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FREE GROWTH AND OTHER SURPRISES
Draft
Gordon Getty
FOREWORD BY THE AUTHOR
How Come This Book?
A few months ago, Robert Trivers was kind enough to send me his new book. The
title is “Wild Life”. Perfect two ways. Bob is a world authority on wildlife, to wit
evolutionary biology. But his books and papers about that are already well known.
His new one is about his own wild life, with his ideas in the background.
I’ve started my own book three for four times over the past decade. Bob’s got me
started again. Try it. It’s Bob’s real voice. One of his papers, co-authored by Huey
Newton(!), is about deception and self-deception. I never saw much of either in Bob.
I never saw a guy less anxious to impress. Fine if you knew his achievements, and
fine if you didn’t. What he wanted to talk about was great new ideas by others. It
was from him that I first heard about the Hamilton-Zuk parasite theory, and Paul
Ewald’s complementary one about parasites stabilizing population density of hosts.
Both are beautiful examples of the obvious-in-hindsight.
I realized that my book could take a cue from his. My own life hasn’t been wild. It
has been interesting because the genius of my father gave me interesting places to
be and things to do. I could say something about that.
But the book would be mostly about my ideas in economics. Bob’s ideas are well
known to anyone in his field. Mine aren’t. I’m ten years older than Bob, without
much to show for it except in composition. (My last two operas have been getting
some traction, and my SACDs get pretty good radio time.) So I’ll run my economic
ideas up the flagpole, in my real voice, and see if they prove deception or selfdeception
or something worth the time.
Declaring My Biases
I’m a big free market fan. I would love it even if I agreed with socialists that there is
something inherently iniquitous about it. There are bad guys and conflicted motives
Forward By The Author 04/18/16 1
in markets and government both. What I love about it is the chance to prove ideas. I
love Wall Street innovations such as swaps and futures and ETFs and mortgagebacked
securities, even admitting their dangers. And who would have thought that
the San Francisco Bay area, a stronghold of political correctness at the voters’ booth,
would nonetheless innovate Siri and Alexa and driverless cars, in its free market
havens here and there, over the past five years? Remind me the last innovation by a
committee. Who would have thought we would make the world’s best car, the Tesla,
in this labor stronghold? It takes guys who prefer the impossible. It takes guys like
my father.
Yes, that was J. Paul Getty. I’ll declare a bias for him. His faults were just what we
read they were. I liked them fine. My times with him, with an exception I’ll note in
Chapter 1, are some of my favorite memories. I seem to be the opposite of pharaohs
who began their reigns by chiseling off their father’s names from the monuments
and substituting their own. That was something about a ticket to the afterlife. I put
my father’s name on things I build. The afterlife will come as it comes.
Since this book is about growth first, I should say how I feel about growth. Most
economists, which I’m anything but, treat it as a goal. I love innovation, which has
translated to growth, while worrying plenty about growth itself. What happens
when anyone can make a doomsday weapon on his desktop? Depressed people do
away with themselves every day. Some might take the rest of the world with them if
they could. Armageddonist religions wouldn’t be needed. Not even destructive
intentions need be. A doomsday weapon bought at the five and ten might go off by
accident.
Then why do I root for innovation when I’m scared stiff about its consequences?
Because alternatives are scarier still. Humans will innovate anyhow, while Big
Brother or the religious authorities aren’t looking, and I don’t like the prospects of
innovation driven underground. We’ll have to find some way to face the risks and
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manage them. This book doesn’t say how. It will open that can of worms, and others
too, and try to track some but not all to their destinations. One look leads to another.
This shows that I’m not an optimist in the sense of making rosy predictions. But I
seem to show that bias in evaluations. I’m two thirds Panglossian. (Doctor Pangloss
was the guy in Voltaire’s Candide who said that this is the best of all possible
worlds.) I side with the good doctor in that I cannot imagine an improvement to this
world or to the human race. I see the dangers and evils, such as Armageddonists, as
somehow part of the scheme. The world would not be better if it posed no threats
and challenges to solve. To solve them is not to wish them away. The stories of
Aladdin’s lamp and the monkey’s paw tell us that each wish after the first is to undo
the one before. I think that’s what Shaw was telling us in Don Juan in Hell. Don Juan
and the others are free to go to heaven whenever they like, and occasionally do.
They come back because they can’t stand the boredom.
Where I find fault, and differ with Pangloss, is as to the doctrines we are taught.
Whatever I study, I seem to find a good measure of nonsense taught along with
wisdom. This book is about what I find of both in economics. And a problem I try to
solve, not wish away, is the danger of losing sight of the points on which Pangloss
was right. My verse and music try to remind us.
And I’ll admit a bias for the surprises my title promises. I love upending what we
had all assumed. Fun! And all the more fun when I can show that famous economists
had already seen and said some of the same things I do when we read those
economists again. Surprise need not be true novelty. My free growth theory is really
John Stuart Mill’s, although no one seems to have noticed the paragraph I quote
from him. My next generation theory really belongs to my 17 th -century rhymesake
Sir WilliamPetty, who happens to be my nominee for greatest economist of all time.
In a way, I could also credit it to the period of production theorists John Rae, Nassau
Senior, William Stanley Jevons and Eugen von Boehm Bawerk. They need only to
have considered human and total capital as explained by Petty two centuries before.
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This reveals my bias for economic history. It seems dry as a bone until you find
something terrific like those insights. It happens that I had written both theories,
and published one, decades before I found those great precedents. Should I have
been chagrined? Of course not. Forgotten or unnoticed precedents are at least as
much fun to point out as the surprises they showed ahead of me.
I will also reveal a bias for evolutionary biology. Its main axiom, the biological
imperative, becomes one of mine. The idea is that behaviors are selected for
successful reproduction. I will try to show that the classical school treated this as
axiomatic from Petty through Smith, Malthus, Ricardo and Mill. Malthus was only
the most obvious case. It lapsed from attention when a brilliant new insight called
marginalism preferred to do without explanations for tastes.
Above all comes my bias for the great thinkers in those fields. We saw that as to Bob
Trivers. Although I often cite them to disagree with them, I see all as giants from
whose shoulders I slip in trying to climb. I don’t kick sand on 97-pound weaklings.
Mill was a mensch who gives us all lessons in attribution and generosity, particularly
to schools he disputed, and who nonetheless didn’t mind being a minority of one in
his books or in parliament.
Petty was something beyond. Polymath, self-made tycoon, anatomist, music teacher,
father of national accounts, originator of present value theory and human capital
and next generation theory, and esteemed by both Adam Smith and Karl Marx for
other innovations I don’t mention. Such men are understood slowly and
incompletely.
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CHAPTER 1: RECOLLECTIONS
I never finished a course in economics. I started one at the University of San
Francisco sixty years ago, and dropped it when I couldn’t see the foundations. But
the bug had bitten me. I knew that one day I would try on my own.
I always loved logic. My favorite philosophers at USF were the pre-Socratics who
liked nothing better than to confound common sense. A brilliantly vexing example
was Zeno the Eleatic and his argument that Achilles can never catch up to the
tortoise; Achilles must first reach the line where the tortoise was last, and the
tortoise has since moved on. Logic can play such tricks. But I sensed that economics
was the place to try its limits. Dropping the course didn’t mean giving up, and logic
would be the key.
Neither did I take a course in business administration or investment. My major was
English literature. As a grade schooler I had asked my father about this. Where and
what should I end up studying? He had read economics and petroleum geology at
Oxford, and I supposed he would advise something like that for me. I got a surprise.
Career-oriented majors were fine but not necessary. A grounding in the liberal arts
could be as much or more. The trick was to learn how to learn. That sounded right,
and anyhow right for me. So I chose USF, a twenty-minute walk from home until my
mother moved us to San Rafael, a half hour drive across the Golden Gate Bridge, and
followed my intuitions toward English lit and history and music and philosophy.
I graduated with a degree in English lit in 1956. This was the time of skittish peace
between the Korean and Vietnam wars, and the Reserve Forces Act meant I had to
report for six months active duty starting in the spring of 57. Meanwhile I worked
for my father. I and my brother Paul, later Sir Paul, started at the bottom pumping
gas and changing oil at separate gas stations not far from our home in San Rafael.
That left time for a few weeks at a bulk plant (oil warehouse and tank farm) in San
Francisco, still working at the bottom, before I reported. Paul had served in the
Chapter 1: Recollections 1/06/16 1
Korean war, and was now exempt. I was a shavetail second lieutenant, thanks to the
ROTC program at USF, in the quartermaster branch at Fort Lee, Virginia. My
eyesight was never good enough for the combat branches.
Ike, who was then president, had started in the quartermaster too. My military
career was not so glorious. Somehow I finished the six months at Fort Lee and seven
and half years of inactive duty following, obligating me to one weekend per month
at military posts near home, without being promoted even to first lieutenant. By
policy, I should have been promoted or busted to the ranks. I later learned that my
school chum Manuel Teles, who worked at Fort Presidio in San Francisco, had
somehow fixed the record. Thank God for old friends.
My weekends of saluting were postponed when Paul and I went back to work for my
father in 1958. My father then lived in the Ritz Hotel in Paris. He liked ordinary tworoom
suites. The sitting room was his office. His filing system was a steamer trunk.
Our job was to sit and listen as he met with executives or art people or old friends.
He would usually take us along to lunch and dinner, and wangle us along when he
had been invited out. He was the world’s most attentive father whenever we were
with him, at least, if focused elsewhere when we weren’t.
Paul went on to learn refining and marketing in Italy, after those few weeks in Paris,
while I went to the oilfields my father had just found and developed in the Neutral
Zone between Saudi Arabia and Kuwait. Paul soon learned Italian, became general
manager within two years, and ran things well. I learned only a little Arabic, but also
became manager in 1959, and soon blundered my way into two weeks’ house arrest.
I had got crossways with the local emir, Mohammed bin Nasr, not a bad guy, about
perks and privileges he and his staff expected Getty Oil to pay for.
The case against me was rigged. One of our junior staff drivers, a Kuwaiti I think,
had accidentally rammed and damaged a pipeline. He had fled the country to avoid
jail. Jails there were no fun. His supervisor, Jim Kinnell, was warned that he (Jim)
was accountable under Saudi law, and would be sent to jail instead. Jim came to me.
I realized what was brewing. Laws are flexible, and Jim would have got off with a
Chapter 1: Recollections 1/06/16 2
caution at most if I weren’t at odds with the governor. I was obviously next. But I
was not about to gamble that the threat to Jim was a bluff. I told him that if I were in
his shoes, I would go back to England. He did. That left me. But I was in my shoes.
The blunders had been mine, and I would face the music.
My two weeks of house arrest went peacefully. The plain cement-block house had
been built for my father at our port camp of Mina Saud when he lived in the Neutral
Zone in 1953. The Emir’s identical house was a few steps away. My father’s favorite
maple sugar was still in the fridge. I read the few Shakespeare plays I hadn’t read in
college, and read or reread the complete poems and plays of John Keats.
The house arrest was probably as much dressing-down as I deserved. Paul, or
anyone else, would have handled the perks and privileges more adroitly. But our
host country, Saudi Arabia, may have picked up on something too. Getty Oil was not
one of the concession companies in the Middle East named in the baksheesh
(bribery) scandals that made the front pages over the few years remaining before
most concessions were negotiated away and host countries ran things themselves.
Back to my father in Scotland, where he was visiting his old friends the Maxwells
near Inverness, and then to the two-room suite at the Ritz in London about like the
one in Paris. He drove the six hundred miles between, in a vintage Cadillac, taking
two days and stopping to visit historic sites and museums. He needed no guidebook.
I sat in on meetings and events everywhere with him in London as in Paris. I
assumed that the Saudis had cleared the house arrest with him, and I would have
agreed as he did. He too was in different shoes. He was right. He had solved a real
problem with minimum damage. Lesson learned, and no hard feelings either way.
It was clear to both of us that I was not cut out to be a line officer, meaning one who
runs things from day to day. My mind goes off on tangents instead of tracking
arguments in real time. It works for me, but not as an administrator. We decided to
try me as a consultant.
Chapter 1: Recollections 1/06/16 3
That began at my father’s Spartan Aircraft Company in Tulsa, Oklahoma. He hadn’t
meant to buy it. He had bought control of Skelly Oil, centered in Tulsa, and Spartan
turned out to be one of its holdings. Then came Pearl Harbor. My father was 48
years old, and had been a yachtsman. He took a navigation course at USC along with
kids half his age, led the class, and volunteered for sea duty. His old friend James
Forrestal, Secretary of the Navy, steered him to Spartan instead. Spartan could make
training planes and could train pilots. My father accepted. He paid himself a salary of
one dollar a year.
He had decisions to make when MacArthur and Matzushita signed the peace treaty.
The training planes were not meant to leave the ground. Spartan lacked the
capacity to make the real thing up to competition. The demand for training planes
pretty much ended with the war. My father could sell out or find another use. He
decided to make house trailers. It worked. I had lived in a Spartan trailer in the
Neutral Zone, like the rest of the senior staff, when I stayed at our Wafra oil field
rather than the house at Mina Saud. We and the market had liked them fine.
Herschel Shelton had been one of my father’s right-hand men during the conversion
to trailers. He said that the place to look for him was never in his office. You would
find him in overalls under a trailer on the factory floor, with a welding iron or
riveting gun. He liked to be able to do any job his workers did. How else would he
know if they were doing it right?
I stayed in my father’s house at Spartan, as at Mina Saud. It stood at the opposite end
of the runway from the offices and trailer plant. I drove another seasoned Cadillac
that my father had left in case he came back. Max Balfour, who ran Spartan, called it
a clunker. It clunked me around the countryside on weekends, or to Jamil’s
restaurant or Cap Balfour’s house for dinner, or downtown to the movies or
symphony or opera house. Cap (Captain) Balfour had flown in World War I, and
showed crippled hands from when his plane caught fire. He was cranky, urbane and
razor-sharp. His problem was that Spartan couldn’t seem to come out in the black.
He worshipped my father, and figured he had let him down. He seems to have
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brought his moods with him after work, which my father generally didn’t. That cost
him his sunny young wife. I somehow got a pass. I could understand him, and I was
my father’s son.
My advice in the end was that my father should sell. Meanwhile I was taking an
interest in economics again. Business was about rate of return. Spartan’s was
negative. What was the benchmark? I did a little study.
It is easy to see that return tends to even out from one company or industry to the
next. We pour investment into high-return prospects, and unintentionally drive that
high return down toward the norm by expanding the capital denominator. I didn’t
know that Robert Turgot had written the same in 1766. But what struck me was the
impression that return, net of inflation, seemed to revert to a norm over time. Why
were interest rates, averaged over business cycles, about the same then as in
Dante’s time or Julius Ceasar’s? Why should human impatience be a steady norm?
That puzzle nagged me for about a quarter century until I found the answer.
Another decade or two would pass before I learned that Sir William Petty had found
it in the seventeenth century.
I went home in 1961 to study harmony and counterpoint at the San Francisco
Conservatory of Music. I had found time to compose a few things at the house at
Mina Saud with a piano I had bought in Kuwait. They included an a cappella
(unaccompanied) choral setting of Tennyson’s “All Along the Valley”, and something
to which I later fit Emily Dickenson’s poem “Beauty Crowds Me” in my song cycle
“The White Election”. The composer Charles Haubiel published “All Along the Valley”
in his Composers’ Press in Los Angeles in 1959. The one change he suggested, an
unexpected D flat major resolution, is the best touch in the piece. I had noticed
copies in music shops in Tulsa. So it seemed about time to develop that interest too,
and the conservatory back home seemed the logical place.
Chapter 1: Recollections 1/06/16 5
I studied there from fall 1961 through spring 1962. I was probably the only
composition student already published. My teacher in both the fall and spring
classes was Sol Joseph. He was a legend there. Most of what he taught confirmed my
instincts. Maybe five percent was old rules I didn’t think much of, and five percent
good ideas that hadn’t occurred to me. All was useful anyhow as a guide to what
leading authorities have thought and taught. That was the point. We were to accept
what we liked, and anyhow learn the lingo.
Those two courses covered traditions of the eighteenth and nineteenth centuries.
Most composers in the 1960s, and probably some or most of my classmates, thought
of that as a stepping stone toward study of the serialism and other atonalism then in
vogue. I skipped those classes. I realized that I was a nineteenth-century composer
at heart. Now the world seems to have spun back to where I was all along. For most
composers now, atonalism is one of the colors on our palettes. Even I use some. So
did Bach. We reach for that color when we want to express disorientation or angst. I
found I could get more said most of the time with major-minor scales.
Five short piano pieces I wrote then were published by Belwin Mills in 1964. As my
father’s son, you might imagine that I was asked to pay the costs. Nope. Neither had I
paid a cent to Composers’ Press. Vanity press exists, but that was not the business
model of those two firms. I got standard royalties from sales, not amounting to much,
and they got the rest.
Six published pieces by age 31 would not have impressed Mozart or Schubert. By
lesser standards, it was a pretty good start. There are distinguished composers who
have never found a publisher. Tomorrow the world! I would write operas and
symphonies! What happened instead was sixteen years of writer’s block, or eighteen
since finishing the pieces in 1962. I suppose I was trying to say “Shazam!” and turn
into something I wasn’t. The ice would break in 1980, when I realized that Billy
Batson would have to do. But that gets me ahead of my story.
I married Ann in 1964, making it a banner year on that count even more than the
publication, and went back to work for my father. That took us to New York in 1965.
Chapter 1: Recollections 1/06/16 6
Tidewater Oil Company, which would merge into its parent Getty Oil Company a few
years later, had red ink problems in its Eastern Division. My job was to see why.
Eastern Division was run by “Jim” Jiminez, an upbeat guy I liked. I don’t think he
took the red-ink problems home with him as Cap Balfour had. He reported to my
half-brother George at corporate headquarters in Los Angeles, and George reported
to my father in London. George had earned his job as president by outstanding
performance at every level on the way up, which is more than you could say for me
in the Neutral Zone. But George was touchy. He had a chip on his shoulder. I think
my father liked to ride him, and he sometimes felt unappreciated. You have to shrug
that off. George was doing fine. The problem in Eastern Division was not in him, and
it was not in Jim Jiminez. Then what?
I looked at the books. The red ink had nothing to do with management. Eastern
Division did refining and marketing. Its new refinery in Delaware had been
optimized to process heavy Wafra crude oil, which then was over a dollar cheaper
per barrel on the market than the lighter and easier-to-refine crude we produced in
Texas and the Central Basin. Tidewater’s Western Division refinery at Martinez, by
contrast, had all the cheap oil it needed in our own San Joaquin field. The Martinez
refinery was old, and more expensive to operate. But the net advantage still went to
Western Division by about a dollar per barrel. Meanwhile gasoline sold for about a
dollar less per barrel, although only two or three cents less per gallon, in the
refinery-loaded east than in California.
Management can’t do much about import quotas and market conditions. I reported
to my father that Eastern Division was at least as well run as Western Division,
where the ink was black thanks to cheaper crude and pricier gasoline.
Then could we cut costs or boost receipts in other ways? I proposed that we close
our old and inefficient Boston Harbor terminal, where barges unloaded gasoline into
our tank farms to be trucked to stations, and supply Boston from our new terminal
at Providence two hours’ drive away. If that worked, other distribution
consolidations seemed possible. I later proposed much the same thing for our
Chapter 1: Recollections 1/06/16 7
operations in Japan, where the new terminal at Kawasaki could theoretically obviate
the older and clumsier one in Tokyo Harbor. I realized that plant-closing might be
unthinkable in Japan, but thought that something good might come of the idea.
Sometime a little later came my lawsuit against my father. It isn’t my happiest
memory. There had been a stock dividend years before, when I was still in school.
We had treated it a certain way on the books. I read the law as saying it should have
been treated another way. The law was probably on my side, and common sense on
my father’s. Judge Peery wisely found a way to make common sense win in the end.
Meanwhile I had accused my father of nothing worse than oversight. My visits to
Sutton Place, now with Ann and the boys, went the same as before. The lawsuit
seldom came up and was discussed in easy terms when it did. I suggested to him, for
example, that he might want to settle with my stepmother Teddy in case there could
be claims by the estate of my late half-brother Timmy. He did. Somehow we got
through the lawsuit without bad blood. One would not have guessed so much was at
stake. The stock dividend had been a huge one. What I learned from my father, then
most of all, was perspective. He believed in an even keel. Zeno the Stoic, not the
Eleatic, would have met his match.
The lawsuit lasted from 1966 through 1971. In hindsight, thank gosh he won. If I
had, tax consequences would have been ugly all around. Again I had learned a lesson,
and again there were no hard feelings either way.
I continued to do consulting jobs for him throughout the lawsuit and after. I charged
expenses, but no fee. And I didn’t pad expenses. If I had, you can believe he would
have seen it. I stayed in a single room in the best hotels, ate three squares a day, and
paid for anything else myself. I was trying to make the point that I didn’t want to be
paid. Neither had my father at Spartan during the war. The idea was for me to be of
use. I was paid like everyone else when working for my father full-time, but never
on consulting jobs.
Those now came once or twice a year, and lasted for a week or two each. Composing
was still on the back burner. I was keen on physics, economics, human origins and
Chapter 1: Recollections 1/06/16 8
city planning. It became clear that all but the third needed better math skills than I
had. So I bought the Barnes and Noble textbook on College Mathematics, got through
it in a week of hard work, and then began on the Johnson and Kiokemeister textbook
on calculus along with Halliday and Resnick on physics. Together they took me
nearly a year. At the end, I was allowed to sit in on the freshman physics finals at Cal
Berkeley, where the same two textbooks were taught.
It was the finals for physics majors, and meant to be tough. Cal took physics
seriously. Not every freshman was destined to go farther. Some should be steered
towards engineering, which pays better anyhow. There were 10 questions. Three
hours were allowed. Each of us had a calculator and nothing else. Not even a table of
integrals. My God. I had to remember them or rederive them. There are some that
had taken even Newton and Leibnitz months to solve. I don’t remember any of the
questions. There were 200 to 300 kids in the room. Maybe 20 or 30 orientals, about
three women, no blacks. Not one finished early. And some figure to be Nobelists by
now. We’re talking about Cal. I had answered seven questions when the three hours
were up. Was that good enough? I got a call in a few days. I passed, and beat the
class average.
My old friend Matt Kelly warned me about this time that George was in trouble. Matt
had known George’s new wife Jackie, and had been invited to dinner there. Matt’s
impression was of out-of-control mood changes. He said that George at one point
had drawn him aside, shown a pistol and warned him about paying too much
attention to Jackie. The next minute they were back at the table in jolly spirits. I
learned later what was wrong. George thought he had a weight problem, although I
never noticed one. Doctors prescribed amphetamines in those days to control
appetite. They revved him up and made it hard to sleep at night. So the same doctors
prescribed barbiturates at night to get him to sleep. Uppers and downers are
dangerous enough. Add a drink or two and you’ve got trouble.
Of course I should have told my father. But I didn’t want to be the one. I liked to
boost my brothers. Many must have seen the symptoms Matt saw. Let them break
Chapter 1: Recollections 1/06/16 9
the news. But the others must have felt as I did. We waited too long. I got a phone
call in 1973. George had died at Mount Sinai Hospital. There was an empty bottle of
sleeping pills.
My father’s death came in 1976. Ann and I had got word it was coming a few weeks
before. We were there. So was Norris Bramblett, an accountant who had worked for
my father since I was in school. My father trusted him. So did I. He had only a fourth
grade education, but a PHD’s worth of character and sense. My father, Zeno the Stoic
when things got tough, cracked jokes to the end. Norris alone could understand him
by then. He translated patiently. My father was giving me one more lesson. He
lapsed into a coma. Ann and I were called down from our bedroom when he died.
That left me and Lansing Hays co-trustees of the trust controlling his companies.
Lansing ran the law firm that handled nearly all my father’s business and little else.
It was a big job. Lansing was smart, abrasive, and dead honest. He didn’t mind
hurting people’s feelings. I was not immune. It didn’t matter. It wouldn’t have
mattered to my father. What mattered was that Lansing knew what trust meant, and
put the Trust first. That’s what I cared about.
Lansing was already on the Getty Oil board. I was invited to join too. We met four
times a year, most often in Los Angeles. Harold Berg, an oil engineer from Colorado,
had become CEO (chief executive officer) and chairman after George died. Sid
Petersen, an accountant, was COO (chief operating officer). Harold was a warmer
and more approachable personality. That’s what you’d expect in an oilfield guy. Sid
was reserved and analytical. That’s what you might expect from an accountant,
although Norris Bramblett fit anything but the stereotype. Harold and Sid were both
clearly well chosen. Neither then nor later did I doubt that Getty was run at least as
well as its big oil rivals.
The board too were top people. But trouble was brewing. The trust, meaning
Lansing and I, owned about 43% of the shares. The Getty Museum, also chaired by
Harold, owned another 11%. Boards and managers prefer scattered ownership, so
that they can operate more freely. Second-best would be concentration in docile
Chapter 1: Recollections 1/06/16 10
hands happy to follow the board’s guidance. But my father had made it clear to
Lansing and me that we were to trust our judgment. We should be ready “to vote the
management in and out.” Since stockholders elect boards and boards hire managers,
that meant to vote the board in and out.
No wonder they were concerned. Lansing and I were both boat-rockers. Wouldn’t it
be safer if there were a corporate co-trustee? These are usually safety-minded banks,
and many banks did business with Getty Oil.
Concerns rose when Lansing died in 1972. That left me as the sole trustee. I was less
obstreperous than Lansing, but also less predictable. Hostile takeovers were
common then, where bids are made directly to shareholders rather than cleared
through the board. Getty was rich in oil reserves per dollar of share price. It could be
a target. Board members tend to feel that they know stockholders’ interests best,
and that the angels are on the side of “friendly” or board-approved takeovers if any
at all. Stockholders don’t necessarily feel that way.
Temperatures rose when I pushed serious study of the possibility of taking Getty
private. The idea was to give up our corporate structure to escape the corporate
double tax. Management and its investment banker, Goldman Sachs, advised against.
I now think they were right, although my idea had good precedents. I pressed on,
unwisely, by trying to convince the Museum to back me. They had better sense.
It was time to heal the breach. Marty Lipton of Wachtell, Lipton, a top mergers and
acquisitions law firm, represented the Museum. He proposed a moratorium (the
“tripartite agreement”) where the Trust, Museum and company would hold the
status quo for one year. Harold Berg had retired as chairman of Getty Oil, and Sid
was now chairman and CEO. His COO was Bob Miller, a keen petroleum engineer.
Harold Berg still chaired the Museum, although Harold Williams was its CEO and
main voice. We all signed. But Getty Oil had its fingers crossed. A few days later, the
company petitioned the court to appoint a co-trustee. It proposed Bank of America.
B of A’s chairman, Chauncey Medberry, sat on the Getty Oil board. Paul and George’s
daughters joined the plaintiffs.
Chapter 1: Recollections 1/06/16 11
The Museum was more outraged than I was. Marty felt that he had been used. He
and Harold Williams, a business-savvy guy who had chaired the SEC under Jimmy
Carter, realized that if I could be hog-tied, the Museum with its 11% was the next
domino.
This was in November of 1983. Within a few weeks, the Museum and I signed a
“consent of shareholders” taking over the company. The required public disclosure
of this, on top of the tripartite agreement and co-trustee lawsuit before, was blood in
the water.
Pennzoil launched a hostile takeover bid in December. My concern was that the
trust should not be locked in a minority position. I met with Pennzoil in New York.
We resolved that to my satisfaction. The Getty Oil board met, also in New York, on
January fourth. The mood was not sunny. Harold Stuart, one of the brightest and
finest board members, assumed that I had invited the Pennzoil bid. Chauncey
Medberry thought I should be sued. But Sid and the board acted responsibly overall.
We countered with a higher price, Pennzoil accepted, and we went home thinking
we had a deal.
Texaco offered a higher bid two days later. Was Getty Oil already bound to Pennzoil?
Its lawyers and mine said it wasn’t until the final agreement was signed. I had my
doubts. But I liked Texaco’s offer better, and my duty was clear. The Trust and
Museum would be paid cash for their shares, rather than locked in. I had insisted on
language in the Pennzoil agreement that bound me only as “consistent with my
fiduciary duty.” My duty, in the light of legal advice, was to accept Texaco’s offer. I
did, and voted the same way as a member of Getty’s and the Museum’s board. Those
were fiduciary duties too.
Pennzoil sued Texaco, and eventually won punitive damages of some eleven billion
dollars. The Museum and Trust had cashed out. We were not parties. The Pennzoil
and Texaco filings both spoke well of me. But there was still the lawsuit seeking a
corporate co-trustee. That would have been very dangerous before the sale to
Texaco cashed us out. A corporate co-trustee might well have assented to “corporate
Chapter 1: Recollections 1/06/16 12
defenses” blocking a sale and effectively locking the trust in a minority position. But
now that danger was over. The remaining plaintiffs were my three nieces and Paul. I
couldn’t blame them. How could a corporate co-trustee hurt?
But I was still worried. I now wanted to split up the trust into four separate ones for
my family, Paul’s, George’s, and my other half-brother Ronnie’s. Corporate cotrustees
tend to prefer the safety of acting only as required, and anyhow might not
be keen to vote themselves out of a job.
Were Paul and my nieces mad at me? Believe it. Lawsuits get that way. Lawyers on
both sides say nasty things. That lasted because splitting the Trust took time. The
math was easy, but the legal precedents were vague. My lawyer, Mose Lasky,
thought we needed new California law. Plaintiff’s counsel didn’t think so. I was
accused of stalling. Someone had the bright idea to approach Willy Brown as
Speaker of the Senate. The law Mose wanted had already worked in other states,
and Willy liked it. He pushed it through. Problem solved. The Trust was split into
four in 1988, and an unhappy chapter ended. My nieces and I are as close as ever. So
were Paul and I until his death in 2002.
My interests by the time of the split were composing, verse, economics, human
origins and evolutionary biology. Composing was going pretty well. My writer’s
block had melted away in the summer of 1980. Ann and I and the boys were in Paris
then. We wandered into Smith’s English language bookstore. I bought the Thomas
Johnson variorum of Emily Dickenson’s 1800-odd poems. “Variorum” means
including Emily’s own variations when she mailed the same poem to different
people, or put a copy in the chest at the foot of her bed.
I read them all over the next two days. Emily had been one of my favorites at USF.
She died in 1886. She had published only eleven poems. Squabbles among the heirs
delayed publication of about half the rest until Johnson published them in 1959,
three years after I graduated. Many already published had been “bowdlerized” to fit
conventional rhyme and grammar. Johnson gave us the real McCoy from her
manuscripts. All was new to me.
Chapter 1: Recollections 1/06/16 13
I had no piano in our hotel room in Paris, but set a few of the poems in my head to
write down later. More followed. One of her poems I didn’t set begins “Mine by the
right of the white election…” Election meant choice. Her white smock hangs today by
her bed in Amherst where she was born and died. White is the color of weddings
and burials. Her choice, I think, was a death marriage to the reverend Charles
Wadsworth of the Arch Street Church in Philadelphia. He was happily married. She
met him about three times in her life. I would tell her story in 31 of her poems, one
in two different settings, in my cycle “The White Election.”
It was completed in 1981, and broadcast on National Public Radio two years later. It
seems to have made a good impression. Slava Rostropovich had kind words, and
invited me to write something for cello and orchestra that he could schedule on his
upcoming tour in Russia. Placido Domingo invited me to write a song for him.
Renata Scotto wanted me to choose five or so of the White Election songs that she
could include in her concerts. All were big opportunities. Somehow none happened.
Other stuff was coming out the pipeline.
That included my opera “Plump Jack.” Here I would tell the rise and fall of Falstaff in
Shakespeare’s Henry the Fourth and Fifth. This was riskier. Now the
accompaniment would be orchestra, not piano, and I had no background in
orchestration. Composing and orchestrating are not the same. Composing is like
writing a play, and orchestration is like casting the play. There are composers that
don’t orchestrate, and orchestrators who don’t compose. Most of us do both. I
always did my own orchestration because no one else would know what I wanted. I
gradually learned from my mistakes. Now I can probably hold my own in
orchestration, although many do that better.
Plump Jack was completed scene by scene over some twenty years. I would think it
was finished, and then decide it wasn’t. My next two operas, each running about an
hour, would be composed much faster. I set “Usher House” to my earlier libretto
based on Poe’s story in about six weeks in 2008 and 2009. “The Canterville Ghost”,
on Wilde’s short story, took me about two weeks each, with two months between,
Chapter 1: Recollections 1/06/16 14
for libretto, composition and orchestration. The last two operas have been
premiered at major opera houses. Usher House ran again at San Francisco Opera.
Upcoming performance of the “scare pair”, meaning Usher and Canterville as a
double bill, have been announced in other cities. Plump Jack is still waiting its turn.
My interest in human origins led me to the Leakey Foundation. I had read about
Louis Leakey in the papers, and had met him a few times in Las Angeles and San
Francisco. Brilliant, courtly, fierce. He let you know what was wrong. I became a
fellow in 1973, a trustee the next year and chairman the next.
Clark Howell, who taught anthropology at Berkeley, chaired our science committee.
His co-chair was Dave Hamburg, a Stanford psychology professor who specialized in
great ape studies or primatology. Most leading scientists in either field were
members or regular advisors. They recommended grants, and we trustees funded
them. We took a venture capital role, usually making grants of a few thousand
dollars to promising new prospects rather than bigger amounts to steady-state
projects already proved. Those proved ones included Jane Goodall’s chimp studies at
Gombe or Richard Leakey’s digs at Lake Turkana. National Geographic, or the
Wenner Gren or World Wildlife or National Science Foundations tended to fund the
known winners. We’re a lot bigger now. I am one of the few living links to those
great people and times. We’ve evolved with the science. But we stick to the venture
capital role.
That always left time to organize lectures and symposia. A few of us including Nancy
Pelosi, long before she tried politics, put together an all-star two-day symposium at
the Palace of Fine Arts in the San Francisco Marina district in 1973. Tickets sold out,
and hundreds watched on screens set up in the lobby. Julian Huxley regretted, but
sent his good wishes on tape. The octogenarian Raymond Dart recounted his
discovery of australopithecus africanus at Taung cave near Johannesburg in 1924.
Louis Leakey had died the year before, but his equally legendary widow Mary
updated us on the digs at Olduvai. Dick Hay filled us in on the geology there. Jane
Goodall gave the news from Gombe. Dave Hamburg reported on the new
Chapter 1: Recollections 1/06/16 15
chimpanzee compound near the linear reaction at Stanford. Clark Howell briefed us
on his work at Torralba and Ambrona in Spain, where our ancestors half our size
had hunted elephants twice the size of modern ones. (Elephants go back at least as
far as mammoths and mastodons.) Desmond Clark covered African archaeology in
general and his discoveries at Kalambo Falls in particular. Sherry Washburn showed
the way in which our DNA is 98% the same as a chimp’s. All were my close friends.
It was at a symposium in 1974, in Washington I believe, that I first heard and met Irv
DeVore. His talk was on evolutionary biology and Hamilton’s rule. Both were new to
me. Irv was a champion speaker. Students packed his anthropology classes at
Harvard. He became a Leakey stalwart and a particularly close friend.
I liked his topic. Genes code for traits, and traits more adaptive to niche pressures
are likelier to carry the genes that encode them into the next generation. The
likeliness is “fitness”. A beauty of this is that you can predict traits from the
environment (niche), and the environment from traits. That promised the kind of
logical challenge that I loved.
Survival of the fittest was not news to us. What was news was that bright scientists
like Irv were specializing in that logic, and making testable predictions for creatures
generally, humans included, rather than sticking to the groups they studied most.
That meant people I could talk to.
Hamilton’s rule was put up as the prime example. It starts from the principle that
the end game in biology is investment in the next generation. Hamilton had
reasoned in 1965 that genes coding for most efficient investment in closest kin, who
were likeliest to carry copies of those genes, ought to leave most copies in the next
generation. We would invest in them when consanguinity was greater than
cost/benefit ratio measured in fitness given up and fitness gained at the other end.
I didn’t like this. Something was missing. The logic was seductive. But Achilles does
overtake the tortoise. Traits compete, like those racers, for niche space. The winner
is the fittest at meeting needs of the niche. Hamilton’s rule seemed to leave that out.
Chapter 1: Recollections 1/06/16 16
It got Darwinism backward. Darwin’s idea was that the best-adapted leave most
progeny, not that leaving most progeny or other close kin somehow bootstraps itself
into adaptiveness.
The math of Hamilton’s rule didn’t work either. In diploids like us, where each
parent carries two sets of chromosomes, closest relatedness without inbreeding is
½. That meant that fitness would have to double or more with each generation. The
reason is that fitness not expected to be transmitted to successors would be a
contradiction in terms. If it cannot be transmitted (invested) at less than a 2:1
efficiency ratio (benefit/cost ratio), then it must be expected to double or more with
each reinvestment. But aardvarks and flatfish aren’t 1024 times fitter than their
ancestors of ten generations ago. They aren’t even a smidgen fitter, by any measure
of fitness known to me, unless the population has grown. Population growth in
nature usually fluctuates around zero.
But his rule was right in important ways. Nepotism is common in nature. The Trust
passed my father’s wealth to direct descendants. Most wills do, or favor nephews
and nieces as a secondary choice. Chimp mothers maneuver to push their offspring
up the social ladder. Worker ants and bees, who don’t breed, push the chances of
their younger half-sisters. Hamilton’s rule was clearly a good rule of thumb, even
though the math needed tuning. Why should it usually work? I couldn’t know then
that Hamilton himself would find the biggest missing piece of the puzzle in 1982.
Economics was always somewhere on my screen. It was the biggest challenge
because I had to reinvent it from scratch. I had dropped the course at USF because I
couldn’t find the foundations. But we don’t build a foundation without knowing
what we want to top. I had to reinvent everything at once. Does that mean I thought
I was best qualified for such a task? No. Plenty of people are better at logic than I am.
Rather I seemed to be the only volunteer.
Explicit economic axioms are seen as a nineteenth century thing. There are implicit
ones to a degree. Macroeconomics is said to rest on microeconomics, and
microeconomics on the logic of supply and demand. Good so far. But I felt the need
Chapter 1: Recollections 1/06/16 17
of a logical context for those. Too darned much was being taken for granted. What
do we really want from economics? As we gradually figure that out, we can figure
out the most efficient vocabulary for description and prediction. That’s was what
Newton did. I didn’t like the lazy assumption that those problems had already been
solved.
Newton lucked out in that old words like mass, force and energy would mostly do if
he gave them exact definitions within their usual ranges of meanings. Brand new
terms would have made tougher reading, and his Principia Mathematica was tough
enough in 1687. I had the same luck in the end. But I didn’t know that until I had
collected textbooks and economic dictionaries, along with most books on economic
history I could find, and meanwhile worked out what I thought the right vocabulary
ought to be. We pretty well have to solve every section of the jigsaw puzzle at the
same time. I’m my father’s son, by the way, and balked at the three-figures prices of
some of those textbooks, even though I might fork up as much for a bottle of wine.
My ideas on growth theory and capital theory (explaining rates of interest and
return) will get plenty of coverage later. It happens I have also taken a lifelong
interest in banks and money theory. This book isn’t about that directly. But banks
and money are part of the story of growth and interest, and anyhow are worth
attention in themselves.
Money has been defined elegantly in terms of what we want from it. We want a
measure of value and a medium of exchange. The qualities to give those things are
“moneyness”. Money should be “transportable”, for one, in that we don’t really want
to lug bags of wampum around. It should be stable in value, so that we can contract
over the future with least uncertainty. It should have the same value in different
places as well as at different times, to minimize the nuisance of conversion. There
should be enough of it that shortage doesn’t drive us to the clumsiness of barter. It
should be “divisible” into tiny units, as hundred-dollar bills into tens and ones and
pennies, for exact payment with nothing owed back. It should be fungible in that one
Chapter 1: Recollections 1/06/16 18
unit, say dollar, is worth exactly the same as another. Most essential of all, money
should be something actually and reliably valued.
What meets all these criteria? Gold has been a contender since ancient times. But
how reliable is its value? Spain and Portugal stockpiled gold and silver from the new
world for two centuries, and bought nothing but inflation for their trouble. Gold is
good for filling teeth, and for displaying status so long as it is rare. Then what is
better?
Two brilliant and dangerous adventurers, the Scotsman John Law and the Irishman
Richard Cantillon, proposed land. France in 1720 had no new world mines, and
needed money. It had plenty of land in Mississippi. Law and Cantillon put two and
two together. I think they sincerely believed their advice to The Duke D’Orleans, the
regent after the death of Louis XIV, that land could be the most reliable basis of
value then known. More than that, I think they were probably right. But it wasn’t
reliable enough. Early investors in paper rights to the land had made a mint as
others crowded in. Market euphoria led to more paper rights than underlying value.
You’ve heard that one before. Law and Cantillon saw the crash coming. It would be
called the “Mississippi bubble”. Cantillon sold out just in time. Law preferred to face
the music, as I would in the Neutral Zone a quarter millennium later. Land wasn’t
the answer.
I can’t call Law and Cantillon good guys like the emir. Both seem to have committed
murder for money, Law long before and Cantillon long after, in scandals in London
having nothing to do with the bubble. But they had good days. Cantillon’s book,
which I know only from descriptions by economic historians, seems to be a
masterpiece of the obvious-in-hindsight. Law went down with the ship, like a
mensch, and seems to have kept the trust and friendship of many backers he had
bankrupted. I mention the plusses of these two men to remind us that the truth is
seldom black and white, and to mitigate the folly of the French in trusting them.
Money today, in the United States and elsewhere, is not backed by any commodity. It
is “government fiat money” backed by the taxing power of government. That may be
Chapter 1: Recollections 1/06/16 19
the best solution tried so far. The value behind the taxing power is the total capital
of the nation, meaning human as well as physical capital. And the dollar has proved
pretty stable since Paul Volker’s tough reforms in the early 1980s. That means that
government fiat money in this county is working about as well as anything we have
known.
But there are problems. Government tools for stabilizing government fiat money,
which has no value in itself, are limited to control of its supply. The tools are
monetary and financial policy. Monetary policy is mostly “open market operations”
where government sells bonds to soak up excess money, and buys them back again
to put money back in the system. You can also raise or lower Central Bank interest
rates to get the same effects. Fiscal policy trims money supply by raising taxes and
cutting government expense, and pumps money back into people’s hands by
lowering taxes and raising government expense. Monetary policy is the tool of
choice because it has acted must faster. But either policy, or any mix, is a tightrope
walk. Too much money courts inflation by motivating people to spend rather than
save. Too little courts recession by motivating the opposite. That’s why
macroeconomics is said to rest on microeconomics. Are we wise to push our luck on
that tightrope forever?
Another problem is that our current money system may depend too much on banks.
Banks buy and sell back the government bonds, for example, and create the money
they lend by writing it into the borrower’s checking account and booking the
promissory note as value received in return. The problem is that banks are failureprone.
I mean plain commercial banks which do nothing but accept deposits and
make loans, not the still more dangerous commercial/investment hybrids which
rose and fell after repeal of the Glass-Steagle Act.
The danger is leverage. Depositors must be attracted at some cost, say checking
services. Borrowers must be attracted at a rate covering those costs to give profit in
the first place. Then equity investors must be attracted at an equity rate, generally
higher because equity imposes risk. These rates and costs are market givens rather
Chapter 1: Recollections 1/06/16 20
than what the bank decides. Then how can profit from lending rates, watered down
by costs of attracting depositors, translate into higher equity rates?
Easily, but dangerously. That’s where the leverage comes in. If the amount borrowed
is much larger than the amount invested as equity, absolute profit from borrowing
might be large compared to the amount invested. If hens lay only one egg per day,
but I own three hens, then I can eat three eggs a day.
More money lent out, compared to equity invested, presupposes more deposits to
lend. The leverage needed, or deposits/equity ratio in the bank’s case, works out to
equal the market equity return for investments of equal risk, divided by the market
borrowing rate for loans of such term and risk, net of expense percent including
costs of attracting depositors. This has tended to pencil out at about ten to one.
Firms in general are considered risky when leverage (debt/equity in that case)
reaches one to one. Four to six is more typical. Not ten to one. Banks invest in loans,
which are safer. But not ten times safer. Few people today would risk their money in
bank deposits without federal deposit insurance. My own reading of history finds
that deposit-and-lend banks have failed systemically, or needed bailouts, about once
per generation since they were innovated in Marco Polo’s time. They failed because
borrowers default in high winds, and defaults are magnified tenfold in effects on
stockholders’ investment. We rebuilt them, and the tenfold leverage, because we
blamed the high winds rather than the rickety structure. The Practical Pig knew
better.
It began occurring to me in the mid 90s that mutual funds might replace bank
deposits, and deal with the tightrope problem too. Too much money burns holes in
pockets today because money earns nothing while we hold it. Mutual funds pay
returns, and are owned for their own sake. If their shares were somehow money,
people would feel no impatience to spend it, and no supply would be too much. I
gradually figured out how the obvious problems in fungibility and divisibility and
other moneyness qualities could be addressed.
Chapter 1: Recollections 1/06/16 21
Nobelist Franco Modigliani heard of this, and invited me to MIT for a presentation.
He talked like Gepetto in Disney’s “Pinocchio”. There were a few other top brains,
including Ruddiger Dornbusch and2Julio Rotemburg, in the small classroom where I
spoke. Sometimes Modigliani interrupted. “Getty, you don’ta consider this.” “You
forgeta that.” I guess I thought I wasn’t doing so well.
My talk ended, and he and I were standing by a window. To lighten the mood, I said
something about the Red Sox. He said “Getty, I getta papers on banka reform every
week. Yours isa the best.”
Milton Friedman, another nobelist, had a different take. We had given talks at a Cato
Foundation symposium in San Francisco. He hated my idea. No great surprise. He
had written that money ought to earn nothing so that we wouldn’t own too much.
Any attempt to back money with anything, he told me, would meet John Law’s fate
in the Mississippi bubble. The backing commodity would become inflated and then
crash. So Nobelists can disagree.
My version of the same idea today looks first to ETFs (exchange traded funds),
which are more liquid and money-like than mutual funds. ETFs are usually index
funds, which replicate index holdings with no active management and so charge
very small expense ratios. But mutual funds might become money too. My idea, dead
opposite from Friedman’s, is that both money supply and money yield should be
held as high as possible.
What would happen to banks? Major angst, but not much damage. They would
devolve into their separate deposit and lending specialties, with separate
stockholders and only incidental interaction. Deposits would be invested in ETFs or
mutual funds. Federal deposit insurance would wither away as unneeded. There are
no runs on ETFs. Lending banks would have to raise funds to lend from investors
expecting a return.
Is there a downside? There is certainly a risk of one. The devil we don’t know is
what would happen to lending rates and what the consequences might be. That had
Chapter 1: Recollections 1/06/16 22
been one of Modigliani’s points in his interruptions. Federal deposit insurance
subsidizes cheap money and keeps lending rates low. Most tradition associates easy
money with growth and prosperity. Higher interest rates are associated with
restraint in investment and consumption both. Modigliani was right to worry.
My guess is that the bank reform and money reform I propose would drive
borrowing costs up, borrowing volume down, and equity investment up to fill the
gap. Corporations would issue new stock to retire corporate debt. Newlyweds
would rent, not buy, until their incomes were high enough to bring other options.
Modigliani was also worried that monetary policy would become impossible. It
would as we know it. I have argued elsewhere that fiscal policy can be made to work
as well and as fast. And I will argue for an unusual and more direct form of monetary
policy. But no one knows.
These concerns are reasons to go slow. I think that the reforms I describe are
developing now, with no input from me, and will continue if they succeed.
Depositors will be attracted away from banks to ETF accounts of equal liquidity and
full return. Federal deposit insurance will not be advantage enough to hold them.
Banks will get the message and join the parade by spinning off their loan
departments and investing deposits in ETFs. If Modigliani’s valid concerns haven’t
found good answers, the parade will stop until they do. It could backtrack to the
starting point. The reforms I believe in ought to work, but can be scrubbed without
much mess if they don’t.
I am not their only advocate. Others argue for splitting up commercial banks more
or less as I would. Meanwhile many people maintain liquidity in ETFs or mutual
funds rather than banks. There may be some originality in putting the two reforms
together.
This personal account can end with more thoughts about my father. My stepmother
Teddy’s touching book about their marriage, out a couple of years ago, tells the truth,
the whole truth and nothing but the truth. That what she does. He seems not to have
Chapter 1: Recollections 1/06/16 23
been the easiest guy to be married to. He pinched pennies, went on trips while she
held up the home front, came home late. My mother had about the same story. But I
saw different sides of him at different times and places.
Twice I saw him cry. Once we were listening to a Caruso record. He might well have
heard Caruso, although I don’t recall that he said so. He would already have been 28
when Caruso last sang at the Met. One of the two books he wrote by himself shows
him as an opera buff when on his own in Germany in the 1930s. He wrote what
operas he had heard, who sang, and what he liked. My mother said the same. Once
they arrived late at a performance of La Boheme somewhere on the Riviera, couldn’t
find a program, liked the tenor, decided to help him, and learned that they had failed
to recognize Beniamino Gigli.
The other time was about his and Teddy’s son Timmy. Timmy’s brain tumor was
inoperable and growing. He was 13. The doctors had told them to prepare for the
worst. We were in London. The papers said something about young toughs called
Teddy boys. My father started crying. Timmy wouldn’t make it, and the Teddy boys
would.
I’ve now lost a son myself. You thank the graces for what’s left to do. What’s left to
do includes composing, verse and economics. The first has panned out okay. A fair
bit of the verse was set in the music. At least that makes it read and heard. Aside
from the kind words of Modigliani and a few others, I can’t say as much for my
economics. So here goes again.
Chapter 1: Recollections 1/06/16 24
CHAPTER 2: FAST FORWARD
I dropped the course on economics because I couldn’t see the foundations. Not that
they should be clear from the start. That isn’t how the mind works. We see, do and
understand in that order. The pyramids rose four thousand years before people like
Galileo and Newton found the laws that made them possible. Practice comes first,
and science last. Science is abstraction from the particular to the general. It is fewer
rules predicting more outcomes more exactly. The pyramid builders knew rules for
this kind of stone and that kind of wood or rope. Newton gave rules for mass and
force. Those are not particular things like stone and wood and rope. They are
qualities of all things. Their rules are tougher to get our minds around, but predict
everywhere once we do.
What a book or course should offer from the start, even before the foundations, is an
inkling that it should be worth finishing. We have to sense that we’re on to
something. The price of getting there will be the nuisance of abstraction from things
to qualities, and we need to see a reason to pay it. I didn’t in the course on
economics. Now it’s my turn. I’ll try a fast forward through free growth theory and
my other arguments to give an idea where we’re headed and why it matters. The
foundations and then the slower tour will follow.
Free Growth
What I call free growth theory will probably count as the chief surprise, at least to
non-economists, because the argument and the supporting evidence call for a major
reversal in tax policy of this and other nations. But it is not original. John Stuart Mill
wrote the same idea in his Principles of Political Economy in 1848. I will quote what
he said in my Chapter 4. Although Principles became a leading textbook for decades,
the paragraph I quote seems to have been overlooked. Economic historians
including Joseph Schumpeter describe him as a champion of growth through belttightening.
The paragraph I will quote makes the opposite clear. We now have
means to prove his idea. I will show how to test it, and will show test results in
charts and tables taking up about 20% of this book. They imply that tax laws
Chapter 2: Fast Forward 1/06/16 1
encouraging investment over consumption and plowback over dividends,
particularly in the last half century, have led to dangerous overinvestment in the
private sector. The empty eyesores and bulldozer bills of 2008 are symptoms of proinvestment
policies founded in many countries after World War II. They did no
harm when the world needed rebuilding anyhow. But I suggest that output growth
slowed because of them, not despite them, after 1970 or so. I will argue that optimal
investment at the national scale, strange as it sounds, is depreciation plowback and
nothing more. Mill showed how that could be true. The same growth will arrive, say
he and I and the charts and tables, with no consumption sacrificed. More
consumption at no cost to growth adds up to more output. Output nosed down
since 1970 or so because we squelched consumption to no purpose.
That means only private sector overinvestment, prompted by unwise tax motives,
and only at the collective scale. Government follows different motives, and has
somehow followed them to an opposite problem in this country. Our infrastructure
rusts and crumbles. It seems that our good friends in the Tea Party think that roads
and bridges undercut market freedom.
Growth is interesting, even without these opposite distortions, because history is
interesting. Growth is our history. It is not the history of other creatures, who repeat
norms from generation to generation once evolved. That’s why the math of
Hamilton’s rule doesn’t work. And we care about it because there are emotional and
moral and belly issues attached. I gave an idea of its dangers in the foreword. The
past has proved survivable. The future has not. Then what about its cost? Does
faster growth need consumption restraint at the start? Is it a reward for sacrifice?
That’s what Mill tried to answer in 1848.
He started with the idea that output, meaning creation of capital, must mean growth
of capital (“investment”) plus consumption. I will call this the Y = I+C (or Y = C+I )
equation from the standard notation economists use. I will argue that it is true with
two adjustments. Investment must include investment in human capital, and
Chapter 2: Fast Forward 1/06/16 2
consumption must exclude any schooling or nurture already counted in that
investment. (Schooling counts as consumption.) Mill would have understood the
human capital concept, defined by Sir William Petty nearly two centuries before, but
economists only recently have begun to take it seriously. Mill’s meaning of the
Y = C + I equation, and the one accepted everywhere in macroeconomics even today,
leaves out the growth in human capital and includes all consumption.
That equation, which I will try to prove correct if we make the two adjustments,
shows that less consumption brings faster growth if output holds still. But nothing
in the equation says it will. It says that less consumption means either more growth
or less output. It doesn’t say which. John Maynard Keynes, probably the most
famous and influential economist of the 20 th century, put this fact of math a special
way in his General Theory of 1936. In his analysis, saving through less consumption
is either invested or not. Since output is consumption plus investment, saving
uninvested is so much less output. I like to put the same idea with a range of degrees.
All saving is invested, as I use the word, but finds different returns. Saving under the
mattress is investment at zero return, and drops output just as Keynes said.
Investment at the current average return keeps output unchanged. That’s what
Keynes meant. But investment at lower returns lowers output, and conversely.
Keynes’ version sees intended saving (consumption restraint) as either invested or
not, and sees it as translated dollar for dollar into actual capital growth if it is. Mine
allows any degree of capital growth below or above the actual cost of investment in
consumption given up.
This is a surprising concept, either in Keynes’ version or mine, because it seems to
fight personal experience. Until the next raise or job change or layoff, our incomes
seem to be known quantities. If we skip desert, and watch TV instead of going to the
movies, we can put more in the bank. At least our incomes will not drop because we
saved those costs. But it is different for all of us collectively. When the whole nation
saves, and either does not invest or invests less productively, output drops. Keynes’
analysis says the same, but leaves out the “less productively”.
Chapter 2: Fast Forward 1/06/16 3
My reading of the Mill paragraph says that if we plowed back only depreciation
investment, without invading consumption for more, we would still grow if that
investment paid off in higher returns than the current norm. Then capital would
grow faster without making consumption grow slower. The gain in output, even
though we had invested only enough to make up for depreciation while keeping
consumption the same, would have been split into some for capital growth and
some for more consumption. And Mill gave the reason for the gain in output. The
driver was “whatever increases the productive power of labor”. He was talking
about better ideas. We would make returns higher if we could make capital more
productive at the same cost.
This possibility troubled Nobelist Robert Solow, who came reluctantly to a
conclusion most of the way toward Mill’s a century later. He felt that growth should
not be a gratuitous deux ex machina arriving at its own whim. How could Mother
Nature say “Shazam” and turn less into more whenever new ideas come along?
Didn’t the capital chicken have to grow before the output egg? Didn’t we have to
tighten belts to invest in new plant applying those new ideas? But the evidence
seemed to say that the rise in output came first. Rise in capital followed. Thrift
seemed to play little role. Tests by others have tended to find the same thing since.
My own tests, using new data from national accounts and my own new testing
method shown in my charts and tables, reduces the role of thrift to zero. How could
that be?
How could better kinds of capital arrive without costing more, at least at the start,
than the kinds we already knew? My best guess is that the cost of innovation in
failure rates and learning curves is the cost of being human, that we pay it about the
same every day, and that growth happens when the worth of innovation proves
more than the cost. It can because we are human. The cost of being human means
the cost of adapting. It is how we cope. We turned in our fangs and fur in exchange
for the savvy to make tools and fire and clothing do better. Other creatures adapt
Chapter 2: Fast Forward 1/06/16 4
too, but we became the specialists. Adaptation grades into innovation whenever it
somehow becomes a norm. That too happens with other creatures, but not as often
or as lastingly. Their new norms almost always revert to the old ones. Our
innovations collect and accrue. That’s why growth is our history.
Its costs are failure rates and learning curves. Many innovations are blind alleys, and
most others need shakedown runs. But we’re stuck with those as the cost of being
human. And we’re stuck with them whether the result right now is growth or not.
They were our cost of survival during our million years as homo erectus, when the
archeological record shows little overall change in the stone tools we made. Growth
and lasting innovation picked up marginally with the emergence of Ancestral Eve
and bigger brains about 200,000 years ago, and began accelerating about 50,000
years ago. Growth happened because the more or less constant cost of adaptation
and innovation became less than the payoff. New ideas finally found traction at no
added cost. Mill’s idea was that more payoff in growth need not presuppose more
sacrifce.
Does that mean that all we need for growth is new ideas and the courage to trust
them? Well, no. We still have to plow back depreciation as the cost of holding even.
We need practical savvy and patience too. Sometimes great new ideas must wait for
an opening. That may be why our bigger brains showed little effect on the kinds of
tools we made until about 50,000 years ago. And I will argue that innovations need
laws and customs that welcome them. Otherwise they will make a few bucks for the
local warlord rather than wealth for the originator and the world. But what they
don’t need, say Mill and I and the data, is tighter belts.
Adam Smith, in his Wealth of Nations published in 1776, proposed growth by belt
tightening. Most tradition has agreed, with the proviso that new ideas must come
first. Solow raised doubts about the role of consumption restraint, but stopped short
of denying a need for it. Mill acknowledged both ways to grow. My charts and tables
will confirm that only the kind that troubled Solow has actually happened, in every
Chapter 2: Fast Forward 1/06/16 5
country and period tested. I call it free growth. My own free growth theory
acknowledges growth by consumption restraint, which I call thrift, only as a
mathematical possibility which doesn’t seem to happen. So my idea, taking account
of data Mill didn’t have, is different from his. I must be careful not to put my ideas in
his mouth. When I say “Mill’s idea”, from now on, I will mean some of both.
No one had the data to prove him right until national accounts began reporting
market-valued capital in 1990 or so, and reconstructing it for a few decades before.
What they had earlier was the book measures of capital that we see in balance
sheets. They don’t reveal enough. Book measures assume depreciation norms.
Outcomes converge to norms over time, but meanwhile might be anything. National
accounts follow a form of this book or depreciation accounting. They now report
market-valued capital too, but still prefer book methods to calculate investment I
and output Y in the Y = C + I equation. That doesn’t work well. Did you know that
national accounts in France, Germany, U.K. and the United States all reported
positive net investment in the crash years 1929, 1930, 1937 and 2008? Net
investment, meaning net of depreciation, is intended to show growth in capital value.
Do you think values really went up in those crash years? And national accounts can
be just as wrong in the opposite direction. In the boom year 1933, when stock
markets were up 42%, 67%, 96% and 46% in those four countries, Germany and U.S.
reported net investment (capital growth) as negative while France and U.K.
reported it up less than half a percent. All this shows in my charts and tables.
Reports of net investment in national accounts tend to prove radically wrong in
years of unexpected upturn or downturn because they don’t get the news of wars or
national disasters or discoveries or business cycles until new assets are bought or
new products sold. Purchases and sales are normally the only input into the books.
Average time between original purchase and realization in sales is the “holding
period” or “turnover period” of capital. For all physical capital together, it runs
several years. Accounts in those slump years were reporting the good news of boom
years shortly before, including the booms of 1935 as well as 1933 preceding the
slump year 1937. Accounts in the boom year 1933 were finally getting the news of
Chapter 2: Fast Forward 1/06/16 6
the crash. (Yes, some of the strongest boom years in history came during the world
depression.)
This is not to question the need for national accounts. We could not manage without
them. But the genius of accountancy is in its reporting of cash flow items.
Depreciation, even its sophisticated form used in national accounts, is a makeshift
approximation better than nothing. I argue that it is obsoleted by our access to
market-valued capital appearing in the last few decades.
Mill’s argument was that capital growth might be explained by productivity gain as
well as by thrift in deferred consumption. The way to test between them that I will
describe takes measurements of market-valued capital, its year-to-year change in
these, and consumption at the same time. I call it the simultaneous rates method. In
any year and country where consumption restraint explains growth, although the
data show none, rise in growth rate would equal current drop in consumption rate
(consumption/capital) while rate of return (output/capital) holds unchanged. When
productivity gain is the explanation, as the data confirm so far, it is consumption
rate that holds the same while growth rate and return rise equally. That’s what I
test. Data in charts and tables for those four nations from 1870 through 2010, and
from Australia, Canada, Italy and Japan from 1970 through 2010, show that faster
capital growth coincides with higher consumption rates in the same year as often as
not. Less consumption has simply meant less output with no growth to show for it.
That is the sense in which growth is free.
These countries and periods are not cherry-picked to support Mill’s idea. They are
all I have found. My source for national accounts including market-valued capital
was the website of Thomas Piketty and Gabriel Zucman adjusting their data to
uniform accounting standards and measuring them in 2010 currency units. It also
collects recent and past research by other economists modeling what national
accounts, again including accounts of market-valued capital, would have shown in
years before they were founded in 1930 or so. Simon Kuznets, for example, who
Chapter 2: Fast Forward 1/06/16 7
founded the national accounts in the 1920s and reorganized them along Keynesian
lines when the General Theory was published, reconstructed them back to 1870 for
the U.S. economy. Piketty and Zucman incorporate this research and others. They
have acted as editors only. As a layman, I would hardly be qualified to find and
interpret original sources. Even most economists might lack that specialty. I simply
trust Picketty and Zucman. They will have compounded misreadings and editors’
bias in those sources by adding their own, and I will have added mine. They and I
have plenty. Editing is bias by definition. But we can’t do without it. We manage as
best we can.
To make sure, I also test Mill’s idea on stock market data from the same nations and
periods. Here my source was the Global Financial Data website marketed by
Bloomberg. Market cap corresponds to capital, dividend yield to consumption and
total return to output. Charts and tables show free growth as essentially all of
growth in stock markets too.
Now try a first look at the charts and tables. The lollipop-shaped Greek letter ϕ
(phi) is something I call the free growth index. It reads 1 in years when growth is
explained as Mill described, 0 in years when belt-tightening was the explanation,
and something in between when there was both. The free growth index will be
explained in chapters 4 and 5. The charts can be messy, and the data jumps around.
There are spikes, both up and down, which tend to disappear in the charts which
screen out small absolute values of the denominator (capital acceleration). But the
free growth index clearly jumps around 1, not zero, both before or after the
screening. It is as often above 1 as below. That means that growth is as likely to
coincide with belt-loosening as belt-tightening. My free website
FreeGrowth&OtherSurprises.org shows how everything was calculated.
Economists will not be as surprised as they might have been a century ago. Growth
theory since Solow’s revolutionary papers in 1956 and 1957 has marginalized
Chapter 2: Fast Forward 1/06/16 8
capital accumulation or thrift, and has seen most growth at the national scale as
“exogenous” or unexplained by whatever we suppose that we give up in exchange.
This book takes the next step in the same direction. The role of thrift is zero. It is
politicians, not economists, who will be flummoxed. The double tax and the tax
preference for capital gains are examples of policies favoring investment over
consumption to benefit growth. The record shows no such benefit in any country
ever. From all evidence so far, free growth theory is free growth fact.
A New Way to Measure
What this book tries to add is not only the next step in Solow’s direction. My
simultaneous rates method offers a new means of testing. Twentieth century growth
theory, led first by Keynes’ colleague Sir Roy Harrod and then by Solow, has tried to
gauge the effectiveness of consumption restraint by a different method from Mill’s
and mine. It has looked for effects on later output rather than on current capital
growth. I call it the lagged flows method. Why the lag? Because if output is growth of
wealth (capital) plus consumption, a shift from the third to the second cannot
change output at the same time. Rather output should benefit after a lag of a few
years for the capital that produces it to accumulate. Capital investment plants a tree,
and output growth is the new fruit expected to follow.
The lagged flow method makes sense, and there was nothing better until data for
market-valued capital began appearing in 1990 or so. But the lag tends to blur
causality. Later changes in output could have later causes. And output itself, after
the lag, could not be measured reliably for lack of the same data. It has been
measured as gross or net domestic product, reported as the sum of consumption
and book investment. Books don’t get the news until new assets are bought or new
products sold. We just saw the anomalous book results reported for 1929, 1930,
1933 (the opposite distortion), 1937 and 2008. Those are not the only examples. My
method measures output as consumption plus change in market-valued capital. It
seems to me that Piketty and Zucman ought to have shown output this way, at least
as an alternative version. Isn’t it inconsistent to measure capital at market, but to
Chapter 2: Fast Forward 1/06/16 9
measure its change (net investment) at book? And isn’t it better to measure the
effectiveness of thrift with neither the lag nor the well-known problems of book
depreciation?
I will show the math of my simultaneous rates method in Chapters 4 and 5. Chapter
4 reasons from the Y = C + I equation, even though I don’t accept it, while Chapter 5
translates findings into the new version I do accept. Charts and tables show both
versions for all eight countries reported, over all years reported, and run the
averages. The thrift index, or ratio of the supposed cost to actual growth, averages
zero. I found it best to show separate charts for each country by each of the two
versions of the Y = C + I equation and by each of three levels of denominatorscreening
(none, then two progressively wider screens). Other charts track other
data that seemed informative. That explains why charts take up so much of this
book.
This completes my first survey of free growth theory and its support in the data.
Chapters 4 and 5 will cover the same ground again from new perspectives. So it will
be with other themes of this book and other chapters. My problem is to sell
unfamiliar ideas, although not necessarily new ones, and in somewhat unfamiliar
language too. My “simultaneous rates method”, yet to be clarified, is an example. I
use the standard language of economics where I can, but must sometimes tweak
words or coin them. We will see that in Chapter 3. I try to cope with that double
challenge – unusual ideas in unusual terms – by the same strategy of restatement
from new perspectives until all fits together.
Fixing the Y = I + C Equation
If I had any sense, I would pretend to accept the Y = I + C equation as Mill and all
other economists seem to do. Then I could have done with only half as many charts,
and made this a book about free growth only. Any fool knows that a book should
pick a focus. The data confirming Mill’s idea would have made a spectacular finale.
Why undermine my own case by questioning his assumptions? So I should probably
Chapter 2: Fast Forward 1/06/16 10
have played dumb and quit ahead. But that would have left out half the story and all
the other surprises. I confessed that the surprises are the features I can’t resist. If
they are fun for me, I can accept the challenge of making them fun for the reader.
Anyway, I already opened that can of worms by showing that I don’t accept the
Y = I + C equation even though others do. I gave an idea why, and can sketch my
reason out a little farther.
It begins with something I call the total return rule or total return truism. The
truism is that creation of value equals growth of value plus cash flow, where cash
flow means value taken out less value inserted from outside. I don’t think anyone
doubts this truism, which is fundamental everywhere every day in the investment
world. I will prove it anyhow, just for good measure, in the next chapter. It is
probably the reason that the Y = C + I equation is readily accepted. Net investment I
is meant to show physical capital growth. It could look to be the growth in value, if
we don’t consider human capital, and consumption C could look to be the value
taken out.
But a second look is needed. The logic doesn’t work unless we consider all value
including human capital. Some consumption is invested in human capital, and only
the rest exits the whole economy in satisfying tastes. Then the equation would still
be true if the invested part of consumption equaled human capital growth.
The reason why it doesn’t starts with what we already know about human capital.
Petty in 1664 had hit on the idea of this as time-discounted future lifetime pay.
Adam Smith in 1776 saw it equivalently as accumulated past investment in nurture
and schooling. The Americans Irving Fisher and Frank Knight revived both ideas in
the early 20 th century. The tempo picked up after World War II at the University of
Chicago. Jacob Mincer rederived Fisher’s present value equation in 1958, and
modeled investment in human capital through job training. Nobelists Theodore
Schultz and Gary Becker soon joined in. New insights included the realization that
human capital grows from the self-invested work of learning, as well as the outside
Chapter 2: Fast Forward 1/06/16 11
input of nurture and schooling, and then depreciates gradually to zero just as
buildings do. Yoram Ben-Porath combined these ideas and more in a masterly lifecycle
model published in 1967. We’ll get to it soon.
Schultz called the part of consumption exhausted in taste satisfaction “pure
consumption”. The part invested in human capital was “pure investment”. I change
that to “invested consumption” to avoid confusion with investment in physical
capital. Since there is no settled term for the part of work invested in learning, I call
it “self-invested work”. I call the part of work sold for pay “realized work”. Then the
consensus view formed in the 1960s held that human capital growth equals
invested consumption plus self-invested work less human depreciation. I agree,
with a clarification as to possible deadweight loss that I’ll come to in Chapter 6. I call
it the Ben-Porath equation, although he drew it from the Schultz-led consensus. It is
really a summary of the first four of the equations in his 1967 paper taken together.
This explains my critique of the Y = I + C equation. The equation would be true if
human capital growth equaled invested consumption. In fact it equals that plus selfinvested
work less human depreciation. The corrected equation would read “output
equals consumption plus investment plus self-invested work less human
depreciation”. I call this the “Y rule”.
Upending the Y = I + C equation is big news. Macroeconomics and the national
accounts are founded on it. That’s one reason, although not the main one, why I
think that macroeconomics should start over. It doesn’t follow that national
accounts in themselves need much change, aside from reporting net investment at
market as well as at book, because accountants must measure what they can.
Human depreciation and self-invested work elude market measurement. But
economists can allow for them, and they are huge flows. Human depreciation is
depreciation of the larger factor. And self-invested work includes more than
learning. Ben-Porath showed, as we will see, that it equals all growth in human
capital not explained by inflows of nurture and schooling less outflows in human
Chapter 2: Fast Forward 1/06/16 12
depreciation. That implies that it includes all free growth of the larger factor. And
these huge flows would figure to be uncorrelated. Depreciation of either factor is a
steady drag on growth, while free growth is revealed in the charts and tables as a
bucking bronco which might be double-digit positive one year and double-digit
negative the next. No wonder that national accounts cannot reliably tell good years
from bad.
Another distortion in the Y = I+C equation is the undue prominence given to
consumption. Physical capital, in most views including mine, is only a third to a fifth
of total including human capital. Human capital is the lion’s share. Pure
consumption is most of consumption, in my view, but not all of consumption. If the
factors grow in mutual proportion, then, the ratio of total capital growth to pure
consumption will be much higher than of net investment to all of consumption. That
explains, I think, why national accounts have reported not a single year of negative
net product in any of the eight countries since inception. Balanced portfolios report
negative total returns every few years. So would net product, were it not dominated
artificially by the steady positive of consumption. It is as if a portfolio dominated by
investment grade bonds were taken as representative of a realistically balanced
portfolio.
Solving the Age-Wage Puzzle
I will now try to solve a feature that troubled Ben-Porath and has troubled many
economists since. I call it the age-wage puzzle. Age-wage profiles are published
reports comparing pay earned by all working ages at the same time. Since all
cohorts (same-age sets) are compared at once, as in a family portrait, age-wage
profiles do not show effects of technological growth over time. They show effects of
age and experience alone. What appears is that pay or wage rises steadily until
retirement or near it. Meanwhile human capital is present value of remaining
lifetime pay, and shrinks steadily as approaching retirement and mortality leaves
fewer future paydays to discount. Most students of human capital including Ben-
Porath reason that self-investment must end when time left for recovery in higher
Chapter 2: Fast Forward 1/06/16 13
future pay runs out. So do I. The puzzle is how pay could rise while human capital
shrinks smoothly to zero.
This would not be a puzzle if we were speaking of oil wells whose oil might continue
to be pumped out at a steady or even rising rate until the well ran dry. We are
puzzled because pay is generally believed to equal and compensate work. Work
means the output of human capital. How could less capital steadily produce more
output, meaning creation as distinct from depletion of value, particularly if some
work is self-invested rather than marketed for pay? That would imply exponentially
rising productivity, meaning rate of return, and rising to infinity at the end.
Think about it. Strictly speaking, human capital is present value of future pay less
spending on future childhood nurture plus textbooks or tuition or job training
(collectively called “schooling” by Mincer) invested in human capital. Ben-Porath
knew that, as had others before, but reasoned that investment in anything must stop
when not enough time remains for recovery. I think so too. And I argue anyhow,
from observation rather than logic, that invested nurture and schooling
substantially end when we enter the full-time job market sometime in our twenties.
Then human capital in adulthood is essentially present value of expected pay, or
even less if Ben-Porath and I are wrong and nurture or schooling continues to the
end. When only a year of pay is left ahead of us, human capital at most is timediscounted
present value of one year’s pay. When one day is left, it is at most
present value of one day’s pay. Yet age-wage profiles show pay (wage) holding level,
or even rising, as human capital grades smoothly to zero. This is the famous agewage
puzzle. I’ll flesh out the same thought experiment later in what I call the
parable of the boss and her secretary.
Economists have recently proposed solutions which I see as farfetched. Possibilities
that human capital indeed grows more productive with age, or depreciates all at
once, seem implausible in each case and cannot begin to explain enough. I think
Becker hinted at the answer in 1964. Becker pointed out that job training at the
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employers’ expense is part of investment in human capital, and reasoned that
employers won’t pay it unless they expect eventual recovery with interest.
What Becker stopped short of saying is that the same is true of any investment in
anything by anyone. When we invest for our own benefit, we expect recovery by
ourselves. When we invest for the sake of others, we expect recovery by them.
Recovery means recovery of depreciation. Our parents would not have invested in
our human capital without expected recovery of our human depreciation by us, and
the young further invest the work of learning in themselves because they expect
that to be recovered with interest as well.
There is another proof which I call the deadweight loss rule. Capital of any kind is
present value of cash flow, meaning expected realizations in transfer or taste
satisfaction. Deadweight loss means decapitalization with neither. It follows that
deadweight loss, although a common reality, is implicitly unexpected. But human
depreciation, like plant depreciation, is expected from first investment. That rules
out deadweight loss, and makes human depreciation expected as cash flow by
elimination of alternatives.
Each proof is sufficient. The first expresses what I call the maximand rule: we
maximize risk-adjusted rate of return. Robert Turgot observed this in 1766. I’ll say
more about that in the next chapter. It takes little thought to realize that maximizing
risk-adjusted return begins with recovery of investment, and that this means
recovery of depreciation or amortization. We are depleted like the oil well, although
we create value too. The second proof needs only the assumption that human
depreciation is foreseen. It adds the specification that human depreciation is
realized in human cash flow. That turns out to mean that it is realized in pay. The
solution to the age-wage puzzle is that pay does not equal and compensate realized
work above. It compensates that plus human depreciation. I call this the “pay rule”.
Chapter 2: Fast Forward 1/06/16 15
The pay rule joins free growth theory and the Y rule as the three major surprises
promised in my title. Recovery of human depreciation in pay changes a lot of
equations. It does not impact public policy and tax laws as radically as free growth
theory, but I will argue that it impacts them enough. Even if it didn’t, it is probably
the most startling assertion in this book from an economist’s viewpoint. And
although I now know better than to claim originality for any idea in economics, this
one just might pass the test. If someone out there knows a precedent closer than
Becker’s, as I eventually found ones for what I had thought were my own free
growth and next generation theories, all the more fun in finding those unsuspected
precursors. (Next generation theory will be outlined soon.) And the two proofs
leave no doubt. I will add a few more as we go. It is never overkill to drive another
stake through the heart of entrenched misperception. Meanwhile we can already be
as sure of that expected recovery, not actual recovery, as of anything we know. The
arguments from the maximand rule (Turgot’s insight) and the deadweight loss rule
are unanswerable.
An analogy from something else we all know leads to the rest of my argument. Pay
over working careers is something like payments over the period of a decliningbalance
mortgage. Mortgage payments are partly amortization and partly interest.
Amortization is like depreciation, although without the same sense of physical wear
and tear behind it, and interest is like the worker’s output marketed to employers.
The declining balance is like human capital. Mortgage payments are almost all
interest at the start of the loan, when the declining balance is almost the whole loan
amount, and then gradually less interest and more amortization as the balance
shrinks. As the balance approaches zero at the end, the payment approaches all
amortization while the interest share approaches zero.
My depreciation theory, which we’ll come to soon, argues that depreciation follows
the same logic and the same math. I will argue, in the face of what has seemed to be
contrary evidence, that depreciation of both factors begins at zero and grows
Chapter 2: Fast Forward 1/06/16 16
exponentially to become all of cash flow at the end. This completes the explanation
of age-wage profiles as we see them. Pay is all human depreciation at the end.
What I Thought Once
Chapter 6 will compare accounting for human capital to accounting for a firm. Pay,
in this analogy, is the worker’s revenue. The firm deducts outside operating costs of
labor and supplies to leave gross realized output. The analogy for human capital
would be maintenance consumption enabling life and activity. But I don’t deduct
this in reaching the workers’ gross realized output (gross realized work) because I
take it as part of the net output we intend in itself rather than a cost in return for
what we intend. I see adult consumption as mainly Schultz’ pure consumption
exhausted from the universe of capital, including human capital, in satisfying our
taste for adult survival.
Opinion is divided here. Some economists have treated the maintenance
consumption that keeps workers going as new investment in human capital for the
sake of higher pay in future. Some in the 18 th century expensed it, like maintenance
in the firm, as a cost recovered in keeping up the worker’s revenue (pay) now,
rather than invested for later. I did that for years. I now treat it as recovered neither
in pay now nor pay later. Even though we couldn’t earn without it, I count it in pure
consumption exhausted in satisfying tastes for survival.
When I thought it was recovered in pay and work products, up to about five years
ago, I realized that human depreciation could not also be. There would be nothing
left for pure consumption except Mill’s “unproductive consumption” neither
replacing nor maintaining human capital. That would stand biology on its head.
Biology is precisely about replacing and maintaining us. Unproductive consumption,
for which there seem to be parallels in other species, is something biology has yet to
justify. It cannot be the unique taste satisfaction that behavior reveals.
Chapter 2: Fast Forward 1/06/16 17
I found a solution that seemed to make sense then. It was the exact opposite of what
I think now. If maintenance consumption were recovered in pay and work products,
as I now think human depreciation but not maintenance consumption is, then
human depreciation instead of maintenance consumption could be exhausted in
taste satisfaction! That seemed less macabre to me then. I looked for ways in which
human depreciation, hardly the biological end in itself, could somehow be its
measure. It was not unreasonable, I thought, to interpret human depreciation in
aging as the cost of survival. The old gag says that aging is not so bad when you
think about the alternative. Age-wage profiles could be explained, I thought then, as
recovery of maintenance consumption rather than of human depreciation in pay.
And I had those precedents from the 18 th century. I knew that Francois Quesnay
and the physiocrats, in Adam Smith’s time, had argued too that consumption could
be recovered in earnings. Mill could be interpreted that way, in his definition of
“productive consumption”, as could Piero Sraffa in a paper from 1960. I thought I
was on the right track.
What brought me to my senses was the thought experiment about a boss and her
secretary I mentioned earlier. Picture them together at the beginning of the last year
of human capital for each. The boss earns ten times as much. Human capital for each
is one year’s pay, or even less in the unlikely case that invested consumption
continues to the end, less one year’s discount. If pay measured work, rate of return
(work/human capital) would be something over 100% per year for each. It would
be even more in the unlikely case that some work remains unrealized (self-invested)
until the end. Yet their time preferences measured by return to their other
investments, say securities, is less than a tenth as much. This already states pretty
clearly that pay covers more than work.
In case there was doubt, go on to the beginning of the last day. Age-wage profiles
show that pay for each is about what it was a year before. Rate of return to each is
now a little over 100% per day. At the beginning of the last second, it is a little over
100% per second. At the end of the last second it is infinite. Yet the securities in their
Chapter 2: Fast Forward 1/06/16 18
portfolios are chosen for returns no higher and riskier than the year before. They
will tend in fact to be lower, judging from logic and evidence for a decline in risk
tolerance with age.
Then what besides work is recovered in pay? The two possibilities I was weighing
were maintenance consumption and human depreciation. The winner was obvious.
The higher-paid usually consume more, but not always and not in proportion. The
fact that we must generally be paid enough to cover consumption does not imply
that we are paid to consume. We are motivated to do that anyhow. We are paid to
apply skills, and are paid in proportion to skills applied. Human capital is skill sets.
Pay measures its transfer to products, whether in realized work currently created or
from capital in place through human depreciation.
That’s how I came to the pay rule. We see why it ought to startle economists.
Macroeconomic tradition teaches the doctrine that wage measures work, and
teaches it so confidently that it uses the notation W for either. Human capital
tradition recognizes that some work is self-invested, but effectively treats human
depreciation as deadweight loss. That’s why I use “pay” in place of the more usual
“wage”.
Refuting a Piketty Argument
There are practical uses for the pay rule aside from solution of the age-wage
problem. These are the impact on tax laws and public policy that I promised. Piketty
has shown correctly that the ratio of pay to net profit rose substantially during the
world wars, world depression and welfare state period following, and has declined
since. Piketty argues for higher capital taxes in consequence. His argument follows
tradition in comparing pay and net profit as the shares of workers and investors in
income. But tradition is wrong. Pay is the worker’s gross realized income, meaning
gross of human depreciation. Depreciation, for either factor, is a steadier flow. This
makes gross output for either less responsive to upturns and downturns. It is a
particularly high share of realized income or output in hard times when dislocation
Chapter 2: Fast Forward 1/06/16 19
of both factors (human and physical capital) drives net output down. Comparison
between net income and gross realized income can mislead. Piketty is right about
the data, but wrong about its interpretation.
Depreciation Theory
This is the explanation I promised when I said that depreciation is essentially like
amortization. Accounting tends to practice straight-line depreciation over standard
depreciation periods. A well-known refinement, allowed but not much practiced in
business, is called current cost accounting. The idea is to correct distortions due to
past inflation. The problem is that books reflect long-term assets and their
depreciation at original cost at date of booking. Current cost accounting adjusts both
to the equivalent in current dollars. It shows both net worth and depreciation as
higher if prices inflated since booking, or lower if prices deflated. That seems to
make sense.
A further adjustment called replacement cost accounting does the same, but also
replaces linear depreciation with a curve believed more realistic. National accounts
adopt this method. It is sound in principle. But they shape the curve in the wrong
direction. They rely on records of actual sales of plant to model depreciation as
steep initially and slower later. I suggest that this record is misleading.
My starting point is that value of any capital is discounted cash flow. To keep things
simple at first, suppose that cash flow in constant dollars is expected to hold steady
for fifty years before asset life ends. Also suppose a constant time discount rate.
Present value at the outset is fifty years of discounted cash flow. At the beginning of
the second year, it is 49 years present value of the same cash flow at the same
discount rate. All that has been lost is present value of the 50 th and most-discounted
year. At the start of the third year, capital has dropped again by present value of the
49 th and second-most discounted year. So it continues until the end as the discount
Chapter 2: Fast Forward 1/06/16 20
period approaches zero. Depreciation increases absolutely each year, and increases
even faster in ratio to capital.
What I have just modeled is depreciation rising exponentially from zero at the start
to a maximum at the end. National accounts show the exact opposite. They show it
decreasing exponentially from a maximum at the start. The reason for the difference
is instructive. I would rather trust the present value formula to show what assets
are worth subjectively to their owners. The national accounts prefer to trust
evidence as to what they are worth to others if sold. That’s a solid method too if the
evidence is likely to prove representative. It isn’t in cases where transactions are
more likely to have been driven by pressure to sell than pressure to buy. Plant is
generally tailored to purposes of its first owner, and not meant to be resold. Plant
sales tend to follow disappointing results. These are likelier to come early as
business plans are first tested. That could explain why evidence without logic has
suggested that depreciation tends to start fast and slow down with time.
I would recommend that national accounts continue tracking actual sales as an
indicator of true depreciation curves, but limit the study to rental buildings
expected from the start to be resold several times. I mean apartment buildings,
office buildings and warehouses designed along standard lines. Many investors
specialize in buying and selling these tradable assets for portfolio purposes.
Pressure to buy and pressure to sell tend to balance.
I can testify that prices bid for them are found either by discounted cash flow or
internal rate of return (IRR) methods. IRR is a variant of the same thing. A bid price
is modeled as the original negative cash flow in evaluating the proposed purchase.
Then the positive cash flows at each year’s end are modeled, and the discount rate
found which nets present value of all flows together to zero. If this rate is judged
competitive, the purchase goes ahead. This method was originated by Keynes in the
General Theory as his “marginal product of capital”.
Chapter 2: Fast Forward 1/06/16 21
And I repeat that most other structures are not meant to be resold. Productive plant
is customized to original owners. Tract housing is not, but becomes adapted to them.
Original plant operators and homeowners typically expect to stay put. Most do.
When they do, their own valuations are higher than would likely be realized in sale.
Owners’ valuations matter. Economics is more than prediction of sales prices. It is
prediction of behavior. It is the owner’s valuation of an asset, not a hypothetical
outside valuation, that predicts what he will do to exploit and defend it.
My depreciation theory does not jolt settled belief as forcibly as free growth theory
or the pay rule and Y rule do. It contradicts only a minor feature of the national
accounts. But it contradicts that diametrically, and adds clarity to the pay rule too. It
is also original as far as I know. Who has said such a thing before? All the more fun
and satisfaction in finding out and setting the record straight. There are giants out
there, whether I ever make it to their shoulders or not, and economic history means
identifying them.
Retirement Theory
Retirement generally means the period or first moment when people end the
careers for which their training has been specialized. The reason is typically not
diminished skills and performance just yet, as age-wage profiles show no little or no
drop in pay toward the end. I think it is more that we and our bosses see the drop
coming.
Literal pay is typically zero in retirement. Instead we earn imputed pay for taking
care of ourselves and one another, and for driving the grandkids to the zoo. These
services are tangible, not psychic, in that they save the hire of others to do the same.
The imputed pay is what the others would have charged. But it typically is not
enough to meet our consumption needs. Retirees must typically draw down savings
or depend on “social transfer payments”, meaning support from government or
family or foundations, to make ends meet.
Chapter 2: Fast Forward 1/06/16 22
It seems that these infusions from savings or gift cannot be interpreted as invested
consumption to be recovered with interest later, but are rather pure consumption
recovered now in the satisfaction of survival. Then human cash flow, or pay less
invested consumption, remains positive to the end if we recognize imputed pay.
Economists should, I think, because it figures into predicting behavior as much as
literal pay. So does psychic pay.
It follows that human capital, meaning present value of all pay in the absence of
invested consumption to deduct, continues after retirement. That shows that my
parable of the boss and her secretary is oversimplified. Parables tend to be. The
secretary may happen to have better skills as a full-time caregiver, which both she
and the boss will figure to be in retirement, and so may reverse the disparity in
human capital then. All models, I guess, assume ceteris paribus (other things equal).
My retirement theory leaves much unexplained. It tries to throw a little light here
and there. I believe it achieves some surprise, and even originality until we know
better, in my argument that human capital continues after retirement. Yet this
follows directly from Ben-Porath. Invested consumption must end when time for
recovery runs out, whether or not I am right in ending it with job entry decades
before, and human capital must last as long as literal or imputed pay does. The
endurance of human capital through to mortality is not logical certitude, but need
not be doubted either.
Retouching the Ben-Porath Model
Ben-Porath’s life cycle model seems right enough in all features but one. Equations
in his 1967 paper imply that pay measures realized work alone. This should be
adjusted to show the pay rule. I would also model invested consumption as ending
at independence, or a few months later to allow for initial job training. That does not
contradict Ben-Porath, who leaves such a possibility open. I would further apply
depreciation theory to model human depreciation as growing from a negligible
share of pay at first employment to substantially all of pay at the end.
Chapter 2: Fast Forward 1/06/16 23
My model is the same as Ben-Porath’s from birth to independence. All consumption
and all work are invested, for modeling purposes, until schooling ends at full-time
job entry. I model this transition at age 20. Pay, realized work, human depreciation
and pure consumption all begin at that point, although human depreciation begins
at essentially zero.
Self-invested work continues as an important but diminishing share of work until
late in careers, just as in Ben-Porath. I differ from him mildly in that I model all adult
consumption as pure consumption. Ben-Porath allows adult invested consumption
without assuming it. I regard it as real but negligible. Age-wage profiles are
explained by self-invested work and depreciation theory alone.
I model this self-invested work as subliminal accumulation of job experience. My
reason is personal observation. What I have seen in plants and offices is people
working full time on the job. We don’t take time off to learn. Experience simply
arrives, much as free growth does. I think that my view on this contradicts Ben-
Porath’s marginally. He seems to allow some such allocation of time to help explain
age-wage profiles.
Next comes retirement. I model this as just shown. Later I will expand this model to
include acquisition and disposal of physical capital too. The combined model will
give most of the math and mechanics of next generation theory.
Risk Theory
For practical purposes, economic risk is usually measured as expected standard
deviation in rate of return. Safer assets vary less from their return norms. Shortterm
treasuries are thought safest because they combine fixed nominal return with
fast liquidity in case inflation threatens. The market overall bids safer expected
outputs up and riskier ones down. Since asset value is the denominator in rate of
return, and output the numerator, the effect is make risker assets higher in return.
Chapter 2: Fast Forward 1/06/16 24
Risk tolerance might be anything in any individual. As a norm, it tends to be a
function of age, gender and wealth. Effects of age and gender are better understood.
Teens and young adults, particularly males, seem readiest to take chances. Prison
populations and medal of honor rolls feature young males. Part of the explanation, I
think, is biologist R. A. Fisher’s sex ratio theory of 1930, or equally Bob Trivers’
differential investment theory of 1971. Young males show greatest variance in
reproductive prospects. Females are almost always assured of a few offspring.
Young males might leave none or many. Nature arranges tournaments or displays to
give fitter males the advantage.
Another reason is that the young, of either sex, have most time left to outride
downswings. The older we get, the more risk-averse.
Some businesses and assets are inherently riskier than others. Nerf balls are safer
than hand grenades. But I prefer to look past the asset owned to the owner. We tend
to own assets suited to our risk preferences. And we tend to operate it as safely or
riskily as we like. That is true particularly of human capital, although it was first
designed according to our parents’ goals rather than ours. Human capital is
probably the most versatile asset, even so, and is adapted to our purposes rather
than theirs. We make it as risky as we choose. The risk-averse can become florists or
Trappists. Risk lovers can try bullfighting or skydiving. What does that tell us about
the relative risk of the factors?
Human capital is owned disproportionately by the young. We own very little
physical capital, legally or in practical effect, until maturity. Pay at first is barely
enough for survival. We accumulate it gradually as pay rises with age, and then
deplete it in provision for the young and in our own retirement. Since physical
capital is owned disproportionately by the older and more risk-averse, and human
capital the contrary, human capital figures to be higher on average in risk and return.
Chapter 2: Fast Forward 1/06/16 25
There is another useful inference. Adults own assets in the business and housing
sectors. Older adults tend more to own debt claims on these sectors, and younger
adults to own equity claims. But all adult ages collectively own both sectors
collectively. It does not follow that the sectors are equal in risk, as older individuals
might tend to own one sector predominantly, and younger ones the other. As a
layman, I don’t really know.
What I happen to know is that the publicly traded corporate sector, meaning stocks
particularly but also bonds, is far more liquid than the housing sector, and that the
rest of the business sector is far less liquid than either. Risk in general includes
liquidity risk. This leads me to the hypothesis or hunch that the housing sector in
general should be safer than the business sector, ceteris paribus, but that the
publicly traded corporate sector, cap-weighting debt and equity claims on it, may be
safest of all.
The idea that stocks and bonds cap-weighted are safer than houses might have been
laughed to scorn a few years ago. It doesn’t seem so funny after 2008. I view it as an
idea to be tested, not trusted, until more is known. If it holds up, it will rank as
another surprise.
The effect of individual wealth on risk tolerance is less understood. Here I judge
more from hunch and impression than from data. Given that human needs are fairly
uniform, as with the private and the general, more wealth gives more insulation
from want. Talent is wealth in human capital, and gives the same. Less, in either
factor, gives less margin for error. My hunch and impression is that the wealthier in
either factor should tend to be more risk tolerant so long as human capital itself is
not put in harm’s way. Human capital operates physical capital, and gives the means
of recovery. The wealthier, in talent or net worth, should prove the least tempted
toward sky diving and Russian roulette.
Chapter 2: Fast Forward 1/06/16 26
In this book I will usually be modeling risk and return at the collective scale or at the
cohort one. A cohort means the set of all same-aged individuals. It turns out that the
ratio of females to males tends to rise with each older cohort, for reasons Bob
Trivers explains, as does wealth up to a point. But in cohort analysis, both effects
(wealth and sex ratio) are incorporated into effects of cohort age. That will simplify
modeling.
My risk theory is another example of what looks to be surprise and novelty until
shown otherwise. The unusual idea lies in projecting the owner’s time
preference/return rate onto the asset rather than conversely. Thus all the owner’s
assets of both factors are selected or modified to fit her current risk profile. This
would count her liquid securities portfolio, cap weighted, as a single asset. All other
assets are too illiquid for practical rebalancing. We own the assets best suited to our
risk profiles, if for no better reason than that we wouldn’t be the winning bidders
for any others if we wanted them. As our risk profiles evolve with age, we modify or
trade them. We will tend to have anticipated this need, and to have factored
modification or trading costs into our bid price. It turns out that this interpretation
can simplify the math of present value and present cost.
It helps in supporting the pay rule, and explaining age-wage profiles, by rebutting a
hypothesis, sometimes argued, that productivity of human capital might rise with
age. Productivity, rate of return and time preference rate all mean the same. My risk
theory argues that we know a cohort’s risk tolerance from the return to its capweighted
securities portfolio as a whole. All other assets of the same cohort,
including human capital, will tend to agree with it in return. Return to security
portfolios tends to be transparent. It declines with adult cohort age. I infer that
return to human capital does the same.
My risk theory and depreciation theory together add a finishing touch to the pay
rule. The key supporting evidence is age-wage profiles. Depreciation theory offers
solid logic, in the face of apparent contrary data, that pay is all human depreciation
Chapter 2: Fast Forward 1/06/16 27
at the end. Risk theory reinforces that impression by adding that the contribution of
productivity in the form of realized work/human capital actually declines. One
cannot pound too many stakes through the heart of the doctrine that pay
compensates realized work alone.
Next Generation Theory
I also treat rate of return. This combined free growth theory with insights of Petty
in 1662 and William Stanley Jevons in 1871. Petty’s idea was that each generation
passes the baton to the next. Our investment horizon is the generation length. Its
reciprocal, or one over that period, gives our time preference rate. Jevons also saw
time preference as the reciprocal of the period of production, but did not connect
that to the generation length. I adjust Petty’s estimate of the length from his 21
years to 28.5 by allowing for later births as well as firstborns. The reciprocal is 3.5%
per year. I add free growth as an exogenous and unspecified variable.
As with Mill and free growth theory, I have to walk a fine line between crediting
Petty and putting my ideas in his mouth. Petty dictated his books and pamphlets,
and is not always clear. My idea, probably but not certainly the same as his, is that
each generation invests everything in the next in trust that it will do the same. All
our capital of both factors, although Petty spoke only of a cornfield, is exhausted in
putting the next generation in place. The time horizon to get this done is the
generation length.
This 28.5 years, as I model it, becomes Jevons’ “period of production”. Its reciprocal,
meaning one over it, gives rate of return. The idea of a period of production whose
reciprocal gave rate of return had begun with Rae in 1934, if you don’t count Petty,
and passed through Nassau Senior to Jevons and Boehm Bawerk. All assumed
growthlessness for simplicity. Return is growth rate plus cash flow rate. It simplifies
to the pure consumption rate at the collective scale. All these men, even Petty, were
really modeling the pure consumption rate. 28.5 years gives the period of
replication, in my view, or period of production if there were no growth.
Chapter 2: Fast Forward 1/06/16 28
Free growth then arrives at its whim, like a deus ex machina, without calling for
more than this steady effort of replication. I find myself focusing more and more on
that cash flow component of rate of return, or pure consumption rate at the
collective scale, as the part we can predict and model.
The generation length is a biological norm which probably has not varied by more
than a factor of two since Ancestral Eve some 200,000 year ago. This suggests that
next generation theory can be tested against data from any period. Meanwhile it
predicts only at the collective scale. Collective return is average risk return. Subtract
collective growth rate to leave cash flow rate. Return and growth are two of the
most closely measured rates in economics. That says that tests of next generation
theory should be practical. I will show tables broadly in support.
Next generation theory is a blockbuster. An explanation of interest and return has
been the Holy Grail of capital theory. Boehm Bawerk contributed a big advance by
revealing return as an artifact of time preference rather than the other way around.
Some including Irving Fisher have seen that beautiful insight as enough.
Not me. What explains and quantifies time preference? What turned out to be
Petty’s idea occurred to me about 40 years ago, when I first took an interest in
evolutionary biology. My friend Alan Rogers, a population geneticist I didn’t know
all the time, was thinking in the same direction. His two published papers on this are
in my appendix. Neither of us knew about Petty’s priority.
The idea would have been a still bigger blockbuster before the wall came down.
Wars were being fought about whether return has any legitimacy at all. Karl Marx,
ironically a champion of Petty, may have missed his argument on that.
Petty’s idea is really the biological imperative I discussed in Chapter 1. The first
priority is survival and reproduction. I will argue that this was implicitly accepted
Chapter 2: Fast Forward 1/06/16 29
throughout economic history until new insights now summarized as the marginalist
revolution began in 1871. The marginalists, mentioned in the forward, swapped the
telescope for the microscope. They left aside the grand teleologies of Smith and
Ricardo and Mill and Marx to refocus on the mechanics of choice. Reasons for tastes
or choices were treated as irrelevant. By 1900 or so, the marginalists had given us
microeconomics much as we know it today. A century would pass before
bioeconomics took form in response to Hamilton’s rule.
Summary
That gives the outline. It is a layman’s view of what a proper economist might not
have attempted. Fools rush in. I will cite sources in economics and biology not to
pretend that I am an authority, but to give real ones a chance to check. My case rests
on the charts and tables. Mill might have been astonished to find that the kind of
growth he described is the only kind to appear in the record.
What makes my book different, aside from my lack of credentials, is the surprises
and the unusual degree of abstraction leading to them. Not many writers try to
follow a chain of inference as far without the comforting touch of the stone and
wood and rope. If Becker had been as venturesome, he might well have solved the
age-wage problem in 1964. I see no other path. Economics is all inside. It is tastes
expressed in choices. Capital is foreseen satisfactions discounted by whatever our
taste for impatience is. Most of it is human capital leaving little market record
beyond its rental cost in pay. Logic is about all we have left.
But the story cannot end in thin air. Few would pay the nuisance cost of so much
abstraction without prospect of surprising and testable prediction. I will try to
deliver that. Mill’s idea is a surprise to politicians, if less so to economists, and could
hardly be tested more thoroughly and successfully. When new ideas are thought up,
Mother Nature says “Shazam” and embodies them at no cost beyond the
depreciation plowback we needed anyway. The data could not be more supportive if
Mill and I had invented them. Even my proposed solution to the age-wage problem,
Chapter 2: Fast Forward 1/06/16 30
which must have seemed hopelessly stuck in subjectivity, paid off finally in that
solution and in a refutation of Piketty’s argument. Risk theory and depreciation
theory, each surprising enough, reinforced that solution and the pay rule. I said
nothing in the this chapter about bank reform because I covered that in Chapter 1.
Predictions of behavior can work because tastes converge to market equilibria.
What stands behind the convergence, I argue, is biology selecting tastes that
maintain and reproduce us. The idea that we act out the biological imperative is
clear in Petty and Malthus, and in the equilibrium wage theory of Adam Smith and
David Ricardo, where pay converges to the level preserving the work force. But if I
say everything about that now, I will have nothing to say later.
Chapter 2: Fast Forward 1/06/16 31
CHAPTER 3: FOUNDATIONS
Historically, foundations and science itself emerge at the end of centuries of
practical application. A logical place for foundations in textbooks is the beginning. So
it was with Halliday and Resnick on physics, which began with Newton’s kinetics
(motion in time and space) and then this three laws. Only in the last chapter did the
authors remind us that Einstein later put two of these three into question, and even
the kinetics. Halliday and Resnick reasoned, correctly I think, that we sometimes
learn more efficiently by learning something slightly wrong first and fixing it later. I
will do that, in a sense, by reasoning first through free growth theory as if the Y = C +
I equation were true, and then again with the two corrections. The sometimes
counterintuitive logic of teaching and learning, including that, is “heuristics”.
Building on explicit axioms was common in economics throughout the classical
period running from Petty in the 17 th century through Mill in the 19th. Then came
the major shift in focus, beginning in 1871, called the marginalist revolution. What
mattered was less our goals, and more the market mechanisms that aligned supply,
demand and price. The meeting point was the margin. Axioms about goals
disappeared, including the usual one of prioritizing survival and reproduction, and
axioms kept were usually left implicit. The implicit ones, essential to marginalism in
my view, included convergent tastes and predictions. I will make those two and
others explicit, and eventually add back the goals.
This book on the whole is about second-guessing what is taught. This chapter is
different. The nearest thing to a surprise in it is the idea that economics needs
explicit foundations in the sense of axioms and basic definitions and equations. All
the ones I choose are well accepted. Why I pick which should seem obvious in
hindsight. But some mini-surprises will accumulate. Why do I take such pains to
prove every feature of what everyone accepts already? Why all the boilerplate and
bulletproofing? I need them because I will later try to shoot down other beliefs
everyone accepts. We must know what is sound to find what is not.
Chapter 3: Foundations 1/11/16 1
Another mini-surprise is the physics-like care in definitions. The reason is that my
arguments later will drive logic pretty far. Logic needs words that are like algeraic
symbols in meaning the same thing all along.
Figuratively and literally, foundations are groundwork. They will be less a chore if
you love logic. And you’d better if you’re going to like the later chapters. Let’s get
started.
Orientation
Economics itself, I think, is a quantitative rationale of choices. Psychology is a sister
study not explicitly quantitative, and accounting for subliminal behavior as well as
deliberate choices. The two fields cooperate and overlap. Economics is quantitative
in that it asks how much as well as what, and focuses on numbers. It is science-like
in that it looks for surprising and testable predictions in the end. It is philosophylike
in that choices are subjective and that the larger factor, human capital, leaves
little market evidence from which to reason upward. Both facts put the burden on
reasoning downward from axioms.
Much of the evidence for both factors, meaning physical and human capital, comes
from the records of literal markets where we rent and hire and buy and sell. Most
economics looked no further until Gary Becker and others expanded the boundaries
about 50 years ago. The expansion made sense. A rationale of choices in literal
markets alone is a silly concept. It is silly to acknowledge only choices that ring cash
registers. We are the same people everywhere. Logic is the same everywhere. We
have little interest in axioms that aren’t the same everywhere. Becker was right to
see choices in marriage and even crime as predictable in terms of supply and
demand and price.
That includes psychic price. Once we follow Becker past literal markets, we accept
psychic value and yield. We must anyhow. Value is in the mind. Economics works as
Chapter 3: Foundations 1/11/16 2
a rationale of choices, hence values, because human nature leads minds to converge.
The literal market adds a measure. When we step outside it, we make do without the
measure and trust logic alone.
A Diamond Ring Parable
I like a picture of a diamond ring to show something about psychic value and yield,
and even about what output and exhaust in consumption are. The ring brings
psychic yield to its wearer. If it didn’t, it would have no value. Its yield is each
psychic satisfaction, and its value sums all time-discounted prospective ones
together. Value therefore drops just a little as each yield is finally realized. It is as
with apples dropping from a tree. Yet the ring is inert. It ostensibly produces
nothing. It also keeps all its value as a ring from day to day. Then where does the
outflow of the value in the exhaust come from? How can value go out if none was
deducted and none produced? In the tree, we can see the apples growing and falling.
The answer is that some value was produced in the ring, and some deducted too.
What we didn’t notice was the constant shortening of remaining discount periods.
As each day passes, each future yield comes one day closer. These are the apples
slowly ripening on the tree. Present value of each rises because the discount period
covers less time. This creation of value is output by definition, even though nothing
has moved but the hands of the clock. As the discount period reaches zero, the
expected yield eventuates to explain the taste satisfaction. These yields are the
apples falling to be eaten. The ring holds its value intact because the exhaust of
value it surrendered has exactly offset the output of replacement value as time alone
shortens discount periods. Yet not an atom stirred.
The whole point is that the value of the ring or anything else is discounted present
value of foreseen satisfactions. They are discounted because there is such a thing as
“time preference”; we value satisfactions now over foreseen ones later. This is not
quite the same as the difference between birds in the hand and birds in the bush.
That says that we value certainties over probabilities. Time preference also values
Chapter 3: Foundations 1/11/16 3
present certainties over future certainties. The reason is studied in a branch of
economics called “capital theory”. My next generation theory, really Petty’s of 1662,
proposes what the average-risk time discount rate is and why. Present value of each
expected instant of future satisfaction grows at that rate as time shortens the
discount period. It disappears, as apples from the tree, when expectation matures
into reality.
This diamond ring parable is full of useful lessons. I think it contains substantially all
of economics. “Consider the lilies of the field.” “They also serve who only stand and
wait.” A chemist would testify that the ring has done nothing. An economist sees
plenty happening. Economics is abstraction. Physical capital is not things, and
human capital is not people. It’s all in the mind. What an economist sees is present
value evolving with time as expectations ripen and eventuate. Output is not what we
do, although it has to do with what we do. It is the passage of time. Exhaust is the
fruition of time and the harvest reaped.
Only when we allow psychic values can we say that all behavior is economic
behavior. It is choices among alternatives. That’s what makes economics philosophy.
Axioms
Then what should its axioms be? We would like empirical or real-world certainties. I
find none beyond Descarte’s cogito. Philosophy is certain of next to nothing. We
settle for working assumptions. We want ones as safe and few as possible. Those of
economics have usually been left implicit since the marginalist revolution. I dropped
the course because I felt their need. It should do no harm, at this point, to risk the
opposite extreme. Let’s try putting everything on the table.
My first axiom, in that spirit, will be unguided natural causality. This need not alarm
the devout. It is the working assumption of all science. Working assumptions are
not creeds. I cannot rule out the possibility of occasional or even continuous
intervention by God to explain what we see. But we know to act as if we ruled it out
Chapter 3: Foundations 1/11/16 4
when our science hats are on. Even philosophy, in the Western tradition, leaves
revelation aside. A practical consideration is that debates of how God is likely to be
motivated to intercede have tended to find little consensus or traction. Science gets
some.
I tipped my hand on my own views in Chapter 1. As chairman of the Leakey
Foundation for more than 40 years, I pretty clearly buy evolution theory and
unguided natural casualty as working assumptions. But I invite those who don’t to
read further before deciding that we will disagree on conclusions. If I foresaw a
conflict with the devout, which I don’t, I would feel obligated to warn them now. I’ll
bring this up again as we go along.
My next few axioms, lumped together, are a mortal and reproducing population
which competes, cooperates and freelances to act on convergent predictions. It acts
to satisfy convergent tastes in a world of limited resources. I will model the
population as human, although other species would do insofar as my axioms hold
for them. “Convergent” means non-identical from individual to individual or place to
place or moment to moment, but converging to norms with increasing scale in space
and time. Predictions converge to outcomes as well as to one another.
The point is that tastes and predictions must be convergent enough for markets to
form and hold. A market, as Becker knew, is where anyone makes any choice among
alternatives. A literal market is where a choice leaves a quantitative record. Markets
cannot form and hold if we cannot predict where to find them and what they supply
and when they are open. They cannot form and hold without some consensus that
what we predict they will offer includes something we want. Clothing stores can
work because our sizes and shapes fall mostly within standard ranges. Their
business would be in trouble if we did not agree in number and rough placement of
arms and legs and head. Restaurants can work because we can find what we want
on a finite menu. Most crucially, clothing stores and restaurants cannot hold unless
there is consensus on what their wares are worth in return. All this convergence
Chapter 3: Foundations 1/11/16 5
suggests a single species, although the axiom only said population. The ants and the
picnickers can compete for the lunch, but they cannot bargain for it. The bar in Star
Wars is a great gag because it thumbs its nose at this home truth. We converge in
taste for the hilarious.
I will add the biological imperative as a separate axiom later, although much of that
at least may be implicit in the first one of natural causality. We hate unnecessary
axioms, from good Occamite principle, but we hate unsupported inference or
question-begging worse.
I spell out the axiom of mortality and reproduction because I know I’m heading
towards Petty’s insight and next generation theory. Of course we design foundations
to support what we want on top. It seems to me that my axioms mention nothing
about rationality, whatever that might mean, except in the sense of assumed
convergence of predictions to outcomes. And that assumption itself might not be
critical. What seems critical that is the predictions should converge to a known
function of outcomes. If they converge to something predictably overoptimistic or
overpessimistic, we’re still in business. Lacking even that, economic science is
stillborn. We can’t predict chaos.
That’s an example of the principle that axioms need not be strictly true. They must
be true enough. We’re still in business if God intervenes a little here and there. Much
more than that, and the convergent prediction axiom runs into the problem of
predicting the mind of God.
The two convergence axioms, of tastes and predictions, are implicit in all
microeconomics. “Micro”, as economists call it, is about supply meeting demand at
price equilibrium. This insight was the main theme of the marginalist revolution. It’s
exactly what can’t happen without convergent tastes and predictions. It’s exactly
why the bar in Star Wars is a hoot. Ants find price equilibria in ant markets, and
people in people markets. Ants and people find no meeting of the minds. Then if
Chapter 3: Foundations 1/11/16 6
macroeconomics (“macro”) rests on micro, the convergence axioms say only what
economics has accepted implicitly since micro began. The “law of one price”,
meaning market equilibrium, actually begins a century and a half earlier with
Cantillon. But Jevons, in co-founding the marginalist revolution in 1871, effectively
made it an axiom.
I don’t want to seem to claim that the convergence axioms are safe because they are
accepted. Arguments ad majoritatem or ad auctoritatem prove nothing. But markets
do seem to form and hold, and the convergences seem implied. Authority and
majority are sometimes right.
Not all economists have agreed. There have been “historicists” and
“institutionalists” who mistrust the idea of convergent tastes, and prefer to see
idiosyncratic national tradition or power groups or mindsets as the prime movers in
place of uniform human nature. Heinrich Schmoller, a historicist who stressed
national differences, tangled with Carl Menger, an independent co-founder of the
marginalist revolution in 1871, in a childish feud for which Menger was at least as
much to blame. If you must answer your critics, be gracious. Thorstein Veblen, an
institutionalist from Wisconsin, coined the term “neoclassicism” for what we now
call marginalism. He made fun of it for missing the role of institutions in driving
economies for institutional or collective goals rather than individual human ones.
I think there’s something there. My main theme in this book is growth theory at the
collective scale. I argue that collective growth flourishes where laws and practices
and cultures nurture and protect it. These are national institutions. New ideas, by
definition, are opposite from the fungible commodities for which supply and
demand meet at price equilibria. Somehow they come. Dogs bark, cats climb, people
innovate. I’m with Menger and Jevons and the marginalists and human nature, but
with asterisks there too. There is plenty left for historicists and institutionalists to
help explain.
Chapter 3: Foundations 1/11/16 7
Vocabulary and Catechism
The words microeconomics and macroeconomics, by the way, didn’t exist until
Ragnar Frisch coined them in the 1920s. We use terms retrospectively to describe
old arguments in language familiar now. That segues into the next steps in the
foundations. What should be the basic vocabulary and catechism, meaning basic
logic, in terms understood today?
Consideration of purpose always comes first. The purpose of economics is
prediction. We happen to know that one of the most powerful predictors of
economic behavior is maximization of risk-adjusted return. This was Robert
Turgot’s insight of 1766, although he left the risk variable unsaid. (His real first
name was somehow Anne, so we’ll go with the second). He wrote that return
equilibrates across markets as investors leave low-return businesses to crowd into
higher-return ones. The shift bids up capital denominators in the higher-return
businesses, and conversely, until return converges. It was David Ricardo, in 1817
who added that the convergence is more exactly for businesses judged equal in risk.
The evidence is everywhere we look. I call this the maximand rule: all behavior
maximizes perceived risk-adjusted rate of return. I’ll show its proof below. That
means all behavior in all markets, and markets are where any choice among
alternatives is made. Return means ratio of (net) output to capital generating it.
Then the vocabulary wanted might as well include capital and output.
But what is capital? Economics is choices, and the measure is price or value. Price
can’t be measured exactly outside literal markets, which is why economists follow
those markets, but is measured in principle by what we give up in exchange. The
price of any capital, even human capital, is given by the present value rule as timediscounted
cash flow. Then cash flow and its positive and negative components
belong to the basic vocabulary, while the present value and maximand rules both
belong in the catechism. Output is total return, so the total return truism belongs in
the catechism too.
Chapter 3: Foundations 1/11/16 8
What other basic terms do we need? Cash flow at the collective scale, where
transfers cancel internally, and there is no source of investment from outside,
simplifies to exhaust of value in taste satisfaction. There is no negative component
because there is no external source of new investment. Tradition through most of
economic history has called this exhaust consumption. Schultz recognized some
consumption as investment in human capital, I said earlier, and limited the exhaust
to “pure consumption”. I will use this and the term “exhaust” interchangeably. Then
transfer, consumption, exhaust and pure consumption belong in the vocabulary too.
So does “invested consumption”, my restatement of Schultz’ “pure investment” in
human capital.
This seems to be the right track. The object is prediction of behavior. The maximand
rule predicts all behavior, and I have sought to build a vocabulary and catechism to
clarify its terms. The right vocabulary, thank gosh, is mostly the one we have all used
since Adam Smith or even Petty. It has needed only a little tweaking and
clarification, as to the two kinds of capital and consumption for example.
There is a “fundamental theorem” of calculus showing how differentials and
integrals fit together. Its proof takes a lot of thought. There is a simpler one for
algebra. Might a fundamental theorem of economics be helpful? Obvious candidates
would include the maximand rule predicting all behavior, the total return truism
explaining the output numerator of the maximand (rate of return), and the present
value rule explaining the capital denominator. For years I chose the maximand rule
as the fundamental theorem. Then I preferred the present value rule as more
fundamental since it explained the denominator. But so would be the total return
truism in explaining the numerator. Now I opt for the judgment of Paris. Let the
three together be the fundamental theorems of economics. The maximand rule is
the centerpiece, and the other two define its terms. All three together are much
easier to follow, mercifully, then the one of calculus.
Chapter 3: Foundations 1/11/16 9
The vocabulary can also include the standard distinction among stocks, flows and
rates. These are only definitions, not assumptions. Stocks means value measured in
money units, say dollars. This is not the same as stock in the sense of equity
securities, although those can be examples. Flows means processes such as output
for consumption measured in dollars per unit time. Flows are to stocks as verbs to
nouns. Percent rates are flows divided by stocks, as rate of return or growth rate,
and are measured in pure numbers over time such as 5% per year.
Now for the fundamental theorems. Take the present value rule first. It starts from
the axiom that we satisfy convergent tastes in the light of convergent predictions. In
a simple case, we foresee that an asset (stock) is likely to yield a certain amount of
taste satisfaction flow at a certain future time. We discount that expected amount at
a time preference or time discount rate given by our taste for impatience, tempered
by our taste for risk avoidance, to find its present value. Present value of the whole
asset is the sum of present values of all the expected future satisfactions together.
A more general case allows for transfers. The future events we foresee and discount
are not always exhaust in taste satisfaction by ourselves at the time. Some might be
foreseen liquidations to reinvest in other assets or to give away so that we or the
donee can realize the taste satisfaction later. Either reinvestment or gift is called
transfer. I call it “transfer out”, meaning out from the generating asset. Then
transfer out = reinvestment + gift. (3.1)
There can also be transfer in. Sometimes future realizations, in taste satisfaction or
transfer out, are not explained as production by the asset as it is now. The asset
might grow later by new investment from outside, and the investment in between
might help explain the later yield. If an eighth-grader is destined to become a doctor,
for example, her foreseen earnings as a doctor will presuppose investment in high
school and college and med school in between.
Chapter 3: Foundations 1/11/16 10
The expected future flow we discount to present value, allowing for transfers too, is
exhaust plus transfer out less transfer in. This net difference is called cash flow. That
is,
cash flow = exhaust + transfer out – transfer in. (3.2)
That’s the logic behind the present value rule interpreting capital as discounted cash
flow.
Human cash flow may not be defined in those words anywhere but in this book. But
the flow discounted to find human capital is understood everywhere, I think, as pay
less what Schultz called pure investment and I call invested consumption. I
defended this idea in my analogy between human capital and the firm. Thus I
endorse the tradition that human capital is pay less invested consumption
discounted to present value. That is,
human cash flow = pay – invested consumption.
It turns out that this is not logical certitude, or an inference from axioms already
given, and so it is not strictly part of the foundations. I will defend it in later
chapters.
The great convenience of the present value rule and its application to human capital
is that it allows the factors to be added as a dollar sum. That helps in understanding
the total return rule.
That rule begins with the truism that growth of anything is internal creation plus
flow passed in less flow passed out. That shows as
growth = creation + flow passed out – flow passed in. (3.3)
Chapter 3: Foundations 1/11/16 11
Algebra now allows
creation = growth + flow passed out – flow passed in,
(3.3a)
since terms can change sides if they reverse signs.
Economics is interested in creation and growth of value. Value in the stock sense
means capital in general. Most economists most of the time use the word to mean
only the “physical capital” we buy and sell. But the truism works for anything. I
sometimes prefer the generality of “value”, meaning any amount of any mix of
human and physical capital. This again can be called either “total capital” or value
interchangeably.
Flow of value passed out is exhaust plus transfer out, and flow passed in is transfer
in. Creation of value is output in the net sense. Then (3.2) and (3.3a) give the total
return rule
output = growth + cash flow.
(3.3b)
“Income” means rights to output, and is implicitly equal to output. Like most writers
in economics, I will use these words more or less interchangeably too.
Now comes the centerpiece. A good starting point is the present value rule. We
assemble value or total capital to satisfy foreseen tastes. But we also satisfy current
tastes by spending current cash flow. At the scale of the total capital (value) of the
individual, were reinvestment cancels internally, cash flow simplifies to exhaust in
taste satisfaction plus gift given less gift received. Then
individual cash flow = net gift + exhaust, (3.4)
where net gift means gift given less gift received.
Chapter 3: Foundations 1/11/16 12
Consider net gift. Its negative component, gift received, is concurrently added either
into total capital growth or into exhaust. Thus it is the contribution to those two
desiderata explained from outside, rather than by the individual’s behavior. Net gift
deducts that negative component (gift received) from the positive one to leave the
part which the individual’s behavior explains. Thus individual output, as the sum of
growth and net gift, is the sum of desiderata realized by behavior. That makes it the
unique behavioral maximand as a flow. Division by the individual’s total capital,
which is her whole means of behavior, gives total capital rate of return as the rate
maximand.
This can be summarized in a slightly different way. Cash flow measures the means of
taste satisfaction now. Total capital growth measures gain in means of expected
satisfactions, discounted according to our taste for impatience (time preference)
tempered by our taste for risk aversion. Output is their sum. Behavior reveals and
maximizes the taste satisfaction including provision for future satisfaction.
Therefore risk-adjusted output is the flow maximand. Capital of both factors, at
present value, is defined as the whole means of that satisfaction, and implicitly of
behavior. Therefore risk-adjusted return, the ratio of the flow maximand to its
means, is the rate maximand.
What Turgot said in 1766, in his Reflections, was
“. . . as soon as the profits of one employment of money. . . increase or
diminish, capitals turn in that direction. . . or withdraw and turn to other
employments. . . Whatever the manner in which money is employed, its
product cannot increase or diminish without all the other employments
experiencing a proportionate increase or diminution.”
Turgot did not allow for risk in this quick summary, but otherwise explained the
mechanics that tend to equalize return.
Chapter 3: Foundations 1/11/16 13
The rule does not say that risk-adjusted return tends to hold constant over time. To
the contrary. Return equals growth plus cash flow, and my charts show the growth
component as a bucking bronco. The maximand rule says only that risk-adjusted
return is always the maximand. It is not always the same as time changes
circumstances. Proof is in Turgot’s equalization of return at each moment, not from
one moment to the next. That is what we see wherever we look.
There is a quibble worth attention. Behavior seldom expresses taste exactly. We say
one word when we mean another. We reach for the coffee, and accidentally spill it.
That was the point of my axiom that predictions converge to outcomes, as well as to
one another, only on average. Outcomes are generally a little better or a little worse
than predicted. There can even be systematic bias where all people together seem
overoptimistic or overpessimistic accordingly to circumstances, as shown in the
psychological economics of Hanneman and Tversky. The axiom requires that these
biases offset over scale and time. That sounds plausible, and anyhow makes analysis
easier.
The maximand rule would be ridiculous if terms were defined in a literal market
context only. Markets must be defined as wherever any choice is made. It would be
ridiculous if cash flow were understood to presuppose literal cash, or even the
necessity of some quid pro quo to explain motivations. Unreciprocated gift down the
generations drives lineage survival.
All behavior means all behavior. The miser maximizes the growth component in
return, the parent or philanthropist maximizes the net gift component, and the
good-time Charlie maximizes exhaust.
Have I gone too far in this claim? Try to imagine an exception. What kind of behavior
might not maximize perceived risk-adjusted return? What if I jump out the window?
Deliberately drive my car into a tree? Sell a cow for a handful of beans? Maximize a
Chapter 3: Foundations 1/11/16 14
pile of nuclear waste in my safe instead of cash and securities? Drive a truck filled
with dynamite into a crowd of unbelievers? Write a book on economics when I have
no credentials? Sing when I have an atrocious voice? All express my tastes. There is
no escape. Behavior reveals taste satisfaction in the broad sense including provision
for future satisfactions.
Tastes, Aims and Ends
I usually mean the word “tastes” as objectives whose satisfaction exhausts capital
value. By that usage, as we just saw, the truism that behavior reveals tastes must be
interpreted carefully. We see current taste satisfaction at mealtimes. Between meals,
we mostly see buildup of capital to satisfy tastes in future. And we sometimes are
motivated to give capital away, as in raising the generation to succeed us. I
sometimes use the term “aims” to mean the sum of this exhaust plus gift plus
buildup. Then to say that output realizes growth plus cash flow is to say that it
realizes aims. All behavior reveals and maximizes aims explained by ends. This
again puts the maximand rule in a different way.
As capital of both factors is our whole means of behavior, and as it is present value
of foreseen taste satisfaction and nothing else, we might first suppose that taste
satisfaction is our unique final goal. But that too could mislead. Biology shapes our
tastes, and shapes them to replicate the generations. I treat the biological imperative
as the “ends” driving tastes and aims. Our two complementary ends are adult
survival and replication of both factors for survival of the young. This idea underlies
next generation theory.
What we maximize is risk-adjusted present value of current plus foreseen taste
satisfactions by ourselves plus donees. Current taste satisfaction or exhaust by
ourselves is counted at full value, and foreseen ones are added at a time discount.
Transfer is part of the mechanics. The exhaust plus growth plus gift are the aims, in
whatever proportion we like, and our subliminal deeper motive of lineage survival
is the ends.
Chapter 3: Foundations 1/11/16 15
Subjective Certitude
Tautologies or truisms are logical certitudes. My three fundamental theorems are
cases in point. The total return truism is a classical example. Since growth is
creation less net outflow, creation is growth plus net outflow. This gives unqualified
certitude to the doctrine that output, or creation of value, is growth of value plus
cash flow (net outflow of value).
The other two fundamental theorems are certitudes in a subjective sense. What they
predict infallibly is intentions. The present value rule must give capital value as we
see it individually. Only under the convergence axioms does it predict observed
market equilibria. The same is true of the maximand rule. This rested on the same
axioms and the one that a population acts to satisfy tastes (in the sense of aims).
There are schools of thought, including Popperians and deconstructionists, which
disapprove of logical certitude on grounds not clear to me. They are wrong. A rose is
a rose. Nor are all examples as inane as that one from Gertrude Stein. All of math is
derived as logical certitude. Its proof comes from analysis, not experiment. Proof of
Fermat’s last theorem eluded some of the finest minds in the world for three
centuries until Andrew Wiles published the solution in 1995. Philosophy is precisely
a search for hidden truisms or tautologies. Economics is philosophy when it does
the same. The pay rule shows that their inferences can be startling. Age-wage
profiles are technically illustration, not proof, of the proposition that human
depreciation is expected to be recovered in pay. That follows from definitions and
needs no evidence in proof.
The pay rule is not wholly logical certitude because it also proposes that
maintenance consumption is not recovered in pay. Rather I argue that from the
biological imperative: maintenance is exhausted in satisfying our taste for adult
survival. The fact that few can have doubted this since the physiocrats has nothing
to do with proof. The shock, anyhow, is in the expected recovery of human
Chapter 3: Foundations 1/11/16 16
depreciation. This opened a can worms. It contradicts the Y = C + I equation, and the
related belief that output equals profit plus pay. I will try to track down some of the
worms, as I promised, and release new ones in the process if I must.
This book will continue to hunt for certitude, absolute when possible and subjective
otherwise. If the convergence axioms are trustworthy, behavior will reveal aims
well enough.
Output Exhaust
I define output as creation of value, and equivalently of capital. Does this overlook
the possibility that output might also create taste-satisfying pure consumption
directly, without passing through a capital phase first?
Such a thing is possible in math, but not in economics. Since capital is foreseen
eventual exhaust, exhaust not drawn from capital in place would be implicitly
unforeseen. This is the flip side of the deadweight loss rule. Economics is a rationale
of choices, and neglects unforeseen taste satisfaction as unable to influences choices.
Those unforeseen and hence costless satisfactions are called “free goods”, and
ignored as outside the economic purview. They why not ignore free growth too?
Growth is roughly foreseen and factored into choices, for one thing, even if I am the
first since Mill to foresee it as free. For another, even unforeseen events are of
economic interest if they affect means or choices after. Free growth does. Costless
satisfactions leave no trace.
Note in any case that the total return truism (3.2) through (3.3b) does not depend
on this inference. Those equations describe creation of value, not necessarily of
capital alone. Output exhaust would be added both to output and to exhaust, and
would disappear in their difference.
Chapter 3: Foundations 1/11/16 17
Basic Glossary
I use standard terms when I can find them, and coin new ones like “aims” and “ends”
when I can’t. But even standard ones are ambiguous. The vocabulary of economics is
not settled. Look up “capital” or “output” or “cash flow”, for example, in any
economic dictionary. It will show ranges of meanings, and appreciably different
ones from one dictionary to the next. I coped by defining as I went along, and would
have had to do the same even if this book were meant for economists only.
Otherwise the ambiguities would have left loopholes.
Definitions include:
Aims:
Capital:
Cash flow:
Ends:
Exhaust:
Flow:
Human capital:
Income:
Invested consumption:
Maximand rule:
Net transfer:
Intention to maximize the sum of current taste
satisfactions plus gift, plus growth in means of future
satisfactions and gift.
Means of aims; human plus physical capital; present
value of expected cash flows.
Capital passed out, in transfer or exhaust, less capital
inserted from outside.
Rationale of aims; biological imperative.
Termination of capital in taste satisfaction.
Any process measured in capital per unit time.
Present value of skill sets; capital whose outside
operating cost is exhausted in taste satisfaction; present
value of pay less invested consumption; present cost of
past invested consumption less pay.
Rights to output; equal to output.
Transfer into value of human capital.
All behavior is maximization of perceived risk-adjusted
output and return as a flow and a rate respectively.
Transfer out less transfer in.
Chapter 3: Foundations 1/11/16 18
Output:
Physical capital:
Present value rule:
Profit:
Pure consumption:
Rate:
Stock:
Tastes:
Total return rule (or total
return truism):
Transfer in:
Creation of wealth, or equivalently of capital of either
factor.
Capital whose outside operating cost does not satisfy
tastes.
Capital of either value is expected cash flow discounted
at our time preference rate.
Output of physical capital.
Same as exhaust.
Quantity measured as a flow over a stock, and
equivalently as a pure number over time.
Quantity measured in dollars alone. Same as capital.
Intentions whose satisfaction terminates capital in
exhaust.
Output equals capital growth plus cash flow.
Value inserted from outside. Same as new investment
from outside.
Transfer out:
Wage:
Work:
Value passed out and recovered fully in other assets
rather than exhausted.
Same as pay.
Output of human capital.
Summary
When I first thought these foundations through, maybe 25 years ago, I was just as
happy to see that they held so little originality. The vocabulary is about the same as
in Adam Smith, and the three fundamental theorems are well accepted. Any
composer knows that originality should be incidental. Our music says what we think
Chapter 3: Foundations 1/11/16 19
needs saying. If it does, that tends to mean that it is new to the current conversation.
It need not be new to the world.
All three fundamental theorems are part of the daily conversation of investors and
finance economists. They are not much on the screens of microeconomists and
macroeconomists. There may have been some originality in spelling out the implicit
axioms behind them, and in generalizing them into all capital including human
capital if we trust those axioms.
One of the mini-surprises was that gift appeared in my very first equation. Cash flow
at the scale of the total capital of the individual, where reinvestment cancels out,
simplifies to gift and exhaust alone. Obvious in hindsight, but surprising if we have
been taught that economics is all about numero uno. I think it is about adults giving
to the young to keep the generations turning.
That sets the theme of this book. Old ideas will find unfamiliar combinations and
applications. Those are originality enough. But so many little stretches of the tried
and true can be hard to track.
Economics needs a special and counterintuitive mindset. The guiding principle is the
analysis of the diamond ring. Economics means taking our minds off the physical
substrate. That goes to the corners of our eyes, not the focus. Capital is not people
and things. It is present value of foreseen cash flows. Output is the ripening of these
foreseen flows with time, and exhaust is the harvest eventually reaped. Economics
takes us through the looking glass to a place the same but different.
Chapter 3: Foundations 1/11/16 20
CHAPTER 4: MILL’S IDEA
Mill’s Paragraph
It always seemed obvious to me that growth is free. Survival costs investment in the
next generation, but growth costs nothing more. It seemed to me that innovation is
the human specialty, that we pay its cost every day as the cost of being human, and
that growth happens when genius or circumstance somehow gives it traction. I
spent most of my life assuming that all economists, but not politicians, thought the
same. I since learned that economists, following Solow, teach something close but
different. So I guessed that I had hit on something new.
I hadn’t. We read economic history to learn that our ideas are seldom original.
Thomas Malthus, contradicting his friend and rival David Ricardo, wrote something
like my or Mill’s free growth theory in 1820. Chapter 7 of his Principles 1 says this in
several ways. One example is
“When we have attained…increased and steady profits, we may then begin to
accumulate, and our accumulation will then be effectual. But if, instead of
saving from increased profits, we save from diminished expenditure; if, at the
very time that supply of commodities compared with the demand for them,
clearly admonishes us that the proportion of capital to revenue is already too
great, we go on saving to add still further of our capital, all general principles
concur in showing that we must of necessity be aggravating instead of
alleviating our distresses.”
John Rae renewed this theme in 1834. Book 1, Chapter 10 of his New Principles 2
includes
“If an improvement, for instance, in the art of baking bread were effected, by
which, with half the labor and fuel, equally good bread could be produced, it
would not benefit the bakers exclusively, but would be felt equally over the
whole society. The bakers would have a small additional profit, the whole
society would have bread for the product of somewhat less labor, and all who
1 Principles of Political Economy Considered with a View to their Practical Applications
2 Statement of some New Principles on the Subject of Political Economy
Chapter 4 Mill’s Idea 1/11/16 1
consumed bread, that is, every member of society, would from the same
outlay have somewhat larger returns. The whole series of instruments
owned by the society would be somewhat more productive, and would be
carried to an order of quicker returns.”
The clearest expression, and probably clearest even today, came from Mill in 1848.
He put it that output growth can precede and explain capital growth as well as the
reverse. Crediting Rae, he wrote:
There are other cases in which the term saving, with the associations usually
belonging to it, does not exactly fit the operation by which capital is
increased. If it were said, for instance, that the only way to accelerate the
increase of capital is by increase of saving, the idea would probably be
suggested of greater abstinence, and increased privation. But it is obvious
that whatever increases the productive power of labor creates an additional
fund to make savings from, and enables capital to be enlarged not only
without additional privation, but concurrently with an increase of personal
consumption. Nevertheless, there is here an increase of saving, in the
scientific sense. Though there is more consumed, there is also more spared.
There is a greater excess of production over consumption. It is consistent
with correctness to call this a greater saving. Though the term is not
unobjectionable, there is no other which is not liable to as great objections.
To consume less than is produced, is saving; and that is the process by which
capital is increased; not necessarily by consuming less, absolutely. We must
not allow ourselves to be so much the slaves of words, as to be unable to use
the word saving in this sense, without being in danger of forgetting that to
increase capital there is another way besides consuming less, namely, to
produce more.
The words “accelerate” and “concurrently” show that Mill understood calculus. His
autobiography says that he hadn’t really learned it from his father James, who had
bought a book and was trying to teach himself and the 13-year old son at the same
time. The son studied it in his later teens at school in France. He like me was writing
for everyone, and preferred to keep explicit math off the page. But the quote
reminds us that the only alternative in economics is implicit math in sentence form.
The paragraph implies the Y = C + I equation: output equals consumption plus
investment. I go a tad farther, starting one chapter ago, by offsetting my word
equations from the running text. These show equal signs and plus and minus and
Chapter 4 Mill’s Idea 1/11/16 2
division and multiplication signs, rather than keeping them inside the paragraph
and writing out such words as “equals” and “plus”. These word equations are
usually easy enough to read. My appendix will cover them and more in notation.
Mill’s equation may be as old as economics, although I haven’t found it put explicitly
before Keynes wrote it in his General Theory 1936. It is now foundational to national
accounts and macroeconomics (the art of balancing full employment with price
stability). I showed why I agree only if we add a couple of imaginary asterisks. We
have to mean total capital growth and pure consumption. Mill and tradition have
meant physical capital and all consumption.
That leaves me with something like the heuristic problem of Halliday and Resnick.
They started with Newton as something familiar and accessible and commonsensical.
I will follow suit. I will reason as if Mill’s equation were right. My own
argument is exactly the same if we remember the hidden asterisks. That saves us all
the trouble of going through it twice. Chapter 4 will restate it in terms of total
including human capital just to make sure.
It is an unsettling argument either way. It unsettled Solow. Chapter 2 showed why.
We are probably more comfortable to think of income as something known which
we can slice into consumption and saving slices as we like. Less of one would mean
that much more of the other. That would put us in charge. We can always consume
less by will power. If less consumption meant more growth, we could grow at will.
Keynes showed otherwise by invoking the old paradox of thrift. If everyone put
money in vaults instead of consuming, consumption would go down while money
piled up. But the added money would find less output to buy with it, as nothing new
was created to compensate for the drop in consumption. The value of the piled-up
money would vanish in inflation. Saving would equal investment in the end because
both disappeared. The Y = C + I equation shows the math. It say that less
Chapter 4 Mill’s Idea 1/11/16 3
consumption C means either more investment I or less output Y. It doesn’t say
which happens.
Investment, for Keynes, meant creation of new productive assets. He was right in
seeing that as the goal. But his analysis leaves too much outside. What I miss is a
variable for investment quality. Investments in new productive assets in 1929 or
2008 yielded negative return. Money in vaults did better.
I prefer an approach which takes our minds off the ultimate goal in new productive
assets. I drop all distinctions between saving and investment. Either word means
the other. What matters is its intended and realized return. That is the missing
quality variable. Notice that I don’t have to specify “risk-adjusted” return because
Keynes and I are describing only at the collective (national) scale. Risk of all
investments collectively is average risk. This can be implicit whenever I describe at
the collective scale.
Keynes’ analysis and equations appear in his General Theory. He was addressing the
world depression. A theme was that households do most saving, while businesses do
most investing. Banks collected the saving and made it available for business to
borrow and invest. But business lacked the “animal spirits” to take such a risk in a
slump. We saw the same story after 2008. Keynes’ proposal was for government to
do the borrowing and investing instead. That’s part of the “fiscal policy” I described
in Chapter 1. Here we tend to agree. That would explain his sense of urgency as to
new productive capital as the most direct way to put idle plant and workers back to
work.
I prefer to suspend judgment on what is a new productive asset and what isn’t. I
think my way of putting things is both simpler and subtler than Keynes’, although at
sacrifice of his explicit focus. Saving and investment, in my language, are the same
from the start. The maximand is return. Consumption foregone will translate into
Chapter 4 Mill’s Idea 1/11/16 4
capital growth insofar as rate of return actually realized matches the current norm.
Less return makes less growth than consumption sacrificed, and more makes more.
But collective return can be a surprise. Boom years and bust years arrive unforeseen.
The cost of investment in consumption given up, whether individually or collectively,
never agrees exactly with what it proves to be worth at market. Gunnar Myrdal, in
1939, coined the terms ex ante for the first and ex post for the second. The bucking
bronco describes the ex post picture overall.
Ex ante (at cost) and ex post (at market) investment agree when market-realized
return holds unchanged. Lower return means that ex post outcomes fell short of ex
ante cost and expectations. Higher return means the reverse. That gives the context
of Mill’s idea. And he clearly isn’t talking about growing or declining by random luck.
His prime mover is “whatever increase the productive power of labor.” He knew
that this meant innovative ideas. Can we dial them in as we like? All he says is that
they need cost nothing in consumption missed. Then how might that work?
Gross and Net Investment
Keynes, accepting the Y = I + C equation, defined saving S as gross income less
consumption C. I draw the impression that he implicitly defined output as creation
of economic value. So do I. He defined gross investment I as gross output less
consumption. Gross in both cases meant gross of depreciation. He knew that income
and output are equal, at all scales, since the first means rights to the second, and
gave both the symbol Y as I do. It followed that saving and investment are also
equal. The meaning was that actually realized saving, as distinct from consumption
restraint in hopes of saving, had to be realized in investment. This is the home truth
which I accept but prefer to rephrase.
I have traced Keynes’ argument and language on these points because I think it is
now generally accepted by Keynesian and anti-Keynesian and neo-Keynesian
schools alike. That’s why I think my own interpretation differs from a general
Chapter 4 Mill’s Idea 1/11/16 5
consensus rather than supports one school over another. I think it is the consensus
view, as well as Keynes’, that his “attempted saving” means gross saving (gross
income less consumption) not invested in new productive assets. That can be
written as
Keynesian attempted saving – transfer payments
= Keynesian net saving = Keynesian net investment,
at any scale.
I accept Keynes’ definition of transfer payments, and I recognize the importance of
his distinction of those from investment in new productive assets which put idle
plant and workers to work. My interpretation, even so, is that it is better to leave
them idle than to put them to work unproductively. Keynes made his opposite view
crystal-clear with his brilliant tongue-in-cheek parable of money buried in
mineshafts and idle workers hired to dig it up. He had a sense of theater as well as a
great mind. And he just might have been right. But I think my way of putting things
encompasses that possibility. His mineshaft scenario works if it somehow
maximizes return in the big picture.
My language differs from Keynes’ in several ways. I prefer Myrdal’s ex ante – ex post
dichotomy, published three years after the General Theory, to Keynes’ equivalent
attempted-realized one. Like Myrdal, and unlike Keynes, I apply it to investment as
well as saving. That’s why I treat them as synonymous. And I prefer to recognize
human capital explicitly. Keynes surely understood the concept. He was the star
pupil of Alfred Marshall’s later teaching career, unless he shared that distinction
with his lifelong personal friend and professional adversary Arthur Pigou, and
Marshall and Pigou both describe human capital in principle. Marshall wrote that he
neglected it as something outside what he saw as the main sequence ending with
consumption. Keynes could have agreed, or could have meant to provide for it
implicitly by defining output as investment plus consumption while realizing that
Chapter 4 Mill’s Idea 1/11/16 6
some consumption is investment in human capital. I said what I think this overlooks
(self-invested work) and what it forgets to exclude (recovered human depreciation).
My own way of putting things mightn’t strictly need the terms investment or saving
except to translate my ideas into the language we all know. That translation is
essential if I hope to be understood. It will first take account of the fact that Keynes
meant investment and saving as to physical capital only, with labor or human capital
to arrive exogenously as an outcome somehow of consumption. That led to the
Y = I + C equation
output = investment + consumption. (4.1)
Gross and net versions of (4.1) meant gross and net of depreciation. Thus
gross output = gross investment + consumption
(4.1a)
and
net output = net investment + consumption.
(4.1b)
In the General Theory, where (4.1) appears in his Chapter 6, (4.1) it means the gross
version unless otherwise specified. I prefer the opposite, and mean the net version
(4.1b) unless otherwise specified.
My ex ante investment corresponds to Keynes’ “intended saving” through
consumption restraint. My “depreciation investment”, or “depreciation plowback”,
means just enough ex ante investment to offset actual depreciation, not book
depreciation, of physical capital. I assume that we intuit roughly how much this is
when I say that optimum ex ante investment is depreciation plowback. Now let’s
consider how that could be true.
Chapter 4 Mill’s Idea 1/11/16 7
Growth Mechanics
Start with simplicity. Imagine a changeless world where people and things replicate
themselves exactly. Chapter 3 showed that in total capital terms including human
capital, although neither Mill nor Keynes used them, depreciation of both factors
together, net of transfers from one to the other, equals exhaust in taste satisfaction.
“Replacement investment,” or “depreciation investment,” is just enough to turn the
generations over as new (net) output makes up the loss to consumption exactly.
Ideas hold unchanged. That wouldn’t be too far from the truth for our million years
as homo erectus, or our millennia after as homo sapiens until some 50,000 years ago,
or our centuries in the dark ages after Rome fell. Most of the new norms we
innovated, although not all, eventually regressed to the old ones.
Next imagine growth of everything at a constant rate. Capital, consumption and
output all grow in constant proportion. Economists now call this “balanced” growth.
Mill had described that possibility in 1844. Balanced growth isn’t driven by
consumption restraint, as consumption never lags. And it isn’t driven by
productivity gain, meaning more output per unit capital, since output grows no
faster. What drives it?
Suppose first that there are still no new ideas. If we are pioneers in a new world or
empty niche, we might be able to increase numbers of exactly the same things and
skill sets until we reach niche limits. Then what would pay for capital growth in that
case? Zeno the Eleatic might insist that depreciation investment is never enough
because it chases a moving target. But depreciation moves just as fast. Identical
capital means identical in depreciation rates. That means the ratio of depreciation
(pure consumption) to capital. The two racers hold neck and neck indefinitely.
Depreciation investment is still enough, just as it was in the growthlessness before.
In balanced growth, as in standing still, it is the only need for of capital replacement.
Now comes a tougher problem. Niches in the real world are typically more or less
full. Here old ideas alone can’t bring growth. David Ricardo, Thomas Malthus and
Chapter 4 Mill’s Idea 1/11/16 8
Edward West had written in 1815 that in economies already developed, there isn’t
much room for more capital of the same kind. Its productivity disappears in capital
glut and diminishing returns. There could still be growth when some of the new
ideas would need only redeployment of existing kinds of capital, as in relocating
production nearer to the market or cutting out the middleman. This redeployment
was Solow’s “disembodied growth.” But growth after that have to come from capital
new in kind. Hourglasses might have to give place to pocket watches, or sailing ships
to steamships. Those were Solow’s “embodied” growth.
The apparent problem here is that novelty is expensive. There are blind alleys and
failure rates and learning curves that rote replication avoids. This is true somewhat
even in disembodied growth, where redeployment is already a step into the
unfamiliar. If depreciation investment is barely enough for balanced growth without
new ideas, how can it also pay for the failure rates and learning curves?
A tough question. And Mill was posing an even tougher one. The paragraph quoted
is clearly describing capital acceleration. Capital as he describes it is not only
innovating consistently as it keeps up with consumption, but picking up the pace,
and still taking the innovation costs in stride. Is that too much even for Achilles?
It is not. Charts and tables show that the kind of growth Mill describes has proved
the only kind in every country and period where tests are practical. It has proved
the only kind whether capital was growing faster or shrinking faster or anything
between. The growth bronco bucks, and the consumption rider stays on. This is
what clearly happens, or anyhow has happened so far, despite so many reasons to
think it is impossible. What would explain it?
First take the lesser puzzle. Balanced growth, where capital, output and
consumption all grow at the same constant rate, must make do with depreciation
investment. How can it in crowded niches where growth compels the costs of
innovation? Chapter 2 showed my inference that these are the costs of being human.
Chapter 4 Mill’s Idea 1/11/16 9
We were paying them as homo habilis two million years ago. The cost went up, but
the value of innovation just as much, when homo erectus arrived a little later. Both
rose again with the emergence of Ancestral Eve 200,000 years ago. Adaptation is the
human specialty. Its what gets us through the day. Innovation is adaptation that
happens to become new norms. It started leaving a record of embodied growth
about 50,000 years ago. That doubled pace about 400 years ago. The costs of being
human are the same failure rates and learning curves whether the payoff in
adaptation/innovation means faster gain in good times or slower decline in bad
ones. We row at a steady stroke, and gain against the shoreline when our new ideas
are particularly good ones and the current is right.
My idea, whether or not Mill’s, is that these costs might be about the same for
breakthroughs or meta-ideas or paradigm shifts as for modest upgrades, or even for
holding even in a world of daily surprises. Ideas trade in an inefficient market. Cost
is dissociated from value, and cause is desynchronized from effect, by the vagaries of
genius and the whim of circumstance.
Now the tougher puzzle. How can consumption keep up with capital even in
accelerations? That’s what Mill described, and that’s what happens. Can Achilles
catch the tortoise even when the tortoise speeds up? Put your money on Achilles.
Here it is Gunnar Myradal to the rescue. The apparent problem is that ex ante
depreciation investment is never enough in acceleration. But the charts and tables
show unanswerably that ex post depreciation investment is. We sow the first, but
reap the second. Plowback of depreciation investment is up to us. Growth is
whatever is added by genius or happenstance. The difference between market value
and cost is sometimes luck, which neither loses nor gains in the long run, but
sometimes imagination. Mother Nature and Gunnar Myrdal simultaneously say
“Shazam”, and convert new ideas into embodied or disembodied growth without
surcharge for the novelty.
Chapter 4 Mill’s Idea 1/11/16 10
That still leaves the mystery only half solved. How exogenous (sourced from
outside) are the genius and happenstance? Can we coax them along by policy? That
isn’t really my field. What seems reasonably clear is that growth flourishes in
secular free markets with solid infrastructure and rule of law. How to get those
things is the problem. I will suggest that the answers, whatever they are, will be
developed outside the usual marginalist perspective of supply and demand.
The Free Growth Equations
Now back to Mill’s argument. Notice first that he puts it all in the present tense.
Modern growth economists have preferred what I called the lagged flows method:
spikes in investment are compared to later ones in output. Mill here is substituting
what I called a concurrent rates method: he compares changes in consumption rate
to changes in capital growth rate at the same time. He writes that “whatever
increases the productive power of labor … enables capital to be enlarged …
concurrently with an increase of personal consumption.”
Let’s follow that. Mill’s root assumption is the Y = I + C equation in its net form
(4.1b). Put the ex post version as
output = growth + consumption, (4.2)
meaning net output, growth of physical capital and all consumption. The Y rule says
the same with the hidden asterisks after growth and consumption. So it will
continue for the rest of this discussion. (4.2) shows that less consumption implies
more growth, or less output, or some of both. Mill was asking which. To show how
to find out, first arrange (4.2) as
growth = output – consumption,
(4.2a)
again because terms can change sides if they change signs.
Chapter 4 Mill’s Idea 1/11/16 11
Mill and Keynes and tradition hold (4.2) and (4.2a) as logical certitudes which hold
constant over time. I agree if we imagine the asterisks. Constancy over time would
imply
change in growth = change in output – change in consumption. (4.3)
I take the trouble to derive this as a road I haven’t preferred to follow. I will reason
instead in rates rather than flows. Rates, or ratios of flows to capital, effectively
cancel capital from numerator and denominator. That frees them to show
comparison between smaller and larger economies among the eight I test. Mill’s idea,
or anyhow mine, is that the ratio of consumption to capital in all those countries can
hold constant. That is what the charts and tables show.
To follow that lead, divide (4.2a) by capital. This finds
growth
capital
= output
capital – consumption . (4.4)
capital
That can be put more compactly as
growth rate = capital productivity – consumption rate,
(4.4a)
where rate always means ratio to capital. That needs a caveat because consumption
rate in macro means ratio to output. Capital productivity in this sense is also called
rate of return.
For more compactness still, define
thrift rate = – consumption rate,
allowing (4.4a) to be restated as
Chapter 4 Mill’s Idea 1/11/16 12
growth rate = capital productivity + thrift rate.
(4.4b)
Notice that we must change the sign before “consumption rate” to find thrift. Change
downward in consumption rate is change upward in thrift rate, and conversely.
Further
change in growth rate = change in capital productivity
– change in consumption rate, (4.5)
by the same logic as with (4.3). Save space again by reexpressing (4.5) as
acceleration = productivity gain + thrift gain.
(4.5a)
Finally divide by acceleration to reach
1 =
productivity gain
acceleration
+
thrift gain
acceleration , (4.6)
if acceleration is nonzero. Reexpress as
1 = free growth index + thrift index, (4.6a)
where indexes are undefined if acceleration is zero.
I think this gets at what Mill meant, and anyhow what I mean. We both describe
acceleration as well as growth. One night think that his “whatever increases the
productive power of labor” is the opposite from my “change in capital productivity.”
But they are about the same. Better machines make their operators more productive
whether skills have changed or not.
Chapter 4 Mill’s Idea 1/11/16 13
(4.5) shows something about “balance” or the state where capital, consumption and
output grow at the same rate. It confirms the standard teaching that balance is
possible, although not compelled, when growth rate is constant. It also shows that
balance is impossible when growth rate changes. No one disputes that capital
productivity (output/capital) always leads, and consumption rate
(consumption/capital) always lags, in accelerations up and down. Output gets the
bad news first and the good news first. What the equations leave unspecified is
where capital itself joins the sequence. That is what the evidence in the charts and
tables tells us.
In the case where the free growth index equals one, for example, the above
equations show
thrift index =
thrift gain
acceleration = 0,
implying
– change in consumption rate
thrift gain = change in growth rate = 0, and
change in consumption rate = 0, or equivalently
consumption rate = consumption
capital
= constant, (4.7)
if acceleration is non-zero. (The reason for that qualifier is that zero acceleration
means zero change in growth rate, and division by zero is a no-no.)
In the opposite case where the thrift index is one, the same equations would show
free growth index =
productivity gain
acceleration
=
changein productivty rate
change in growth rate
= 0,
Chapter 4 Mill’s Idea 1/11/16 14
implying
productivity rate = output
capital = constant,
(4.7a)
assuming again that acceleration is nonzero.
This shows how to find the position of capital in the sequence led by output, and
how to test between free growth and thrift theories. The market-valued capital
denominator in (4.7) and (4.7a), and the consumption numerator in (4.7), can be
taken directly from national accounts data collected at the Piketty-Zucman website.
The output numerator in (4.7a) can be constructed as consumption plus current
change in market-valued capital. By (4.7), free growth theory (Mill’s idea) predicts a
roughly constant consumption/capital ratio, even in accelerations and decelerations
and reversals. Then capital acceleration would lag alongside consumption
acceleration while output led alone. Thrift theory makes the opposite prediction of a
roughly constant output/capital ratio, so that output and capital would lead
together while consumption lagged alone. There is no need to measure and test both
indexes, as either is defined as one less the other. My charts and tables track the free
growth index. They confirm free growth theory in all countries and periods.
Defining Free Growth and Thrift
(4.2) through (4.7a) defined the free growth and thrift indexes, but not free growth
or thrift themselves as flows. Since I will use those terms often, I’d better clear that
up now. Define
free acceleration = productivity gain = gain in rate of return,
thrift acceleration = thrift gain = drop in cash flow rate,
and
so that those sets of terms become interchangeable. Then (4.5a) can be put as
Chapter 4 Mill’s Idea 1/11/16 15
acceleration = free acceleration + thrift acceleration.
(4.5b)
Rates are flows divided by capital expressing them. Then define the two flows as
free growth = capital ∗ free acceleration, and (4.8)
thrift = capital ∗ thrift acceleration, giving (4.9)
growth = free growth + thrift. (4.10)
These equations apply equally in continuous or discrete-period time. In the latter,
they leave the periods of acceleration and growth unspecified. Marginal or current
free growth, as with the speed of a car, is the sum of free accelerations since some
past origin when growth was zero. So it is with current thrift. That need not place
the origin with Ancestral Eve. Surprising as it might seem in the growth age, zero
points appear to recur every few minutes at the longest. Online stock index numbers
reverse direction at least that often. They pass through zero each time. Debt claims
on the corporate sector figure to be less volatile, but equity (stock) ones outweigh
them. Then marginal free growth means accumulated free acceleration, or rise in
rate of return, since the last zero growth point no more than a few minutes ago
when return and cash flow were equal. Growth is free whenever cash flow rate rises
or holds steady.
The Charts and Tables
Mill lacked data to test whether growth tends to lead with output when it changes,
or to lag with consumption, or something else. So did all economists until national
accounts began reporting market-valued capital in 1990 or so, and reconstructing it
backward over a few decades before. The equations through (4.7) show how to test
from data in the Piketty-Zucman and Global Financial Data websites.
First I downloaded the Piketty-Zucman data for market-valued capital and
consumption for all countries and periods. I chose their “private wealth” data for the
Chapter 4 Mill’s Idea 1/11/16 16
former. I neglected “government wealth” net of national debt, which is small and
often negative, as I don’t feel that I understand it well enough. I took consumption as
the sum of personal consumption expenditure (PCE) and government consumption
expenditure (GCE). I also downloaded real stock market rates of growth, dividends
and return from the Global Financial Data website for the same years and countries.
Yearly change in capital in each country gave each year’s capital growth as a flow. I
added this to consumption to give what I call market-valued output. I said earlier
that Piketty and Zucman should logically have done the same. This gave the values
for (4.1) and (4.1a).
I then divided by year-end capital to give values for (4.3). I next found annual
changes in those three to give acceleration, productivity gain and thrift gain as
shown in (4.5) and (4.5a), and divided by acceleration to find the two indexes of
(4.6) and (4.6a).
The test from Global Financial Data took fewer steps. Stock market growth rate, rate
of return and dividend rate were downloaded directly. I took them as corresponding
respectively to growth rate, capital productivity and consumption rate in (3.3a). I
found their annual changes to find values for (3.4a), and again divided by
acceleration to reach (3.5a).
This allows tests of Mill’s idea from national accounts data for all eight nations
reported at the Piketty-Zucman website, and over their entire reporting periods
through 2010. (The website also reports for Spain, but only since 1993 and without
data for consumption.) In each year, for each country, change in capital growth rate
is compared to change in consumption rate (consumption/capital). If consumption
rate grows faster than capital growth rate while both grow, or declines faster if both
decline, the free growth index in that year is greater than one. If they change at the
same rate in the same direction it is one exactly. If both change in the same direction,
but consumption changes less, the free growth index is between zero and one. If
Chapter 4 Mill’s Idea 1/11/16 17
either grows while the other declines, the index is zero or less; zero if one grew as
much as the other declined, and less if the change in capital growth rate was larger
than the opposite one in consumption rate.
Interpreting the Charts and Tables
Now look again at the charts captioned “free growth index” in the appendix. I will
summarize them and all other charts and tables only briefly here, and save most
description for there. They cover all eight countries. Each chart covering free growth
tracks three separate versions of the free growth index labeled !
ϕ(K), !
ϕ(K T
) and
! ϕ(SM). The one I have discussed so far is ! ϕ(K). ! ϕ(K ) is a version including human
T
capital, and !
ϕ(SM)is taken from stock markets only. will be explained in the
! ϕ(K ) T
next chapter.
The powerful spikes both up and down in the free growth charts were described in
Chapter 2. Spikes tend to be explained by the fact that acceleration, the denominator
in both the free growth and the thrift index, is occasionally close to zero. Near-zero
denominators, whether above zero or below, can magnify mismeasurements. Some
charts report the free growth index every year, and show all the spikes. Others filter
out years where denominators fall below a chosen threshold, and spikes disappear
accordingly. Filtration is unbiased in that free growth index is corrected down as
often as up.
What jumps out from all those charts is that all versions of the free growth index ϕ
fluctuate around one. That means that the unshown thrift index fluctuates around
zero. We just saw that the thrift index will show as negative whenever the thrift
numerator and acceleration denominator disagree in sign, meaning that thrift gain
coincided with deceleration (negative acceleration) or conversely. Charts and tables
show that thrift gain, meaning drop in consumption rate, coincides as often with a
lower as a higher capital growth rate. Growth by thrift is a theoretical possibility
Chapter 4 Mill’s Idea 1/11/16 18
which doesn’t actually happen. The means of growth Mill describes in the paragraph
quoted is the only kind that appears in the record.
Evidence from Stock Markets
Market-valued capital, reported in national accounts since 1990 or so and
assembled at the convenient Piketty-Zucman website, is measured by a common
standard in principle. Measurement begins with stock markets. It should. The stock
market is the most exact source of economic information that I know. With due
reservations about connivance and “stale prices,” meaning outdated prices from
earlier days because the stock has not traded since, or anyhow not enough for
confidence, we know pretty well what markets think stocks are worth from tick to
tick.
We would know better if markets were perfectly efficient. Proof that they aren’t
shows in medium-term autocorrelation or trend. Autocorrelation (in price) is
tendency for markets to be up tomorrow if up today, and down if down. Trend is a
shorter word for the same. Perfect efficiency ought to show a “random walk” where
prices change captures all current news, news captures reality without optimistic or
pessimistic bias, and tomorrow’s price direction is as unpredictable as tomorrow’s
news. The only exception should be long-term uptrend with productivity gain
through innovation. In this case it is not surprise in the news that brings growth, but
gradual gain in present value as a foreseen better future is less discounted as it
draws nearer.
There is chicanery as well as inefficiency. Insiders, braving the legal risks, may take
advantage of outsiders. But it is not clear to me that insiders are likelier to be sellers
than buyers. National accounts follow prices of publicly traded shares collectively,
where some chicaneries should offset others.
Allowing for all this, I think national accounts are wise to accept stock prices as the
best measure of underlying assets. Intangibles such as patents or market advantages
Chapter 4 Mill’s Idea 1/11/16 19
are factored into share prices because they are realities that would be valued as
such by bidders for the assets themselves. It is a mistake, I think, to suppose that
shares prices would be less volatile if more descriptive of real value underneath.
The existence of trends suggests the opposite. Trends would be expected from
systematic underreaction to the news, so that reaction catches up later, while
systematic overreaction ought to be followed by adjustment in the opposite
direction. This gradual rather than immediate digestion of the news would tend to
smooth out price response. Trends imply systematic underreaction, not
overreaction. Market evidence shows something near that random walk as a usual
rule, implying neither systematic overreaction nor systematic underreaction, but
with some episodes of the latter. What would the reason be? My first guess would be
something delaying the mechanics of price reaction when news is particularly
surprising. Our sense of where prices should go right now seems not to get them
there until later. Prefect reaction to perfect news ought to mean more price
volatility, not less, from day to day.
Stocks are more volatile then most assets because most are “leveraged.” Firms may
issue bonds, and may borrow shorter-term from banks. Fixed interest on those debt
claims is paid first. Shareholders get the rest of net output, which itself fluctuates
around expected norms and is sometimes negative. If a firm’s net profit (net output)
is one million dollars one year, and one dollar higher the next, net profit will have
varied only one ten thousandth of a percent. But if interest payments take up the
same million dollars per year, every year, profit left for shareholders will have
grown from nothing to one dollar. Its growth rate will have been effectively infinite.
If the firm earns two dollars less the year after, it will have to invade capital to pay
the interest, and owners take a one-dollar loss. Again the difference is trivial
percentage-wise to net profit, but diametric to equity investors. The more fixed debt,
the more surprise and volatility in whatever is left for shareholders. The ratio of
debt to that remainder, called “equity,” is the leverage meant. Stock in this security
sense means the same as shares or equity.
Chapter 4 Mill’s Idea 1/11/16 20
Now I’ll try to pull this together. Stock prices collectively, meaning all shares at
current prices, is called “market cap.” (Cap is capitalization.) Market cap does not
measure the whole underlying value of the issuers, meaning firms that issued the
stock, since there are debt claims that must be paid off first. It measures the equity
residue. It measures that imperfectly because some inefficiency and chicanery are
here to stay. It is more volatile than the debt claims because it is leveraged, but
probably less volatile, given the observed reality of trends showing smoothed-out
reaction of share prices to news over time, than what would be bid for the
underlying assets, including intangibles, subject to the same debt claims that must
be paid off first.
National accounts measure market-valued (physical) capital by beginning with
market cap. They then add the market value of debt claims on the same issuers,
along with equity and debt claims on the rest of the business sector, and then the
same for the housing sector. The sum is “private wealth.” Consumer durables such
as cars and refrigerators are excluded as impractical to price. Government wealth
net of national wealth is tracked separately, and tends to show as slight or negative.
Finding the Free Growth Index for Stock Markets
My concern in this chapter is the stock market as a data source for testing free
growth theory. Here (4.2) would read total return in place of (net) output, while
growth would be in market cap. Consumption in (4.2) would become dividend yield
in the sense net of capital concurrently raised in new stock issues. The Global
Financial Data website summarizes the history of world stock markets from
inception in about 1700 for U.K., about 1800 in U.S., and later elsewhere. A nice
feature of this data source, and most other sources for stock and security
performance, is that market values are shown from the start. This left no need to
correct for the inevitable lags in depreciation accounting, which gets the news only
in purchases or sales.
Chapter 4 Mill’s Idea 1/11/16 21
Global Financial Data reports annual rate of return, growth rate in market cap, and
“imputed dividend rate” as the difference. Dividend rate itself is reported as
something a little different. I made no attempt to get to the bottom of this distinction,
just as I made none to allow for editorial bias in the Piketty-Zucman website. I chose
the imputed version for logical consistency.
This direct information obviates the chain of reasoning from (4.2) to (4.5), and
allows me to jump to the latter. “Productivity gain” in (4.5) is simply annual change
in reported rate of return. Acceleration is annual change in reported market cap
growth rate. (4.6a) defines the free growth index as their ratio. !
ϕ(SM), the green
line, tracks it in the charts. It too fluctuates around the number one. Gains in
dividend rate have coincided as often with gains in market cap growth rate as with
drops.
This seems only to expound what everyone knows. Of course firms are likelier to
raise dividends in years of growth, and cut them in years of decline. I never claimed
that free growth theory does more than state the obvious. What is made obvious by
the data is that a change in total return is the prime mover enabling market cap and
dividend rate to accelerate or decelerate as a pair. What is made obviously wrong
would be a thrift theory casting dividend restraint as the prime mover. Were that so,
market cap acceleration would coincide with lower rather than higher dividend
rates.
This pretty much completes my evidence for free growth theory. I have not found
other promising data sources. One is tantalizingly close to hand. There is not much
reason why corporate bond history is less transparent to the world than corporate
stock history. A qualified expert might reconstruct market caps of both, side by side,
to show a picture of the whole corporate sector. Surely I am not the only person who
would take interest. What is the history of leverage, and of total return, and its
growth and yield components, to debt and equity claims cap-weighted together?
Chapter 4 Mill’s Idea 1/11/16 22
It would be nice to test from such a dataset, again starting from (4.6), to see if free
growth theory holds again. Who knows? Meanwhile, I think, the case is closed. All
growth at very large scales is free until proved otherwise.
Where Does Opinion Stand Now?
What should we make of this evidence for free growth in national accounts and
stock market data? Lawmakers would probably demand a recount or an
investigation. Tax laws discourage consumption and dividends to encourage growth.
Yet data show that lower consumption rate coincides as often with lower as higher
capital growth rate for eight nations over four to fourteen decades. They will show
the same for dividends when we come to that.
Economists would be less surprised. Solow has prepared them for the news. In 1956
and 1957 he showed evidence that most growth is not explained by capital
accumulation, or saving through consumption restraint. His Nobel prize acceptance
speech in 1988 includes:
… In the beginning, I was quite surprised at the relatively minor part the model
ascribed to capital formation. Even when this was confirmed by Denison and others,
the result seemed contrary to common sense. The fact that the steady-state rate of
growth is independent of the investment quota was easy to understand; it only
required thinking through the theory. It was harder to feel comfortable with the
conclusion that even in the shorter run increased investment would do very little for
transitory growth. The transition to a higher equilibrium growth path seemed to
offer very little leverage for policy aimed at promoting investment.
The formal model omitted one mechanism whose absence would clearly bias the
predictions against investment. That is what I called “embodiment,” the fact that
much technological progress, maybe most of it, could find its way into actual
production only with the use of new and different capital equipment. Therefore the
effectiveness of innovation in increasing output would be paced by the rate of gross
Chapter 4 Mill’s Idea 1/11/16 23
investment. A policy to increase investment would thus lead not only to higher
capital intensity, which might not matter much, but also a faster transfer of new
technology into actual production, which would. Steady-state growth would not be
affected, but intermediate-run transitions would, and those should be observable.
That idea seemed to correspond to common sense, and it still does. By 1958 I was
able to produce a model that allowed for the embodiment effect. … If common sense
was right, the embodiment model should have fit the facts better than the earlier
one. But it did not. Dension (1985) , whose judgment I respect, came to the
conclusion that there was no explanatory value in the embodiment idea. I do not
know if that find should be described as a paradox, but it was at least a puzzle.
Edward Denison was another leading growth economist Solow consulted.
Remember that Solow had defined disembodied growth to mean better use of
existing assets, as when ships carrying coal to Newcastle are inspired to reverse the
business plan. It is easy to see how disembodied growth could come more or less for
free. But Solow puzzled how embodied growth, which needs “new and different
capital equipment,” could arrive without “ a policy to increase investment.”
It can for the same reason that Achilles can overtake the tortoise. Solow’s problem, I
think, may have been that new and different capital equipment stands to embodied
novelty as a new and different chicken laying a new and different egg. We can see
how the different capital might come first through saving from consumption
deferment. And it seems clear that the embodied novelty could not. But one of the
beauties of calculus is that it allows chicken and egg to evolve simultaneously.
Neither novelty precedes the other at the instant of first embodiment.
This time it is Newton and Leibnitz to the rescue, along with the trusty Gunnar
Myrdal, if I guess right about Solow’s misgivings. Since he understands calculus and
Myrdal far better than I do, I may guess wrong. So let me try another way. It seems
to me that embodied growth is still disembodied growth at a finer and more basic
Chapter 4 Mill’s Idea 1/11/16 24
scale. Instead of redeploying finished goods, we recombine raw materials. We aren’t
creating something from nothing. And growth is not so free that it needs no cost at
all. It still needs depreciation plowback. Net investment would mean any in addition.
The charts and tables, as I read them, show a steady stroke of deprecation plowback
paying for all innovation, embodied or disembodied, that copes as best it can with
good times or bad.
The steady stroke metaphor, showing how cost (the steady stroke) and growth
(against the shoreline) could be desynchronized, explains the possibility of free
growth. It does not explain why the record shows no other kind. My best guess as an
explanation would look to biology. The biological imperative shapes our tastes and
behaviors for lineage survival in some sense of family or population or species.
Other species crowd their niches. They cannot gain by consumption restraint for the
two excellent reasons that there is no consumption to spare and no niche space if
there were.
Ricardo, Malthus and West all warned against rote replication in economies already
developed. We must create means to make more from less. I suspect that we are up
against that wall more or less continually. Innovation pushes the wall back when
genius and happenstance are at their best, and helps us survive the rest of the time.
It costs the same either way. Consumption sacrifice is sacrifice to gods who work
their will heedless of it.
My implication that we have no consumption to spare could mislead. Rather we
have none safe to spend. All creatures hold back reserves against adversity.
Economies usually carry more capital, producing more consumption, than they need
for now. It is a rainy day fund to be drawn down in lean times and built back in
plush ones. Many nations invaded capital to keep up consumption during the world
wars and world depression between, and reversed course since. But we would be
fools to spend it for return over time when the next crisis might come tomorrow.
Chapter 4 Mill’s Idea 1/11/16 25
What exactly do I picture as this capital reserve? Is it vodka distilleries that might be
converted to orange juice plants in a pinch? I don’t really know. Human capital itself
is versatile. Some retirees could unretire, and vodka plant workers might convert
with not much retraining. I will explore some of this idea later.
Harrod’s Knife Edge
Solow’s neoclassical growth model developed from ideas published a decade earlier
by Roy Harrod. Harrod had described a “warranted growth path” given by the pace
of technological innovation. He reasoned correctly that any effort to push
investment faster must soon founder in the diminishing returns foreseen by Malthus,
Ricardo and West in 1815. But how could we get investment exactly right? There
was a critical “knife edge” with little margin for error. He was right to stress the
dangers of overinvestment. I do the same. But free growth theory, and the
overwhelming evidence that it is right, bring a new perspective.
What Solow and other economists teach today , judging from the textbooks I read, is
more or less Harrod without the knife edge. We are taught to figure out the
warranted growth path, meaning the rate of technological growth, and then invest
just enough, ex ante, to exceed depreciation by that margin. But my charts and tables
show that any investment beyond depreciation recovery is deadweight loss. There is
no need to know the warranted growth path because optimum investment is not a
function of whatever it might be. Depreciation investment captures the whole of
technological growth, and further investment adds no more. It is money left on the
table. Optimum ex ante investment, at the collective scale, is depreciation
investment. Ex post results will reveal the warranted growth path.
What about Underinvestment?
One indication in the charts and tables might leave us puzzled. It is easy to
understand the futility of ex ante investment (consumption restraint) beyond
Chapter 4 Mill’s Idea 1/11/16 26
depreciation plowback in light of the diminishing returns described by Ricardo,
Malthus and West two centuries ago. We might crowd our niche, like other
creatures, and leave neither consumption safe to spare nor room for capital
accumulation before diminishing returns set in. But too little investment could seem
a tougher challenge. No thrift at all, meaning not even depreciation plowback, would
mean no growth at all. Then consumption rate would vary inversely as capital
acceleration, just as predicted in in thrift theory. And underinvestment, meaning
plowback of less than current cost depreciation, ought to happen about as often as
overinvestment. If each year of underinvestment tended to fit the predictions of
thrift theory even a little, free growth indexes should average something less than
one in the end. But they don’t. The index varies, but averages more than one as often
as less in every country and period.
The explanation I suggest is already implied in that insight of two centuries ago. Just
as overinvestment and capital glut diminish returns, underinvestment and capital
shortage augment them until supply of capital catches up to demand. Even if there
were no plowback at all in some years, higher returns to capital already in place
would help take up the slack. There would be real danger in sustained
underinvestment or overinvestment. The saving grace is in market forces restoring
equilibrium as investors maximize return.
Summary
This gives the outline of free growth theory. It is my best speculation on how to
make sense of the charts and tables. It follows Mill more or less exactly, and risks
the next step in the bold new direction pointed by Solow.
My prize exhibits are the charts and tables. Better this book should show them alone,
with an explanation of my testing equations and the data sources, than all the rest
without them. They could hardly support free growth theory better than if Mill and I
had rigged them. The consequences are huge. We must get rid of the corporate
double tax ASAP, and raise the corporate tax rate enough to make the overall
Chapter 4 Mill’s Idea 1/11/16 27
adjustment revenue-neutral. That should help get both parties on board. We must
tax capital gains at the same rate as ordinary income. Dividend rates should revert
to the 4% - 6% range typical over the centuries before the pro-investment policies
put in place after World War II. We must do whatever we can to level the
consumption-investment playing field.
Obvious qualifiers are worth spelling out. (4.1) and all consequences are meant to
describe at the collective scale, where growth cannot be explained by transfer. Free
growth theory assumes depreciation investment, not zero investment. My charts
and tables will never be exact. There are inevitably errors and judgment biases in
the national accounts and research assembled by Piketty and Zucman, more added
by them, and more by me. These cautions will apply to later chapters as well.
Chapter 4 Mill’s Idea 1/11/16 28
CHAPTER 5: BRINGING HUMAN CAPITAL IN
Human capital is labor measured as a dollar sum rather than as so much per hour or
year. It treats pay less invested consumption as our cash flow, and finds our present
value (to ourselves) as expected lifetime cash flow discounted by our own time
preference rates, meaning what we would charge for delay. Measurement in this
way usually finds it as something near three fourths of all capital. Physical capital,
much better understood because it can be bought and sold as well as hired, is only
the visible tip of the iceberg. The term human capital itself is touchy because it can
suggest that life has a price. Irving Fisher used it in quotation marks in 1898 1 ,
attributing it to earlier sources I haven’t found, but not in his two great books on the
topic in 1906 2 and 1907 3 . Wikipedia is mistaken in attributing the term to Arthur
Pigou a generation later.
History of the Idea
The concept began with Petty in 1664 4 . He estimated the aggregate pay of English
workers, and divided by the discount rate he had modeled in A Treatise of Taxes two
years earlier. I have not read Verbum Sapienti, but have read two of his later
versions of the same argument 5 .
Petty’s method was criticized by William Farr in 1854 6 , also in a paper I haven’t read,
for neglecting what I call invested consumption. Farr, if I read the right description
of his argument, was both right and wrong. Petty was modeling human capital of
aggregate workers. These were mostly adults, who no longer receive invested
consumption if my model is right. That makes his method sound in principle for
measuring adult human capital separately. It follows that he underestimated the
human capital of England, rather than overestimating it as Farr claimed, by leaving
1 The Nature of Capital.
2 The Nature of Capital and Income.
3 The Rate of Interest.
4 Verbum Sapienti.
5 Political Arithmetic (1676) and A Gross Estimate of the Wealth of England (1685).
6 Vital Statistics.
Chapter 5 Bringing Human Capital In 1/13/16 1
out the human capital of children. But Farr deserves credit for pointing out that
human capital in general capitalizes pay less invested consumption.
Keynes’ teacher Alfred Marshall agreed with Farr in 1990 7 . As I read this passage,
Marshall interpreted maintenance consumption as investment. So did B. F. Kiker 8 in
1968. I interpret it as exhaust in taste satisfaction enabling energy to earn pay
concurrently, while preserving but not increasing pay expectations in future.
Invested consumption would mean addition to human capital concurrently for
expected realization with interest in higher pay later.
Meanwhile economists had developed the complementary idea of human capital as
present cost of investment accumulated before. Adam Smith 9 in 1776 wrote
…The acquisition of such talents, by the maintenance of the acquirer during
his education, study, or apprenticeship, always costs a real expense, which is
a capital fixed and realized, as it were, in his person.
The conversion of some consumption into human capital was a favorite theme of
Frank Knight a generation before Schultz. Only the rest is what Schultz called pure
consumption eliminated from the economy in satisfying tastes. Becker added in
1964 that this investment must be expected to be recovered with interest, at least
when paid by employers in job training. Schultz had also pointed out that human
capital depreciates, and invests some work in itself in the effort of learning to
complement the exterior investment of nurture and schooling. Ben-Porath,
expressing a Schultz-led consensus, added in 1967 that human capital growth is
invested consumption (the nurture and schooling) plus self-invested work less
human depreciation. All these ideas are now accepted everywhere in human capital
studies.
7 Principles of Economics.
8 A History of Human Capital. I learned of Farr from Kiker.
9 The Wealth of Nations.
Chapter 5 Bringing Human Capital In 1/13/16 2
Jacob Mincer seems to have been first in print with the post-war revival of interest
in human capital, in his 1958 paper 10 rederiving Irving Fisher’s present value
equation and stressing job training. Schultz impresses me as the main idea man
among these post-war contributors. He usually avoided math, unlike the others, and
is probably the best source for quotes in plain English. His paper Investment in
Human Capital, published in 1961, includes:
… Much of what we call consumption constitutes investment in human capital.
Direct expenditures on education, health and internal migration to take advantage
of better job opportunities are clear examples. Earnings foregone by mature
students attending school and by workers acquiring on-the-job training are equally
clear examples.
… This use of leisure time to improve skills and knowledge is widespread… I shall
contend that such investment in human capital accounts for most of the impressive
rise in the real earnings per worker…
… Measured by what labor contributes to output, the productive capacity of human
beings is now vastly larger than all other forms of wealth taken together…
… the curve relating income to age trends to be steeper for skilled than for unskilled
persons. Investment in on-the-job training seems a likely explanation…
… We can think of three classes of expenditures: expenditures that satisfy human
preferences and in no way enhance the capabilities under discussion – these
represent pure consumption; expenditures that enhance capabilities and do not
satisfy any preference underlying consumption – these represent pure investment;
and expenditures that … are … partly consumption and partly investment, …
In 1962 11 he added:
… the investment in human capital can conveniently be classified in (1) nurture and
higher education, (2) postschool training and learning, (3) preschool learning
activities, (4) migration, (5) health, (6) information, and (7) investment in children
(population) …
10 Investment in Human Capital and Personal Income Distribution
11 Human Capital: Policy Issues and Research Opportunities
Chapter 5 Bringing Human Capital In 1/13/16 3
… But unlike the wonderful “one-hoss shay,” the productive life of educational
capital typically does not go to pieces all at once. It depreciates along the way, it
becomes obsolete, it is altered by changes in retirement and by the state of
employment …
… As already noted, educational capital, like reproducible physical capital, is subject
to depreciation and obsolescence. The established tax treatment takes account of
both depreciation and obsolescence in the case of physical capital, but this
accounting is not extended to education capital… In brief, our tax laws… appear to
be all but blind to the fact that educational capital entrails maintenance and
depreciation, becomes obsolete, and disappears at death…
These excerpts clearly show Shultz’ meanings of pure and invested consumption,
and of human deprecation. He says “pure investment” in place of my “invested
consumption”, but I prefer to follow tradition by applying “invested” to physical
capital alone. We also see his belief, with which I disagree, that substantial invested
consumption continues after independence and physical maturity. For example, he
writes “Direct expenditures on … health and internal migration … are clear
examples.” I interpret these outlays, when applied to adult workers, as maintenance
consumption preserving rather than adding skills, and enabling current pay rather
than invested for higher pay later.
I agree that self-invested work “to improve skills and knowledge … accounts for
most of the impressive rise in the real earnings per worker …”. But I don’t share
Schultz’ view that the “use of leisure time” accounts for much of this improvement.
My years in plants and oilfields and offices have given me an impression of some
study by workers during leisure time, but mostly passive accumulation of
experience and insight while fully at work on the job.
Practical Uses
One obvious use of the human capital idea is to compare the factors (human and
tradeable capital) in the same dimension. Capital and labor cannot be added, as
Petty knew, since capital is measured in dollars where labor is measured in dollars
Chapter 5 Bringing Human Capital In 1/13/16 4
per unit time. But Petty showed that the idea of human capital as discounted cash
flow measured in a money sum allows the factors to be summed together. The
revival of interest at the Chicago school soon introduced the term physical capital
for land and man-made things that can be bought and sold, and total capital for the
sum. Physical capital is a misnomer in that we are physical too. But I have used it
throughout so that economists can follow me and general readers can pick up some
of their language.
From the Y = C + I Equation to the Y Rule
Chapter 2 summarized my argument adjusting the Y = C + I equation to the Y rule.
Chapter 4 spelled out the former in (4.1). The Y rule made the hidden asterisks of
the Y = C + I equation explicit. I said in both chapters that the free growth equations
are the same for both when we allow for the asterisks.
Let’s go through the derivation of the Y rule again. (4.1) shows
output = investment + consumption.
I generally mean the version of this where “ex post net” is understood before both
“output” and “investment”. I said that this idea is implicit in the Mill quote, and is
probably as old as economics. Net output, here or anywhere, means creation of
value. Then the equation would be guaranteed by the truism, at the collective scale,
if net investment meant growth of all value existing, meaning total capital, while
consumption meant elimination from total capital collectively and nothing else. But
net ex post investment as meant throughout this book, and anywhere in macro,
means growth in physical capital alone. Consumption includes Schultz’ invested
consumption transferred into human capital as well as his pure consumption
eliminated from total capital as a whole. What the truism guarantees is rather
output = total growth + pure consumption, (5.1)
Chapter 5 Bringing Human Capital In 1/13/16 5
at the collective scale and where “ex post net” is again understood before “output.”
(5.1), but not (4.1), guarantees that terms are mutually exclusive and exhaustive.
Total growth means this ex post net investment (growth of physical capital) plus
growth of human capital. The latter would have puzzled us before the contribution
of Ben-Porath. Equation (4) in his 1967 paper, summarizing the first three, shows
human growth = invested consumption + self-invested work
– human depreciation, (5.2)
using my terms rather than his.
Chapter 6 will argue that this equation needs to be clarified. I gave a preview in
Chapter 2, and will update it now. Work is the output of human capital. Output is not
always positive. It is negative whenever growth and cash flow sum to less than zero.
A negative sum of these two shows unrecovered decapitalition (also called
deadweight loss). That would include unrecovered human depreciation. If (5.2)
meant all including negative self-invested work less all including unrecovered
human depreciation, it would subtract unrecovered human depreciation twice. Then
it must be corrected either to
human growth = invested consumption + positive self-invested work
− human depreciation, (5.3)
or equivalently
human growth = invested consumption + self-invested work
− recovered human depreciation.
(5.3a)
It is clear that Ben-Porath meant (5.3), as other evidence shows that he treated
human depreciation as unrecovered. So does all tradition, mistakenly I believe, with
Chapter 5 Bringing Human Capital In 1/13/16 6
the partial exception of Becker. I will generally prefer (5.3a), although the two are
identical in meaning.
Schultz’ analysis of consumption found
consumption = invested consumption + pure consumption. (5.4)
This plus (5.1) and (5.3a) combine for
output = total growth + pure consumption
= investment + human growth + pure consumption
= investment + invested consumption + self-invested work
– recovered human depreciation + pure consumption
= investment + invested consumption + self-invested work
– recovered human depreciation + consumption
– invested consumption
= investment + consumption + self-invested work
– recovered human depreciation. (5.5)
“Ex post net”, as always, should be understood before both “output” and
“investment”.
Chapter 6 will revisit this logic once again, and add a second way to the same
conclusion.
The Growth Equation Under the Y Rule
(5.1) can be arranged as
total growth = output – pure consumption,
(5.1a)
as a counterpart to (4.1a). Total growth means growth in total capital. My argument
continues as in Chapter 4. Since (4.2) was a blind alley, skip to (4.3). That now
becomes
Chapter 5 Bringing Human Capital In 1/13/16 7
total growth
total capital = output
total capital − pureconsumption , (5.6)
total capital
which can be written as
total growth rate = total capital productivity
− pure consumption rate,
(5.6a)
as with (4.3a). Since (5.6a) is always true, and not only under occasional
circumstances, we also get
change in total growth rate = change in total capital productivity
− change in pure consumption rate. (5.7)
This parallels the logic of (4.4). Again save space by reexpressing this as
total acceleration = total productivity + total thrift,
(5.7a)
where “total” means “of total capital”. Now divide by total acceleration to reach the
counterparts of (4.5) and (4.5a).
I will sometimes save space, from now on, by expressing these arguments in the
equations of Chapter 4, as for example in leaving the words “total” and “pure”
implicit if the context shows that I mean them.
The Slave Paradox
Say that Phil enslaves Bill. Bill’s maintenance consumption had been taste-satisfying
pure consumption to Bill when Bill was free, and so was not deducted from his pay
to find his gross realized output as valued by himself. But Bill’s maintenance
consumption satisfies no tastes of Phil. Cash flow is gross realized output less
plowback from revenue less new investment from outside, for either factor, while
Chapter 5 Bringing Human Capital In 1/13/16 8
net output is gross realized output less depreciation plus proprietary output. Both
drop by the amount of Bill’s maintenance consumption on Phil’s books as a
slaveowner. So then does Bill’s present value of that cash flow.
This noir thought experiment is worth thinking through. It shows that even if
slavery were legal and common, its market evidence would neither show the value
of human capital nor refute the fact that human capital is inalienable. It is
inalienable for the reason, if none other, that our maintenance consumption satisfies
no one else’s tastes. Phil did not acquire Bill’s human capital. He converted it to
livestock worth much less.
Another useful point is that assets in general tend to be worth more to their owners.
This does not contradict the convergence axioms. We buy or build to taste. That
difference is particularly important as to assets not meant to be traded, such as
productive plant. I suspect that this is what the national accounts missed in
adjusting depreciation.
Maintenance Learning
Ben-Porath argued, persuasively I believe, that both kinds of investment in human
capital must end when not enough time remains for recovery with interest. Those
two are invested consumption, including schooling, and self-invested work. I
propose that invested consumption substantially ends at maturity and
independence. Self-invested work of learning continues long after, as there remains
no other adequate explanation of age-wage profiles. When does it stop?
Learning itself continues to the end. Yet if Ben-Porath is right, and he is, selfinvested
learning stops well before. What continues, I think, is what I call
“maintenance learning”. It is defined as learning to keep up pay now rather than to
enhance pay later. At all ages, we must learn the names and traits of new clients and
co-workers and suppliers and regulations continually to do what we are paid for.
Chapter 5 Bringing Human Capital In 1/13/16 9
This observation helps clarify my hypothesis that job learning costs no time that
might otherwise have been spent earning pay. My deeper meaning is that invested
learning and maintenance learning are the same process costing the same time but
with different economic effect, much as with invested and maintenance
consumption.
Evidence that hourly if not yearly pay rises until retirement, or very near, would
refute Ben-Porath’s claim if human capital ended at retirement. But it continues
through retirement because imputed pay does.
Mill and a few economists before him acknowledged “productive” and
“unproductive” consumption. The productive kind was what I call maintenance and
invested consumption. Unproductive consumption meant any written invested for
higher pay later nor supporting survival pay now. That would give
pure consumption = maintenance consumption + unproductive consumption (5.8)
and
consumption = invested consumption + pure consumption
= invested consumption + maintenance consumption
+ unproductive consumption. (5.9)
Investment and maintenance contrast in human capital as in a firm. Investment is
valued only in the expectation of future maintenance. No maintenance later, no
value now. To count maintenance as new investment would count part of the old
investment twice. Where the accounting treatments differ is in disposition.
Maintenance in the firm is recovered in pay and products. I thought before that the
same was true of human capital. Thanks to the parable of the boss and her secretary,
I now I think it is exhausted in satisfying our taste for lineage survival.
Chapter 5 Bringing Human Capital In 1/13/16 10
Restating the Three Fourths Rule
Petty, neglecting human capital of children, measured total capital as about 2.5
times physical capital in 1664. Most estimates since have run higher. I myself model
4:1 or so as a first approximation. The ratio of human to physical capital might hold
to some such lasting norm for the same reason that number of shepherds should
hold in proportion to number of sheep. They own as many as they can manage.
Human capital means value of skills, including skills in acquiring and employing
physical capital. If the value of physical capital changes, so should the value of its
management. There is truth behind the old doctrine that a rise in the productivity of
labor explains growth in value of physical capital. But old skills can also be more in
demand when improvements in physical capital productivity can get more good out
of them. Drivers are worth more when there is more valuable freight to be trucked.
A rise in either kind of capital tends to invite a rise in the other.
The ratio of pure to invested consumption is unsettled in human capital studies. I
just showed why I think Schultz gave the right clue in 1961 when he defined
invested consumption as an outlay to be recovered with interest in consumption
over the future, and pure consumption as an outlay bringing taste satisfaction now.
It is the same distinction as with investment and operating expense in the firm. A
professional’s meals and doctor bills, and even his subscription to trade journals, are
expenses needed to keep his earning power intact rather than investment to raise it
over the future. It seems to me that once we are physically mature, the only avenues
of investment in skill building, not exhuast in skill maintenance, are self-invested
work and job training or other adult education.
And I argued that there is probably not much adult education. Only a few go back to
school. From what I’ve seen, job training is concentrated in our first few months
when schooling is over and full-time work begins. That’s why I think that the rise of
pay with age, implying a rise in skills marketed, is explained more or less entirely by
self-invested work in the mainly subliminal accumulation of job experience. (Work
Chapter 5 Bringing Human Capital In 1/13/16 11
means the output of human capital, and nothing in the definition of output implies
effort or even awareness.)
I agree with Ben-Porath that all consumption and all work should be modeled as
self-invested until independence and full-time job entry, given that models must
simplify. But I just showed why I model all consumption after, or anyhow after a few
months of job training, as Schultz’ pure kind. Here I would fault Mincer and his pupil
Becker, but not Schultz or Ben-Porath, for too much focus on the potential of job
training. It exists and is crucial. But it is so small a fraction of invested consumption,
judging from my experience, that I prefer to neglect it in modeling. Job learning,
conversely, seems to explain all rise in pay with age.
Biology might predict the same. Nature’s plan is that we first develop and then
reproduce. Some creatures follow sharply-defined somatic and reproductive phases
showing first only development and then only reproduction. A mature butterfly
does not eat. It may even lose mouth parts. Its time is spent in reproduction alone.
Other creatures including us like eating too, but nature gives them that taste for the
sake of the one behind. Adult consumption, as I see it, is more or less all pure
consumption exhausted from total capital in satisfying our taste for life and energy.
Consumption by the young is invested because that is the big idea. Nature’s plan is
reproduction to maturity.
Now suppose for simplicity that consumption is age-independent. Nobelists Milton
Friedman and Franco Modigliani, mentioned earlier for their opposite reactions to
my banking idea, separately argued something like that in the 1950s for adults. My
extension backward to birth seems defensible when we remember to include
unpaid parental care and then schooling in invested consumption. I model human
capital as continuing after retirement as present value of implicit pay by ourselves
and others for caring for ourselves and those others. Then if adulthood runs from
ages 20 to 80, those simplifying assumptions would give pure consumption as three
fourths of all consumption.
Chapter 5 Bringing Human Capital In 1/13/16 12
I also modeled human capital as three fourths of total capital. My tag for the two
ideas together was the “three fourths rule.” The agreement of the two ratios as
modeled is a convenient coincidence. If they differed, this book would have to be a
few sentences longer. Each is first-order approximation only.
The Free Growth Index for Total Capital
Given the three fourths rule, the free growth index for total capital is derived by
reading “pure” and “total” before the words consumption and capital in the
equations of Chapter 4.
Now back to the charts and tables. The free growth index for total capital is tracked
in the red line and labeled !
ϕ(Kt). It too fluctuates around one in each country, but in
a much narrower range than does the blue line !
ϕ(K). The reason is the three
fourths rule. The thrift index, not shown in the charts and tables, is one minus the
free growth index. It is derived in Chapter 4 as thrift rate over acceleration, where
thrift rate is change in consumption/capital ratio times minus one. By the three
fourths rule, where pure consumption is three fourths of all consumption while total
capital is four times physical capital, the pure consumption/total capital ratio is only
3/16 (3/4 divided by 4) the size of the consumption/physical capital ratio. The
yearly changes in these ratios reflected in the numerator of the thrift index will hold
to the same proportion. The denominator is acceleration, which is always the same
for physical as total capital by the assumption that they hold in 1:4 proportion
throughout. This explains why the unshown thrift index, or numerator over
denominator, is automatically 3/16 as large for total as for physical capital, and why
the shown free growth index runs nearer one in consequence.
I have just given an idea why it can be worthwhile to brush up the algebra we all
learned in high school or before, and to suffer the nuisance of mathematical notation.
I have made a very simple truth, obvious in hindsight, seem complicated by making
Chapter 5 Bringing Human Capital In 1/13/16 13
do with words alone. One less something nearer zero, whether that something (the
thrift index) is positive or negative, is nearer one. The wonderful books of Einstein
(with Enfeld) and Steven Hawking, not to mention Mill, show that even calculus can
be put that way. My task has been to follow their tough act. But I will now start to
infiltrate notation where I think that that form of shorthand should help more then
it hurts.
Summary
The data for the free growth index of total capital ϕ(Kt) in the charts and tables do
not represent a separate test. It is the same test adjusted to the three fourths rule.
That was proposed as a convenient rule of thumb. I would have shown a true
separate test if I knew how. Pure consumption might become separately measurable
some day, but human capital will not. The Phil and Bill parable shows that not even
evidence from slave markets would be on point. Human capital has no possible
value to any but its original owner.
Whether in words or notation, I hope to make the point that Chapter 4 and the
charts and tables showing !
ϕ(K)are likely to understate the case for Mill. Those
showing should be nearer the truth. Physical capital and pure consumption
! ϕ(K ) T
are less than the whole. My three fourths rule will never be exact because reality
cares little for the convenience of modelers. Proportions between the kinds of
consumption will not hold exactly constant and will never exactly agree. But I don’t
think the three fourths rule is so wrong that the real value of ϕ(K ! T
)doesn’t run
nearer one than the real value of !
ϕ(K). (The infiltration begins.)
Then the data support free growth theory convincingly enough if we trust equation
(4.1), as do all macroeconomists as far as I know, and probably more convincingly
when human capital is considered too.
Chapter 5 Bringing Human Capital In 1/13/16 14
The cautions at the end of Chapter 4 apply even more. My charts and tables for
! ϕ(K ) repeat the accumulated error and bias of those for T !
ϕ(K), and add the crude
simplification of the three fourths rule. (5.4) expresses my understanding of what
Ben-Porath means in equation (4) in his 1967 paper, where variables are defined in
his three equations before. If (5.4) doesn’t capture his idea faithfully, it anyhow
captures mine. Likewise my (5.5) may or may not do justice to Schultz. Some but not
all possible interpretations of what he might have meant give (5.5). Again, it is my
belief whether or not his.
What Farr, Marshall and Kiker have shown, by deducting both invested and
maintenance consumption from pay to get adult cash flow discounted to present
value, is human livestock value to a slaveowner. It is very little. The parable of Phil
and Bill argued that Bill’s maintenance is expensed on Phil’s books, but treated as
net output and positive cash flow on Bill’s. I said I can’t prove that from axioms and
definitions so far, and will need the biological imperative.
Chapter 5 Bringing Human Capital In 1/13/16 15
CHAPTER 6: PARALLELS WITH THE FIRM
My Own History with These Ideas
For sheer shock value, at least to economists, the pay rule and the Y rule must count
first amount the surprises I promised. Who would have thought that human
depreciation is expected to be recovered in revenue (pay) and product value just as
with plant depreciation? Heresy! Yet nothing is more easily proved. Either the
maximand rule or the deadweight loss rule is enough.
Free growth theory and next generation theory give more scope and policy
implications. But the pay and Y rules have plenty of those, and may be new to the
world. Mill and Petty beat me to the others.
I have been arguing the pay and Y rules from the time I reversed course from
Quesnay’s idea some five years ago. I will rederive both in new ways at the end of
this chapter. My change of mind was a classical epiphany. I had been resisting the
obvious for years. I showed how my parable of the boss and her secretary got me on
track.
My depreciation theory is a lesser shock. It occurred to me over the Christmas
holidays this year. It contradicts the national accounts, whose Capital Consumption
Adjustment corrects book depreciation from linear to exponentially falling. That
would make depreciation fastest at the start, and progressively less. No one has
objected because practical experience seems to say the same. If we resell a new car
or house after only a few months of use, we take a big hit. If we resell a new factory,
which would have been tailored to our unique business plan, we take a bigger one.
My counter-argument is that premature resale reflects adverse selection. The usual
motive for premature trade is bad news and pressure to sell, not pressure from
others to buy.
Chapter 6: Parallels with the Firm 2/4/16 1
I point instead to the millions who don’t sell. I argue that depreciation and
amortization are the same in essence. Loan payments are all interest at the start,
and all amortization at the end, by inference from the present value rule.
My risk theory is a mini-surprise. It shifts focus from the risk of the asset to the risk
aversion of the owner. Another mini-surprise is the feature of my growth truism
pointing out that deadweight loss means negative unrealized output.
I will revisit these topics in more depth after I cover the necessary groundwork in
comparing the accountancy for human capital and the firm.
Assets, Owners and Revenue
Assets means examples of capital of either factor. Their owners are all members of
the reproducing population assumed in the axioms. Each, from newborns up, owns
human capital at least. Value and growth and cash flow and output are properties of
capital. Tastes, aims and ends are properties of owners. Human capital reads its
owner’s aims, and manages both factors to realize them. Positive cash flow is
outflow from assets to owners, to exhaust or reinvest or give away as they like. In
the last two cases, the owner is mediating transfer out. She also mediates transfer in
from reinvestment or gift received.
Think of capital as source and present value of foreseen cash flows. Owners are the
foreseers, the recipients of positive cash flows, the exhausters of some in taste
satisfaction, the deciders of the time preference rates giving present value, and the
mediators of transfer out and transfer in (negative cash flow). In the case of the
diamond ring, the psychic positive cash flow arrived without mechanics. The more
typical case reaches the same outcome indirectly.
(Net) output of an asset is its value added, or creation of value. Output can be
realized as outflow to owners for reinvestment or gift or exhaust, or it can be left in
as growth. The part left in is proprietary or unrealized or self-invested output.
Chapter 6: Parallels with the Firm 2/4/16 2
Outflow to owners can also include decapitalization from capital already in place, as
in withdrawals from a bank account. I say decapitization, rather than depreciation,
because the appropriate term might rather be amortization or depletion or
liquidation in sale, depending on circumstances and the nature of the asset. The sum
of the realized output and decapitalization can be called “gross cash flow”, meaning
gross before deducting plowback and negative cash flow (transfer in). Then
gross cash flow = cash flow + plowback + transfer in
= realized output + recovered decapitalization. (6.1)
Here I specify recovered decaptalization because I treat deadweight loss as
decapitalization too. Cash flow as accountants and businessmen use the term
usually means gross of plowback, although net of transfer in. My meaning, net of
both, is the one always applied in finding total return and present value.
Although cash flow might be in kind as well, I will follow convention by treating it as
if realized from sale in cash. The owner can then spend the revenue on exhaust
(pure consumption) or reinvestment or gift as she likes, but might also plow some
or all back into the originating asset. The general principle is
positive cash flow = gross cash flow – plowback. (6.2)
In simple cases, revenue measures and equals gross cash flow for each asset. But
revenue as the term is actually used is likelier to sum contributions from many
assets and owners. To keep that usual meaning separate, define this asset’s share as
“earned revenue”. Then
gross cash flow = earned revenue. (6.3)
Another way to put the same idea is
Chapter 6: Parallels with the Firm 2/4/16 3
revenue = collective gross cash flow = collective earned revenue (6.4)
from all contributors to revenue together. Then revenue and earned revenue would
be the same if there are no other claims.
Earned Revenue and Cash Flow
A classical illustration of revenue generated collaboratively is the firm. The firm
proper can be interpreted as a single asset of physical capital. Its typically many
owners agree to hire outside management, meaning outside themselves, to contract
and trade on their behalf. The firm through its managers hires the other employees,
contracts with suppliers, and generates a joint product representing all its own
gross cash flow plus any contributed parts of gross cash flow of others. The product
is sold for revenue in the collective sense. Revenue is first applied to satisfy claims
on it by those outside contributors. Claims recovered include current purchases
from suppliers realized in sales. Others are pay to management and other
employees, along with rent, interest, utilities, other services, and whatever is due to
the tax man. The principle is to include all outlays by the firm needed to secure
revenue now, as distinct from outlays invested for the sake of more revenue later.
The share of revenue due the firm proper is any residue after all those prior claims
are met. Then
gross cash flow = revenue – prior claims = earned revenue (6.5)
gives the contribution of the firm proper.
Earned revenue may or may not be passed to owners. Management is typically
authorized to plow back any part as reinvestment, say in replenishing inventory or
cash or in buying new plant and equipment. Any revenue left over after that
plowback is transferred out to owners as dividend yield.
Chapter 6: Parallels with the Firm 2/4/16 4
Negative cash flow, or transfer in, always means new investment added from
outside. Plowback from revenue is excluded, as it is already recognized as a
deduction from positive cash flow. For the firm, the only source of positive cash flow
is proceeds from new shares issued. With this understood,
where
cash flow = gross cash flow – plowback – transfer in
= earned revenue – plowback – transfer in
= positive cash flow – negative cash flow, (6.6)
positive cash flow = earned revenue – plowback, and
negative cash flow = transfer in. (6.7)
Firms use the term gross realized output to mean the same thing as what I call gross
cash flow. A common definition is
gross realized output = realized output + depreciation.
Now we come to the subtle point allowing for deadweight loss. The total return
truism shows that output equals value growth plus cash flow. Then output is
negative wherever the sum of growth and cash flow is less than zero. Natural
disasters and bad investments can make them so. Those unexpected setbacks are
examples of deadweight loss. It amounts to unrecovered depreciation, meaning
depreciation not recovered (realized) in positive cash flow. I’ll get back to that soon.
The point at present is that the equation above really means
gross realized output = realized output + recovered depreciation.
Here too I prefer the generality of “decapitalization” over “depreciation”, and define
gross realized output = gross cash flow
= realized output + recovered decapitalization
= earned revenue + recovered decapitalizaton. (6.8)
Chapter 6: Parallels with the Firm 2/4/16 5
The terms gross cash flow, earned revenue and gross realized output will be used
interchangeably. “Realized” and “recovered” will likewise be synonymous, as will be
“proprietary”, “unrealized” and self-invested”.
(A6.1) allows
realized output = cash flow + plowback + transfer in
– recovered decapitalizaiton. (6.1a)
Define
unrealized output
= output – realized output
= growth + cash flow – realized output
= growth – plowback – transfer in
+ recovered decapitalization, (6.9)
by (6.1a) and the total return truism.
Proprietary Output and Deadweight Loss
Unrealized or proprietary or self-invested output of the firm is creation of value not
yet sold or not meant to be sold. This can be something as workaday and
perfunctory and automatic as output to inventory. Other illustrations could be
where a construction firm builds its own offices, or a car manufacturer makes cars
for its executive fleet. (6.9) shows that it includes all growth not explained by
plowback plus transfer in less recovered decapitalization. This implicitly includes all
free growth. Judging from my charts and tables, free growth seems to mean all of
growth at the collective scale. What effect might it have on the firm?
Free growth includes random windfall gain and deadweight loss as well as the
overall upward trend expressing new ideas. Deadweight loss is unrecovered
decapitalization, meaning not recovered in cash flow, That makes it negative output
Chapter 6: Parallels with the Firm 2/4/16 6
as the sum of growth and cash flow, and specifically negative unrealized output.
Then
deadweight loss = unrecovered decapitalization
= negative output
= negative unrealized output
= max (0, – output)
= max (0, − unrealized output). (6.10)
Also
positive unrealized output = max (0, proprietary output), (6.11)
and
output = unrealized output + realized output. (6.12)
The Growth Truism
In general,
Here
Also
growth = capitalization from outside + capitalization from inside
– decapitalization. (6.13)
capitalization from outside = negative cash flow = transfer in, and
capitalization from inside = positive unrealized output + plowback.
Then
decapitalization = recovered decapitalization + unrecovered decapitalization
= recovered decapitalization + deadweight loss.
growth = transfer in + positive unrealized output + plowback
– recovered decapitalization – deadweight loss, (6.14)
or more simply
Chapter 6: Parallels with the Firm 2/4/16 7
growth = transfer in + positive unrealized output + plowback
− decapitalization.
(6.14a)
(6.14a) can also be expressed as
growth = transfer in + unrealized output + plowback
− recovered decapitalization.
(6.14b)
For convenience, define
gross transfer in = transfer in + plowback,
So that (6.14) through (6.14b) can be put more compactly as
growth = gross transfer in + positive proprietary output – decapitalizaiton
= transfer in + unrealized output – recovered decapitalization. (6.14c)
Any of these versions of (6.14) can be called the growth truism. The new term gross
transfer in will help shorten equations for human capital.
Management as a Quasi-Owner
Owners (shareholders) typically allow management wide latitude to cope with
needs. It stands in place of owners. Accounting tradition, and this book too, reasons
out the steps from revenue to dividend yield as if management itself were the owner.
Otherwise there would be little to say. From the shareholder viewpoint, revenue is
simply dividend yield.
But the bottom line is the same. The maximand is output, or growth plus cash flow.
Positive cash flow, in the sense net of plowback, is dividend yield on both the firm’s
books and the shareholder’s. Negative cash flow on the books of shareholders
individually is purchase of any shares in the same firm. On the books of
shareholders collectively, where sales and purchases of existing shares offset, it
simplifies to purchase of new stock issues alone. This too is just as on the books of
the firm.
Chapter 6: Parallels with the Firm 2/4/16 8
My purpose in this analysis of the firm has been to derive equations valid for any
capital of either factor. The firm is a good model for several reasons. Its accounting
traditions are centuries old, and have been well thought through. It is rich in
possibilities because it has to be. It must describe firms of many kinds. It must allow
for contingencies whether or not they apply. For many simple assets, say the firm’s
shares as opposed to itself, revenue and positive cash flow can be the same. But the
complexity and versatility of the firm itself, and the person-likeness added by its
internal management, make it a useful model for any and all capital of either factor.
Not that I claim to follow accounting tradition closely, or even to understand it
closely. I am even less an accountant than an economist. My terms and concepts
tend to be idiosyncratic. The main thing is for the logic to hold together.
Human Capital by Analogy to the Firm
It is reasonable to define pay as the revenue of human capital. Earned revenue for
the firm is typically less than revenue. There are prior claims to offset contribution
by worker and suppliers. The counterpart in human capital, I said in Chapter 2, is
maintenance consumption. I believed for years that this cost counted as a prior
claim on pay, just as with the firm. I may have been the only person to think so since
Quesnay and the physiocrats, although Mill and Sraffa might be interpreted that way.
But who has thought what doesn’t matter. Quesnay’s idea is a mathematical
possibility that must be addressed. I’ll get there soon.
Human capital is inalienable. That means that its decapitalization simplifies to
human depreciation. The firm’s added possibilities of depletion and liquidation
don’t apply. The output of human capital is called work. Then (6.1) through (6.8),
applied to human capital, give
earned revenue = pay – prior claims
= gross realized work
= realized work + recovered human depreciation. (6.15)
Chapter 6: Parallels with the Firm 2/4/16 9
The pay rule argues that prior claims are zero and that all human depreciation is
expected to be recovered in pay and work products as a norm.
Chapter 2 offered two logical proofs of the second point. The alternative to recovery
is deadweight loss. Capital is discounted foreseen cash flow, and cash flow is
realization in transfer or taste satisfaction. Deadweight loss, or unrealized
depcatialization, is therefore implicitly unforeseen. Human depreciation, like plant
depreciation, is foreseen from the start. Aging and mortality come as no surprise. It
is therefore foreseen as realized in pay.
The second proof, stated in part by Becker, follows from the maximand rule. All
behavior is maximization of perceived risk-adjusted return to the individual’s total
capital. This follows from definitions, not from axioms. There are no exceptions
because there are no square circles. The rule says that no one invests in anything
without expected recovery with interest. Recovery means recovery of depreciation.
We do invest in human capital, of ourselves and our children, and consequently
expect recovery of human depreciation by ourselves or them. It’s that simple.
Other proofs looked to evidence and experience. I offered the parable of the boss
and her secretary, which had been decisive in converting me from Quesnay’s view.
Let’s go through it once more. Assume that investment in each has ended before the
last year for each. First take the possibility that neither maintenance consumption
(the supposed prior claims) nor human depreciation is recovered in pay. Then work
and cash flow for each have simplified to realized work and pay. Human capital of
each is remaining pay less the time discount. At the beginning of the last year, it is
something less than one year’s pay. If pay measured work, return to each
(work/human capital) would be something over 100% per year. It would rise to
100% per day at the beginning of the last day, and 100% per second at the
beginning of the last second. At the end of the last second it reaches infinity. Yet the
portfolio assets of each reveal their rates of time-preference (return) as only a few
percentage points per year.
Chapter 6: Parallels with the Firm 2/4/16 10
This is enough to rule out the idea that pay recovers neither maintenance nor
depreciation. Does it say which is recovered? It does if we look at the cases of the
boss and her secretary separately. Each earns the same pay throughout, and the
boss earns ten times more. By the beginning of the last day, the human capital and
work of each is negligible. Pay is all depreciation recovery if I am right, or all
maintenance recovery if Quesnay was right, or maybe both. The boss’s pay, anyhow,
remains ten times higher. Is that because her maintenance is ten time more, per
Quesnay, or because her depreciation is?
The answer is easy. I concede that the higher-paid usually consume more. But not
always, and anyhow not in proportion and not because they have to. I learned in the
quartermaster corps that the consumption needs of the general and the private are
not much different. The commanding officer, in the field, is expected to be the last to
eat, the last to sleep and the first up in the morning. Maintenance consumption, as
opposed to the rest, is what we need to keep up strength and vitality and
performance. We can’t make do with less. More pay is more motive, but need not be
spent on more consumption unless by choice.
The boss and her secretary are paid to apply skills. They are in trouble if the worth
of those skills doesn’t cover their maintenance needs. But they will tap savings if it
doesn’t. Retirees need no money motive to consume. All they need is the means. The
source of skills applied is human capital. The application is gross realized work. The
difference between its human depreciation and realized work components matters
because the maximand is net output (work) rather than gross. But it is not a
difference in kind. Skill applied is skill applied. Pay is all depreciation at the last
second for the same reason as with the mortgage payment. There is no balance left
to earn interest.
This argues strongly that human depreciation is recovered in literal pay and
transferred to work products. It also argues that maintenance is not. The problem is
Chapter 6: Parallels with the Firm 2/4/16 11
in the exact 10:1 proportion required throughout. Whatever was contributed to pay
by maintenance recovery, on top of depreciation recovery, would have to hold the
same ratio in order for pay to cover both. Experience shows this as unlikely in any
case, let alone all cases. The boss and her secretary probably couldn’t hold
maintenance consumption to that ratio if they tried.
Another strong argument against the hypothesis of prior claims on pay is lack of a
source. The claimant would be whoever other than the worker had paid for the
maintenance consumption and needed to be made whole. Thus the employing firm
would hold a valid claim if it had provided the maintenance consumption in order to
enable the work. That would put the firm in the position of a farmer who must feed
the livestock and must earn enough profit to recoup the cost. We went through this
in the parable of Phil and Bill. But the employer firm does not advance the cost
because it has no motive to do so. It knows that the worker will pay it anyhow if
means allow. Where means don’t allow, as in retirement without adequate savings,
the worker looks to transfer payments from society generally rather than from the
firm alone.
Now comes the evidence of age-wage profiles. This evidence is the substance behind
the parable of the boss and her secretary. The evidence is apt. Wage generally
means hourly pay, while “earnings” means yearly pay. Wage-earnings profiles show
a rise with age, but peaking and reversing as workers reach their fifties or so. The
reason is that they tend to work fewer hours. I consider pay per hour a better
measure of human capital than pay per year. If someone is worth $30 per hour half
time, my impression is that she would be worth $30 per hour full time. If she prefers
to stay home, her leisure must give her that much psychic pay instead. Psychic pay
cuts just as much ice with me.
My boss and secretary were cases preferring to work full time. Age-wage profiles
bear out the scenario I imagined for them. They illustrate the logical certainty that
human depreciation is expected to be recovered in pay, and support the
Chapter 6: Parallels with the Firm 2/4/16 12
convergence axioms leading from prediction to probable outcome. More than that,
continuance of the 10:1 ratio through the last day tends to confirm that no
maintenance consumption is recovered alongside human depreciation. If it were,
age-wage profiles show that it would have to hold the same 10:1 ratio throughout.
Exhaust Pay
The present value and maximand truisms affirm that all including human
depreciation is expected to be recovered in positive cash flow. Positive cash flow is
transfer out plus exhaust. In human capital it is pay less plowback. Might some
human depreciation be realized in exhaust? I thought all was when I also thought
maintenance consumption was recovered in pay and work products. The boss and
secretary parable turned my thinking around on that. But it doesn’t follow that none
is.
Some pretty clearly is. I argued that even suicide expresses the maximand rule.
Deliberate self-maiming exists and expresses it again. Just as Citizen Kane destroyed
his showcases because the fit was on him, some destroy their bodies. So long as the
destruction is intended and compos mentis, it counts as economic behavior.
Are there sunnier examples? What about voluntary unpaid vacations and voluntary
retirements? What if the boss and her secretary enter convents in mid-career?
These choices surrender human capital on the face of things because they surrender
literal future pay. But the psychic pay of leisure makes up for it. Otherwise we would
have stayed on the job track.
Then some human depreciation is exhaust. Call the psychic pay for it “exhaust pay”.
It seems mercifully small in the big picture. I tend to neglect it in modeling for that
reason, just as with invested consumption after full-time job entry. But I claimed
logical certitude as to expected recovery of human depreciation in pay. I’d better not
leave loopholes. There are none. Some of the pay is psychic, and some of the tastes
satisfied are not pretty.
Chapter 6: Parallels with the Firm 2/4/16 13
Tweaking the Axioms
My last argument reasoned from experience that we need no money motive to
consume, and that pay tends to cover our maintenance needs. But that wasn’t
strictly in the axioms. I assumed a mortal and reproducing population strategizing
for means to satisfy tastes, and more generally aims. I didn’t say out loud that the
population in fact survives. Now I do. Let’s specify that the population has motive
and means for lineage survival, whether in a group selection or kin selection sense.
The means can be specified as skill sets, as an adult norm, sufficient to earn
maintenance consumption needs for themselves and invested consumption needs
for their young together. As to motive, I will specify at last that maintenance
consumption is exhausted in satisfying our taste for survival. I already as much as
assumed this in arguing that we need no money motive to consume.
This assumption of motive and means amounts to the biological imperative. It is
hardly new to economics. It is the essence of Petty’s overlapping generations model
of 1662 in A Treatise of Taxes. It is the essence of the equilibrium wage theory of
Smith in 1776 and Ricardo 1817, where pay converges to the level holding the work
force intact. It is the essence of Malthus’ population principle of 1798 and 1801,
chosen by Senior as his first axiom in his Outline of 1836. It is the essence of the
productive consumption theory developed from Malthus through Mill in 1848.
It lapsed from attention with the marginalist revolution beginning with Jevons and
Menger in 1871, ironically the year of publication of Darwin’s The Descent of Man,
because the marginalists treated explanations of tastes as irrelevant. I happen to be
a huge fan of the marginalists. But they’ve made their point. The microeconomics
they founded is a rich and mature science. It needs no assumptions as to what
explains our tastes. But macro is not doing so well. I believe that it must start over,
and that a grasp of motives helps.
Chapter 6: Parallels with the Firm 2/4/16 14
Quesnay’s Idea
What Quesnay wrote, in his entry for “man” in Diderot’s Encyclopedia of 1750, was
“Those who make manufactured commodities do not produce wealth…they
spend their receipts in order to obtain their subsistence. Thus they consume
as much as they produce…and no surplus of wealth results from it.”
Quesnay, like Petty a century before, came to economics from medicine. He was
personal physician to Madame de Pompadour, and then to the royal family. His
argument was that value is added in agriculture alone, not in manufactures. His
conclusion that only landowners can afford to pay taxes did not enchant the landed
aristocracy of Versailles.
Mill’s Essays 1 includes
“as much as is necessary to keep the productive worker in perfect health and
fitness for his employment, may be said to be consumed productivity. To this
should be added what he expends in rearing children to the age at which they
become capable of productive industry.”
Mill’s Principles of 1848, which I quoted earlier, said the same:
“What they consume in keeping up their health, strength and capacities of
work, or in rearing the productive laborers to succeed them, is productive
consumption.”
Sraffa’s parallel idea is expressed in his 1960 paper Production of Commodities by
Means of Commodities.
My impression is that Quesnay’s “surplus of wealth” means value added, and that he
thought maintenance consumption should be deducted from revenue in finding it.
Mill can’t have meant what I think Quesnay did, in view of Mill’s evident belief that
output is investment plus consumption. Rather, when I like Quesnay argued that
1 Essays on Some Unsettled Questions of Political Economy (1844).
Chapter 6: Parallels with the Firm 2/4/16 15
maintenance is recovered in pay work products, I thought Mill and Sraffa might have
reasoned partway there.
My belief then that human depreciation is exhausted is satisfying tastes seemed
defensible then. I argued, sensibly to a point, that getting older meant surviving. I
suppose I might still argue the same but for the parable of the boss and her
secretary.
Another Look at Depreciation Theory
My pay rules, illustrated in the parable of the boss and her secretary, depends on my
idea that depreciation and amortization are the same. Capital means present value
of a typically finite series of forseen cash flows. As each year passes, present value of
the most distant and most discounted one is lost. Depreciation/amortization is that
loss. It begins at a maximum, and rises steadily as the end point nears.
I faulted national accounts for projecting an opposite trajectory from evidence of
actual sales. I suggested a second look at likely circumstances and motivations.
Depreciable assets are mostly structures and equipment. They tend to have been
designed and modified for original users. Original users typically expect to own and
operate them to the end. Then what is the likely driver of exceptions? Are secondary
trades of plant and equipment likelier to be driven by pressure to buy or pressure to
sell?
Human capital, anyhow, is exempt from both pressures. We’re struck with what we
have. We can invest more, as a homeowner might add a pool room, but we cannot
sell. The years roll by, and present value of the most distant one’s pay is lost.
Consider what happens when the expected end point changes. Say that the boss and
her secretary, at the beginning of what was to be the last day, are both persuaded to
re-up for another five years at the same pay. Human capital of each jumps from a
little less than one day’s pay to present value of five years’ pay. But human
depreciation of each is sharply reduced! At the beginning of what seemed the last
Chapter 6: Parallels with the Firm 2/4/16 16
day, it was substantially to be the whole of pay. Now it becomes present value of a
day’s pay five years off.
Another Look at Risk Theory
I made the point that the boss and her secretary reveal their time preferences in the
security portfolios they assemble, and discount their pay at the same rate of return
to reveal their human capital. Is that too simple? Does it overlook risk, or other
factors?
I argued that human capital is the risker and higher-return factor because its
exceptional versatility makes it as risky as we like, and because it is owned
disproportionately by the risk-tolerant young. Does that make the bosses’ or
secretary’s human capital riskier and higher in return than her portfolio assets? It
does not. She molds all capital to her single risk-preference level at her current age.
This is not to claim that age is the only determinant. Gender seems to count too, with
males usually more risk-tolerant. Bob Trivers tells us why. And there is a wealth
effect. We tend to tolerate more risk when wealth gives us more cushion against
setbacks. But each of us, in present circumstances, has just so much tolerance.
Tastes are properties of owners, not of assets. We assemble and modify assets of
both factors to suit them. Human capital is not inherently riskier. It is riskier at the
collective scale only because it is owned disproportionately by the risk-prone young.
Each cohort, from youngest to oldest, molds it to suit that cohort’s characteristic risk
profile. The boss and her secretary each molds all her assets of both factors to her
single risk tolerance at the time.
Tweaking the Life Cycle Model
I consider Ben-Porath’s life cycle model of 1967 the most important paper in 20 th
century economics. I agree with all of it more or less. Now it needs clarification and
completion.
Chapter 6: Parallels with the Firm 2/4/16 17
All studies of human capital, as far as I know, effectively treat human depreciation as
deadweight loss. Ben-Porath’s model seems no exception. How does he model pay?
He multiplies human capital by a productivity factor, and then again by the fraction
marketed for pay rather than self-invested. That gives what I call realized work. Pay,
if I am right, measures gross realized work. That is the main amendment I would
propose for his model.
Ben-Porath’s first three equations summarize what I call the growth truism (6.14).
In my terms, not his, he models
human growth = invested consumption + self-invested work
– human depreciation.
He means positive self-invested work in the form of learning. Meanwhile the
inalienability of human capital leaves its depreciation as its only avenue of
decapitalization. Invested consumption corresponds to gross transfer in as meant in
the growth truism (6.14c) while self-invested work is the same as proprietary
output. Then (6.4c) applied to human capital could show as
confirming (5.2) and (5.3a).
human growth = invested consumption + positive self-invested work
– human depreciation,
= invested consumption + self-invested work
– recovered human depreciation,
Logic also seems to agree with Ben-Porath’s interpretation that self- invested work
continues late into careers, and that it must stop when time for recovery runs out.
But I would specify that invested consumption stops, for modeling purposes, at fulltime
job entry or a little later to allow for initial job training.
This needn’t follow from my adjusted axioms. It’s just an impression from what I see.
I don’t agree with Schultz that outlays on medicine or worker relocation are
investment. I see them as maintenance consumption preserving skills, not
Chapter 6: Parallels with the Firm 2/4/16 18
investment building skills. I don’t see much avenue for investment in adult human
capital except through textbooks and tuition. Some happens. I went back to school at
the Conservatory myself, and I buy lots of textbooks. But I just don’t see enough of it
around me. Models must simplify. Mine would end invested consumption at
independence more or less.
I would also model adult self-invested work as subliminal and costless job
experience. I don’t see it as taking a second away from work for pay. This again is
meant to describe the usual rule only. Ben-Porath’s model, I think, allows an
impression that workers can choose between earning and learning by allocation of
time. The quotes from Schultz in Chapter 5 described that as common. I just don’t
see much of it happening. Rather we tend to work fewer hours at the end of careers,
not the beginning or middle when time for recovery of self-invested work remains.
I said that Ben-Porath’s equations imply
pay = realized work.
I would substitute the pay rule
pay = gross realized work
= realized work + human depreciation
= work – self-invested work + human depreciation, (6.17)
as a norm or expectation. It isn’t a guaranteed outcome because deadweight loss
happens to human capital too. We may be hit by a bus, or lose our jobs in a slump, or
be sent to prison or drafted into the army. The pay rule means that recovery is
foreseen. If (6.17) were stated in terms of outcomes, “recovered” would have to be
inserted before “human depreciation”.
Chapter 6: Parallels with the Firm 2/4/16 19
I believe that the case for this rule is very strong. The deadweight loss rule and the
argument from the maximand rule give logical certitude that human depreciation is
expected to be recovered in pay. The convergence axioms would then give actual
recovery as a norm. The rule disallows the prior claims hypothesis, or possibility
that maintenance is recovered too, from an accumulation of implausibilities that led
me finally to rule them out by adjusting the axioms.
The life cycle model should also specify that human capital continues after
retirement. I admit that this rules out the simplicities assumed in the boss/secretary
parable. It continues because we earn imputed pay until the end, and human capital
remains as its present value.
I would also model in my depreciation theory. Pay, like the mortgage payments, is
all realized work (interest) at the start and all human depreciation (amortization) at
the end. No other explanation of age-wage profiles will hold water.
A New Approach to the Pay Rule
I reasoned to the pay rule from the maximand and deadweight loss rules. Another
approach can reach the same conclusion.
The total return truism finds
output = capital growth + cash flow.
(6.16) expressed Ben-Porath’s equation as
human growth = invested consumption + self-invested work
–recovered human depreciation.
Cash flow is the flow discounted to present value. Tradition, since Farr in the midnineteenth
century, has seen human capital as present value of future pay less what
Chapter 6: Parallels with the Firm 2/4/16 20
I call invested consumption. I argued in Chapter 3 that this tradition is sound,
although not logical certitude. I put it as
human cash flow = pay – invested consumption. (6.18)
Work is defined as the output of human capital. Summing (6.16) and (6.17) now
shows the pay rule
work = pay + self-invested work – recovered human depreciation,
after cancellation of invested consumption.
This says that the pay rule is not so exotic after all. It has been staring us in the face
since the Schultz-led consensus, with Ben-Porath, figured out the human growth
equation a half a century ago. We had effectively recognized human cash flow as
pay less invested consumption since Farr a century before, without putting it in
those words. The total return truism does the rest.
A New Approach to the Y Rule
The marginalist tradition, which has dominated economic thought since its
introduction by Jevons and Menger in 1871, has treated all consumption as the end
point exhausting capital in satisfying tastes. It doesn’t follow that marginalists were
unaware that some is invested in human capital. At least three of the leading ones
understood human capital well. That includes Leon Walras, a third co-founder of the
marginalist revolution in 1874. I also mentioned Marshall, who agreed with Farr in
disputing Petty, and Irving Fisher. But all three, and marginalsts in general,
preferred to locate human capital outside the economy proper. Whether they spoke
of labor measured in dollars per unit time, or human capital meansured in dollars
alone, the larger factor was taken to arrive exogenously. It provided its services
from outside and was paid their market value in return, as if on the books of a firm.
Chapter 6: Parallels with the Firm 2/4/16 21
Marshall’s pupil Keynes was thoroughly a marginalist, as are economists in general
today and as am I. One of the features of his General Theory of 1936 was a kind of
double-entry accounting for national product. Product was output and equivalently
income. Output meant the sum of prices of final products produced within the year,
while income meant the shares of that sum paid to the workers and investors
producing it. His double-entry idea can be put as
output = investment + consumption = income = pay + profit. (6.19)
I showed why I disagree. But let us see how the total return truism might seem to
have led to that inference if we leave workers or human capital outside the economy.
To treat them as arriving exogenously from outside is essentially to treat the
national economy as if it were a single firm. Output inside is simply profit. Output
outside is work, meaning creation of value by the workers. This gives the truism
output = work + profit,
confirming that total output is the sum of factor outputs.
So far, so good. But now Mill and Keynes and most tradition slip by arguing that pay
equals and compensates all of work and nothing else. That’s why (6.18) equates
output to pay plus profit. Schultz and Ben-Porath and other students of human
capital correct this in part by recognizing some work as self-invested rather than
marketed for pay. My pay rule adds that pay recovers human depreciation as well as
realized work. (6.19) should have reasoned
output = income = work + profit
= pay + self-invested work – human depreciation + profit. (6.20)
Chapter 6: Parallels with the Firm 2/4/16 22
Where Keynes and Kuznets and macroeconomic tradition have been right is in
reasoning that pay and gross profit, meaning gross of depreciation, sum to the
“expenditure” spent on consumption and gross investment. This fact of arithmetic is
the logic behind Say’s law: pay plus profit are always enough to buy what is
produced. We saw that this truism gives cold comfort when calamity or
misjudgment make profit negative, as with the subprime houses of 2008. What it
certifies, anyhow, is
expenditure = pay + gross profit = consumption + gross investment. (6.21)
We can subtract depreciation to reach
pay + profit = consumption + investment. (6.22)
Now (6.19) can be corrected as a whole to show
income = pay + profit + self-invested work – human depreciation
= output
= consumption – investment + self-invested work
– human depreciation. (6.23)
My main goal in this book has been to further the work of Solow in exogenizing
growth, and also the work of Ben-Porath in endogenizing human capital as
something produced within the economy. It was in that spirit that I derived the Y
rule in Chapters 2 and 5 by putting human capital inside. I reached
output = investment + human capital growth + cash flow.
Here “ex post net” is understood before output and investment, so that investment
means physical capital growth. (6.16) applies the growth truism to human capital.
The cash flow truism shows that cash flow is net transfer plus exhaust realized in
Chapter 6: Parallels with the Firm 2/4/16 23
taste satisfaction. These are all ex post descriptions of realized outcomes rather than
intentions. Together they give
output = investment + invested consumption + positive self-invested work
− human depreciation + net transfer + exhaust
= investment + invested consumption + self-invested work
− recovered human depreciation + net transfer + exhaust. (6.24)
This much is certitude. I now apply (5.9), which includes
consumption = invested consumption + pure consumption,
to reach the Y rule in its general form:
output = investment + consumption + self-invested work
− human depreciation + net transfer. (6.25)
The net transfer term disappears at the collective scale.
Although (6.24) is logical certitude infered from definitions, (5.9) and consequently
(6.25) are not. I cannot rule out the possibility of a third kind of consumption
recovered in work products as per Quesnay. I hope that my interpretation of agewage
profiles in the light of the boss-secretary parable has revealed that as
improbable. The same holds for my derivation of the pay rule through Ben-Porath’s
equation and (6.18). (6.18), my inference that human cash flow equals less invested
consumption, also trusts that all maintenance consumption is exhausted in
satisfying tastes.
Summary
Accounting for human capital is much like accounting in a firm. Expected recovery of
human depreciation in pay is logical certitude illustrated in age-wage profiles and in
the boss-secretary parable. The pay rule is not entirely logical certitude, however, as
it also asserts that maintenance consumption is not recovered. Age-wage profiles
Chapter 6: Parallels with the Firm 2/4/16 24
support this hypothesis too, as the constancy of pay differences to the end would
otherwise be improbable. I made it the Darwinian axiom: maintenance is exhausted
in satisfying our taste for survival.
Ben-Porath’s life cycle was adjusted to express these features. Factor risk theory
argued that human capital is the riskier and higher-return factor because capital of
any kind takes on the risk characteristics of its owners and human capital is owned
disproportionately by the risk-tolerant young.
The Y rule contradicts the Y = I + C equation, while the pay rule contradicts the
dogma that output equals pay plus work. National accounts are founded on both.
That means I can expect tough resistance. I have tried to prepare for it by adding a
little more to each argument with each chapter.
Throughout this chapter, and throughout this book, I have bent over backwards to
distinguish logical certitudes from falsifiable hypothesis. Economics needs both. But
it needs to know which is which. The pay and Y rules, for example, are each
certitude in part. The certain part is the heretical one. The present value and
maximand rules follow from definitions, and compel expected recovery of human
depreciation in pay. I then relied on the convergence axioms to infer actual recovery
as a norm, not a invariable outcome, and on the new axiom of the biological
imperative, as well as evidence from age-wage profiles, to infer that maintenance
consumption is exhausted rather than recovered in pay as well.
Chapter 6: Parallels with the Firm 2/4/16 25
CHAPTER 7: PETTY’S IDEA
How We Got to this Point
I said that if I had any sense, I would have left the worms in the can by pretending to
believe (4.1) as Mill did and as the rest of the world seems to do. Charts and tables
confirm his prediction in his and their terms as well as mine. But Piketty’s argument
was rightly criticized for leaving human capital out. Someone might or might not
have faulted mine on the same ground if I had stopped at the end of Chapter 4.
Whether they would have or not, every composer knows that the critic to hear is the
one inside. What that critic told me was to gamble a case already won, open the can,
and follow the argument and worms wherever they lead. That’s why my title
promised other surprises.
I risked following it past clarification into digression when I argued the pay rule. I
since tried to justify the digression, if there was some, by showing how that rule
could explain Piketty’s data for pay/net profit ratios in the twentieth century. And I
tried to show how the pay rule and depreciation theory combined, making pay all
human depreciation and no realized work at the end, gives the only convincing
explanation of age-wage profiles showing rising or steady pay as human capital
grades smoothly to zero. Risk theory reinforced this argument by revealing time
discount rates for human capital as those made plain for physical capital owned by
the same ageing cohorts. Every step was an adventure, and every step led to the
next one. But I opened other questions and cans along the way, and the same critic
tells me to follow the worms a little farther.
I said that the cost of survival is adult consumption for the sake of investment in the
next generation, that pure consumption is more or less the same, and that we will
understand the maximand when we understand pure consumption. These threads
lead into evolutionary biology, which reasons how traits are selected for lineage
survival. The faithful need not take alarm. Although I mean natural selection, divine
Chapter 7 Petty’s Idea 2/3/16 1
selection should probably do as well. We are all at peace with the fact that people
and other creatures care for their young.
Economics and evolutionary biology are much the same. Helen Keller, born blind
and deaf, might still have reasoned her way through much of both. Hamlet would
have loved them. I love them most when they test the limits of logic, and consult the
data only at the end. The theme from which both reason, as Herbert Spencer taught
in the nineteenth century, is what he called “survival of the fittest.” Another
philosopher, Karl Popper, found fault with this idea a century later. Popper was one
of those I mentioned who disapprove of truisms. I haven’t read Popper, but gather
that he thought it improper to define fitness as potential survival, and then measure
it as survival. That objection is close to being understandable from an anti-truism
viewpoint. But the reason why it is not quite a truism is instructive. Measurement
implies an “empirical” world of data in external and observable reality. Spencer’s
insight, really his paraphrase and generalization of Darwin’s, is not quite a truism
because it carries the hypothesis that “potential” has an empirical meaning.
Aristotle’s idea that potency precedes and explains act is called causality. Adam
Smith’s friend and fellow Scotsman David Hume scarcely doubted causality, but
argued correctly (I think) that it cannot be proved either by logic or by experiment.
The fittest prove themselves such by surviving if and only if Aristotle was right.
Natural selection simply means the untestable but little-doubted theory of causality.
Spencer or Darwin or Gertrude Stein might be faulted for insulting our intelligence
by stating the obvious. That shoe would fit Gertrude Stein. But Spencer and Darwin,
like the little boy in Hans Christian Andersen’s The Emperor’s New Clothes, were
stating the obvious unseen. Andersen’s point was that intelligence was not the thing
lacking or what the little boy supplied. It was about how tradition and mind-sets and
in-groups might sometimes need a look from outside. Peer review is not enough.
Sometimes it perpetuates nonsense. The little boy was not a peer, but he could tell
clothes when he saw them. (“Peer”, as any theorist knows, means someone who
pees on your theory.)
Chapter 7 Petty’s Idea 2/3/16 2
I confess that this book casts me as that little boy crashing the economic party, and
maybe the evolutionary biology one too, in trust that outsiders might have better
chances to spot the obvious unseen. What else was the pay rule? I derived it easily
from doctrines already accepted, I think, and anyhow hard to refute. Those were the
total return turism and Ben-Porath’s equation for human growth. The maximand
rule or deadweight loss rule would prove it as well. How could Becker have missed
that what holds for investment in job training by employers holds for any
investment by anyone in anything? How could students of the age-wage problem
have missed the obvious solution? Investment implies expected recovery with
interest, by the investor or a chosen donee, and recovery means recovery of
depreciation. I belabor this point because tradition dies hard, and naturally tends to
circle wagons under attack. I doubt that my surprise attack will meet the resistance
Darwin’s found. Darwin’s met resistance founded on faith. I took pains to show that
my version requires only selection for lineage survival, and that a benign Artificer
might ordain the same.
Evolutionary Biology and Hamilton’s Rule
Economics, meaning any quantitative rationale of choice, normally describes
humans and human choice. That goes for this book too. But some treatments of
economics including this one are meant to fit other creatures as well. My axioms
have kept that in mind. The mortal and reproducing population need not be human.
Much of the animal kingdom, I think, shows convergent tastes and predictions or
acts as if it did. The biological imperative is meant to apply to all. All, as I see it, own
capital of both factors. Even protozoans own (“monopolize”) the nutrients they
assimilate and the space they occupy. Humans are exceptional in their cultural
accumulations of learning and technology shown in our secular (lasting) growth.
But I did not make those features axioms.
I argued that economics tended to reason explicitly or implicitly from the biological
imperative, meaning what I call “ends” in lineage survival, from Petty through Smith
Chapter 7 Petty’s Idea 2/3/16 3
and Ricardo and Malthus and Mill, until the marginalist revolution shifted focus
from objectives to the mechanics in supply, demand and price. Bioeconomics awoke
a century later, largely it seems in response to the challenge of Hamilton’s rule. Now
I will look at it too.
My term “lineage survival” is unusual. It is meant not to take sides between “kin
selection” and “group selection.” The kin selection idea was another word for
Hamilton’s rule from his doctorial thesis in 1964. It said that genes encoding
investment in close kin encode investment in likeliest sharers of those genes, and
should tend to entrench and perpetuate themselves. His condition for investment
was r 〉 bc . r here meant relatedness: ½ for offspring or siblings, ¼ for nephews or
nieces or grandoffspring, and so forth. b meant benefit to the donee, and c meant
cost to the investor. The sign > means “greater than”. The cost and benefit were
measured in fitness itself, meaning chances to survive and breed. But that too meant
“inclusive fitness” where investing in kin counted as breeding when adjusted for
relatedness. The idea was that I give up some of my chances if I can increase yours
to my net genic advantage in the long run. Hamilton allowed for exceptions
including meiotic drive, which sometimes forecloses gene competition. His rule
prevailed because it made mostly good predictions. Humans and creatures in
general usually care for their own young first, if they have any, and for closely
related young if not.
Hamilton made it clear that cost c and benefit b in his hurdle rb > c respectively
meant fitness given up by the investor and fitness grained by the investee. He
further made it clear that fitness could be measured as R. A. Fisher’s “reproductive
value” V(x) published in 1930 and 1957. V(x) meant likelihood at age x of
reaching each successive age times expected offspring at that age. V(x), or Bob
Trivers’ “reproductive success” RS, which simplifies V(x) to expected remaining
offspring, is implicitly constant at the population scale unless there is population
growth (Fisher’s “Malthusian parameter”). For creatures other than us, the
Chapter 7 Petty’s Idea 2/3/16 4
parameter typically fluctuates around zero and group fitness holds about where it
started.
Hamilton’s rule, applied to diploids like us where closest relatedness r absent
inbreeding is ½, forbids investment where fitness gained (benefit) is less than twice
fitness given up (cost). I see no escape from the inference that fitness would double
with each generation, or more to account for cases where relatedness fell below ½. I
see no relief in an interpretation, say, that each successive generation cures this
imbalance by investing only half or less of its fitness and letting the rest lapse.
Fitness is likelihood of leaving descendants of equal fitness. It is not strictly
conserved, because likelihood is generally not identical to outcome. There is ex ante
and ex post fitness. But the ex ante kind is meaningless unless potency, in Aristotle’s
terms, is expected to converge to act. Hamilton’s rule should not have escaped this
critique for half a century. It clearly has merit, but needs some different expression.
Such a reformulation might treat rb/c as a maximand within practical constraints.
We can see how it might be by looking at the context. Darwin’s idea is a competition
for breeding success. This biological imperative is a powerful predictor in nature. It
predicts that traits are selected for successful reproduction to the exclusion of all
else. Evidence is impressive. “Semelparous” creatures who breed only once and do
not invest postpartum care, like salmon and soybeans, die within hours. An octopus
mother breeds only once, cares for her young a few weeks, and dies as they disperse.
Nature is on a tight budget. Resources wasted soon become resources lost to
thriftier lineages.
Hamilton saw this. He was right in stressing the role of competition among
individuals and individual heritable traits. Darwin did the same. One thing
Hamilton’s rule leaves out, which is not to claim that he overlooked it, is that traits
and their genes best at prioritizing self-replication might for that reason hurt
chances of achieving it. We know this happens. Human tradition everywhere resists
and punishes nepotism when it crosses a line. Jane Goodall reported the same for
Chapter 7 Petty’s Idea 2/3/16 5
her chimps at Gombe. I think I have seen it among the pack of dogs, led by my
father’s favorite “Sean”, at Sutton Place. That would count as one of the practical
constraints. Too little support for family over equally deserving others is seen as a
fault, and too much as another.
The reason is obvious. Jack’s ambitions for kin will eventually conflict with Zack’s,
just as with ambitions for food and nest sites and mating opportunities. Not
everyone’s firstborn can be king of the hill. Social creatures evolve agonistic rules to
settle such conflicts peacefully. Losers in mating tournaments, or in contests where
males display and females choose, usually survive to compete again next year. The
contest is in the group interest because the traits of strength and skill proved in the
winner will be those passed on. Our genes tell us to compete as best we can for the
sake of a fair test, and to stop when the verdict seems clear. And soon enough it does.
The quarterback tries his best for three downs to move the yardsticks, but trots to
the sidelines on fourth down for the sake of another chance later. If genes can
encode this farsighted strategy for those other kinds of competition, why not for
nepotistic competition too?
For decades, biologists wondered why genes need so much selecting in species long
established. Shouldn’t earlier contests have selected the fittest genes once and for all,
with no need for further ones but to screen out recent and harmful mutations?
Shouldn’t the best traits have become clear millennia ago? Why need males contest
in tournaments or beauty contests every breeding season, with mostly the same
contestants, when best genes ought to have proved themselves soon after the
species began? Then there would be no genetic diversity except for recent
mutations not yet screened out. Population genetists such as Fisher, J. B. S. Haldane
and Sewall Wright had written mathematical models showing that even the slightest
selection pressures should drive a gene to fixity, and its rivals to extinction, within a
few generations if selection favored it consistently. Their argument was Malthus’
insight: breeding success is geometric. Yet there is rich allelic diversity wherever we
look. There are some gene sites in some species where the most common allele
Chapter 7 Petty’s Idea 2/3/16 6
holds frequencies under ten percent, and those frequencies are constantly shifting.
The flux proves that losers are allowed mating opportunities too, though not as
much, and leave young to compete in the next generation.
Hamilton explained why that could make sense in a paper published with Marlene
Zuk in 1982. George Williams in 1976 and John Tooby in 1980 had argued that
fittest genes in one generation might not be fittest in the next if niche pressures
varied to counter current gene choices. Tooby had pointed to parasites and
pathogens, particularly single-cell ones whose life cycle runs less than an hour. They
could evolve new strains to outflank our old defenses and call for new ones.
Hamilton and Zuk continued this theme. They suggested that genes might have long
memories, put in human terms, and might have seen the same parasites and
pathogens pull such tricks before. If some individuals in the host population still
carried the antidote gene that worked the last time the same unexpected strain
arose, or something close enough to it, hosts collectively could weather the threat if
that antidote gene could be identified and spread fast enough. Then how? Hamilton
and Zuk proposed that what winning males display in contests of singing or
croaking or agility or symmetry, or bright colors in the right places, was possession
of the genes needed to counter the current strains of pathogens and parasites.
Losers in the same contests carried genes that had proved best against strains of the
past and might come back in the future. Nepotism practiced by winners would
speed up the spread of the current antidote. But losers carried genes that had
worked against other strains that might recur. A way had to be found to keep all
those potential antidotes somewhere in the medicine cabinet. Current losers had to
be saved for later. Gene diversity was the key to group survival in the long run. The
quarterback trots to the bench on fourth down because that is better for himself and
the team than being carried to the hospital. He realizes that other players are best
for punts or field goals or defense until he gets the ball again. Selection pressures do
not favor the same traits and genes every time.
Chapter 7 Petty’s Idea 2/3/16 7
Hamilton’s Parasite Theory
My take on Hamilton’s 1982 paper, which I consider his masterpiece, is a blend of
his thoughts, Bob Trivers’ from a decade before, Richard Alexander’s, and maybe
mine. Mine sees a population arranged in local “demes” which intrabreed in most
cases for best adaptation to local pressures including pathogens and parasites. A
local strain to which the local deme is adapted might spread to other demes which
are not. Hosts in the invaded demes become sick. Female ones there intuit the
degraded conditions, breed less often, and breed mostly females (mothers can
choose) because males with their now ill-adapted anti-parasite (histocampatability)
genes will find few willing mates. This begins the part from Trivers. I’ll come to
Alexander’s later.
Mothers in the source deme see an opposite picture. Conditions are not necessarily
better than before, but they are better than in the invaded demes. They intuit this,
breed more often, and breed mostly males. The males migrate to those invaded
demes, carrying histocompatibility genes pre-adapted to the invaders, and find
willing mates there if they can show the signs. The idea that mothers choose to
breed mostly males in prosperous conditions is the other half of Trivers’ idea. The
idea that the invading parasite and the males with antidote genes might tend to
originate from the same deme may be mine.
That presupposes that females can trust the signs. Nature makes sure they can. She
provides resistant males with hard-to-feign ones to prove it. This was one of
Hamilton’s key insights. His idea has been called the “truth in advertising” theory.
Symmetrical antlers, deep croaks, accurate songs and bright colors where they
should be tell the females whose genes can be trusted. Parasites and pathogens
would fake them in afflicted host males if they could. It seems they can’t.
Hamilton, I believe, had solved three nagging puzzles at once. Why does nature
waste resources on beauty displays that seem at first glance to hinder fitness? A
Chapter 7 Petty’s Idea 2/3/16 8
peacock’s tail feathers are an encumbrance in running from predators. And why give
the expensive displays mostly to males? Why do males exist at all in species where
they contribute genes but no care?
We just saw the answer to the first. Answers to the second two again build on an
insight of Trivers in 1973. Males produce cheap sperm carrying genes alone.
Females produce eggs packed with costly nutrients. A male can pass genes to many
descendants through many mates if they approve his signs. That speeds up the fight
against parasites. Nature evolved males and their self-promoting signs and their
contests for fastest spread of antidote genes to catch up to shifts in parasite load.
Where Do Losers Go?
A key point in the Hamilton-Zuk theory is that losers’ genes in the beauty contest are
typically not driven to extinction. They are driven to low frequencies until needed
again. Kin selection, up to a point, helps maintain genic diversity by preserving
current losers within the gene pool. Selection pressures punish and restrain kin
selection when it conflicts with preservation of other genes whose time will come
again. I met Hamilton at a conference in Squaw Valley, where Bob Trivers had
helped us attract him, and told him this reason why I thought his 1982 paper helped
complete and qualify his 1964 paper. He was the absent-minded professor to
perfection. Moody, distracted, profound. He smiled, a rare thing for him, and said
“It’s been a long search.”
This explains what I mean by lineage survival or fitness. Much of this book assumes
its maximization even among modern humans, who create our own urban
environments in place of the ancestral savanna for which we were adapted. And
much of economic history, although written in cities by city-dwellers, appears to
assume the same. Chapter 2 listed some examples. Let’s review them. There was
Petty’s of 1662. The similar equilibrium wage theories of Smith and Ricardo
expected pay to converge to the level maintaining and replacing the work force,
which is trusted to spend it on both. Malthus’ population principle in 1798 and 1801
Chapter 7 Petty’s Idea 2/3/16 9
added the mechanics. Nassau Senior made that principle his first axiom in his
Outline of 1836. The biological imperative lapsed from attention when the first
generation of marginalists, led by Jevons and Menger, with Walras soon to follow,
thought it unscientific to explain or justify tastes. It reemerged a century later in
bioeconomics, much of which looked for economic implications of Hamilton’s rule.
We will see how it might clarify pure consumption and the maximand.
Enlightened Kin Selection
Hamilton’s rule needs completion because the quarterback and his genes have
figured out that the bench is better than the hospital. What really happens, I think, is
a long-range example of Bob Trivers’ “reciprocal altruism” of 1971 as generalized by
Richard Alexander. Bob wrote that creatures might invest in non-kin if the
investment were expected to be repaid with interest. Alexander added that the
repayment could be to the investor’s kin with equal genetic benefit if Hamilton’s
hurdle rb > c were cleared from the investor’s perspective. The quarterback yields
to special teams on fourth down, and they to the defense until possession changes
again, for the best interests of each and all in the long run. The interest they receive
in turn for deferring to non-kin is the cost of maintaining themselves on the bench. It
does not accrue and compound because it is paid out continuously. It is an insurance
cost that each temporary winner dares not trim. Group selection is enlightened kin
selection.
Three or four decades ago, this much acknowledgement of group selection would
have met more resistance than I expect now. It shouldn’t have. Half the beauty of the
Hamilton-Zuc scenario is in explaining allelic diversity as a result of agonistic rather
than lethal competition. Zack and Jack and their genotypes are rivals now because
they are teammates in the big picture.
Kin selection is a help until it crosses the line and becomes a hindrance. Some
mothers in the source deme will carry higher frequencies of the antidote gene than
others. They will tend to be healthier, and so able to invest more energy in more
Chapter 7 Petty’s Idea 2/3/16 10
young. If all mothers invest preferentially in their own, or maximize Hamilton’s
standard rb > c , healthier mothers will produce more young with higher doses of
the antidote genes, while sicklier mothers will produce less with less. Here it is
females who compete to prove the same better genes that males just proved in the
tournaments or beauty contests.
The race against parasites speeds up again with Trivers’ fine insight about healthier
mothers choosing to dial up the ratio of sons to daughters (“primary sex ratio”), and
to expand the reproductive period at both ends with shorter birth spacing for more
male offspring still. (Some of this may be my idea rather than his.) Nature proves
best current genes twice. Fathers prove them by duking it out or strutting their stuff.
Mothers carrying the same best genes prove it by winning the breeding contest
against other mothers after.
The ex ante/ ex post distinction counts as much in biology as in economics. Here it
accelerates the selection process. Offspring carrying the antidote gene to meet
current parasites will generally not on that account cost more ex ante invested
consumption to raise. If they are males, who can turn that advantage into many
offspring, the ex post value of that same investment can be far higher. The converse
works for offspring lacking the gene. Their mothers can make the best of it by
producing females who will find breeding opportunities anyhow with mates
carrying the gene, since she knows which they are and males always have cheap
sperm to spare, and will so keep their own genes in the gene pool.
Parasites got the last laugh by killing Hamilton on research in Africa a few years
after I met him. I never knew well enough to call him Bill. Bob Trivers called him the
deepest thinker in the world. That couldn’t be wrong by much.
Parasites and Demes
Ernst Mayr, Bob Trivers’ doctoral advisor at Harvard, defined a deme as a race or
subpopulation that intrabreeds at least 95% of the time. I hypothesize that it does so,
Chapter 7 Petty’s Idea 2/3/16 11
in some cases, to maximize frequency of a histocompatibility gene which is an
antidote to the local strain of parasite or pathogen. This idea could complement the
Hamilton-Zuc parasite model nicely. It would give a safe home to which both gene
and parasite could retreat until their times come again.
Period of Production Theory
Back to economics. Chapter 4 mentioned John Rae as a contributor to what later
developed into Mill’s free growth theory. Rae’s book, published in 1834, also begins
what was called period of production theory. The idea was that production took
time, and that profit compensated the investor’s patience over the production
period. Senior, who had sent Rae’s book to Mill, adopted this idea in his own betterknown
Outline in 1836. Rae’s book itself found few readers, despite its warm
endorsement by Mill in his own magnus opus of 1848. Jevons adopted the idea from
Senior in 1871, and Boehm Bawerk from Senior and Jevons in his book of 1889.
Boehm Bawerk soon learned of Rae’s work, and dedicated later editions to him.
Period of production theory thrives today in the Austrian School, which had been
founded by Boehm Bawerk’s teacher Carl Menger in 1871. (Menger was the guy who
squabbled with Schmoller in Chapter 2.)
It has found little favor elsewhere. The period seemed impractical to define or
measure, and so gave little predictive value. Joseph Schumpeter, a student of Boehm
Bawerk who disagreed with him on this point, argued in 1911 that the period of
production is zero; capital is present continuously. Frank Knight, who had
anticipated Schultz in realizing that some consumption is investment in human
capital, argued as Schumpeter had.
But the theory is true by definition. Any rate is the inverse or reciprocal of a period.
The inverse of 4% per year is 25 years. Return is the ratio of net output to capital
producing it, meaning the rate of production, and its reciprocal is the period of
Chapter 7 Petty’s Idea 2/3/16 12
production. Where the critics were right was in finding a lack of clarity and
predictive value in the theory. Where does it lead? Rabbits and redwoods have
different periods of production, at first glance, but should nonetheless agree in
return if in risk. Jevons wrote that he meant production of the “wage fund” as a
whole, meaning the universe of consumer goods. But he pointed to wine and timber
as examples to help pin down the period. Boehm Bawerk picked nine years for no
reason I can see.
All went wrong by considering physical capital only. The factors blend into each
other; physical becomes human capital through invested consumption, and
conversely when human depreciation is recovered in products. The generation
length gives the replacement period for total capital if total capital is interpreted as
fitness and if all fitness of each generation is passed to the next.
Jevons and Boehm Bawerk assumed growthlessness for simplicity, and would have
realized that they were modeling only the replacement component in net output.
Boehm Bawerk’s contribution, anticipated by Petty, was his insight that time
preference rate explains rate of return by pricing the capital denominator, and not
the reverse. This had not been clear in Rae or Senior or Jevons. I give all four high
marks for a near miss. But they could have come closer. Remember that Senior’s
first axiom had been Malthus’ population principle. He and the others would also
have known of Petty’s human and total capital idea, which was occasionally revived
and critiqued. They didn’t quite connect the dots.
Next Generation Theory
Petty wrote A Treatise of Taxes in 1662. The whole title continues to about as many
words, counting ampersands, as pages in the book or pamphlet. His son tells us that
Petty dictated his books overnight to secretaries who slept by turns. It is easy to
believe that Petty didn’t need much sleep. He was a go-getter who had sailed to
Chapter 7 Petty’s Idea 2/3/16 13
Ireland as chief medical officer to Cromwell’s ironsides, stayed on to survey the Irish
land with which Cromwell would pay his troops, and then got Parliament’s approval
to invest in that high-risk land to make a fortune. It is rare for a man of practical gifts
to be a deep thinker too. Petty, like my father, was both. His Verbum Sapienti of 1664
was first to apply the ancient capitalization formula to both factors, meaning
workers as well as tradeable things, and so originated the concept of human capital
as present value. He applied this insight there and his Political Arithmetick in 1676,
and again in The Total Wealth of England in 1683, to measure the total wealth of
England including human capital. That makes him the father of national accounts.
But his greatest achievements, I think came in A Treatise of Taxes.
Chapter 4, paragraph 9 of that book begins with
19. Having found the Rent or value of the usus fructus per annum, the
question is, how many years purchase (as we usually say) is the Fee simple
naturally worth? If we say an infinite number, then an Acre of Land would be
equal in value to a thousand Acres of the same Land; which is absurd, an
infinity of unites being equal to an infinity of thousands.
Petty clearly recognizes that time preference, meaning our taste for impatience,
explains productivity, or ratio of output to capital, rather than the other way around.
This powerful and counterintuitive insight is usually credited to Boehm Bawerk in
1889, who showed that it is true for man-made things as well as land. The utility or
usus fructus being a given, we bid less for the land or other capital producing it if we
are less patient, and more if more. Bidding less for this denominator of rate of return
bids that rate itself up if the numerator is a given, and conversely. That’s why riskier
assets offer higher return. Petty’s reductio ad absurdam of a hypothesis of infinite
patience is obvious in hindsight, but may not have been written down before. Petty
continues:
Chapter 7 Petty’s Idea 2/3/16 14
Wherefore we must pitch upon some limited number, and that I apprehend
to be the number of years, which I conceive one man of fifty years old,
another of twenty eight, and another of seven years old, all being alive
together may be thought to live; that is to say, of a Grandfather, Father and
Childe; few men having reason to take care of more remote Posterity: for if a
man be a great Grandfather, he himself is so much nearer his end, so as there
are but three in a continual line of descent usually coexisting together; and as
some are Grandfathers at forty years, yet as many are not till above sixty, and
sic de eteteris.
20. Wherefore I pitch the number of years purchase, that any Land is
naturally worth, to be the ordinary extent of three such person their lives.
Now in England we esteem three lives equal to one and twenty years, and
consequently the value of Land, to be about the same number of years
purchase. Possibly if they thought themselves mistaken. . . .(as the observer
on the Bills of Mortality thinks they are. . .)
21. . . . But in other Countreys Lands are worth nearer thirty years purchase,
by reason of the better titles, more people, and perhaps truer opinion of the
value and duration of three lives.
23. One the other hand, Lands are worth fewer years purchase (as in
Ireland) . . . by reason of the frequent rebellions. . .”
The “other Countreys” could include France and especially Holland, then models of
prosperity. Petty had made his fortune in Irish mortgages, and knew the years
purchase there.
But the argument is a puzzle. There is a focus on longevity and mortality, as if the
generations are providing for old age. But Petty’s overlapping generations model
cannot be much like Paul Samuelson’s of three centuries later, where a generation of
productives leaves a nest egg for retirement. Samuelson’s productives are
replenished exogenously, with children left to the imagination. Why would Petty
have mentioned their ages? And retirement at age 50, as a norm, would have made
no sense to Petty or his readers. The grandfather will stay in harness.
Chapter 7 Petty’s Idea 2/3/16 15
The one and twenty years could mean remaining life expectancy at age 50. But Petty
could easily have spelled that out, or the implied 71 year terminus. He does spell out
the ages of the three generations. Their average difference in age rounds to 21
years.
Petty’s readers, like Smith’s and Ricardo’s after, would have taken it for granted that
each generation provides for the next. “Few men having reason to take care of more
remote posterity” would have registered in the context of that provision. “Posterity”
usually meant and means descendants.
His description, like mine, is incomplete. He may mean that life expectancy is also a
factor in calculating the years purchase. If so, he apparently leaves that thought to
be followed up later. There is also room to argue that the grandfather looks two
generations ahead, so that the years purchase becomes 42 years. But that would
give the usus fructus at 2.3%. All the rates Petty reports elsewhere in the tract are
much higher. One generation length is what he seems to apply. My reading is that
the grandfather provides for the grandson by passing all to the son.
Petty’s overlapping generation insight has been one of his least noticed, just as with
Mill’s on output growth preceding and explaining capital growth. I first read of
Petty’s idea in a collection of Lionel Robbins’ lectures at London School of
Economics delivered in 1979-1980, but published in 2000. I learned from these
lectures that Gustav Cassel had published the same idea in his The Nature and
Necessity of Interest in 1903. I hunted that down. Robbins misremembered in telling
his students that Cassel had arrived at the idea independently. In fact Cassel and
Robbins both quote the same excerpts from A Treatise of Taxes that I just did. Cassel
inferred that interest rates cannot stably be less than 2% per year.
Chapter 7 Petty’s Idea 2/3/16 16
I arrived at the same idea independently, anyhow, and published it in Social Science
Information in 1989. To date it is my only publication in a refereed journal, and
remains uncited as far as I know. Alan Rogers, a biologist at University of Utah,
published almost the same idea in 1994 1 and 1997 2 . Neither of us knew of Petty or
Cassel or each other. Both of Rogers’ two papers are included in my appendix.
Petty’s great idea has otherwise remained unnoticed as far as I know.
His idea in modern terms comes from the same ancient capitalization formula.
Sumerian temples knew how to evaluate land as well as mortgages and annuities by
discounting to present value. In the simplest case, where cash flow is expected to
hold constant forever, the logic begins with the definition
cash flow rate =
cash flow
capital
.
Algebra allows
capital =
cash flow
cash flow rate
. (7.1)
Years purchase, given those simplifying assumptions, meant
years purchase =
1
cash flow rate , (7.2)
1 The Evolution of Time Preference.
2 Evolution and Human Choice over Time.
Chapter 7 Petty’s Idea 2/3/16 17
Suppose for example that cash flow rate is known to be 4%. Using (7.2), we would
figure
years purchase =
1
4%/ year = year
4% = year
4 /100 = 100years = 25 years.
4
That allows (7.1) to be reexpressed as
capital = (cash flow) x (years purchase). (7.3)
Where cash flow and cash flow rate are assumed constant over time, they become
identical to profit and rate of return. Sumerians realized that return is the universal
maximand, three millennia before Turgot wrote that down, and that competition
tended to equalize it to a current market norm. Then it would also equal years
purchase.
Petty was searching for the rationale of years purchase, and found it in the
generation length. Petty’s idea I think, and mine anyhow, could begin with
capital = means of accomplishing goals= means of lineage survival= fitness. (7.4)
Nature’s way is transmission of all fitness, meaning total capital for humans, to the
next generation. Nature cares just as much for later generations, but trusts each
generation of immediate descendants to know best what their own immediate
descendants will need for that long-range goal. Each passes the baton and retires.
We invest everything in the next generaton precisely because we care about the
ones after. Hamilton’s rule reflects this reality. Grandoffspring are only ¼ related to
Chapter 7 Petty’s Idea 2/3/16 18
donors, while offspring are ½ related. Hamilton thus predicts grandoffspring to
receive investment only when benefit/cost ratio is double. My own analysis allows
more role for group selection, without saying how much, and shifts attention from
who benefits to when.
Petty’s idea, if I understand him, is
years purchase = generation length = 21years, (7.5)
which would give
cash flow rate
1
generation length = 1
21 years
= 4.7%/year. (7.6)
This would tally well enough with rates of return and interest rates as Petty knew
them.
I would adjust Petty’s estimate of the generational length. Petty’s primogeniture
model may have been true to law and custom for land inheritance, but it is not true
to biology. I prefer R. A. Fisher’s 3 method equal-weighting all births from first to last,
and equal-weighing ages of both parents at each birth. We have some evidence that
the maternal generation length in recent decades, by that method, has run near 26
years over recent decades. If fathers are five years older on average, Fisher’s method
would arrive at 28.5 years. Rogers found 28.9 years from other sources. Then (7.6)
would give
cash flow rate =
1
= 3.5%/year. (7.7)
28.5 years
3 The Genetical Theory of Natural Selection (1930).
Chapter 7 Petty’s Idea 2/3/16 19
All this has assumed has assumed constant cash flow indefinitely. That would imply
zero growth. Only under zero growth do output and rate of return simplify to cash
flow and cash flow rate.
Now let’s model growth in. I divide the Y rule by total capital, as in Chapter 4, to get
output
total capital
=
total capital growth
total capital
+
cash flow
total capital ,
or more compactly
rate of return = growth rate + cash flow rate. (7.8)
At the collective scale, cash flow rate simplifies to pure consumption rate. That
would be written
rate of return = growth rate + pure consumption rate, (7.9)
as in Chapter 4. Then (7.6) through (7.9) allow
rate of return = growth rate + 3.5%/year (7.10)
at the collective scale.
(7.10) would be wrong if growth rate were a function of cash flow rate. I said that
politicians, and even economists to a degree, teach that faster growth needs
consumption restraint first. That corresponds to cash flow restraint in (7.10). Free
Chapter 7 Petty’s Idea 2/3/16 20
growth theory says such restraint doesn’t happen. Data say the same. I apply the
same idea in next generation theory.
My 3.5% is a rough estimate. What counts is the generation length. The length was
probably higher, and the rate lower, before medicine and sanitation lowered
mortality rates, and let two or three births per couple meet the need for population
replenishment.
The cash flow or pure consumption rate modeled at 3.5% might also vary for
reasons other than changes in the generation length. My charts show the pure
consumption/total capital rate as higher in the middle part of the twentieth century
as people drained capital reserves to keep up consumption in times of world-wide
depression. I’ll say more about these reserves.
First Interpretation
Next generation theory says in effect that R. A. Fisher’s version of the generation
length, not Petty’s primogeniture version, gives the period of production of total
capital. We would miss the point if we focused on the period production of human
capital separately. Total capital is our means of lineage survival. This reinforces my
theme that human capital does not mean humans. It means skill sets priced at
present value of foreseen cash flow. Skill sets are not enough for lineage survival.
We also need things. We should not fall into the trap of surplus value theory, which
had been taught by communists for decades before Karl Marx joined their ranks, in
supposing that skills make things. It is only half the truth. Skills plus things make
skills plus things as the generations repeat.
Nor should we make the mistake of supposing that the generation length begins and
ends uniquely from birth to birth, so that the remaining period of production grows
shorter over adult life and the time discount rate steeper. The period of a cycle is the
same at any point. The young, simply by maturing, are already investing in their
Chapter 7 Petty’s Idea 2/3/16 21
counterparts in the next generation. Each cohort (same-age group) invests
effectively in its immediate descendent. Eight-year-olds are investing in the next
generation of eight-year-olds, and so to the end. That’s why Fisher’s version of the
generation length is best. It prioritizes each cohort and gender without judgment as
to which matter more. The period of production gives our patience horizon. The
horizon and its reciprocal, the pure consumption rate, both hold the same at any age.
Cash Flow and Risk
The maximand rule notes that time preference and return vary with risk. Return is
growth rate plus cash flow rate. Is variance with risk captured more in one of these
two components than the other?
We might intuit that riskier and higher-return assets grow faster on average, over
enough time for the bumps of risk to even out. But if that tended to be true, the
universe of assets would grow progressively riskier over the decades and centuries.
That is not my reading of history. My impression is that smoother and rockier
periods come and go without overall trend. In the world we know, then, it is cash
flow rate rather than growth rate that varies from asset to asset with risk.
For illustration, consider factor risk. I argued that human capital figures to be the
riskier and higher return factor because assets tend to reflect the risk appetites of
their owners. The young are more risk-tolerant, and own human capital
disproportionately. If this higher return were reflected in higher growth, rather than
in higher cash flow, the ratio of human to physical capital would tend to rise steadily
over the millennia. Most readings have tended to see it the other way around. I
myself favor the neutral assumption that the factors keep pace. Then cash flow rate
becomes higher for human than physical capital, with 3.5% the cap-weighted
average.
Chapter 7 Petty’s Idea 2/3/16 22
Consider also the history of corporate leverage. Equities are riskier because bond
interest is paid first. If equities grew faster, however, leverage would constantly
decline. That is not what we see.
This inferred concentration of risk premium in cash flow rate is convenient for
testing. Growth and return are two of the most closely followed variables in
economics. We have no direct measure of the pure consumption rate, or cash flow
rate at the collective scale. Nor have we any direct measure of growth and return to
total capital at any scale. But we have a good idea of average return and growth and
cash flow to securities and business assets. By the maximand rule, return to human
capital should be the same but for differences in risk. I model human capital as
somewhat riskier, for reasons just given, and human capital is the larger factor.
Then if I am right in placing the risk premium within the cash flow component of
return, and in estimating average-risk cash flow rate at 3.5%, cash-flow rate to the
business sector as a whole should be somewhat less.
Next generation theory predicts at the collective scale. Collective return is implicitly
average return, and that means average-risk return. My reading of history, which
rules out progressive growth of higher-risk assets at the expense of lower-risk ones,
simplifies that to average-risk cash flow plus whatever collective or average growth
happens to be at the moment.
Don’t Grandparents Invest?
Next generation theory assumes that each generation invests all its capital of both
factors in the next within the generation length. We expect it to do the same in turn.
We care about grandoffspring too, but serve them best by trusting and enabling
their parents only.
A first reaction is that this denies the obvious. Humans today, in advanced countries,
normally live to nearly three times the generation length. (3 x 28.5 = 85.5). Even
retirement at age 65 comes eight years after twice that length. And job number one
Chapter 7 Petty’s Idea 2/3/16 23
for grandparents seems to be helping take care of grandchildren. Doesn’t that falsify
next generation theory?
Note quite. Retirement typically means dependence on savings or subsidy. The
parental generation subsidizes both the young and the old. Retirees can be
interpreted to some extent as hired though willing caregivers paid for by parents.
That explains part. The rest, I think, is best explained as replenishing a capital
reserve. Nature builds up reserves in good times and depletes them in bad times. A
rise in longevity from what is normally needed for lineage survival is a rise in
human capital reserves. Human capital is the most versatile kind. We geezers have
lost a step. But we remember how it’s done. We particularly remember how
parenting and homemaking are done, since those change least with technology.
Julius Caesar’s nanny, with a few pointers, could probably fill in as a nanny today. If
the parental generation were pulled away to fight a war, or rebuild after a
catastrophe, we oldsters could keep up the home front.
Free growth theory, abundantly proved in the data, is essential to next generation
theory. What each generation invests in the next is all its fitness (total capital). All ex
post growth, up or down, is added or subtracted for free. Catastrophes and windfalls
are the random kind of free growth. Tech gain is the accumulating “secular” (of
ages) kind. I wouldn’t put it past nature to have learned that sustained growth
means rising risk. She could adjust with reserves. We may be selected (a nicer word
than programmed) to build human capital reserves intentionally, whether or not
seeing nature’s motives for the buildup as distinct from our own, when real wealth
doubles with every generation.
That intentional or ex ante part would mean investment in the reserve. It isn’t
targeted to the grandoffspring generation, because they aren’t expected to draw it
down unless needed. All the rest of the buildup of human capital reserves in lifespan
prolongation is best explained as random free growth if my interpretation holds
Chapter 7 Petty’s Idea 2/3/16 24
water. Next generation theory is not contradicted because it describes cash flows
only. It treats all growth at the collective scale as free and exogenous.
Testing Next Generation Theory
The proxies for the pure consumption rate (Schultz’ pure consumption over total
capital) in security markets would be dividend yield for equities, and interest for
debt claims. Ibbotson Associates’ SBII (2012), Chapter 4, shows average real
interest on U.S. corporate bonds as 3.0% over the period 1926-2011. Real corporate
dividend yield rate over the period can be estimated from the same source at about
2.9%. Jeremy Siegel’s Stocks for the Long Run (2002), Table 1-2, reports data
extending back to 1802. Real return over the period 1802 – 2001 is shown as
averaging 3.5% for long-term governments, and 2.9% for short-term governments.
Corporate bond returns would have run somewhat higher.
Global Financial Data shows stock market information for 95 countries. Data for U.K.,
U.S., Germany, Australia and France begin from 1701, 1801, 1870, 1883 and 1896
respectively. My charts and tables, and my website Free Growth and Other Surprises,
show this information along with evidence for free growth.
The eighteenth century is represented by U.K. alone. U.K. then showed real price
return, dividend yield and total return at 21.4%, 7.9% and 29.3%. Volatility of
dividend yield was exceptional. From 1801 forward, U.K. averages for these flows
were 2.2%, 4.2% and 6.4%. U.S. figures from 1801 forward were 2.9%, 5.3% and
8.3%. Global Financial Data also shows collective flows for Europe and the world
since 1926. Here the figures were 3.3%, 3.9% and 7.3% for Europe, and 3.5%, 3.8%
and 7.3% for the world.
Modeling of the pure consumption rate before the emergence of security markets
could refer to the history of interest rates alone. Interest is rate of return to senior
claims. Rate of return to any claim is realization by investors net of all expense.
Chapter 7 Petty’s Idea 2/3/16 25
Investors as to interest means lenders, not borrowers. Interest rates published
historically are rates borrowers are contracted to pay. Interest rates realized by
lenders are less for two reasons. There are friction costs of due diligence,
contracting and collection. Default costs, slight when times are good, can be
catastrophic when times are bad.
Homer and Sylla describe normal contracted rates, not realized rates net of those
costs, as 10% − 40% in Sumer and Babylonia, 6% − 18% in ancient Greece, 5% −
24% in Egypt, and 4% − 12+% in Rome and the Byzantine Empire. 4 After higher
rates in the dark ages, European mortgages and commercial loans found the range
7% − 25% in the thirteenth and fourteenth centuries. 5 The range settled down to
4% − 14% in the sixteenth century, 6 and to 3% − 10% by the seventeenth and
eighteenth 7 . The authors comment: 8 “…interest rates declined during much of the
later Middle Ages and Renaissance. The earliest short-term rates quoted were
somewhat higher than the last and highest of the western Roman Legal limits. They
were not too different from early Greek rates and were within the range of
Babylonian rates… The later Renaissance rates were well within the range of
modern rates and the lowest were far below modern rates in periods of credit
stringency.” Merchants of Venice in Shakespeare’s time and long before borrowed
from banks, not from Shylocks, and at rather lower cost than merchants of the
twentieth century.
Economics and Biology
Bioeconomics has meant economics informed by biology. I argued that this
describes much or all of classical economics from Petty through Mill, then lapsed
when the marginalists preferred to do without any explanations or justifications of
tastes, and revived a century later to explore Hamilton’s rule.
4 A History of Interest Rates, Rutgers, 1996, Table 4.
5 Ibid. Tables 6 and 7.
6 Ibid. Table 9.
7 Ibid. Tables 10 and 14.
8 Ibid. Chapter 10.
Chapter 7 Petty’s Idea 2/3/16 26
I too reason from biological axioms, and from much the same ones implicit or
explicit in the classical period. But I end up framing ideas of biology in the language
of economics rather than the opposite. I begin with
total capital = means of ends = means of replication = fitness,
where fitness is understood as a stock. The concomitant flow and rate would be
output (creation of fitness/total capital) and return (ratio of the two).
Free growth theory gave the inference
optimum ex ante output = optimum controllable output
= exact offset of pure consumption, at the collective scale.
Next generation theory specified the period of this exhaust and recovery as the
generation length.
Consider Hamilton’s rule in this context. All ex ante output, continuing steadily at
the generation rate, must be invested concurrently in the next generation or stored
for later investment within the deadline. It is the problem of Brewster’s millions.
Adults must invest or store as efficiently as practical (the maximand rule) before the
output means has slipped by. And the more stored instead, the more pressure to
invest later within the deadline. Time left for investment is another of the practical
constraints on maximization of rb/c.
What I sense is a watering down of Hamilton’s rule from what seemed logical
compulsion a few decades ago to something more like a target of opportunity. A
prediction maximizing rb/c has proved its value as a useful rule of thumb. I
suggested why some nepotism might be more adaptive than none in my review of
the Hamilton-Zuk parasite theory. It’s about giving all genes a fair but speedy trial.
Chapter 7 Petty’s Idea 2/3/16 27
The quarterback gets three downs, and the batter three strikes, before they go back
to the bench. Some nepotism directs healthier mothers to invest in more and
healthier offspring, and sicker ones conversely, long enough to demonstrate which
is really which. Males passing the test carry the signs to prove it. Females choose
them to spread the antidote gene to the whole population. Losing genes and losing
parasites retreat until their time comes again.
Summary
This chapter trades my wannabe economist hat for my wannabe biologist one.
Herbert Spencer called those fields the same at bottom. I never read Spencer, and
know him mostly from Bertrand Russell’s books on the history of philosophy.
Spencer rates a subchapter there. Yet he was an autodidact with less training in
either field than mine. He even had less training in philosophy than mine. He was a
philosopher all the same, by Russell’s tough standards, and knew that logic comes
first. Data eventually prove their worth when it’s time to test. The data I’ve found
fits net generation theory more or less. What I really have on, all the while, is my
wannabe philosopher hat.
Popperians make no sense. Are we supposed to find that a rose is not a rose? Or that
all reasoning from definition is as transparent as that example? Wiles’ proof of
Fermat’s last theorem ended a search that took some pretty bright minds three
centuries. My best guess would be that Popperians confuse the concepts of logic and
question-begging. They are opposite. Logic (reasoning from definition) means
taking out no more than you put in. Truism or tautology usually means obvious
examples of the same, but sometimes includes subtle ones too. Question-begging
means taking out what you never put in 9 .
9 Circularity is question-begging which claims to take out as inference what it put in as assumption.
Assumption that Socrates is a man and that all men are mortal does not confirm that Socrates is a
man. It confirms that Socrates is mortal if assumptions are sound.
Chapter 7 Petty’s Idea 2/3/16 28
Spencer’s “survival of the fittest’ doctrine would be a truism if we could prove the
theory of natural causality. We can’t by any means known to me. Science takes it as a
working assumption. So did Hume, and so do I. If God intervenes only a little, so that
laws of nature comes close to reality most of the time, we’re still in business.
My critique of Hamilton’s rule proposed that nepotism meets resistance when it
conflicts with nepotistic goals of others. I proposed a modus vivendi through
agonistic rules. Hamilton’s parasite theory with Zuk, written 18 years later, gives the
game plan.
Nepotism, meaning kin selection through Hamilton’s rule, is in the common interest
to a point. It speeds up proof of best genes to beat the current parasites by testing
female genes as well as male ones. Healthier mothers and sisters and aunts carry
more fitness to invest in more young. And females in most K-selected species,
including humans, perform most care of the offspring and siblings and nepotes
(nephews and nieces) that receive it 10 . Male competition alone does not determine
best current genes to nature’s satisfaction. Female breeding competition and
nepotistic investment help prove them farther.
All agonistic rules are about keeping the contest fair and deciding when proof is
enough. Long-term success against future as well as current parasites needs most
losers, not all, to go to the bench (low frequencies; source demes in my version)
rather than to extinction. Most losers survived to enter the contest because they
10 The burden is about 50-50 in pair-bonding birds. Fathers look to be the only caregivers in
territorial fish such as sticklebacks.
Chapter 7 Petty’s Idea 2/3/16 29
were winners once before. Their cost on the bench, or on the taxi squad, is good
insurance.
My version of Hamilton’s parasite theory patched in some of Trivers’ ideas. One was
that mothers intuiting self-health and good prospects should tend to breed higher
primary sex ratios and conversely. Their male offspring can then find willing mates
if health carries reliable signs as Hamilton proposed. Also the investment of
insurance cost by winners in maintaining losers on the bench can be interpreted as
Trivers’ reciprocal altruism to be recovered when winners now become losers later.
My discussion of grandparental investment let still more worms out of the can. It is
clear that humans in advanced economies today normally live to nearly three
generation lengths. I proposed that we are replenishing a total capital reserve,
meaning mainly a human capital one, when recovering from hard times in the world
wars and world depression. No one really knows.
Chapter 7 Petty’s Idea 2/3/16 30
CHAPTER 8: BANKS, MONEY AND MACROECONOMICS
Splitting up Banks
I started to write a book on banks and money a year ago. I stopped when I realized
that I don’t know enough about the subject. I have some experience and have done
some reading in those fields, but not enough to justify a whole book. A chapter, or
part of a chapter, is more like it.
Sumerian temples doubled as banks, mostly for agricultural loans to finance the next
crop. It is from their records, in clay tablets, that we know they understood
compound interest and the capitalization formula.
Deposit-and-lend banks as we know them today emerged in Venice and other
European cities in the twelfth and thirteenth centuries. Chapter 1 said that equity
investors cannot be attracted at leverage (deposit/equity) of less than 10:1, that
even one tenth so much leverage is unstable in high winds, and that we rebuild the
banking system after every systemic failure because we blamed the high winds
rather than the rickety structure.
I said that the solution is to split up banks as we know them into deposit banks
which invest in ETFs on the one side, and lending banks which raise funds from
investors rather than depositors on the other. These entities would have separate
stockholders, and would not interact unless incidentally.
A different kind of bank split-up has been urged since the 2008 crash. Repeal of the
Glass-Steagle act had allowed commercial (deposit-and-lend) banks to operate as
investment banks (brokerage firms). Many blamed the crash on that repeal, and on
investment bank innovations such as mortgage-backed securities. I think those
critics are looking in the wrong direction. The problem, as with most bank crashes
over the centuries, was overleverage encouraged by nearly costless deposits. The
solution is not to peel off brokerage operations from the mix, but to peel off deposits.
Chapter 8 Banks, Money and Macroeconomics 2/8/16 1
I see no reason why lending banks should be separate from investment banks.
Rather the depositors’ money should not be risked in either.
It is also a mistake to blame Wall Street chicanery. Chicanery is a fact of life, and
Wall Street has more than its share. But I can testify, from a ringside seat, that many
sound financiers and first-rate economists genuinely believed in the sub-prime
derivatives they were selling. They were proposed to the trusts I run. I turned them
down as a business proposition because I saw too much complexity and no upside.
But my read was that the presenters were sold themselves.
The problem is not in the people. It is in the inherent fragility of deposit-and-lend
banks. Then what would the world be like without them? The answer first needs a
closer look at the problem.
Credit Risk is More than Leverage
Some leverage is a good thing. Firms issue bonds as well as stocks in order to attract
a wider range of investors. Risk-averse investors may choose the safety of bonds,
whose interest claims are paid first, while risk tolerant ones may be happy with the
iffier but more promising equity remainder. Leverage in general is a way to satisfy
both these constituencies.
Credit risk rises with term (duration) as well as amount of debt. One of the most
telling points in Siegel’s Stocks for the Long Run is that corporate bonds of 15 years
or more have proved more volatile in real total return than equities have. No
wonder. A corporate bond will have ample debt coverage (gross profit/debt service)
at date of issuance, and an appropriate credit rating. What will both be fifteen years
from now?
Homeowners also typically borrow long-term. They expect to have children in local
schools, husbands and/or wives in local jobs, and other roots in the community. But
Chapter 8 Banks, Money and Macroeconomics 2/8/16 2
who knows that husbands and wives will still be married in fifteen years? Who
knows that if they are, their careers will not have taken them to another city?
It seems to me that reducing the dangers of debt means reducing both term and
amount, and that the solution had better find ways that still accommodate the shortterm
and long-term needs of firms and people.
Now let’s look at how deposit banks might invest.
The Omnibus Fund Idea
If I were a couple of decades younger, I would try to create something I call an
omnibus fund. It starts by seeming to contradict what I just said. I said that firms
issue both stocks and bonds to reach different constituencies. The omnibus fund
would first erase that separation. In principle it would reconstruct the firm as a
whole, or put the pieces back together again, by assembling proportionate shares of
the debt and equity claims on it in a single portfolio.
Suppose for example that the market cap (number of shares times current market
quotation) for a firm’s equity shares is one billion dollars, while the market cap of all
debt claims together in half that. Then the omnibus fund, in principle, would buy
each firm’s equities and debt instruments in that proportion at current market
valuation. In practice it could realize the same effect in a simpler way.
The omnibus fund would be a balanced index fund. Index funds are representative
of all the funds in an index, such as the S&P 500, weighted again to market cap. The
omnibus fund would pick a still more inclusive index, say the Russell 3000 or even
the Wilshire 5000. It would add in a corporate bond index, since balanced means
mixing stocks and bonds, and cap weight the two. The object would be to model the
publicly-traded corporate sector as a whole. The simplest way to get there would be
to buy index ETFs (exchange traded funds) directly, rather than duplicating their
work of assembling portfolios of the underlying individual issues.
Chapter 8 Banks, Money and Macroeconomics 2/8/16 3
If it stopped at that point, the omnibus fund would probably attract few investors. It
would offer the aggregate return and risk of the publicity-traded corporate sector as
if it had never borrowed or issued debt. Aggregate means average. No one is exactly
average. Some like me and my father happen to be more risk-tolerant, and opt for
the higher returns that tend to come from higher risk. Some prefer the opposite.
How can the omnibus fund attract both?
The answer is derivatives. Derivatives are obligations whose benefits depend on
outcomes imperfectly foreseen. I said in the forward that I’m all in favor of them so
long as we respect and manage the risks. Equities themselves are the classical
example. Mortgage-backed securities give another. Common forms include futures
and swaps. The idea is about the same. Each typically picks an index, often the S&P
500. One party, the “short leg”, bets so much money, the “notional amount”, that the
S&P 500 index will go down tomorrow. Another party, the “long leg”, bets it will go
up. The short leg gets so much, say Libor plus 20 basis points (hundredths of a
percent) of the notional amount, in any outcome. The long leg gets the index change,
whether up or down, times the same notional amount.
No one actually invests the notional amount. It is called “notional” for good reason.
Rather each side (leg) commits a cash reserve, held by the firm managing the swap
or future, in this case the omnibus fund itself, of 20% of the notional amount. The
reserve is drawn down to meet payments required when market swings are averse,
and replenished when favorable. When it falls to 10% of the notional amount, it is
considered unsafe and the swap or future ends prematurely. Parties are warned,
and new reserves can be committed in time.
Monitoring of the reserve is continuous during market hours. Whenever the reserve
falls to 10%, even in the middle of the day, the account is closed immediately. This
discipline keeps the other party safe.
Chapter 8 Banks, Money and Macroeconomics 2/8/16 4
Risk-averse clients in the omnibus fund can take short legs, and risk-tolerant ones
long legs. Management of the omnibus fund can handle the mechanics of the swaps
or futures.
The effect would be not less leverage per se, since leverage at the individual account
level is substituted for leverage at the corporate level. The difference is duration.
Swaps and futures are short-term commitments. Three months is typical. Futures
trade in active markets, for good measure, and can usually be liquidated in seconds
at current market during trading hours. So can ETFs themselves.
What do these derivatives cost? Essentially nothing. Those who prefer safety and
the short leg are matched with those who prefer return and the long leg, while the
manager charges only for its time in working the mechanics.
What About Asset Allocation?
Where the omnibus fund seems to violate common sense is in merging out what had
seemed to be valuable distinctions. So it would seem with the blending of equity and
debt claims, but for an optional overlay of derivatives such as futures to restore
whatever risk and expected return we want. Many distinctions blended out,
including that one, have been important to principles of asset allocation and modern
portfolio theory. They are important because some investment sectors are less
correlated than others, meaning less likely to risk and fall in lockstep. Lowcorrelation
portfolios are better because less volatile as a whole without sacrifice of
return. That’s why hedge funds typically assemble portfolios judged low or negative
in correlation, and then try to reduce correlation still further with an overlay of
derivatives. The omnibus fund seems to throw away all these options.
Not really. One of the lessons of the 2008 crash is that everything but Treasuries
tends to go down in high winds. Anti-correlation strategies failed when we most
needed them. The omnibus fund isn’t really giving up so much. Its exceptional
diversity makes it begin with less correlation than specializing portfolios. And
Chapter 8 Banks, Money and Macroeconomics 2/8/16 5
nothing would prevent a sophisticated investor in the omnibus fund from
manipulating correlation further down with derivatives as hedge funds do.
Liquidity, Risk and Return
Demand deposits in banks today can be withdrawn at any time. Time deposits
cannot be attracted without either competitive interest or quick liquidity. This
liquidity requirement has been awkward in that bank deposits are usually reloaned
for years. A run on the bank soon finds no cash left to meet withdrawals. The runs
come when the high winds blow, and provide a coup de grace on top of high default
rates.
The omnibus fund meets withdrawals easily because it is invested only in the most
liquid securities. ETFs trade in seconds at current market quotations. Any mutual
fund shares that might belong to the portfolio trade at current close.
Like most funds, the omnibus fund would also maintain cash. Like some others, it
would “equitize” its cash by exposing it to swaps or futures. Equitized cash leaves a
fund fully invested in effect, while adding instant liquidity around the clock. ETFs
give instant liquidity, but only during trading hours. Mutual funds typically trade at
market close only.
A risk-averse investor in the omnibus fund who opts for Libor plus so many basis
points is more or less in the same position as a bank depositor today. She knows
that her account will grow only by deposits and by interest (Libor plus basis points)
left in to compound. She knows that it will decline only by withdrawals. The investor
who prefers the long leg in swaps or futures, or stays unhedged, will also see her
account rise and fall with the market. There are infinite graduations around these
three simple choices. An account might be partly hedged and partly exposed, or
even over-exposed to a notional amount larger than the account size where law and
markets permit. (They usually do.)
Chapter 8 Banks, Money and Macroeconomics 2/8/16 6
Payment Mediation
Banks effect payments from depositors’ accounts. An omnibus fund can do the same.
Payments out are directed “redemptions” in the language of brokerage accounts, or
withdrawals in the language of bank accounts. Payments in are “subscriptions” to
brokers and their clients, or deposits to bankers.
All these payments can be electronic. A payer, typically a customer, might swipe a
card or click a screen. A payee, typically a vendor, typically must verify first that the
account is authentic and covers the payment offered. An omnibus fund could be well
suited to give this quick transparency.
First, it is essentially an index fund. It is composed of a published ratio of index ETFs
and index mutual funds and index-equitized cash. Individual accounts are then
hedged or exposed to index swaps or future overlays administered by the omnibus
fund itself. The fund can track all these indexes online, and knows from tick to tick
what each account is worth. This holds true even for volatile accounts where risktolerant
clients have opted for long legs in swaps and futures. So long as
management effects all payments in an out, and constructs each account of index
exposures itself, and tracks those exposures and payments in real time, it knows
account values exactly.
Risk-tolerant clients will expect daily ups and downs in account size. That means
that they will have to carry larger accounts in order to be sure of covering payments
in the downswings. That would be a problem if accounts yielded zero return, as
checkable bank deposits do. The gist of my answer to Milton Friedman was that no
amount of money is too much if it yields as much return as other assets of equal risk.
Accounts are hedged or leveraged to do so. Omnibus fund accounts burn no holes in
pockets. We do not own one to spend, like a checking account, and treat it as a drag
on earnings until spent. We own it as a fully competitive investment, and spend it
reluctantly when bills are presented.
Chapter 8 Banks, Money and Macroeconomics 2/8/16 7
Why Invest in Indexes?
The last section showed that index funds offer easy trackability over market hours.
What are the other pros and cons?
On sound microeconomic principle, professional asset management will add value
over index results before deduction of fees. Otherwise they couldn’t stay in business.
The same principle says that the fees will converge to that pre-fee value added. Price
converges to marginal utility (value). Investors bid fees up when fees are less, and
down when they are more. As a rule of thumb, investors should expect to do equally
well in managed or index accounts when fee costs are considered too.
The mechanics of convergence is worth a look. Managed and index funds compete in
a kind of density-dependent flux like hawks and doves in game theory. It pays to be
a hawk when the hawk/dove ratio is too low, and a dove when too high. When
hawks have only hawks to fight, they will win only half the time. Fighting becomes a
losing strategy when it risks more than winning stands to gain. More doves will
mean easier contests.
So it is with asset managers. Index funds (doves) avoid commitment (fights) as to
which firms and sectors will outperform. This neutrality saves the costs of research
needed for commitment (fights). Asset managers (hawks) pay those costs, and
recover them when outperformance results. That means outperforming the index.
But if asset managers collectively managed the whole market, they would become
the index. Some would outperform others, but the whole group cannot outperform
itself. Then it could not recover its research costs. Many would have to close their
doors, leaving the field to index funds which don’t pay those costs, until market
equilibrium was restored.
Then what determines equilibrium? Is the critical variable percent of trades by
managed funds? I thought so for a while. Now I think it’s percent of AUM (market
value of assets under management). My reasoning now is that holds by portfolio
Chapter 8 Banks, Money and Macroeconomics 2/8/16 8
managers reveal informed opinion on security values as clearly as trades do.
Research cost is the same for both. If a manger neither buys nor sells, she tells us
that she thinks the price is right. The critical variable is not trade volume, but
percent of aggregate market cap controlled by asset managers collectively.
The number of asset managers is much less critical. There must be enough for
competition within each specialty or sector of investment. Too many is not a
concern. Abler ones, on microeconomic principle, will displace the less able. That’s
why Herbert Spencer taught that natural selection works the same in economics as
in biology.
A particular reason for preferring index ETFs as omnibus fund investments is for
cheaper liquidity. The omnibus fund must compete with banks in accommodating
payments and other withdrawals (redemptions). Popular index ETFs such as
spiders (SPDRs, for Standard and Poor’s Depository Receipts) are bought and sold in
seconds for a fee of a couple of basis points. So are Treasury ETFs. Thus the omnibus
fund might do best not to include actual corporate bond ETFs in reintegrating the
corporate sector. Treasuries of equal value should do about as well at much lower
trading cost. Easy liquidity is essential.
Why Omnibus?
Omnibus means for everyone as well as of everything. It is all-inclusive either way.
Individuals differ in risk tolerance. An omnibus fund provides for all. The portfolio
of index exposures to riskier equity claims and safer debt claims is meant to satisfy
average risk tolerance as a whole. Individual accounts then choose short-leg hedges
or long-leg exposure or anything between. An omnibus portfolio best matches
aggregate risk and return to individual claims on it.
Other approaches would work too. A broad-based equity index fund, targeting say
the S&P 500 or Russell 3000, could give the same tick-to-tick transparency in
individual accounts. Hedging would still be available to cater to individual risk
Chapter 8 Banks, Money and Macroeconomics 2/8/16 9
appetites within the risk-tolerant groups. A broad-based bond index fund would do
the same for the risk-averse.
It seems to me that the omnibus fund would do both jobs at once, and would attract
more clients collectively. Bigger is better for payment processing. The more clients,
the more “two-sided” payments from one client to another. These payments are
always cheapest.
If accounts cost little or nothing to open, vendors would logically need no urging to
open them. That again favors the simplicity and economy and immediacy of twosided
payments by including both buyers and sellers within the fund.
The omnibus fund is also for everyone as a investor as well as a payer. Very few
people have the time or training to beat the market. I myself have not. What we have
is a sense of our degree of risk-aversion. The omnibus fund gives the broadest and
most flexible coverage of risk appetites. It can poll and advise clients on risk
preferences, and mediate hedges and exposures to suit.
How the Omnibus Fund Might Evolve
I said that if I were a couple of decades younger, I would start an omnibus fund. Not
to worry. If the idea holds water, as I think, someone else will.
It seems to me that banks could not offer much competition. Demand deposits
typically pay no interest, and process payments no better. Omnibus clients offer an
infinite range of returns according to client tolerance for risk.
Banks offer the advantage of federal deposit insurance (FDIC). It will not be enough.
The omnibus fund carries no leverage, and needs no insurance. As it grows, banks
will take notice. They can keep up the uneven fight, or they can join the parade. My
working assumption is that many will prefer the latter. Banks are well positioned to
make the most of the idea. They have the needed expertise and systems and
Chapter 8 Banks, Money and Macroeconomics 2/8/16 10
clientele in place. They can spin off their lending operations as separate ventures to
find funds from investors rather than depositors.
If there were no FDIC, there would be no deposits and no commercial banks. People
can read the newspapers. Anyone old enough has lived through periodic bailouts.
I’m a free market fan who dislikes FDIC. But we would be rash to yank the rug from
under banks by repealing it. We shouldn’t even hint that we might. The world we
know is build around banks, and banks are built on FDIC. Let it stand. How can
anyone know for sure that omnibus funds and independent lending banks will do
better? I think omnibus funds figure to win despite that advantage for banks.
Lending Banks
This is the area least clear to me. Banks as we know them begin with expertise,
systems and clientele in the loans business as well as the deposit and payment
processing business. That could position them to take the lead in both if spun off
separately. Lending can stand alone. There are many lending firms other than banks.
They raise funds from investors seeking returns, rather than depositors seeking
liquidity, and somehow mange to compete with banks today. Lending banks
divorced from depositors could do whatever they do.
If interest rates must rise because investors demand competitive returns, some
traditional borrowers will be motivated to attract equity investment instead.
Corporations and other firms could phase out structural (long-term) debt, and float
new stock issues in its place. The effect would be to lower leverage, risk and return
together. Investors could then tailor risk and return more flexibly by hedging or
leveraging their individual holdings through professional services.
If the same rise in interest rates makes it impractical for newlyweds to buy homes,
they can rent until their means improve. In ten or fifteen years their incomes will
double. They will know if they are still married, how much house they need if so,
and where their careers have taken them. Meanwhile they might rent the same
Chapter 8 Banks, Money and Macroeconomics 2/8/16 11
house they would have bought. They will not have missed a sure-fire investment.
The crash of 2008 showed that houses are risky too. The time to commit to huge and
illiquid investments, as houses are, is after ten or fifteen years of business
experience.
I see no reason why lending banks should not make equity investments too. Loans,
convertible loans and equity investments need the same “due diligence”, or research
into prospects of success and return. All might serve the same clients. “Lending
banks” might simply be investment banks. That’s why splitting of investment banks
and commercial (deposit-and-lend) banks may be a step in the wrong direction. The
key is splitting off deposits.
Macroeconomics in General
Splitting up commercial banks into omnibus funds and depositless lending banks
could change the nature of macroeconomics. Macro has meant the art of maintaining
growth and money value stability at the same time. This has proved mostly a
tightrope walk between inflation and recession. Easy money risks the first, and tight
money the second. My idea is to disconnect the problems of underemployment and
money value instability. If medicine for one has no side effect on the other, each can
be treated more freely.
I would first dissociate money value from money supply. No supply is too large if
money earns competitive returns while we hold it. That was one of the main ideas of
the omnibus fund. Milton Friedman thought my early version of this idea was
anathema. Franco Modigliani liked it fine, but asked tough questions. I’ll try to
answer some of them below.
My approach to the problems of underemployment and the business cycle begins
with phasing out deposit-and-lend banks as I described. I more or less agree with
Chapter 8 Banks, Money and Macroeconomics 2/8/16 12
Ludwig von Mises and the Austrian school that slumps come from overinvestment
enabled by overlending. In 1928 1 , a year before the crash, Mises wrote:
Sooner or later, the crisis must inevitably break out as the result of change in the
conduct of the banks. The later the crack-up comes, the longer the period in which
the calculation of the entrepreneurs is misguided by the issue of additional fiduciary
media 2 . The greater this additional quantity of fiduciary money, the more factors of
production have been firmly committed in the form of investments which appeared
profitable only because of the artificially reduced interest rate and which prove to
be unprofitable… Great losses are sustained as a result of misdirected capital
investments. Many new structures remain unfinished. Others, already completed,
close down operations. Still others are carried on because, after writing off losses
which represent a waste of capital, operation of the existing structure pays at least
something.
Here Mises, writing in 1928, describes the crash of 2008 even more vividly than the
one in 1929. “Many new structures remain unfinished. Others, already completed,
close down operations.” These were mostly plant and office buildings in 1929, and
mostly houses in 2008.
Mises argued that money should be backed by precious metals. He was right in
thinking that it should be backed. But precious metals pay no return. The omnibus
fund earns competitive return at the risk level chosen in each account. Accounts are
owned for performance, and only incidentally for liquidity. No amount is so large as
to tempt overspending.
It did not occur to Mises that divorcement of deposits from lending might prevent
the cycle in the first place. Nor did he mention the danger of 10:1 bank leverage, and
often more, in amplifying consequences of bad guesses. His idea was better
governance of commercial banks. Mine is ending them.
Free growth theory also belongs to macroeconomics in that it predicts only at the
collective scale. It predicts that ex ante net investment, or attempted investment
1 Monetary Stabilization and Cyclical Policy.
2 Unbacked paper money. Also called government fiat money.
Chapter 8 Banks, Money and Macroeconomics 2/8/16 13
beyond depreciation recovery, is simply less consumption with no growth to show
for it. My charts and tables show that this has been true wherever and whenever
tested, in eight economies over 40 to 140 years. We crowd our niches like other
creatures, I think, and have no room for growth except as innovation widens the
niche. The charts and tables seem to tell us that innovation costs no more in failure
rates and learning curves that daily coping does.
Macroeconomics and Keynes
Macro emerged in the 1930s under the influence of Keynes. Simon Kuznets, the chief
architect of the U.S. national accounts, was one of the five economists Keynes invited
to proof the chapters of his General Theory as he wrote them 3 . National accounts
were soon reorganized along Keynesian lines.
To read the General Theory, a beautiful work, one would think that counter opinions
were led by his close friend Arthur Pigou. But Pigou was already in print with
recommendations much like Keynes’ when it was published in 1936. Opposition
came rather from Mises, the other Austrians, Lionel Robbins and the Chicago school.
They argued that intervention tends to make things worse. So do many economists
today. Keynes believed in fiscal and monetary policy as I describe in Chapter 1. He
favored fiscal policy.
Chapter 2 said that he made a basic distinction between investment producing new
things and repurchase of things already produced. Only the first counted as real
investment. The difference matters because only the first puts plant and people to
work. Transfers neither add nor subtract value. Even so, my own language counts all
as investment, and ranks investment only by return. I make no distinction among
investment adding new plant and equipment, or investment in stocks and bonds
already issued, or in existing structures, or even under the mattress.
3 The others were Harrod, Sraffa, Joan Robinson and Ralph Hawtree.
Chapter 8 Banks, Money and Macroeconomics 2/8/16 14
What matters is return. I don’t have to specify “risk-adjusted” return so long as I
describe the collective scale alone. Collective return is implicitly average-risk return.
I prioritize it on the reasoning that optimizing employment of people and plant is
implicit, and that optimizing means putting them to work most productively rather
than over the most hours.
If policy maximizes rate of return, at the collective scale, it will maximize true output
perforce. Return is output divided by total capital producing it. More return is more
output per unit capital. Putting idle plant and people to work, in a slump, is a step in
the right direction. But it doesn’t get the job done unless they work productively.
Even putting money under the mattress is better than investing at a loss. Zero
return is better than negative return. I accept Keynes’ distinction between new
investment and transfer payments. But I see the latter as part of the mechanics that
ends up in the former. Maximize return, and full employment will happen.
Keynes’ opposition is now mostly the Chicago school and other “freshwater” schools
bordering the Great Lakes and along inland rivers. Somehow the taste for Keynesian
intervention resonated best in “saltwater” seaboard school such as Harvard, MIT,
Stanford, and University of California. It is probably no coincidence that the
saltwater states are the “blue” ones tending to vote Democrat, while the freshwater
ones are the “red” ones favoring Republicans. (I call myself a free market Democrat,
whether or not that’s a contradiction in terms.) Freshwater views tend to oppose
intervention, but accept Keynesian basic definitions and equations such as the
Y = I + C doctrine and the distinction between “attempted saving” and investment.
It is these I question.
I don’t think much of his view that intended saving (consumption foregone)
becomes actual saving only if invested, and becomes an equal amount of physical
capital growth if it is. Then (actual) net saving, net investment and physical capital
growth would become synonymous. I said why I prefer a language where saving
and investment are synonymous in the first place. What matters is rate of return.
Chapter 8 Banks, Money and Macroeconomics 2/8/16 15
Investment (saving) under the mattress yields only the psychic value of liquidity.
Actual capital growth depends on rate of return as much as amount invested. If
return holds the same as it was before, growth and net ex ante investment will be
equal. Growth will be less than consumption foregone (remembering the asterisks)
if return drops, and more if return rises.
Keynes saw slumps as investment deficits. I see them as return deficits. Keynes
assumed uncritically, I think, that new investment is the path out of slumps.
Investment will come when prospects of return do.
Although the General Theory was published three years before Myrdal’s ex ante – ex
post distinction, Keynes would have realized the same thing. I think he made the
understandable mistake of supposing that the difference would balance out as
random noise. The charts and tables show otherwise. The optimum ex ante
investment target is enough to offset realistic depreciation exactly.
Keynes was a great thinker, a lively writer and a decent man. I happen to endorse
some of his policy ideas. So did my father. When I asked him what he thought of
fiscal policy, I expected something like Hawtree’s “crowding out” argument:
government investment preempts and prevents private investment. I got a surprise.
My father said “When people are out of work, that’s the time to build a new post
office.” It is, if you need a new post office, because returns can be higher when
contractors strapped for options bid construction cost down.
But it is no disrespect to point that the General Theory was published 80 years ago. I
tend to support Keynes on some points, for example the usefulness of fiscal policy in
relieving slumps, but to agree mostly with Mises on their causes in the first place.
Where I differ from both is in the fundamental anatomy.
Chapter 8 Banks, Money and Macroeconomics 2/8/16 16
Stabilizing Money Value
Modigliani’s main critique was that money earning full competitive return, so that
no amount was too much, would make monetary policy impossible in its usual
forms. My best answer at the time was that full-return money ought to remove
inflationary or deflationary pressures. But I agreed with him that money value
might drift, even so, and that some control would be a safeguard if someone could
think of a way.
The best that occurs to me is continuous revaluation of the dollar. Legal tender laws
specify dollars, or other currency in other countries, as the default means of
payment recognized in satisfying money obligations. Laws could be changed to
specify real dollars instead. Real means corrected for inflation or deflation.
This would have been impractical before the information age. The problem now
seems less. Spendable money, called M1, now means currency plus checking
accounts. Government publishes current inflation figures online. Omnibus accounts
could adjust automatically. They might show values in nominal and real dollars both.
Account value would not change. Correction for inflation would show fewer dollars
worth more each. Correction for deflation would show the opposite.
Currency itself cannot adjust so elegantly. It would remain legal tender, but not
necessarily at face value. Currency would impose a translation cost on its spenders
and receivers. Say for example that the change in legal tender laws was effective as
of January 1, 2020. The real value of the dollar, whether accounts or currency, would
mean its value of that baseline. Nominal value would be that plus inflation since.
Calculators or iPads could keep track of the conversion rate. The cost and nuisance
of this conversion should be manageable. But it would probably reduce demand for
currency where cards or the equivalent do as well. The benefit is in encouraging
long-term contracts and saving “menu change costs.” That means costs of changing
prices. There is no need to change them on account of inflation if prices are specified
in real rather than nominal dollars.
Chapter 8 Banks, Money and Macroeconomics 2/8/16 17
Price stability can matter. The United States has managed to avoid double-digit
inflation since the Volker reforms of the 1980s. But the danger remains. Modigliani
was right to worry.
A law making real dollars legal tender might prompt better measurements of
inflation. Many economists agree that our official ones overstate inflation by
allowing two little for quality improvements. A Lexus or Tesla is not a Model A. That
was the theme of the Boskin Commission report to President Clinton in 1995. The
Boskin panel argued that quality-corrected inflation has run about 1.1% less than
the numbers posted in the consumer price index (CPI). I think so too. But making
real dollars legal tender, even by these imperfect measures, could still give more
confidence in long-term commitments than the status quo.
Speeding Up Fiscal Policy
Designating real rather than nominal dollars as legal tender would amount to an
unfamiliar and more direct form of monetary policy. Meanwhile devolution of banks
into their separate deposit and lending functions, along with emergence of omnibus
funds, need put no constraints on fiscal policy.
Fiscal policy has prescribed tax cuts and government spending in slumps. It
prescribes the opposite, at least in principle, in booms. A problem is that it has
proved slow to implement. There is an “inside lag” while government diagnoses the
problem and calls for a vote in the legislature. An “outside lag” follows until taxes
come due and spending programs are put together and gradually put plant and
people to work.
The inside lag is unavoidable in a democracy unless the executive branch, or an
independent agency like the Fed, is given standing limited authority to diagnose
early signs of unemployment, and to address them with tax cuts or spending. And
there must be enough outside lag to make sure that the medicine has good
prospects in rate of return. Return comes first.
Chapter 8 Banks, Money and Macroeconomics 2/8/16 18
Tax cuts can be faster-acting than spending programs because they obviate the
construction period. Freshwater economists argue plausibly that they are likely to
prove ineffective. They foresee “rational expectations” of taxpayers as predicting
eventual restoration of the taxes when full employment resumes. This gives a
motive to save the tax cut rather than spend it as intended. I see it a little differently.
Most consumption is maintenance or investment to keep up human capital. We will
need that earning power when taxes are restored.
Say’s Law
Jean Baptiste Say, in writings I haven’t read, argued two centuries ago that supply
creates its own demand. The logic is sound to a point. The claims on output simplify
to pay plus profit. The asterisks don’t matter here. Thus pay plus profit is always
enough to clear that market. There could be “partial gluts” when we produced too
much of one thing and not enough of another, but never a “general glut” where
production got ahead of our means to pay for it.
All too true. Consumption plus investment equals pay plus profit. But the sad fact is
that profit can be negative. Deadweight loss happens. When it happens, at the
collective scale, even pay claims may be left unsatisfied. Say’s law gives no comfort
except where outcomes are as expected.
Tax Considerations
Schultz in 1962 argued that educational (human) capital is overtaxed. What he
wrote was: “The established tax treatment takes account of both depreciation and
obsolescence in the case of physical capital, but this accounting is not extended to
human capital”. He was right. Income tax is charged on net profit of firms and pay of
workers. Pay measures gross realized work including human depreciation.
Tax laws now counter that imbalance by applying lower rates to pay as “earned
income”. If we could measure human depreciation, or model it with enough
Chapter 8 Banks, Money and Macroeconomics 2/8/16 19
confidence, we would know how much correction was enough. That’s a reason to
take depreciation theory seriously.
Market-Valued Capital in Macroeconomics
Another reason why macro should be reconceived from scratch is that its defining
equations, written mostly over half a century ago, leave out capital. Change in capital
shows as net investment, but capital itself stays outside. Flows are considered
sufficient for description.
Piketty, a good economic historian, tells us that this did not have to be. It seems that
the largest economies had good records of market-valued capital since the latemiddle
nineteenth century. Piketty does not speculate why macro and national
accounts ignored them when both took form in the 1920s and 1930s.
Physical capital and its changes can be measured at market or calculated by the
perpetual inventory method used in balance sheets. I showed in Chapter 2 why that
method is not the best. Depreciation accounting assumes norms in the loss of capital
value with time, and gets the news of actual outcomes long after. National accounts
reported positive real net investment, meaning growth in capital value, in 1929,
1930, 1937 and 2008. They give little clue to reality in years of surprise.
The neglect of market-valued capital in macro and the national accounts until 1990
or so may have to do with the influence of Keynes. The General Theory includes
some hilarious broadsides on the fickleness of market speculators. He put more
trust in the sober disciplines of accounting. Piketty trusts the market more, and so
do I.
Then why does Piketty track new investment, or change in capital, by the accounting
methods used in national accounts? That seems inconsistent. My charts and tables
track it at market. It seems to me that national accounts should track it both ways,
Chapter 8 Banks, Money and Macroeconomics 2/8/16 20
and let each economist decide which version is more useful. Mine, at least, correctly
describes those same four years as losing ones.
National Accounts Overall
It seems to me that national accounts are doing nothing wrong except in modeling
the depreciation curve from misleading sales evidence. Evidence seems to show
depreciation as fast at first, and slower later. That tends to be true when depreciable
assets are actually sold. Structures tend to be customized for their original owners
and occupants. They tend to be resold when results are disappointing. This
disappointment often comes when expectations are first tested. When distressed
sellers market illiquid structures customized for themselves, prices too will be
disappointing.
Better to trust evidence of structures intended in the first place to pass from owner
to owner, as with many standardized rather than customized apartment and office
and warehouse buildings. Better still, from an economist’s viewpoint if not an
accountant’s, is to trust logic. Capital is present value of expected cash flow. Its loss
of value with time, under simplifying assumptions, is the present value of the most
distant and most discounted cash flow. Depreciation of structures we keep, rather
than sell, is least at first and greatest at the end. It is the same as with a levelpayment
mortgage.
National accounts are nonetheless a magnificent achievement. They need
interpretation just as corporate accounts do. That’s where economics comes in. And
national accounts are not resting on past practices. They can be congratulated on
including market valued capital, even if sixty years too late, and on extrapolating it
backward where practical. This book could scarcely have been written if they hadn’t.
I would recommend the obvious next step. Net investment should be shown
alternatively as change in market-valued, and output as that plus consumption. Let
economists decide which version is good for what.
Chapter 8 Banks, Money and Macroeconomics 2/8/16 21
National Wealth Including Human Capital
By definition, pure consumption rate is pure consumption divided by total capital.
This can be arranged as
total capital =
pure consumption
pure consumptionrate . (8.1)
Next generation theory modeled the pure consumption rate as 3.5% per year.
Historical data showed dividend and interest rates as more or less in this region
since Sumerian times. I model pure consumption as about three fourths of all
consumption. I take consumption as personal consumption expenditure (PCE) plus
government consumption expenditure (GCE) per the national accounts.
GCE includes government outlays, at all levels of government, on education and
welfare. These are easily recognized as consumption. It also includes costs of law
enforcement, national defense, fire control, and maintenance of infrastructure such
as highways and water systems and government buildings. These too count as
consumption, even if we mightn’t have thought so. They are part of the cost of our
survival. That’s why I agree with Kuznets and tradition, although I didn’t always,
that consumption includes all of GCE.
PCE in 2015 shows as $12.429 trillion. GCE is reported at $2.5855 trillion. Both are
in 2015 dollars. their sum is $15.0145 trillion. Three fourths of that is $11.2609
trillion. Then (8.1) gives
total capital =
pure consumption
pure consumptionrate = $11.2609
.035/ year
= $321.74 trillion,
in 2015 dollars. This rough estimate can be borne in mind when we evaluate the tax
base and the risk of national debt. U.S. public and private debt together has been
Chapter 8 Banks, Money and Macroeconomics 2/8/16 22
estimated at a little less than a fourth of this sum. My impression is that this
exposure is not yet dangerous. But it needs watching.
The best method to estimate aggregate adult human capital separately is Petty’s. It
is present value of future human cash flow. That means pay less invested
consumption. If I am right, meaning that Farr, Marshall and Kiker are wrong,
invested consumption is negligible among adults. Then Petty was right to capitalize
pay with no deduction. And he was right to capitalize aggregate current pay, with no
need to model the future. Growth of pay will tend to match growth of human capital.
The discount rate to find its present value is expected rated of return. Rate of return
is growth rate plus cash flow rate. Evaluating human capital as constant current pay
discounted by cash flow rate alone will give the same answer as if we modeled in
expected pay growth, but then discounted at cash flow rate plus the same projected
growth rate.
Total human capital is adult capital plus that of the young. That part might be
measured at current cost. I won’t attempt either of those calculations here, since
they seem to call for economists expert in interpreting national accounts.
To Do List
Books and papers on economics tend to lead to “policy prescriptions”. That means
recommendations on what governments and markets and educators should do. My
list begins with getting rid of the double tax on dividends. To get democrats on
board, make the effect revenue neutral by raising the corporate tax rate. Dividend
rates have been far too low for about 50 years now. They should average 5% to 6%
real, as they did in the nineteenth century. The result of low dividends has been
dangerous overinvestment in the private sector, with growth hampered rather than
enhanced. Charts and tables make it clear that ex ante investment beyond
depreciation recovery is deadweight loss.
Chapter 8 Banks, Money and Macroeconomics 2/8/16 23
I would tax capital gains as much as ordinary income for the same reason. Level the
playing field. Solow saw most of the truth, but didn’t go far enough. Mill saw more.
And even Mill stopped short. All we have to do is look at the charts and tables.
Capital accumulation does not exist. Any attempt lowers consumption with no
growth to show for it.
Keep track of national wealth including human capital by my method here, and also
by Petty’s of 1664, 1676 and 1685. What would we think of corporate management
that added up only the smaller part of corporate assets? We now consider physical
capital only. Political parties debate what taxes and the national debt should be
without the key facts.
Policy prescriptions can also aim at schools and what they teach. Macroeconomics
should start over. It reached most of its present form in the “years of high theory”, in
the 1920s through 1950s, without the concepts of human capital or market-valued
capital. It is founded on the inaccurate Y = C + I equation and the concomitant belief
that output equals pay plus profit. It recognizes ex ante – ex post distinctions only
crudely as to saving, by taking it as either invested or uninvested, and not at all as to
investment itself. By missing the lag between market effects and book reaction, it
misreads some of our worst years as our best and conversely.
The path forward is omnibus funds and devolution of commercial banks. Bank
reform along the lines I suggested should need no help from lawmakers. But for
gosh sakes, let’s not set up barriers against it. Commercial banks and 10:1 leverage
make slumps inevitable. Crashes are as sure as death and taxes until we phase them
out.
Summary
Macro has meant a tightrope walk between the risks of inflation and recession. That
doesn’t have to be. The problems are detachable. Even today, It should be practical
to redefine legal tender as real or inflation-corrected dollars. But the deeper
Chapter 8 Banks, Money and Macroeconomics 2/8/16 24
solution is to devolve commercial banks into their separate deposit and lending
functions, with separate stockholders and only incidental interaction.
It is best for the free market to do this alone. The omnibus fund could be the decisive
innovation. It too is possible today. It would offer clients full competitive return, so
that no supply would be too large. It would match bank deposits in liquidity and
payment services with the low service charges typical of other index funds, while
tailoring risk and return to client needs with essentially costless derivatives. The
intention would be obsolescence of bank accounts, and devolution of banks in result.
Deposit-and-lend banks, inevitably leveraged at 10:1 or more, are the weak link
explaining economic collapses about once a generation since the system was
founded in the Renaissance. Misdeeds and misguesses and world events were only
the proximate cause. Chicanery will be with us forever. Honest bad judgment will be
with us forever. Supply shocks, as when OPEC raised oil prices in 1973, will be with
us forever. Wars will be with us forever. Setbacks for our trading partners will be
with us forever. These bring the high winds. I don’t foresee much payout in trying to
dial down the winds by upgrading human nature. The payout is in stabler structures.
The big bad wolf huffed and puffed, and the brick house stood. Omnibus funds will
carry no leverage. Accounts themselves will be levered to taste, but for short periods
only. Futures trade in seconds. The fund as a whole cannot become worthless until
each and every security in its portfolio does. High winds and leverage can wipe out
the accounts of risk-takers who chose the long leg, but not of those who opted for
contractual interest and safety. That’s as it should be. Risk-takers may name their
poison. Omnibus means for all, and all-inclusive.
Derivatives are central to the omnibus fund idea. Some see them as dangerous. They
can be. They are powerful. But they have a good track record of performing as
contracted. Cash reserves, called margins, have proved enough to escape default
Chapter 8 Banks, Money and Macroeconomics 2/8/16 25
even in 2008 and the flash crash of 2013. Short legs have been protected without fail,
and long legs have got what they bargained for. The reason is that margin
sufficiency is monitored from tick to tick. Checking every few seconds doesn’t rule
out every doomsday scenario, but gives about as much confidence as we’re going to
find in this uncertain world.
Saltwater and freshwater schools debate the wisdom of fiscal and monetary policy.
But both sides frame their arguments in Keynesian language. I find it wanting. The
idea that intended consumption is either invested or not, and realized in equal
capital growth if it is, misses the essential mechanics. It measures employment of
plant and people in hours rather than in production. This is a good reason why
macro should start again from scratch. Another is to recast its basis equations in
terms of market-valued capital as well as flows. Another is to accommodate human
capital, for example by substituting the pay and Y rules for the doctrines that pay
measures work and that output is investment plus consumption.
None of those good reasons refers to the possibility of omnibus funds. They are only
a gleam in my eye. If they come to pass, and succeed as I imagine, macro will have
still more novelty to digest. If they lead to devolution into separate deposit and
lending banks, with the deposit banks operating as omnibus funds, good riddance to
the 10:1 leverage that has brought down economies every generation or so since
Marco Polo’s time.
The lagged flow method of assessing efficacy of ex ante investment is outdated by
the simultaneous rates one outlined in Chapter 4. It should go to honorable
retirement whenever market-valued capital is available. It superimposes the
inevitable unintended lag of accounts themselves, even under best practices, onto
the intended one needed for the new tree planted to bear fruit. Both lags blur
causality.
Chapter 8 Banks, Money and Macroeconomics 2/8/16 26
Some famous economists are tougher on the current state of macro than I am.
Recent books argue that it should no longer be taught, and should receive no Nobel
prizes. My diagnosis is about the same. But my prescription is opposite. Reconceive
it from scratch, and teach it right. Award Nobel prizes to those who help. My first
nominees would be Piketty and Zucman. Not that I think much of Piketty’s
arguments. But his website with Zucman is as powerful a new resource for
scholarship and the database as national accounts were eight decades ago.
Chapter 8 Banks, Money and Macroeconomics 2/8/16 27
CHAPTER 9: SO WHAT’S NEW?
To claim originality in any field is rash. It is safer to say that some things in this book
are new as far as I know. I know at least what I can’t remember reading elsewhere. I
am more confident in judging what will surprise in the sense of conflict with what is
taught today. There we need only keep up with the current conversation. Judging
originality with confidence means having read everything before.
My surprises were not all new, and my novelties (if such) where not all surprises. A
few ideas met both descriptions. They pay rule, and the equally heretical Y rule,
probably count as both although Becker came within a step of getting there first.
Depreciation theory is likely to be both. Other possible candidates might include my
observation that holds by money managers reveal prices as clearly as trades do, and
my hawks-and-doves analogy inferring from this that index funds should
outperform managed ones when aggregate AUM held by money managers, not
trades by them, exceeds a critical percentage of the market to be determined. There
may also be both surprise and novelty in my suggestion of monetary policy by
establishment of real dollars as legal tender. In my wannabe biologist role, I just
may have been first to the point out the gaffe in the math of Hamilton’s rule.
Free growth theory takes Mill a little farther by ruling out growth by thrift at the
collective scale. It should prove a major surprise to lawmakers, who incentivize
thrift in the name of growth, and a milder one to economists already prepared by
the insights of Solow. My possible originality here was in the simultaneous rates
equations I derived to test them, and the test itself accessing data for market-valued
capital as well as consumption from the Piketty-Zucman website. My definitions of
market-valued net investment and net output, substituting for the book-valued
versions used in national accounts, were essential for testing. I suppose these rank
as novelties but not surprises.
Chapter 9: So What ‘s New? 3/17/16 1
The advantage of the simultaneous rates test over the standard lagged flows one is
great. It avoids both lags, meaning the intended one to allow more capital to show
its effect in more output, and the unintended one in the inherent unresponsiveness
of accounts to market effects on capital already booked, while also gaining from the
superiority of market measures of capital growth over book ones even when lags
end. The method itself is no surprise because the math is high school algebra. The
shock is in what it reveals. Solow and Denison were righter than they knew. There is
no such thing as capital accumulation at the collective scale.
Risk theory is probably both marginal novelty and marginal surprise. The part that
might be new, although obvious in retrospect, is that assets take on the risk
characteristics of their owners. We knew all along that people buy assets to fit their
own risk profiles. There may be novelty in my idea that it works the same in the
opposite direction. Assets once acquired are modified to fit those profiles better. A
family home bought by a drug dealer might become a crack house bringing higher
expected return at higher risk of confiscation by authorities.
The next step was to connect risk profiles with age and gender. It seems well
established that risk tolerance peaks in the teens and twenties, particularly in males.
It drops steadily afterward for both sexes. R. A. Fisher in 1930, and Bob Trivers in
1972, suggested why. Males, in humans, produce thousands of cheap sperm.
Females produce eggs, which are few and expensive because they are packed with
nutrients. Young males might end up leaving dozens of offspring or none. Nature
arranges competition to determine which. Females are reasonably sure to leave a
few. They have less to compete about. As both sexes get past their 20s, their
remaining reproductive chances grow fewer and competitive ranking clearer. There
is less to compete about. Risk tolerance grades steadily down with age, and capital
owned reflects the change with lower risk and return. This gives the basic theme.
The next key information was that human capital is owned disproportionately by
the young. We own little else until independence at age 20 or so. Physical capital
Chapter 9: So What ‘s New? 3/17/16 2
builds from then on, and peaks near retirement. But human capital grows quickly in
the 20s and thirties too, as most human and other depreciation is concentrated
toward the end. These are persuasive reasons to think that human capital is the
riskier and higher-return factor overall.
The argument becomes complicated in that most investment in us before
independence comes from parents rather than from self-invested work. Parents
have a a strong say in what risks children run, so that parental risk tolerance
governs too. But it governs most in pre-teen years, when parents themselves are
passing through their own risk tolerance peaks. And human capital is probably the
most versatile of assets in adjustment to our tastes for risk at the time. Cops can
become robbers at will, and robbers can get religion.
We should not slip into the error of concluding that an individual’s human capital is
riskier than her physical capital at the same time. Both adjust to her current risk
profile alike. That’s why the parable of the boss and her secretary falsifies the notion
that pay compensates realized work and nothing else. That would make return of
each in her human capital a little over 100% per day at the start of the last day, and
100% per second at the start of the last second, even while their security portfolios
reveal their time preference rates as a few percent per year. Human capital is not
inherently risker, as hand grenades than nerf balls. Each cohort adapts all its wealth
of both factors, counting balanced security portfolios as single assets, to its single
characteristic risk profile. There may be novelty, but not much surprise, in this
projection of the owner onto the asset rather than conversely.
That parable helped confirm the pay rule and explain age-wage profiles. It brought
another surprise along the way. I grew up being told that houses are safe
investments. But in fact they are owned by about the same age group and gender
mix that owns the business sector. The publicly traded corporate sector is a part of
the business sector that has given up return for safety by providing instant liquidity
to shareholders. The notion that houses are safe took a punch in the gut in 2008. The
Chapter 9: So What ‘s New? 3/17/16 3
notion that they ever were rests pretty much on evidence bolstered by government
subsidies such as FHA and FNMA and FMAC which began before I was born. As it is, I
don’t see enough evidence either way to assert whether houses or the publicly
traded corporate sector, cap-weighting its stock and bonds, should be risker. But
even that uncertainly is a surprise in view of what we all were taught.
Depreciation theory is one of my favorites. It doesn’t upset the applecart as much as
the pay rule does, because little economic theory depends on it. I love it because it
reverses tradition precisely. National accounts model depreciation as declining
exponentially. I model it as rising exponentially. It’s the same equation with a plus
sign in place of a minus sign. I love its obviousness once we think about it. It follows
when we remember the present value rule. Once we do, evidence for both factors
makes more sense. Depreciation theory rounds out the pay rule in explaining how
pay can rise or hold steady to the very end. And we see the same in businesses.
Gross realized profit, analogous to pay, does not tend to decline as firms approach a
date with the wrecking ball. My impression has been that rents go down when
properties aren’t kept up or locations become unfashionable, but not with age in
itself. When it’s time to demolish and rebuild, premises are more typically vacated
with trade still running at norms. Gross realized profit is inevitably all depreciation
on the last day, and would approach zero steadily if tradition were right.
There may have been minor novelty in my derivation of my three fundamental
theorems as at least subjective certitudes following from definitions, and in my idea
itself of subjective as distinct from empirical certitude. A subjective certitude is one
such that contrary evidence would falsify the convergence axioms. I have found little
or no empirical certitude past the cogito. I concede that the idea of subjective
certitude is impertinent. How dare we infer what people must think?
We dare when we infer from definitions. I began with the somewhat unusual
definition of capital (value) as perceived means of foreseen taste satisfactions. The
usual “means of production” is equally valid, but less suited to my purpose here. I
Chapter 9: So What ‘s New? 3/17/16 4
then pictured a future instant’s worth of expected satisfaction. Its perceived value at
that future moment would give its perceived value now save for differences
explained by the time gap between. I adopted the old terms time preference or time
discount rate to account for whatever they might be. There was no assumption as to
whether the rate should prove positive or negative or zero, nor that the same rate
should apply to other future instants. My goal was to leave not even the farthestfetched
of loopholes. If I have succeeded, the present value rule followed as
subjective certitude giving exact expectations, though not outcomes, for each future
instant and thus for all together. Note that my depreciation theory follows, but with
the caveat that the version I have shown adds the usual assumption that time
preference is positive. That part is not certitude, although neither are we likely to
doubt it.
It was not hard to derive the maximand rule as the next step. Once we define tastes
or more generally aims as whatever behavior reveals, the rest follows quickly.
(Remember that I have no problem with mutually circular definitions.)
There were probably a few heuristic novelties. The parable of the boss and her
secretary might itself be new. So might the slave paradox with its parable of Phil and
Bill. Many including Adam Smith have pointed out economic inefficiencies in slavery,
moral criticism aside. I can’t recall mention of this most obvious one. Bill’s
maintenance consumption was taste-satisfying cash flow to Bill, and capitalized in
his present value to himself. It is pure expense to Phil once Bill is enslaved. If all but
one of us were enslaved by the one left, national output would drop by substantially
all maintenance consumption on the books of the one slaveowner.
There may also be minor novelty in my analogy between accounting for the firm and
accounting for human capital in Chapter 6. One possible example is my use of the
term “decapitalization” to include depletion and liquidation in sale as well as
depreciation. It simplifies to depreciation in the case of human capital because that
factor cannot be alienated in reinvestment or gift or sale. One inference was that
Chapter 9: So What ‘s New? 3/17/16 5
deadweight loss, negative output, negative realized output and unrecovered
decapitalization all mean the same. This is obvious enough, but may have been left
implicit before.
Chapter 9: So What ‘s New? 3/17/16 6
CHAPTER 10: THREE PANTHEONS
A few weeks ago I was being interviewed about my opera “Usher House”. How
would I like to be remembered? With a straight face, I said I would like to be thought
the best composer since Mahler, the best poet since Masefield, and the best
economist since John Stuart Mill. The interviewer looked startled. Was she talking
instead to the successor of Don Quixote, Emperor Norton and Walter Mitty?
Probably. But not to worry. Fantasies are good things. They don’t become delusions
until we start believing them. What I believe is that at least dozens of composers
have the knack. There must be hundreds, considering the terrific film scores
attributed to names new to me when I hang on for the credits. Each of us, very much
including film composers, gives the world what we think it needs. We like to be
appreciated, but we don’t give a fig what it wants. We won’t always agree on what it
needs. We’ll defend to the death the other guy’s right to his message. But we prefer
our own. That’s what my answer meant. We’re each the best. But I do have the
temerity to limit the list to those few dozens or hundreds.
Someone might also be surprised at my choice of benchmarks in verse and
economics. Masefield and Mill? A consensus might have picked T. S. Elliot, say, and
Lord Keynes. Masefield and Mill are likelier to be remembered as old-fashioned
fuddy-duddies already outmoded when they wrote. But that’s me. I am Don Quixote.
Not a single idol in my pantheons in those three fields was born after 1900, although
that could change in economics.
My pantheon in music is Bach, Beethoven, Schubert, Wagner and Mahler. Mahler,
the last-born, died in 1911 at 51. What about Mozart? Clearly colossal. Listen to the
slow movements of almost any of his piano concertos. Childlike simplicity, then a
slight surprise, then another, and all at once we are on a trip through the stars. But
my top five show us more. Mozart is too darned enigmatic. He is too darned coy. He
is too darned third-personal. And I like breaking a sweat. Mozart is uniquely the
Chapter 10: Three Pantheons 2/10/16 1
greatest at what he does within the bounds he chooses to set. But I like answers as
well as questions. The five in my pantheon give me those.
Mozart is unrivalled at what he does because no one else plays the same game. What
other composer has put such a premium on delicacy, on poise, on self-effacement?
That doesn’t deny that he was a red-blooded mensch who loved hijinks and good
times as much as the rest of us. His Rondo alla Turca is one of many masterpieces
showing that side. But it only rounds out the impression of a flawless dinner
companion. A maxim of classicism in the Greek spirit is “nothing in excess”. Mozart’s
exuberance and hijinks were just the right amount.
He was the master of moderation. His operas put passion mostly in the mouths of
clowns and villains such as Papageno and Osmin and Queen of the Night. His
sympathetic sorts have feelings too, but keep them circumspect. The perfect
companion cares first about our feelings, not his. Mozart remains that even on our
journeys together through the stars. We are kept safely away from the heat. We are
allowed to feel anxiety because the world is so far below. That was half the point of
the trip. The other half is the happy ending as he leads us safely home. Anxiety, but
not in excess.
That shows him as the master of levitation. Richard Strauss gives the example of
Susanna’s aria “Voi che sapete” (you who know) from Figaro, an innocent ditty
which somehow never lands on the tonic (home note) until the end. The beginning
of Eine Kleine Nachtmusik (a little night music) does this again. But the slow
movements of his piano concertos show it best.
Mozart is not my pantheon, even so. He is moderation in excess. I like the game the
others all play. I like a sense of the first person singular. The five in my pantheon
also take us through the stars. But they take us closer. We feel the heat because they
do. Listen to Bach’s chaconne for solo violin, or passacaglia and fugue for organ.
Listen to the heilige dankgesang (holy song of thanksgiving) from Beethoven’s
Chapter 10: Three Pantheons 2/10/16 2
quartet opus 132. Listen to the slow movement of Schubert’s two-cello quintet opus
163. Listen to Wagner’s liebestod (love death) from Tristan, or Mahler’s adagietto
from his fifth symphony. This music plays for keeps.
The polar opposite to Mozart would be Verdi. Like Mozart, he is not in my pantheon
but close. For Verdi, no passion is too much. He is the master of contrast. He shakes
our emotions back and forth as a dog shakes a rat. Lull and storm are each given
enough time to pack the most punch in the other. He wants only opposites and
extremes. What would the fastidious Franz Joseph have thought? He would have
called the guard.
Somewhere between Apollo and Dionysus, between relativism and frenzy, lies the
true path. The five in my pantheon have found it.
I seldom call myself a poet, since that’s already a tad vainglorious. For better or
verse, I’m a Jack of that trade too. The true poets in my pantheon begin with Keats
and Masefield. I haven’t found a clear choice for third. There are awesome things in
Milton, Blake, Coleridge, Tennyson, Emily, Houseman, Robinson, Dowson, Yeats and
others.
Shakespeare, like Mozart, doesn’t figure in the center of the picture. I take him as the
greatest mind and soul yet known, the greatest playwright, the greatest writer in
general, and all of these because he taps to the bottom of what poetry can be. “Who
is this whose grief/ Conjures the wandering stars, and makes them stand/ Like
wonder-wounded hearers? It is I, /Hamlet the Dane”. Holy mackerel! But these are
touches in his plays. Poetry, in his time, meant something too coiffed and pretty and
mannered for my taste. You can take Venus and Adonis, the Rape of Lucrece, and
the sonnets. That includes the petulant dark lady sonnets, which break the model of
preciousness but find nothing better. Shakespeare simply came along too early. I
credit Milton, in “Lycidas”, for discovering the true vein a few decades later.
Chapter 10: Three Pantheons 2/10/16 3
That leaves economics. Here I really have a one-man pantheon in Sir William Petty. I
suppose that I am the only person to have looked at his portrait alongside Isaac
Newton’s, in the Royal Society which they co-founded, and seen the two as
intellectual equals. Mill seems a clear second, thanks to his superb paragraph on
growth. The candidates for third seem well behind. Maybe Jevons or John Rae or
Leon Walras. Time has not been kind to the teachings of Keynes. I would now rank
his teacher Alfred Marshall higher. I like Myrdal’s magnificent ex ante – ex post
distinction. Boehm Bawerk and the Austrian school are underrated. The pantheon
might have room for him.
Am I being too tough on later economists? We should not forget Schultz and Ben-
Porath. Schultz’ greatest achievement, unless Mincer beat him, was in spotlighting
human depreciation. That left me to ask where this huge flow goes. The answer
becomes inescapable once we focus on the question. It gives the obvious solution to
the age-wage problem. Everything in this book is obvious. Some of it, like that
solution, is the obvious but unnoticed.
Somebody, sooner or later, breaks the news about the emperor’s new clothes. You’d
think Don Quixote would be the last to pipe up. No one in the world was more
devoted to tradition and beautiful creatures of the mind. But it takes a fool. He was
that, and so am I. Der reine tor. There have to be a few of us always. We’ll get a few
windmills before they they get us.
Chapter 10: Three Pantheons 2/10/16 4
APPENDIX A: The Argument in Notation
Output and Cash Flow
My focus will be on absolute rather than per capita values. The usual custom gives
capital letters for the former and lower-case ones for the latter. I will prefer the
upper case for stocks and flows, and the lower one for rates. That need not hold true
for Greek letters.
The total return truism can be notated
Y = !K T
+F ,
(A1.1)
where Y is output, K T
is total capital and F is cash flow. Also
F = τ +C P
and τ = τ +
−τ −
, (A1.2)
where τ (tau) is net transfer, τ +
is transfer out, τ −
is transfer in and C P
is pure
consumption (exhaust in taste satisfaction). Cash flow is the net of positive less
negative components. I define them by
F +
= τ +
+C p
, F −
= τ −
and F = F +
−F −
. (A1.2a)
At the collective scale, where transfers cancel internally, these equations combine
for
Y = !K T
+C p
and F = F +
= C p
. (A1.3)
Math reminds us continually that “equals” does not necessarily mean “is”. (A1.1) and
(A1.3), for example, do not mean that output is growth plus cash flow or growth plus
APPENDIX A: The Argument in Notation 3/7/16 1
pure consumption. Why? Output in itself means creation of economic value.
Mathematically, that could include what I called “output exhaust”, meaning value
exhausted as soon as created. I ruled that out as “free goods”, which happen every
day but are neglected in economics as unable to influence behavior either before or
after. That’s why “equals” cannot mean “is” in (A1.3). And neither does it in (A1.5).
Rather both state that output provides cash flow offset plus total capital growth.
This distinction helps everywhere in economics. We know for example that transfer
out may be drawn either from capital in place or from concurrent output. The
source of first kind is decaptialization D. But decaptialization also includes other
components than transfer out. In Chapter 3, and again just now, I excluded output
exhaust as free goods possible in math but neglected in economics. That makes
decapitalization D the only source of pure consumption C P
. And not all
decapitalization is transfer or exhaust. Some is deadweight loss, defined in (A1.1) as
any negative sum of capital growth !K T
and cash flow F. That can show in
D= D ρ
+D λ
and D ρ
= D τ
+C P
. (A1.4)
Here D ρ
is recovered or realized decapitalization, D τ
is “transfer depreciation” net
of plowback into the same asset, and D λ
is deadweight loss. λ is lambda. At the
collective scale, where transfers cancel internally, (A1.4) becomes
D ρ
= C p
.
(A1.4a)
The dispositions of transfer out may be reinvestment in other assets of the same
owner, or may be gift to donees. Reinvestment can be interfactor as shown in
Chapter 5. Transfer out from total capital of any individual, net of internal transfers,
APPENDIX A: The Argument in Notation 3/7/16 2
simplifies to gift. Transfer in gained by the owner’s total capital, net of the same
internal transfers, is gift received. The math becomes
τ +
= γ +
, γ = γ +
−γ −
, F +
= γ +
+C p
, F −
= γ −
and F = γ +C p
(A1.5)
at the scale of each individual’s total capital as a whole. Here γ (gamma) is net gift,
γ +
is gift and γ −
is gift received.
Divide (A1.1) by K T
to find
Y
K T
= ! K T
K T
+ F K T
. (A1.6)
Define these three terms as productivity or rate of return r, total capital growth rate
g and cash flow rate f. Then (A1.6) can be reexpressed as
r = g + f .
(A1.6a)
(A1.3) combines with (A1.6) to show
Y
K T
= ! K T
K T
+ C p
K T
, at the collective scale. (A1.7)
Define “pure consumption rate” c p
as C p
/K T
, and substitute to show
r = g + c p
, at the collective scale. (A1.7a)
APPENDIX A: The Argument in Notation 3/7/16 3
(A1.1), (A1.6), (A1.7) and (A1.8) are alternative statements of the total return
truism.
In general, define g(Q)= !Q /Q for any variable Q. Note again that g in this book
means growth rate of capital g(K T
) rather than output. g in macro tradition usually
means growth of output g(Y) . Total capital K
T
is the sum of human capital H and
physical capital K. Their outputs respectively are work W and (net) profit P. Their
counterparts to (A1.1) and (A1.6a) are
W = !H+F(H) , r(H)= g(H)+ f(H) , P = !K +F(K) and r(K)= g(K)+ f(K) , (A1.8)
where F(H), f(H), F(K) and f(K) are respectively “human cash flow”, “human cash
flow rate”, “physical cash flow” and “physical cash flow rate”.
Present Value and Present Cost
If there were no such thing as time preference, present and future value would be
the same. All economists known to me concede that we prefer present goods to
future ones, although some like Joseph Schumpter have seen no good reason why. I
suggest a reason in next generation theory.
Present value theory, understood in essence by the Sumerians, considers what we
now call future positive cash flows which are expected to be generated from
external investments (transfer in, negative cash flow) made now or earlier. At the
differential (infinitesimal) scale, we can write the associated future value as
dFV(z)= F +
(z)dz (2.1)
at future moment z. The basic idea of present value PV is
APPENDIX A: The Argument in Notation 3/7/16 4
dPV(x)= F +
(z)e −q(z−x) dz , (2.2)
where q is the appropriate time discount rate.
Note the implication
F +
(z)dz = dPV(x)e q(z−x) , (2.3)
showing that q is the growth rate that raises the value of dPV(x) to F +
(z)dz over
period z− x . Since this differential component of asset value defers all positive cash
flow until moment z , and cannot in itself be affected by later transfers in, q
simplifies by (A1.6a) to rate of return. This was Boehm Bawerk’s insight, although
he was not mathematical, in equating time preference rate to rate of return r. Thus
(2.2) and (2.3) give
dPV(x)dx = F +
(z)e −r(z−x) dz and F +
(z)dz = dPV(x)e r(z−x) , (A2.4)
where r is the appropriate rate of return and time discount rate equivalently.
But what determines appropriate r in these equations? Rate of return varies with
risk among different assets at the same time, and varies over time with economic
circumstances. Most sources I have seen treat r in (A2.4) as a variable to be
integrated over (x, z). I myself long believed the same.
My view now looks to the context. The asset as a whole will typically have received
many differential investments before time x, and may receive many after. Each at
inception will have been priced by the owner’s time preference rate then. But my
theme in risk theory is that assets can be traded or modified to the current owner’s
APPENDIX A: The Argument in Notation 3/7/16 5
risk tolerance now. She discounts each expected future flow not by her foreseen
time preference rate then, but by her time preference rate today. It seems to me that
the appropriate discount rate r in (A2.4) is r(x). She will provide for anticipated
changes in her time preference rate by factoring costs of trading the asset if
tradeable, or modifying it if modifiable, into her evaluations of future value F +
(z)dz ,
and so from present value too. I consequently interpret (A2.4) to mean
dPV(x)= F +
(z)e −r(x)(z−x) dz and F +
(z)dz = dPV(x)e r(x)(z−x) . (A2.5)
The value of the whole asset V(x) at time x will be the sum or integral of present
values of all foreseen cash flows both negative and positive over (x, ω ), where ω
(omega) is the foreseen end point of flows. ω may be infinity ∞ . Thus
ω
V(x)= PV(x)= ∫ F(z)e −r(x)(z−x) dz , x <= z <= ω . (A2.6)
x
The terms value and total capital are interchangeable, as are their notations V and
K T
.
Present cost PC(x) evaluates V(x) as the sum or integral of earlier negative cash
flows compounded at rate r since moment of investment u, and not yet
decapitalized in positive cash flow. The counterpart to (A2.1) becomes
dIC(u)= F −
(u)du and dPC(x)= dV(x)= dPV(x) , (A2.7)
where IC is what I call “investment cost”. The counterparts to (A2.2) and (A2.3) are
dV(x)= F −
(u)e q(x−u) du and F −
(u)du = dV(x)e −q(x−u) . (A2.8)
APPENDIX A: The Argument in Notation 3/7/16 6
q here equals some appropriate r by the same logic as before. Here again, we
usually read interpretations of (A2.8) which treat the appropriate r as an integral
of time preference or equivalently productivity rates over the interim (u,x). I
however see dV(x) as determined by current rate r(x) whether derived by present
cost or present value methods. If the original investor remains the current owner,
and now finds her time preference rate different, she will have factored asset
modification costs into her original decision to bid or invest. If not, she will have
traded to someone whose time preference rate is better suited. My counterparts to
(A2.1) and (A2.6) become
dV(x)= dPC(x)= F −
(u)e r(x)(x−u) dx and F −
(u)du = dV(x)e −r(x)(x−u) (A2.9)
and
x
V(x)= PC(x)= ∫ F(u)e r(x)(x−u) du . (A2.10)
0
These equations seem the most straightforward reconciliation of the maximand rule,
the convergence axioms and the evidence supporting risk theory. They describe
individual assets over time, sometimes passing from one owner to another, rather
than a given owner’s total portfolio. We maximize return within current risk
tolerance, recognize that it will change, and deduct present value of expected
trading or asset modification costs from future value of flows while adding them to
original value. This seems true to life. It allows discounting all expected positive
flows over (x, z), and compounding all past negative ones over (0, x), at a single rate
r(x) because of those adjustments to value or cost of flows. Tradition treats the
flows as fixed givens, and the discount rate as a function of interim time between x
and z or between 0 and x.
APPENDIX A: The Argument in Notation 3/7/16 7
My interpretation that the time discount rate/rate of return we naturally apply in
evaluating both present cost and present value is our time preference rate now,
rather than some retrospective or prospective average, might seem counterintuitive.
I propose it, even so, as the “time discount rule”.
Analogy to the Firm
I follow convention by treating all transfer out as compensated by actual or imputed
revenue. The part exhausted in taste satisfaction gets imputed revenue paid by the
consumer satisfied. Not all revenue compensates transfer out, as revenue is usually
defined as sales proceeds against which prior outside claims must be satisfied first.
These are typically for labor and supplies in the case of the firm. Chapter 6 gave the
logic in word equations. It begins with
ρ − ρ c
= ρ e
,
(A3.1)
where ρ is revenue, ρ c
is prior claims and ρ e
is “earned revenue” as a residual.
Earned revenue, also called gross realized output, is thus remaining share of overall
revenue earned by the firm or other entity that performed the sales, collected the
proceeds, and paid the outside claims on them.
What the the firm or other contributor gives up to earn the earned revenue is the
sum of its realized output Y ρ
and its recovered decapitalization D ρ
. Remember
from (A1.4) that D ρ
includes any pure consumption realized by the owner of the
source asset, although that could not apply where the owner is taken as a firm. The
sum of Y ρ
and D ρ
gives its gross realized output. Then
Y ρ
gross = ρ e
= Y ρ
+ D ρ
,
(A3.2)
where Y ρ
gross is gross realized output. In Chapter 6, I also called Y ρ
gross or ρ e
“gross positive cash flow”. All mean the same. I will usually leave out the notation
APPENDIX A: The Argument in Notation 3/7/16 8
ρ e
from now on, and refer to gross realized output Y ρ
gross alone.
Positive cash flow is that less plowback from revenue. This can be notated
F +
= Y ρ
gross − ρ pb
= Y ρ
+ D ρ
− ρ pb
,
(A3.3)
where ρ pb
is plowback. Negative cash flow is transfer in, notatedτ −
. Thus
F −
= τ −
and F = F +
− F −
= Y ρ
+ D ρ
− ρ pb
− τ −
.
(A3.4)
Cash flow F is the difference
F = F +
−F −
= Y ρ
+D ρ
− ρ pl
−τ −
.
(A3.5)
Gross output is gross realized output plus unrealized (or proprietary or selfinvested)
output. This can show as
Y gross
= Y ρ
gross + Y s
= Y ρ
+D ρ
+ Y s
.
(A3.6)
Think of the subscript s as meaning saved or self-invested. As all output is either
realized or unrealized, we have
Y = Y s
+ Y ρ
.
The terms saved, self-invested, unrealized and proprietary will be taken as
interchangeable.
APPENDIX A: The Argument in Notation 3/7/16 9
(A3.6) combines with (A1.4) and (A1.5) to arrive at
γ +
= F +
= Y ρ
gross − ρ pl
(A3.7)
at the scale of the total capital of the individual or any set of individuals. This fact
will prove helpful in adjusting the Ben-Porath model and in next generation theory.
It should be borne in mind that transfer out and transfer in are both implicitly
defined as net of plowback in the first place. Thus it would be wrong to suppose that
negative cash flow is transfer in less plowback from revenue. That mistake would
deduct plowback twice.
The Growth Truism
Growth of any asset of either factor is capitalization from outside plus capitalization
from inside less decapitalization. This difference can also be called net capitalization.
Capitalization from outside is simply transfer in τ −
. What are the other two?
Our first intuition would be that capitalization from inside is identical to unrealized
output. Here we must be careful. Output is negative wherever the sum of growth
(net capitalization) and cash flow falls below zero. This “deadweight loss” is
implicitly uncovered decapitalization, meaning not recovered in cash flow. To
subtract all including unrecovered decapitalization from the sum of transfer in and
unrealized output would therefore subtract the unrecovered part twice.
To make this clear, define positive and negative output by
Y ( > 0) = max( Y,0) and Y ( < 0) = max( −Y,0) = λ ,
APPENDIX A: The Argument in Notation 3/7/16 10
where λ (lambda) is deadweight loss. Meanwhile negative output belongs in the
unrealized component of output Y s
as with all effects on net capitalization not
explained by transfer in or plowback from revenue. It is the random negative
component in free growth. Then define positive and negative output and realized
output more fully by
and
Y s ( > 0) = max( Y s
,0) , Y s ( < 0) = max( −Y s
,0) = λ , Y s
= Y s ( > 0) − λ , (A4.1)
Y(> 0)= max(Y,0) , Y(< 0)= max(−Y,0)= λ and Y = Y(> 0)− λ . (A4.2)
There is also indirect capitalization from inside in the form of plowback from
revenue. The growth truism sums these inflows less outflows as
!K T
= τ −
+ Y s
(> 0)+ ρ pl
−D=τ −
+ Y s
+ ρ pl
−D ρ
, (A4.3)
recalling that D ρ
shows recovered (realized) decapitalization.
At the scale of the total capital of any individual or set of them, (A1.5) and (A4.3)
give
!K T
= γ −
+ Y s
+ ρ pl
−C p
. (A4.4)
Human Cash Flow
Although I can’t recall seeing the term “human cash flow” in any papers or textbooks
of others, tradition defines the flow discounted to human capital as pay less Schultz’
“pure investment”. The flow so discounted is implicitly cash flow. I rename pure
investment “invested consumption,” and write the traditional view as
APPENDIX A: The Argument in Notation 3/7/16 11
F H
= π −C s
,
(A5.1)
where F H
is human cash flow, π (pi) is pay, and C s
is invested consumption. The
subscript s, as usual, means saved or self-invested.
Pay π can be defined as the worker’s literal or imputed revenue. Self-invested
consumption C s
can be defined as any investment in human capital other than
through self-invested work. This makes C s
all investment from outside in a sense.
But that does not mean that it is limited to transfer in. There is also plowback from
revenue (pay π ), as when we spend pay on textbooks or tuition. I model “pay
plowback” π pl
as minor in the world we know, but definitions must account for it.
This I define
C s
= τ(H) −
+π pl
or t(H) −
= C s
−π pl
, (A5.2)
where τ(H) −
is “human transfer in”. This and (A1.2a), showing F −
= τ −
, give
F(H) −
= τ(H) −
= C s
−π pl
.
(A5.3)
(A3.1) and (A3.2), analyzing the firm, derived
ρ − ρ c
= Y ρ
gross = Y ρ
+D ρ
.
For human capital, this can show as
π −π c
= W ρ
gross = W ρ
+D(H) ρ
,
(A5.4)
APPENDIX A: The Argument in Notation 3/7/16 12
reading “pay less prior claims on pay equals earned pay equals gross realized work
equals realized work plus realized (recovered) human depreciation”.
Prior claims means outflow (transfer out), from sources other than the direct
receiver of revenue, which are recovered in it and owed back to them. Maintenance
consumption can be defined as any transfer out from any asset of either factor,
outside the human capital of the earner, which supports pay in the sense that any
less maintenance consumption would have realized less pay. This meets every
criterion of prior claims but one. Maintenance consumption is the prior claims
meant by π c
in (A5.5) if and only if it is actually recovered in pay or so intended.
I gave my arguments that it is neither, but is rather exhausted in satisfying our taste
for survival, in Chapter 6 and elsewhere. If I am right, (A5.4) gives
π c
= 0 and π = W ρ
+D(H) ρ
= W ρ
gross , (A5.5)
so that pay would measure and compensate gross realized work. This is the pay rule.
By (A3.3), positive cash flow is gross realized output less plowback from revenue.
That comes to
F(H) +
= W ρ
gross −π pl
= π −π pl
.
(A5.6)
Now we have
F(H)= F(H) +
−F(H) −
= π −π pl
−(C s
−π pl
)= π −π pl
−C s
+π pl
= π −C s
,
(A5.7)
APPENDIX A: The Argument in Notation 3/7/16 13
as the application of (A3.5) to human capital. This confirms the traditional view
(A5.1) if (A5.5) is right in interpreting prior claims on pay as zero.
If I was wrong there, and Quesnay and the physiocrats were right, some
maintenance consumption would be recovered in revenue of its suppliers. Then I
should have written something like C = C s
+C τ
+C p
, where “transfer consumption”
C τ
was the value recovered by suppliers. This mathematical possibility, which I do
not claim to have disproved, explains why I do not claim that the pay rule is logical
certainty as a whole. I claim certitude only for its most surprising feature: human
depreciation is expected to be recovered in pay. The rest follows only if (A5.5) is
right as I think it is. Meanwhile (A5.5) also gives
C = C s
+C p
,
(A5.8)
where C is consumption.
Saved work W s
means the self-invested output of human capital. It includes the
subliminal and effortless work of job experience as well as the effort and
opportunity cost of literal schooling, and also includes any free growth of human
capital. Then
W = W s
+ W ρ
.
(A5.9)
The growth truism (A4.3) for human capital becomes
!H = C s
+ W s
(> 0)−D(H)= C s
+ W s
−D(H) ρ
. (A5.10)
Human Capital as Present Value
Note
APPENDIX A: The Argument in Notation 3/7/16 14
g(F⎡
⎣H
⎤ ⎦ )= g(π −C )= 1 d
s
π −C s
dt (π −C )= !π − !C s
,
s
π −C s
(A6.1)
and also
f(H)= F(H)
H
= π −C s
H
= π H − C s
H .
(A6.2)
Pay π , literal and imputed, is the measure of gross realized work if I am right in
(A5.5). I take this as meaning all adult productive activity not self-invested. Then the
ratios π /H and C s
/H , the ratio of invested consumption to human capital, might
both be intuited as biological norms, like the generation length, which tend to hold
steady over time. Meanwhile the definition f = F/K T
in (A1.6) and (A1.6a) is
applied to human capital as
H = F(H)
f(H) = π −C s
f(H) .
(A6.3)
What we want is to quantify f(H) in order to reveal H from measured or modeled
π −C s
. Next generation theory measures cash flow rate of total capital, which
simplifies to the pure consumption rate, at 3.5% a year as a reciprocal of the
generation length. I argued that the risk component in rate of return is captured in
cash flow rate, rather than growth rate, that return at any given moment varies only
with risk, and that human capital as a whole should prove the riskier and higherreturn
factor. Then f(H) should prove generally higher than 3.5% per year.
That could give the key to quantifying collective human capital through (A6.3). I will
not attempt that step here. A reason is that national accounts reflect pay mixed with
APPENDIX A: The Argument in Notation 3/7/16 15
profit when reporting income of proprietorships. I would rather trust an expert in
national accounts to tease them apart, and to judge whatever pay should be imputed
to people in the household sector not literally employed.
The Level Payment Mortgage
(A2.5) gives
ω
V(x)= F∫ F(z)e −r(x)(z−x) dz . (A7.1)
0
Consider the level payment mortgage. F(z) is the constant level payment while r(x)
is the constant interest rate Here (A2.5) simplifies to
V(x)= F
∫
ω
x
e −r(z−x) dz = Fe rx
∫
ω
x
e −rz dz = F ⎡1− e
r ⎣
−r(ω −x)
⎤
⎦ .
(A7.2)
As there is no self-invested output, and no negative cash flow after initial investment
at time 0, decapitilization (amortization) simplifies to − !V(x). Thus
D(x)= − V ′(x)= − d dx
F
⎡
r ⎣
1− e−rω e rx ⎤
⎦ = F r e−rω
d
dx erx = F
e rω erx ,
(A7.3)
confirming that amortization increases exponentially over the term of the mortgage.
Depreciation Theory
Depreciation can be defined as decapitalization which is a function of time since
capitalization alone. When assets change hands, depreciation continues unchanged.
Depletion and liquidation in sale, by contrast, are options available at any asset age.
Amortization can be given the same definition as depreciation, but is customarily
APPENDIX A: The Argument in Notation 3/7/16 16
applied to paper rights such as the mortgage rather than to physical or human
capital itself.
Depreciation of those assets is not as simple as with the mortgage. Cash flow F and
discount rate r are typically variables rather than constants. Depreciation theory
avoids that complexity, much as accountants do, by treating each successive
investment in an asset as if it were a separate asset depreciating in itself.
(A2.5) through (A2.10) gave present value at time x of a differential foreseen
positive cash flow at future time z as
dPV(x)= F +
(z)e −r(x)(z−x) dz ,
(A8.1)
where the differential present value arose from a earlier or concurrent negative
cash flow invested at time u < = x . It was shown that all of asset value PV(x) at any
time x can be explained as a sum or integral of such differential increments
evolving with time alone from investment to eventual realization.
Meanwhile all output within the differential increment of dPV is self invested.
Growth dPV can be understood either as this self-invested output or equivalently
the shortening discount period, as each means growth at rate r. At interim moment
t it is
dP V ′(t)= r(x)dPV(t)= F(z)e −r(x)(z−t ) dt = r(x)F(e)
e r(x)z
e r(x)t
, x <= t <z . (A8.2)
Thus present value rises exponentially as long as the moment of cash flow is
deferred.
APPENDIX A: The Argument in Notation 3/7/16 17
At moment z, self-invested output ends and all change in value is explained by
depreciation alone. It equals the entire accumulated value of dPV at final moment z.
That is,
D(z)dz = −dP V ′(z)dz = dPV(z)= dPV(x)e r(x)(z−x) .
(A8.3)
The following table shows some illustrations:
Depreciation Factor e r(x)(z−x) if z− x is 50 Years
Interim z− x (years): 0 10 20 30 40 50
Factor if r(x) = .035: .174 .247 .350 .497 .705 1
Factor if r(x) = .065: .039 .074 .142 .273 .522 1
This exactly reverses the analysis applied in national accounts, which models the
factor as decreasing rather than rising exponentially.
It should be stressed that these equations and this table describe each successive
differential increment of outside investment (transfer in), not assets overall or
groups of them. If transfer in were constant and continuous in an asset or group,
other things equal, overall depreciation would show as linear.
Free Growth Theory
By the total return truism (A1.6a), showing r = g + f, we derive
g = r − f , dg = dr − df , and Δg = Δr − Δf . (A9.1)
dg or Δg is “acceleration”, dr or Δr is “productivity gain” or “free growth rate”
and −df or −Δf is “thrift gain”. Divide by acceleration to reach
APPENDIX A: The Argument in Notation 3/7/16 18
dr
dg − df
dg = drdt
dtdg − dfdt
dtdg = !r !g − f ! !g = 1 and Δr
Δg − Δf
Δg = 1 .
(A9.2)
drK T
or ΔrK T
give free growth as a flow, while −dfK T
or −ΔdfK T
give the flow of
thrift.
Define the “productivity index” or “free growth index” ϕ (phi) as !r / !g or Δr / Δg ,
and the “thrift index” θ (theta) as − ! f / !g or −Δf / Δg . (A9.2) can then be put as
ϕ +θ = 1 ,
(A9.2a)
in either the continuous time or discrete period sense.
Free growth theory is the prediction that ϕ at the collective scale will average unity
(the number one), implying that θ averages zero, when ϕ or θ is measured for
each year or for shorter periods if practical. Thrift theory makes the opposite
prediction θ →1 and ϕ → 0. The point is to compare simultaneous changes in
acceleration and thrift, and then find the long-term average of these simultaneous
observations, rather than compare long-term changes in the first place. If free
growth is right, they will prove uncorrelated. That is exactly what the charts and
tables show whenever data are available. Acceleration is as likely to coincide with
unthrift, meaning increase in consumption rate C/K, as with thrift.
Division of (A9.1) by acceleration was not essential to the logic. It added the
convenience of index numbers totaling unity.
The test should be as fine-grained as practical. If the Piketty-Zucman website
showed quarterly or monthly data revealing any two of r , f and g, I would have
averaged the largest number of shortest periods. What I try to compare is ex ante
APPENDIX A: The Argument in Notation 3/7/16 19
acceleration, measured as thrift −Δc , and ex post acceleration Δg at the same
moment. Otherwise we don’t have the clearest test between free growth and thrift
theories. Both agree that consumption can keep pace with output and capital over
time. Free growth theory asserts that they keep pace continuously.
Correlations tell the same story. Tables show that coefficients between r and g
run about 1, as with the free growth index, while correlations between f and g run
about zero.
I do not claim that anyone but Mill and I has actually proposed free growth theory,
nor that anyone at all has proposed thrift theory as here defined. It is my impression,
not assertion, that modern consensus fits thrift theory given Harrod’s qualifier that
attempted (ex ante) net saving (thrift) must not exceed the technological growth
rate (warranted growth path). My impression is that Solow and modern tradition
agree, but blunt Harrod’s knife edge. Free growth theory counters that the same
growth arrives costlessly when ex ante net saving/investment is held at zero. Nor do
I claim that data shown in my charts and tables prove free growth theory. Rather
they demonstrate that all growth has proved free wherever measured to date.
Saving/Investment
Unlike Lord Keynes and modern tradition, I define saving and investment as
synonymous from the start. I don’t strictly need either term. My “transfer in”,
“unrealized output” and “plowback” arrive at the same thing. But I know I must do
my best to write in a language already understood. I will usually say “investment” to
mean saving/investment, and will use Keynes’ notation I for both.
Keynes did not explicitly recognize human capital, although he very probably
understood it. He treated investment in physical capital only. I notate this I(K). I also
treat investment in total capital, to be notated I(K T
). Each, as in Keynes, sums
depreciation recovery and “net investment”. The latter, in my treatment, is
APPENDIX A: The Argument in Notation 3/7/16 20
considered in both ex ante and ex post versions. The subscripts xa and xp will show
which.
Ex ante net investment can be notated I(K T
) xa
and defined as identical to thrift flow
−df(K T
) or −Δf(K T
) . Its rate is the same as thrift rate −df or −Δf . Ex post net
investment is actual growth !K T
or ΔK T
/ Δt as a flow, and !g or ΔK T
/(K T
Δt) as a
rate. Free growth theory, supported by data wherever tested, predicts that thrift or
ex ante net investment at the collective scale sacrifices cash flow (pure
consumption) with no growth to compensate. My interpretation is that the optimum
collective ex ante net investment rate is zero, or equivalently that optimum
investment is current cost depreciation plowback from both factors. Then optimum
ex ante net investment becomes
I(K T
) xa
, optimum = 0 , at the collective scale. (A9.3)
(Net) output Y at that scale is total capital growth (net investment of both factors)
plus pure consumption. Here too we can distinguish ex ante output as pure
consumption plus ex ante investment, while ex post output is pure consumption plus
ex post net investment. (9.3) gives
Y xa
optimum = C p
, at the collective scale, (A9.4)
where Y xa
is ex ante output.
Since (gross) investment equals net investment plus makeup for decaptalization,
while decapitalization equals pure consumption C p
collectively by (A1.4a), we can
show I(K T
) xa
optimum = C p
as an alternate statement of (A9.4).
APPENDIX A: The Argument in Notation 3/7/16 21
Summarizing,
I(K T
) xa
optimum = Y xa
optimum = C p
, at the collective scale, (A9.5)
if free growth theory is correct.
Ex ante investment and output mean at cost. They are what we pay for. The practical
importance of (A9.5) is as a guide to macroeconomic policy. It says that we cannot
grow collectively by attempting to produce more than we consume. We do best by
paying to produce just as much, and taking free growth as it comes.
(A9.5) does not say that we cannot influence the growth tides. It says that we cannot
do so by thrift. It seems to be me that growth theory lies somewhere in the province
of historicism and institutionalism rather than in the mechanics of supply and
demand. Judging from history, old and new, growth seems to find traction in free
markets where laws and customs welcome it. These are institutions shaped by
history.
Free growth theory and its equations predict at the collective scale only. Clearly the
Practical Pig can save out of the dissaving of his feckless brothers, while the
individual life cycle is largely a story of each generation giving to the next.
Adjusting the Ben-Porath Model
Human capital begins at zero value at cohort age 0. Invested consumption C s
starts
now, and is immediately compounded by self-invested work of the young. This
means all work before pay begins at age of adulthood and independence A. As
human depreciation is expected to be recovered in pay, that flow too is put off until
age A. Then cohort present cost at any earlier age x , as defined in (A2.10), is
x
H(x)= ∫ C s
(z)e r(x)(x−z) dz , if x <=A . (A10.1)
0
APPENDIX A: The Argument in Notation 3/7/16 22
I argued that outside investment in human young, including the unpaid work of
parenting, might not be far from constant. School costs rise as parenting costs
decline. (A10.1) in that case gives
H(x)= C s
(
r(x) er(x)x −1) , if x <=A . (A10.2)
At maturity (A10.1) becomes
H(A)= ∫ C s
(z)e r(A)(A−z) dz . (A10.3)
0
A
H in adulthood is easiest to model at present value rather than present cost. Human
cash flow is pay π less C s
. Discounted cash flow becomes
ω
H(x)= ∫ (π −C s
)(z)e r(x)(z−x) dz , if x >=A , (A10.4)
x
where r(z) now is best understood as time preference rate. This is identical to
expected rate of return, as shown in the diamond ring parable. Note that there is no
explicit adjustment for asset risk. I argue that human capital is not inherently riskier
than physical capital, but rather adapts to the risk tolerance of its owner. It is riskier
collectively because owned disproportionately by the risk-tolerant young. I treat
risk profile as a function of the owner’s age, gender and wealth. (A10.4) describes
cohort value, and so neglects individual differences in gender and wealth as already
captured in the characteristics of the cohort.
I model C s
as negligible in adulthood because I see so little of it. That would reduce
adult human cash flow to pay alone, and so simplify (A10.4) to
APPENDIX A: The Argument in Notation 3/7/16 23
ω
H(x)= ∫ π(z)e −r(x)(z−x) dz , if C s
= 0 and x ≥ A . (A10.5)
x
Now let’s add some detail and bring in physical capital. Like most, I model
inheritance as zero and physical capital acquisition as beginning after age of
independence A. That can be modeled as age 20. As human depreciation begins then
at zero, if depreciation theory is right, gross realized work (pay) simplifies at first to
realized work. This takes up all the new worker’s time and attention, yet
simultaneously enables subliminal self-invested work in job experience.
It seems reasonable to model pay at job entry as equal to the new worker’s
maintenance consumption, on the reasoning that independence means reaching the
ability to earn it. Thus nothing is left for investment in physical capital at first. But
the quick buildup of job experience soon means pay left for investment. As I model
no pay plowback, that means physical capital acquisition.
Human depreciation rises slowly while the self-invested work of job experience
diminishes, so that overall growth in human capital peaks and then declines.
Physical capital owned does the same as we acquire it and then spend it on the
young. Young arrive, on average, as a cohort reaches age 28.5 (my estimate of the
generation length). The cohort of adults begins divesting its capital of both factors in
nurture and schooling received by the young as invested consumption.
The young reach independence on average when the adult cohort reaches age 57 (2
x 28.5). Some young will have been born after parental age 28.5, and will continue to
receive parental investment over the eight years remaining between age 57 and
retirement modeled at age 65. But my model cannot account confidently for this
eight year gap on the whole, or for the retirement period following, which runs
twice as long. My hypothesis is that retirees are effectively employees hired by
productives to help take care of the kids, while the eight-year gap might show a
human capital reserve against nasty surprises.
APPENDIX A: The Argument in Notation 3/7/16 24
Retirement can be defined in principle as the period when our pay, literal or
imputed, no longer covers our maintenance consumption needs. Human capital
continues, even so, as long as we earn any imputed pay for helping take care of
ourselves and others. Maintenance is not investment C s
, and is not deducted in
finding our cash flow and its present value.
(A4.4) showed the growth truism for total capital of any individual as
!K T
= γ −
+ Y s
+ ρ pl
−D ρ
,
recalling that γ −
is gift received, Y s
is self-invested (unrealized) output of both
factors, ρ pl
is plowback from realized output, and D ρ
is recovered decapitalization.
For the young under age A, I model K T
as H alone, γ −
as invested consumption
provided by adults, Y s
gross as self-invested work, which I model as all work, and D ρ
as zero. Thus (A4.4) is interpreted as
!K T
= !H = C s
+ W s
= C s
+ W = C s
+ rH , if age < = A , (A10.5)
leading directly to (A10.1)
For adults I model gift received γ −
as zero. As physical capital acquisition is modeled
as beginning at independence (age A), Y s
now becomes self-invested output for both
factors. Let this show as P s
for physical capital. ρ pl
means pay plowback π pl
plus
plowback from revenue of physical capital, as with the firm. That can show as ρ(K) pl
.
But I model π pl
as zero because I see so little of it. Rather I allow reinvestment of pay
APPENDIX A: The Argument in Notation 3/7/16 25
into physical capital holdings. That can be notated π τ
. I don’t allow transfer from
physical to human capital in adults, which would mean invested consumption C s
afforded from property cash flow, because I see so little adult C s
(adult education)
on which to spend it. That’s why I model π pl
as zero. Meanwhile realized
decapitalizaiton is decomposed into its human and physical components D(H) ρ
and
D(K) ρ
. This adapts (A4.4) to
!K T
= !H+ !K = W s
+P s
+ ρ(K) pl
+π τ
−D(H) ρ
−D(K) ρ
, if age >= A , (A10.6)
and specifically
(A10.7)
!H = W s
−D(H) ρ
and !K = π τ
+P s
+ ρ(K) pl
−D(K) ρ
, if age >= A .
Next Generation Theory
The period of production, as defined by Jevons and Boehm Bawerk, gave the
reciprocal of rate of production (rate of return Y /K T
) if growth were zero. Output Y
equals growth plus cash flow. Then Jevons and Boehm Bawerk really meant the
period needed for output to make up for losses to cash flow. I call this the “cash flow
period” T F
, equal to the reciprocal of cash flow rate f. That is,
T F
= 1 f .
(A11.1)
Both modeled at the collective scale, where cash flow under the Y = I + C equation
both would have accepted simplifies to consumption C. Adjustment to the Y rule
corrects this to pure consumption C p
. That would specify (A11.1) as
APPENDIX A: The Argument in Notation 3/7/16 26
T F
= 1 C p
, at the collective scale. (A11.1a)
recalling that c p
is pure consumption rate C p
/K T
.
Rae, Jevons and Boehm Bawerk all got nowhere because they modeled physical
capital only. Jevons, in particular, saw the productive cycle as the wage fund
reproducing itself as it was used up in consumption per (A11.1). He was close.
(A11.1a) models it as total capital reproducing itself as it is used up in pure
consumption. My next generation theory, really Petty’s, posits the generation length
as the deadline for transmitting all fitness (total capital) from each generation to the
next.
The generation length in R.A. Fisher’s sense is average age difference between both
parents and all offspring from first births to last weighted equally. It is a flexible
biological norm. It was probably well over 30 years before 1900 or so, when high
infant mortality compelled longer breeding to ensure that two would survive to
breed again. Contraception, known since Roman times, was then less practiced. It
seems to run a little under 30 years today in industrial countries. I model it at 28.5
years. That gives
T F
=28.5 years and c p
= 1 T F
= .035/ year . (A11.2)
(A9.5), inferred from free growth theory, already gives
I(K T
) xa
optimum = Y xa
optimum = c p
,
at the collective scale.
This shows that the output we actually control, meaning ex ante output, is optimized
at just enough to make up losses to pure consumption. Next generation theory
specifies that the loss and make-up period equals the generation length.
APPENDIX A: The Argument in Notation 3/7/16 27
Under the simplifying assumptions of the life cycle model adapted from Ben-Porath,
we would meet that deadline by directing all adult gross realized output less
property plowback ρ(K) pl
to gift to the immediate generation of young received as
their invested consumption. The young would add their part by compounding that
outside investment into their human capital at the rate of their entire ex ante output.
This would prove the most straightforward strategy to exhaust and replace all total
capital by the deadline exactly. This is just as in my adjusted Ben-Porath model with
the addition of the specified deadline.
Here as there, I describe adults collectively and the young collectively. I will not
attempt to model effects of kin selection in individual investment choices. But I have
intended to lay a groundwork. Investment, in Hamilton’s sense, translates to gift γ +
in economic terms. It is a flow of total capital (fitness) from donor to donee. At the
individual scale, as well as for the group scale, it equals gross realized output less
plowback. Gross realized output tends to be a continuous flow, as we see in pay,
rather than one easily sped up or slowed down. This gives an idea of the time
constraints I mentioned in critiquing Hamilton’s rule.
APPENDIX A: The Argument in Notation 3/7/16 28