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