now a little over 100% per day. At the beginning of the last second, it is a little over
100% per second. At the end of the last second it is infinite. Yet the securities in their
Chapter 2: Fast Forward 1/06/16 18
portfolios are chosen for returns no higher and riskier than the year before. They
will tend in fact to be lower, judging from logic and evidence for a decline in risk
tolerance with age.
Then what besides work is recovered in pay? The two possibilities I was weighing
were maintenance consumption and human depreciation. The winner was obvious.
The higher-paid usually consume more, but not always and not in proportion. The
fact that we must generally be paid enough to cover consumption does not imply
that we are paid to consume. We are motivated to do that anyhow. We are paid to
apply skills, and are paid in proportion to skills applied. Human capital is skill sets.
Pay measures its transfer to products, whether in realized work currently created or
from capital in place through human depreciation.
That’s how I came to the pay rule. We see why it ought to startle economists.
Macroeconomic tradition teaches the doctrine that wage measures work, and
teaches it so confidently that it uses the notation W for either. Human capital
tradition recognizes that some work is self-invested, but effectively treats human
depreciation as deadweight loss. That’s why I use “pay” in place of the more usual
“wage”.
Refuting a Piketty Argument
There are practical uses for the pay rule aside from solution of the age-wage
problem. These are the impact on tax laws and public policy that I promised. Piketty
has shown correctly that the ratio of pay to net profit rose substantially during the
world wars, world depression and welfare state period following, and has declined
since. Piketty argues for higher capital taxes in consequence. His argument follows
tradition in comparing pay and net profit as the shares of workers and investors in
income. But tradition is wrong. Pay is the worker’s gross realized income, meaning
gross of human depreciation. Depreciation, for either factor, is a steadier flow. This
makes gross output for either less responsive to upturns and downturns. It is a
particularly high share of realized income or output in hard times when dislocation
Chapter 2: Fast Forward 1/06/16 19
of both factors (human and physical capital) drives net output down. Comparison
between net income and gross realized income can mislead. Piketty is right about
the data, but wrong about its interpretation.
Depreciation Theory
This is the explanation I promised when I said that depreciation is essentially like
amortization. Accounting tends to practice straight-line depreciation over standard
depreciation periods. A well-known refinement, allowed but not much practiced in
business, is called current cost accounting. The idea is to correct distortions due to
past inflation. The problem is that books reflect long-term assets and their
depreciation at original cost at date of booking. Current cost accounting adjusts both
to the equivalent in current dollars. It shows both net worth and depreciation as
higher if prices inflated since booking, or lower if prices deflated. That seems to
make sense.
A further adjustment called replacement cost accounting does the same, but also
replaces linear depreciation with a curve believed more realistic. National accounts
adopt this method. It is sound in principle. But they shape the curve in the wrong
direction. They rely on records of actual sales of plant to model depreciation as
steep initially and slower later. I suggest that this record is misleading.
My starting point is that value of any capital is discounted cash flow. To keep things
simple at first, suppose that cash flow in constant dollars is expected to hold steady
for fifty years before asset life ends. Also suppose a constant time discount rate.
Present value at the outset is fifty years of discounted cash flow. At the beginning of
the second year, it is 49 years present value of the same cash flow at the same
discount rate. All that has been lost is present value of the 50 th and most-discounted
year. At the start of the third year, capital has dropped again by present value of the
49 th and second-most discounted year. So it continues until the end as the discount
Chapter 2: Fast Forward 1/06/16 20
period approaches zero. Depreciation increases absolutely each year, and increases
even faster in ratio to capital.
What I have just modeled is depreciation rising exponentially from zero at the start
to a maximum at the end. National accounts show the exact opposite. They show it
decreasing exponentially from a maximum at the start. The reason for the difference
is instructive. I would rather trust the present value formula to show what assets
are worth subjectively to their owners. The national accounts prefer to trust
evidence as to what they are worth to others if sold. That’s a solid method too if the
evidence is likely to prove representative. It isn’t in cases where transactions are
more likely to have been driven by pressure to sell than pressure to buy. Plant is
generally tailored to purposes of its first owner, and not meant to be resold. Plant
sales tend to follow disappointing results. These are likelier to come early as
business plans are first tested. That could explain why evidence without logic has
suggested that depreciation tends to start fast and slow down with time.
I would recommend that national accounts continue tracking actual sales as an
indicator of true depreciation curves, but limit the study to rental buildings
expected from the start to be resold several times. I mean apartment buildings,
office buildings and warehouses designed along standard lines. Many investors
specialize in buying and selling these tradable assets for portfolio purposes.
Pressure to buy and pressure to sell tend to balance.
I can testify that prices bid for them are found either by discounted cash flow or
internal rate of return (IRR) methods. IRR is a variant of the same thing. A bid price
is modeled as the original negative cash flow in evaluating the proposed purchase.
Then the positive cash flows at each year’s end are modeled, and the discount rate
found which nets present value of all flows together to zero. If this rate is judged
competitive, the purchase goes ahead. This method was originated by Keynes in the
General Theory as his “marginal product of capital”.
Chapter 2: Fast Forward 1/06/16 21
And I repeat that most other structures are not meant to be resold. Productive plant
is customized to original owners. Tract housing is not, but becomes adapted to them.
Original plant operators and homeowners typically expect to stay put. Most do.
When they do, their own valuations are higher than would likely be realized in sale.
Owners’ valuations matter. Economics is more than prediction of sales prices. It is
prediction of behavior. It is the owner’s valuation of an asset, not a hypothetical
outside valuation, that predicts what he will do to exploit and defend it.
My depreciation theory does not jolt settled belief as forcibly as free growth theory
or the pay rule and Y rule do. It contradicts only a minor feature of the national
accounts. But it contradicts that diametrically, and adds clarity to the pay rule too. It
is also original as far as I know. Who has said such a thing before? All the more fun
and satisfaction in finding out and setting the record straight. There are giants out
there, whether I ever make it to their shoulders or not, and economic history means
identifying them.
Retirement Theory
Retirement generally means the period or first moment when people end the
careers for which their training has been specialized. The reason is typically not
diminished skills and performance just yet, as age-wage profiles show no little or no
drop in pay toward the end. I think it is more that we and our bosses see the drop
coming.
Literal pay is typically zero in retirement. Instead we earn imputed pay for taking
care of ourselves and one another, and for driving the grandkids to the zoo. These
services are tangible, not psychic, in that they save the hire of others to do the same.
The imputed pay is what the others would have charged. But it typically is not
enough to meet our consumption needs. Retirees must typically draw down savings
or depend on “social transfer payments”, meaning support from government or
family or foundations, to make ends meet.
Chapter 2: Fast Forward 1/06/16 22
It seems that these infusions from savings or gift cannot be interpreted as invested
consumption to be recovered with interest later, but are rather pure consumption
recovered now in the satisfaction of survival. Then human cash flow, or pay less
invested consumption, remains positive to the end if we recognize imputed pay.
Economists should, I think, because it figures into predicting behavior as much as
literal pay. So does psychic pay.
It follows that human capital, meaning present value of all pay in the absence of
invested consumption to deduct, continues after retirement. That shows that my
parable of the boss and her secretary is oversimplified. Parables tend to be. The
secretary may happen to have better skills as a full-time caregiver, which both she
and the boss will figure to be in retirement, and so may reverse the disparity in
human capital then. All models, I guess, assume ceteris paribus (other things equal).
My retirement theory leaves much unexplained. It tries to throw a little light here
and there. I believe it achieves some surprise, and even originality until we know
better, in my argument that human capital continues after retirement. Yet this
follows directly from Ben-Porath. Invested consumption must end when time for
recovery runs out, whether or not I am right in ending it with job entry decades
before, and human capital must last as long as literal or imputed pay does. The
endurance of human capital through to mortality is not logical certitude, but need
not be doubted either.
Retouching the Ben-Porath Model
Ben-Porath’s life cycle model seems right enough in all features but one. Equations
in his 1967 paper imply that pay measures realized work alone. This should be
adjusted to show the pay rule. I would also model invested consumption as ending
at independence, or a few months later to allow for initial job training. That does not
contradict Ben-Porath, who leaves such a possibility open. I would further apply
depreciation theory to model human depreciation as growing from a negligible
share of pay at first employment to substantially all of pay at the end.
Chapter 2: Fast Forward 1/06/16 23
My model is the same as Ben-Porath’s from birth to independence. All consumption
and all work are invested, for modeling purposes, until schooling ends at full-time
job entry. I model this transition at age 20. Pay, realized work, human depreciation
and pure consumption all begin at that point, although human depreciation begins
at essentially zero.
Self-invested work continues as an important but diminishing share of work until
late in careers, just as in Ben-Porath. I differ from him mildly in that I model all adult
consumption as pure consumption. Ben-Porath allows adult invested consumption
without assuming it. I regard it as real but negligible. Age-wage profiles are
explained by self-invested work and depreciation theory alone.
I model this self-invested work as subliminal accumulation of job experience. My
reason is personal observation. What I have seen in plants and offices is people
working full time on the job. We don’t take time off to learn. Experience simply
arrives, much as free growth does. I think that my view on this contradicts Ben-
Porath’s marginally. He seems to allow some such allocation of time to help explain
age-wage profiles.
Next comes retirement. I model this as just shown. Later I will expand this model to
include acquisition and disposal of physical capital too. The combined model will
give most of the math and mechanics of next generation theory.
Risk Theory
For practical purposes, economic risk is usually measured as expected standard
deviation in rate of return. Safer assets vary less from their return norms. Shortterm
treasuries are thought safest because they combine fixed nominal return with
fast liquidity in case inflation threatens. The market overall bids safer expected
outputs up and riskier ones down. Since asset value is the denominator in rate of
return, and output the numerator, the effect is make risker assets higher in return.
Chapter 2: Fast Forward 1/06/16 24
Risk tolerance might be anything in any individual. As a norm, it tends to be a
function of age, gender and wealth. Effects of age and gender are better understood.
Teens and young adults, particularly males, seem readiest to take chances. Prison
populations and medal of honor rolls feature young males. Part of the explanation, I
think, is biologist R. A. Fisher’s sex ratio theory of 1930, or equally Bob Trivers’
differential investment theory of 1971. Young males show greatest variance in
reproductive prospects. Females are almost always assured of a few offspring.
Young males might leave none or many. Nature arranges tournaments or displays to
give fitter males the advantage.
Another reason is that the young, of either sex, have most time left to outride
downswings. The older we get, the more risk-averse.
Some businesses and assets are inherently riskier than others. Nerf balls are safer
than hand grenades. But I prefer to look past the asset owned to the owner. We tend
to own assets suited to our risk preferences. And we tend to operate it as safely or
riskily as we like. That is true particularly of human capital, although it was first
designed according to our parents’ goals rather than ours. Human capital is
probably the most versatile asset, even so, and is adapted to our purposes rather
than theirs. We make it as risky as we choose. The risk-averse can become florists or
Trappists. Risk lovers can try bullfighting or skydiving. What does that tell us about
the relative risk of the factors?
Human capital is owned disproportionately by the young. We own very little
physical capital, legally or in practical effect, until maturity. Pay at first is barely
enough for survival. We accumulate it gradually as pay rises with age, and then
deplete it in provision for the young and in our own retirement. Since physical
capital is owned disproportionately by the older and more risk-averse, and human
capital the contrary, human capital figures to be higher on average in risk and return.
Chapter 2: Fast Forward 1/06/16 25
There is another useful inference. Adults own assets in the business and housing
sectors. Older adults tend more to own debt claims on these sectors, and younger
adults to own equity claims. But all adult ages collectively own both sectors
collectively. It does not follow that the sectors are equal in risk, as older individuals
might tend to own one sector predominantly, and younger ones the other. As a
layman, I don’t really know.
What I happen to know is that the publicly traded corporate sector, meaning stocks
particularly but also bonds, is far more liquid than the housing sector, and that the
rest of the business sector is far less liquid than either. Risk in general includes
liquidity risk. This leads me to the hypothesis or hunch that the housing sector in
general should be safer than the business sector, ceteris paribus, but that the
publicly traded corporate sector, cap-weighting debt and equity claims on it, may be
safest of all.
The idea that stocks and bonds cap-weighted are safer than houses might have been
laughed to scorn a few years ago. It doesn’t seem so funny after 2008. I view it as an
idea to be tested, not trusted, until more is known. If it holds up, it will rank as
another surprise.
The effect of individual wealth on risk tolerance is less understood. Here I judge
more from hunch and impression than from data. Given that human needs are fairly
uniform, as with the private and the general, more wealth gives more insulation
from want. Talent is wealth in human capital, and gives the same. Less, in either
factor, gives less margin for error. My hunch and impression is that the wealthier in
either factor should tend to be more risk tolerant so long as human capital itself is
not put in harm’s way. Human capital operates physical capital, and gives the means
of recovery. The wealthier, in talent or net worth, should prove the least tempted
toward sky diving and Russian roulette.
Chapter 2: Fast Forward 1/06/16 26
In this book I will usually be modeling risk and return at the collective scale or at the
cohort one. A cohort means the set of all same-aged individuals. It turns out that the
ratio of females to males tends to rise with each older cohort, for reasons Bob
Trivers explains, as does wealth up to a point. But in cohort analysis, both effects
(wealth and sex ratio) are incorporated into effects of cohort age. That will simplify
modeling.
My risk theory is another example of what looks to be surprise and novelty until
shown otherwise. The unusual idea lies in projecting the owner’s time
preference/return rate onto the asset rather than conversely. Thus all the owner’s
assets of both factors are selected or modified to fit her current risk profile. This
would count her liquid securities portfolio, cap weighted, as a single asset. All other
assets are too illiquid for practical rebalancing. We own the assets best suited to our
risk profiles, if for no better reason than that we wouldn’t be the winning bidders
for any others if we wanted them. As our risk profiles evolve with age, we modify or
trade them. We will tend to have anticipated this need, and to have factored
modification or trading costs into our bid price. It turns out that this interpretation
can simplify the math of present value and present cost.
It helps in supporting the pay rule, and explaining age-wage profiles, by rebutting a
hypothesis, sometimes argued, that productivity of human capital might rise with
age. Productivity, rate of return and time preference rate all mean the same. My risk
theory argues that we know a cohort’s risk tolerance from the return to its capweighted
securities portfolio as a whole. All other assets of the same cohort,
including human capital, will tend to agree with it in return. Return to security
portfolios tends to be transparent. It declines with adult cohort age. I infer that
return to human capital does the same.
My risk theory and depreciation theory together add a finishing touch to the pay
rule. The key supporting evidence is age-wage profiles. Depreciation theory offers
solid logic, in the face of apparent contrary data, that pay is all human depreciation
Chapter 2: Fast Forward 1/06/16 27
at the end. Risk theory reinforces that impression by adding that the contribution of
productivity in the form of realized work/human capital actually declines. One
cannot pound too many stakes through the heart of the doctrine that pay
compensates realized work alone.
Next Generation Theory
I also treat rate of return. This combined free growth theory with insights of Petty
in 1662 and William Stanley Jevons in 1871. Petty’s idea was that each generation
passes the baton to the next. Our investment horizon is the generation length. Its
reciprocal, or one over that period, gives our time preference rate. Jevons also saw
time preference as the reciprocal of the period of production, but did not connect
that to the generation length. I adjust Petty’s estimate of the length from his 21
years to 28.5 by allowing for later births as well as firstborns. The reciprocal is 3.5%
per year. I add free growth as an exogenous and unspecified variable.
As with Mill and free growth theory, I have to walk a fine line between crediting
Petty and putting my ideas in his mouth. Petty dictated his books and pamphlets,
and is not always clear. My idea, probably but not certainly the same as his, is that
each generation invests everything in the next in trust that it will do the same. All
our capital of both factors, although Petty spoke only of a cornfield, is exhausted in
putting the next generation in place. The time horizon to get this done is the
generation length.
This 28.5 years, as I model it, becomes Jevons’ “period of production”. Its reciprocal,
meaning one over it, gives rate of return. The idea of a period of production whose
reciprocal gave rate of return had begun with Rae in 1934, if you don’t count Petty,
and passed through Nassau Senior to Jevons and Boehm Bawerk. All assumed
growthlessness for simplicity. Return is growth rate plus cash flow rate. It simplifies
to the pure consumption rate at the collective scale. All these men, even Petty, were
really modeling the pure consumption rate. 28.5 years gives the period of
replication, in my view, or period of production if there were no growth.
Chapter 2: Fast Forward 1/06/16 28
Free growth then arrives at its whim, like a deus ex machina, without calling for
more than this steady effort of replication. I find myself focusing more and more on
that cash flow component of rate of return, or pure consumption rate at the
collective scale, as the part we can predict and model.
The generation length is a biological norm which probably has not varied by more
than a factor of two since Ancestral Eve some 200,000 year ago. This suggests that
next generation theory can be tested against data from any period. Meanwhile it
predicts only at the collective scale. Collective return is average risk return. Subtract
collective growth rate to leave cash flow rate. Return and growth are two of the
most closely measured rates in economics. That says that tests of next generation
theory should be practical. I will show tables broadly in support.
Next generation theory is a blockbuster. An explanation of interest and return has
been the Holy Grail of capital theory. Boehm Bawerk contributed a big advance by
revealing return as an artifact of time preference rather than the other way around.
Some including Irving Fisher have seen that beautiful insight as enough.
Not me. What explains and quantifies time preference? What turned out to be
Petty’s idea occurred to me about 40 years ago, when I first took an interest in
evolutionary biology. My friend Alan Rogers, a population geneticist I didn’t know
all the time, was thinking in the same direction. His two published papers on this are
in my appendix. Neither of us knew about Petty’s priority.
The idea would have been a still bigger blockbuster before the wall came down.
Wars were being fought about whether return has any legitimacy at all. Karl Marx,
ironically a champion of Petty, may have missed his argument on that.
Petty’s idea is really the biological imperative I discussed in Chapter 1. The first
priority is survival and reproduction. I will argue that this was implicitly accepted
Chapter 2: Fast Forward 1/06/16 29
throughout economic history until new insights now summarized as the marginalist
revolution began in 1871. The marginalists, mentioned in the forward, swapped the
telescope for the microscope. They left aside the grand teleologies of Smith and
Ricardo and Mill and Marx to refocus on the mechanics of choice. Reasons for tastes
or choices were treated as irrelevant. By 1900 or so, the marginalists had given us
microeconomics much as we know it today. A century would pass before
bioeconomics took form in response to Hamilton’s rule.
Summary
That gives the outline. It is a layman’s view of what a proper economist might not
have attempted. Fools rush in. I will cite sources in economics and biology not to
pretend that I am an authority, but to give real ones a chance to check. My case rests
on the charts and tables. Mill might have been astonished to find that the kind of
growth he described is the only kind to appear in the record.
What makes my book different, aside from my lack of credentials, is the surprises
and the unusual degree of abstraction leading to them. Not many writers try to
follow a chain of inference as far without the comforting touch of the stone and
wood and rope. If Becker had been as venturesome, he might well have solved the
age-wage problem in 1964. I see no other path. Economics is all inside. It is tastes
expressed in choices. Capital is foreseen satisfactions discounted by whatever our
taste for impatience is. Most of it is human capital leaving little market record
beyond its rental cost in pay. Logic is about all we have left.
But the story cannot end in thin air. Few would pay the nuisance cost of so much
abstraction without prospect of surprising and testable prediction. I will try to
deliver that. Mill’s idea is a surprise to politicians, if less so to economists, and could
hardly be tested more thoroughly and successfully. When new ideas are thought up,
Mother Nature says “Shazam” and embodies them at no cost beyond the
depreciation plowback we needed anyway. The data could not be more supportive if
Mill and I had invented them. Even my proposed solution to the age-wage problem,
Chapter 2: Fast Forward 1/06/16 30
which must have seemed hopelessly stuck in subjectivity, paid off finally in that
solution and in a refutation of Piketty’s argument. Risk theory and depreciation
theory, each surprising enough, reinforced that solution and the pay rule. I said
nothing in the this chapter about bank reform because I covered that in Chapter 1.
Predictions of behavior can work because tastes converge to market equilibria.
What stands behind the convergence, I argue, is biology selecting tastes that
maintain and reproduce us. The idea that we act out the biological imperative is
clear in Petty and Malthus, and in the equilibrium wage theory of Adam Smith and
David Ricardo, where pay converges to the level preserving the work force. But if I
say everything about that now, I will have nothing to say later.
Chapter 2: Fast Forward 1/06/16 31
CHAPTER 3: FOUNDATIONS
Historically, foundations and science itself emerge at the end of centuries of
practical application. A logical place for foundations in textbooks is the beginning. So
it was with Halliday and Resnick on physics, which began with Newton’s kinetics
(motion in time and space) and then this three laws. Only in the last chapter did the
authors remind us that Einstein later put two of these three into question, and even
the kinetics. Halliday and Resnick reasoned, correctly I think, that we sometimes
learn more efficiently by learning something slightly wrong first and fixing it later. I
will do that, in a sense, by reasoning first through free growth theory as if the Y = C +
I equation were true, and then again with the two corrections. The sometimes
counterintuitive logic of teaching and learning, including that, is “heuristics”.
Building on explicit axioms was common in economics throughout the classical
period running from Petty in the 17 th century through Mill in the 19th. Then came
the major shift in focus, beginning in 1871, called the marginalist revolution. What
mattered was less our goals, and more the market mechanisms that aligned supply,
demand and price. The meeting point was the margin. Axioms about goals
disappeared, including the usual one of prioritizing survival and reproduction, and
axioms kept were usually left implicit. The implicit ones, essential to marginalism in
my view, included convergent tastes and predictions. I will make those two and
others explicit, and eventually add back the goals.
This book on the whole is about second-guessing what is taught. This chapter is
different. The nearest thing to a surprise in it is the idea that economics needs
explicit foundations in the sense of axioms and basic definitions and equations. All
the ones I choose are well accepted. Why I pick which should seem obvious in
hindsight. But some mini-surprises will accumulate. Why do I take such pains to
prove every feature of what everyone accepts already? Why all the boilerplate and
bulletproofing? I need them because I will later try to shoot down other beliefs
everyone accepts. We must know what is sound to find what is not.
Chapter 3: Foundations 1/11/16 1
Another mini-surprise is the physics-like care in definitions. The reason is that my
arguments later will drive logic pretty far. Logic needs words that are like algeraic
symbols in meaning the same thing all along.
Figuratively and literally, foundations are groundwork. They will be less a chore if
you love logic. And you’d better if you’re going to like the later chapters. Let’s get
started.
Orientation
Economics itself, I think, is a quantitative rationale of choices. Psychology is a sister
study not explicitly quantitative, and accounting for subliminal behavior as well as
deliberate choices. The two fields cooperate and overlap. Economics is quantitative
in that it asks how much as well as what, and focuses on numbers. It is science-like
in that it looks for surprising and testable predictions in the end. It is philosophylike
in that choices are subjective and that the larger factor, human capital, leaves
little market evidence from which to reason upward. Both facts put the burden on
reasoning downward from axioms.
Much of the evidence for both factors, meaning physical and human capital, comes
from the records of literal markets where we rent and hire and buy and sell. Most
economics looked no further until Gary Becker and others expanded the boundaries
about 50 years ago. The expansion made sense. A rationale of choices in literal
markets alone is a silly concept. It is silly to acknowledge only choices that ring cash
registers. We are the same people everywhere. Logic is the same everywhere. We
have little interest in axioms that aren’t the same everywhere. Becker was right to
see choices in marriage and even crime as predictable in terms of supply and
demand and price.
That includes psychic price. Once we follow Becker past literal markets, we accept
psychic value and yield. We must anyhow. Value is in the mind. Economics works as
Chapter 3: Foundations 1/11/16 2
a rationale of choices, hence values, because human nature leads minds to converge.
The literal market adds a measure. When we step outside it, we make do without the
measure and trust logic alone.
A Diamond Ring Parable
I like a picture of a diamond ring to show something about psychic value and yield,
and even about what output and exhaust in consumption are. The ring brings
psychic yield to its wearer. If it didn’t, it would have no value. Its yield is each
psychic satisfaction, and its value sums all time-discounted prospective ones
together. Value therefore drops just a little as each yield is finally realized. It is as
with apples dropping from a tree. Yet the ring is inert. It ostensibly produces
nothing. It also keeps all its value as a ring from day to day. Then where does the
outflow of the value in the exhaust come from? How can value go out if none was
deducted and none produced? In the tree, we can see the apples growing and falling.
The answer is that some value was produced in the ring, and some deducted too.
What we didn’t notice was the constant shortening of remaining discount periods.
As each day passes, each future yield comes one day closer. These are the apples
slowly ripening on the tree. Present value of each rises because the discount period
covers less time. This creation of value is output by definition, even though nothing
has moved but the hands of the clock. As the discount period reaches zero, the
expected yield eventuates to explain the taste satisfaction. These yields are the
apples falling to be eaten. The ring holds its value intact because the exhaust of
value it surrendered has exactly offset the output of replacement value as time alone
shortens discount periods. Yet not an atom stirred.
The whole point is that the value of the ring or anything else is discounted present
value of foreseen satisfactions. They are discounted because there is such a thing as
“time preference”; we value satisfactions now over foreseen ones later. This is not
quite the same as the difference between birds in the hand and birds in the bush.
That says that we value certainties over probabilities. Time preference also values
Chapter 3: Foundations 1/11/16 3
present certainties over future certainties. The reason is studied in a branch of
economics called “capital theory”. My next generation theory, really Petty’s of 1662,
proposes what the average-risk time discount rate is and why. Present value of each
expected instant of future satisfaction grows at that rate as time shortens the
discount period. It disappears, as apples from the tree, when expectation matures
into reality.
This diamond ring parable is full of useful lessons. I think it contains substantially all
of economics. “Consider the lilies of the field.” “They also serve who only stand and
wait.” A chemist would testify that the ring has done nothing. An economist sees
plenty happening. Economics is abstraction. Physical capital is not things, and
human capital is not people. It’s all in the mind. What an economist sees is present
value evolving with time as expectations ripen and eventuate. Output is not what we
do, although it has to do with what we do. It is the passage of time. Exhaust is the
fruition of time and the harvest reaped.
Only when we allow psychic values can we say that all behavior is economic
behavior. It is choices among alternatives. That’s what makes economics philosophy.
Axioms
Then what should its axioms be? We would like empirical or real-world certainties. I
find none beyond Descarte’s cogito. Philosophy is certain of next to nothing. We
settle for working assumptions. We want ones as safe and few as possible. Those of
economics have usually been left implicit since the marginalist revolution. I dropped
the course because I felt their need. It should do no harm, at this point, to risk the
opposite extreme. Let’s try putting everything on the table.
My first axiom, in that spirit, will be unguided natural causality. This need not alarm
the devout. It is the working assumption of all science. Working assumptions are
not creeds. I cannot rule out the possibility of occasional or even continuous
intervention by God to explain what we see. But we know to act as if we ruled it out
Chapter 3: Foundations 1/11/16 4
when our science hats are on. Even philosophy, in the Western tradition, leaves
revelation aside. A practical consideration is that debates of how God is likely to be
motivated to intercede have tended to find little consensus or traction. Science gets
some.
I tipped my hand on my own views in Chapter 1. As chairman of the Leakey
Foundation for more than 40 years, I pretty clearly buy evolution theory and
unguided natural casualty as working assumptions. But I invite those who don’t to
read further before deciding that we will disagree on conclusions. If I foresaw a
conflict with the devout, which I don’t, I would feel obligated to warn them now. I’ll
bring this up again as we go along.
My next few axioms, lumped together, are a mortal and reproducing population
which competes, cooperates and freelances to act on convergent predictions. It acts
to satisfy convergent tastes in a world of limited resources. I will model the
population as human, although other species would do insofar as my axioms hold
for them. “Convergent” means non-identical from individual to individual or place to
place or moment to moment, but converging to norms with increasing scale in space
and time. Predictions converge to outcomes as well as to one another.
The point is that tastes and predictions must be convergent enough for markets to
form and hold. A market, as Becker knew, is where anyone makes any choice among
alternatives. A literal market is where a choice leaves a quantitative record. Markets
cannot form and hold if we cannot predict where to find them and what they supply
and when they are open. They cannot form and hold without some consensus that
what we predict they will offer includes something we want. Clothing stores can
work because our sizes and shapes fall mostly within standard ranges. Their
business would be in trouble if we did not agree in number and rough placement of
arms and legs and head. Restaurants can work because we can find what we want
on a finite menu. Most crucially, clothing stores and restaurants cannot hold unless
there is consensus on what their wares are worth in return. All this convergence
Chapter 3: Foundations 1/11/16 5
suggests a single species, although the axiom only said population. The ants and the
picnickers can compete for the lunch, but they cannot bargain for it. The bar in Star
Wars is a great gag because it thumbs its nose at this home truth. We converge in
taste for the hilarious.
I will add the biological imperative as a separate axiom later, although much of that
at least may be implicit in the first one of natural causality. We hate unnecessary
axioms, from good Occamite principle, but we hate unsupported inference or
question-begging worse.
I spell out the axiom of mortality and reproduction because I know I’m heading
towards Petty’s insight and next generation theory. Of course we design foundations
to support what we want on top. It seems to me that my axioms mention nothing
about rationality, whatever that might mean, except in the sense of assumed
convergence of predictions to outcomes. And that assumption itself might not be
critical. What seems critical that is the predictions should converge to a known
function of outcomes. If they converge to something predictably overoptimistic or
overpessimistic, we’re still in business. Lacking even that, economic science is
stillborn. We can’t predict chaos.
That’s an example of the principle that axioms need not be strictly true. They must
be true enough. We’re still in business if God intervenes a little here and there. Much
more than that, and the convergent prediction axiom runs into the problem of
predicting the mind of God.
The two convergence axioms, of tastes and predictions, are implicit in all
microeconomics. “Micro”, as economists call it, is about supply meeting demand at
price equilibrium. This insight was the main theme of the marginalist revolution. It’s
exactly what can’t happen without convergent tastes and predictions. It’s exactly
why the bar in Star Wars is a hoot. Ants find price equilibria in ant markets, and
people in people markets. Ants and people find no meeting of the minds. Then if
Chapter 3: Foundations 1/11/16 6
macroeconomics (“macro”) rests on micro, the convergence axioms say only what
economics has accepted implicitly since micro began. The “law of one price”,
meaning market equilibrium, actually begins a century and a half earlier with
Cantillon. But Jevons, in co-founding the marginalist revolution in 1871, effectively
made it an axiom.
I don’t want to seem to claim that the convergence axioms are safe because they are
accepted. Arguments ad majoritatem or ad auctoritatem prove nothing. But markets
do seem to form and hold, and the convergences seem implied. Authority and
majority are sometimes right.
Not all economists have agreed. There have been “historicists” and
“institutionalists” who mistrust the idea of convergent tastes, and prefer to see
idiosyncratic national tradition or power groups or mindsets as the prime movers in
place of uniform human nature. Heinrich Schmoller, a historicist who stressed
national differences, tangled with Carl Menger, an independent co-founder of the
marginalist revolution in 1871, in a childish feud for which Menger was at least as
much to blame. If you must answer your critics, be gracious. Thorstein Veblen, an
institutionalist from Wisconsin, coined the term “neoclassicism” for what we now
call marginalism. He made fun of it for missing the role of institutions in driving
economies for institutional or collective goals rather than individual human ones.
I think there’s something there. My main theme in this book is growth theory at the
collective scale. I argue that collective growth flourishes where laws and practices
and cultures nurture and protect it. These are national institutions. New ideas, by
definition, are opposite from the fungible commodities for which supply and
demand meet at price equilibria. Somehow they come. Dogs bark, cats climb, people
innovate. I’m with Menger and Jevons and the marginalists and human nature, but
with asterisks there too. There is plenty left for historicists and institutionalists to
help explain.
Chapter 3: Foundations 1/11/16 7
Vocabulary and Catechism
The words microeconomics and macroeconomics, by the way, didn’t exist until
Ragnar Frisch coined them in the 1920s. We use terms retrospectively to describe
old arguments in language familiar now. That segues into the next steps in the
foundations. What should be the basic vocabulary and catechism, meaning basic
logic, in terms understood today?
Consideration of purpose always comes first. The purpose of economics is
prediction. We happen to know that one of the most powerful predictors of
economic behavior is maximization of risk-adjusted return. This was Robert
Turgot’s insight of 1766, although he left the risk variable unsaid. (His real first
name was somehow Anne, so we’ll go with the second). He wrote that return
equilibrates across markets as investors leave low-return businesses to crowd into
higher-return ones. The shift bids up capital denominators in the higher-return
businesses, and conversely, until return converges. It was David Ricardo, in 1817
who added that the convergence is more exactly for businesses judged equal in risk.
The evidence is everywhere we look. I call this the maximand rule: all behavior
maximizes perceived risk-adjusted rate of return. I’ll show its proof below. That
means all behavior in all markets, and markets are where any choice among
alternatives is made. Return means ratio of (net) output to capital generating it.
Then the vocabulary wanted might as well include capital and output.
But what is capital? Economics is choices, and the measure is price or value. Price
can’t be measured exactly outside literal markets, which is why economists follow
those markets, but is measured in principle by what we give up in exchange. The
price of any capital, even human capital, is given by the present value rule as timediscounted
cash flow. Then cash flow and its positive and negative components
belong to the basic vocabulary, while the present value and maximand rules both
belong in the catechism. Output is total return, so the total return truism belongs in
the catechism too.
Chapter 3: Foundations 1/11/16 8
What other basic terms do we need? Cash flow at the collective scale, where
transfers cancel internally, and there is no source of investment from outside,
simplifies to exhaust of value in taste satisfaction. There is no negative component
because there is no external source of new investment. Tradition through most of
economic history has called this exhaust consumption. Schultz recognized some
consumption as investment in human capital, I said earlier, and limited the exhaust
to “pure consumption”. I will use this and the term “exhaust” interchangeably. Then
transfer, consumption, exhaust and pure consumption belong in the vocabulary too.
So does “invested consumption”, my restatement of Schultz’ “pure investment” in
human capital.
This seems to be the right track. The object is prediction of behavior. The maximand
rule predicts all behavior, and I have sought to build a vocabulary and catechism to
clarify its terms. The right vocabulary, thank gosh, is mostly the one we have all used
since Adam Smith or even Petty. It has needed only a little tweaking and
clarification, as to the two kinds of capital and consumption for example.
There is a “fundamental theorem” of calculus showing how differentials and
integrals fit together. Its proof takes a lot of thought. There is a simpler one for
algebra. Might a fundamental theorem of economics be helpful? Obvious candidates
would include the maximand rule predicting all behavior, the total return truism
explaining the output numerator of the maximand (rate of return), and the present
value rule explaining the capital denominator. For years I chose the maximand rule
as the fundamental theorem. Then I preferred the present value rule as more
fundamental since it explained the denominator. But so would be the total return
truism in explaining the numerator. Now I opt for the judgment of Paris. Let the
three together be the fundamental theorems of economics. The maximand rule is
the centerpiece, and the other two define its terms. All three together are much
easier to follow, mercifully, then the one of calculus.
Chapter 3: Foundations 1/11/16 9
The vocabulary can also include the standard distinction among stocks, flows and
rates. These are only definitions, not assumptions. Stocks means value measured in
money units, say dollars. This is not the same as stock in the sense of equity
securities, although those can be examples. Flows means processes such as output
for consumption measured in dollars per unit time. Flows are to stocks as verbs to
nouns. Percent rates are flows divided by stocks, as rate of return or growth rate,
and are measured in pure numbers over time such as 5% per year.
Now for the fundamental theorems. Take the present value rule first. It starts from
the axiom that we satisfy convergent tastes in the light of convergent predictions. In
a simple case, we foresee that an asset (stock) is likely to yield a certain amount of
taste satisfaction flow at a certain future time. We discount that expected amount at
a time preference or time discount rate given by our taste for impatience, tempered
by our taste for risk avoidance, to find its present value. Present value of the whole
asset is the sum of present values of all the expected future satisfactions together.
A more general case allows for transfers. The future events we foresee and discount
are not always exhaust in taste satisfaction by ourselves at the time. Some might be
foreseen liquidations to reinvest in other assets or to give away so that we or the
donee can realize the taste satisfaction later. Either reinvestment or gift is called
transfer. I call it “transfer out”, meaning out from the generating asset. Then
transfer out = reinvestment + gift. (3.1)
There can also be transfer in. Sometimes future realizations, in taste satisfaction or
transfer out, are not explained as production by the asset as it is now. The asset
might grow later by new investment from outside, and the investment in between
might help explain the later yield. If an eighth-grader is destined to become a doctor,
for example, her foreseen earnings as a doctor will presuppose investment in high
school and college and med school in between.
Chapter 3: Foundations 1/11/16 10
The expected future flow we discount to present value, allowing for transfers too, is
exhaust plus transfer out less transfer in. This net difference is called cash flow. That
is,
cash flow = exhaust + transfer out – transfer in. (3.2)
That’s the logic behind the present value rule interpreting capital as discounted cash
flow.
Human cash flow may not be defined in those words anywhere but in this book. But
the flow discounted to find human capital is understood everywhere, I think, as pay
less what Schultz called pure investment and I call invested consumption. I
defended this idea in my analogy between human capital and the firm. Thus I
endorse the tradition that human capital is pay less invested consumption
discounted to present value. That is,
human cash flow = pay – invested consumption.
It turns out that this is not logical certitude, or an inference from axioms already
given, and so it is not strictly part of the foundations. I will defend it in later
chapters.
The great convenience of the present value rule and its application to human capital
is that it allows the factors to be added as a dollar sum. That helps in understanding
the total return rule.
That rule begins with the truism that growth of anything is internal creation plus
flow passed in less flow passed out. That shows as
growth = creation + flow passed out – flow passed in. (3.3)
Chapter 3: Foundations 1/11/16 11
Algebra now allows
creation = growth + flow passed out – flow passed in,
(3.3a)
since terms can change sides if they reverse signs.
Economics is interested in creation and growth of value. Value in the stock sense
means capital in general. Most economists most of the time use the word to mean
only the “physical capital” we buy and sell. But the truism works for anything. I
sometimes prefer the generality of “value”, meaning any amount of any mix of
human and physical capital. This again can be called either “total capital” or value
interchangeably.
Flow of value passed out is exhaust plus transfer out, and flow passed in is transfer
in. Creation of value is output in the net sense. Then (3.2) and (3.3a) give the total
return rule
output = growth + cash flow.
(3.3b)
“Income” means rights to output, and is implicitly equal to output. Like most writers
in economics, I will use these words more or less interchangeably too.
Now comes the centerpiece. A good starting point is the present value rule. We
assemble value or total capital to satisfy foreseen tastes. But we also satisfy current
tastes by spending current cash flow. At the scale of the total capital (value) of the
individual, were reinvestment cancels internally, cash flow simplifies to exhaust in
taste satisfaction plus gift given less gift received. Then
individual cash flow = net gift + exhaust, (3.4)
where net gift means gift given less gift received.
Chapter 3: Foundations 1/11/16 12
Consider net gift. Its negative component, gift received, is concurrently added either
into total capital growth or into exhaust. Thus it is the contribution to those two
desiderata explained from outside, rather than by the individual’s behavior. Net gift
deducts that negative component (gift received) from the positive one to leave the
part which the individual’s behavior explains. Thus individual output, as the sum of
growth and net gift, is the sum of desiderata realized by behavior. That makes it the
unique behavioral maximand as a flow. Division by the individual’s total capital,
which is her whole means of behavior, gives total capital rate of return as the rate
maximand.
This can be summarized in a slightly different way. Cash flow measures the means of
taste satisfaction now. Total capital growth measures gain in means of expected
satisfactions, discounted according to our taste for impatience (time preference)
tempered by our taste for risk aversion. Output is their sum. Behavior reveals and
maximizes the taste satisfaction including provision for future satisfaction.
Therefore risk-adjusted output is the flow maximand. Capital of both factors, at
present value, is defined as the whole means of that satisfaction, and implicitly of
behavior. Therefore risk-adjusted return, the ratio of the flow maximand to its
means, is the rate maximand.
What Turgot said in 1766, in his Reflections, was
“. . . as soon as the profits of one employment of money. . . increase or
diminish, capitals turn in that direction. . . or withdraw and turn to other
employments. . . Whatever the manner in which money is employed, its
product cannot increase or diminish without all the other employments
experiencing a proportionate increase or diminution.”
Turgot did not allow for risk in this quick summary, but otherwise explained the
mechanics that tend to equalize return.
Chapter 3: Foundations 1/11/16 13
The rule does not say that risk-adjusted return tends to hold constant over time. To
the contrary. Return equals growth plus cash flow, and my charts show the growth
component as a bucking bronco. The maximand rule says only that risk-adjusted
return is always the maximand. It is not always the same as time changes
circumstances. Proof is in Turgot’s equalization of return at each moment, not from
one moment to the next. That is what we see wherever we look.
There is a quibble worth attention. Behavior seldom expresses taste exactly. We say
one word when we mean another. We reach for the coffee, and accidentally spill it.
That was the point of my axiom that predictions converge to outcomes, as well as to
one another, only on average. Outcomes are generally a little better or a little worse
than predicted. There can even be systematic bias where all people together seem
overoptimistic or overpessimistic accordingly to circumstances, as shown in the
psychological economics of Hanneman and Tversky. The axiom requires that these
biases offset over scale and time. That sounds plausible, and anyhow makes analysis
easier.
The maximand rule would be ridiculous if terms were defined in a literal market
context only. Markets must be defined as wherever any choice is made. It would be
ridiculous if cash flow were understood to presuppose literal cash, or even the
necessity of some quid pro quo to explain motivations. Unreciprocated gift down the
generations drives lineage survival.
All behavior means all behavior. The miser maximizes the growth component in
return, the parent or philanthropist maximizes the net gift component, and the
good-time Charlie maximizes exhaust.
Have I gone too far in this claim? Try to imagine an exception. What kind of behavior
might not maximize perceived risk-adjusted return? What if I jump out the window?
Deliberately drive my car into a tree? Sell a cow for a handful of beans? Maximize a
Chapter 3: Foundations 1/11/16 14
pile of nuclear waste in my safe instead of cash and securities? Drive a truck filled
with dynamite into a crowd of unbelievers? Write a book on economics when I have
no credentials? Sing when I have an atrocious voice? All express my tastes. There is
no escape. Behavior reveals taste satisfaction in the broad sense including provision
for future satisfactions.
Tastes, Aims and Ends
I usually mean the word “tastes” as objectives whose satisfaction exhausts capital
value. By that usage, as we just saw, the truism that behavior reveals tastes must be
interpreted carefully. We see current taste satisfaction at mealtimes. Between meals,
we mostly see buildup of capital to satisfy tastes in future. And we sometimes are
motivated to give capital away, as in raising the generation to succeed us. I
sometimes use the term “aims” to mean the sum of this exhaust plus gift plus
buildup. Then to say that output realizes growth plus cash flow is to say that it
realizes aims. All behavior reveals and maximizes aims explained by ends. This
again puts the maximand rule in a different way.
As capital of both factors is our whole means of behavior, and as it is present value
of foreseen taste satisfaction and nothing else, we might first suppose that taste
satisfaction is our unique final goal. But that too could mislead. Biology shapes our
tastes, and shapes them to replicate the generations. I treat the biological imperative
as the “ends” driving tastes and aims. Our two complementary ends are adult
survival and replication of both factors for survival of the young. This idea underlies
next generation theory.
What we maximize is risk-adjusted present value of current plus foreseen taste
satisfactions by ourselves plus donees. Current taste satisfaction or exhaust by
ourselves is counted at full value, and foreseen ones are added at a time discount.
Transfer is part of the mechanics. The exhaust plus growth plus gift are the aims, in
whatever proportion we like, and our subliminal deeper motive of lineage survival
is the ends.
Chapter 3: Foundations 1/11/16 15
Subjective Certitude
Tautologies or truisms are logical certitudes. My three fundamental theorems are
cases in point. The total return truism is a classical example. Since growth is
creation less net outflow, creation is growth plus net outflow. This gives unqualified
certitude to the doctrine that output, or creation of value, is growth of value plus
cash flow (net outflow of value).
The other two fundamental theorems are certitudes in a subjective sense. What they
predict infallibly is intentions. The present value rule must give capital value as we
see it individually. Only under the convergence axioms does it predict observed
market equilibria. The same is true of the maximand rule. This rested on the same
axioms and the one that a population acts to satisfy tastes (in the sense of aims).
There are schools of thought, including Popperians and deconstructionists, which
disapprove of logical certitude on grounds not clear to me. They are wrong. A rose is
a rose. Nor are all examples as inane as that one from Gertrude Stein. All of math is
derived as logical certitude. Its proof comes from analysis, not experiment. Proof of
Fermat’s last theorem eluded some of the finest minds in the world for three
centuries until Andrew Wiles published the solution in 1995. Philosophy is precisely
a search for hidden truisms or tautologies. Economics is philosophy when it does
the same. The pay rule shows that their inferences can be startling. Age-wage
profiles are technically illustration, not proof, of the proposition that human
depreciation is expected to be recovered in pay. That follows from definitions and
needs no evidence in proof.
The pay rule is not wholly logical certitude because it also proposes that
maintenance consumption is not recovered in pay. Rather I argue that from the
biological imperative: maintenance is exhausted in satisfying our taste for adult
survival. The fact that few can have doubted this since the physiocrats has nothing
to do with proof. The shock, anyhow, is in the expected recovery of human
Chapter 3: Foundations 1/11/16 16
depreciation. This opened a can worms. It contradicts the Y = C + I equation, and the
related belief that output equals profit plus pay. I will try to track down some of the
worms, as I promised, and release new ones in the process if I must.
This book will continue to hunt for certitude, absolute when possible and subjective
otherwise. If the convergence axioms are trustworthy, behavior will reveal aims
well enough.
Output Exhaust
I define output as creation of value, and equivalently of capital. Does this overlook
the possibility that output might also create taste-satisfying pure consumption
directly, without passing through a capital phase first?
Such a thing is possible in math, but not in economics. Since capital is foreseen
eventual exhaust, exhaust not drawn from capital in place would be implicitly
unforeseen. This is the flip side of the deadweight loss rule. Economics is a rationale
of choices, and neglects unforeseen taste satisfaction as unable to influences choices.
Those unforeseen and hence costless satisfactions are called “free goods”, and
ignored as outside the economic purview. They why not ignore free growth too?
Growth is roughly foreseen and factored into choices, for one thing, even if I am the
first since Mill to foresee it as free. For another, even unforeseen events are of
economic interest if they affect means or choices after. Free growth does. Costless
satisfactions leave no trace.
Note in any case that the total return truism (3.2) through (3.3b) does not depend
on this inference. Those equations describe creation of value, not necessarily of
capital alone. Output exhaust would be added both to output and to exhaust, and
would disappear in their difference.
Chapter 3: Foundations 1/11/16 17
Basic Glossary
I use standard terms when I can find them, and coin new ones like “aims” and “ends”
when I can’t. But even standard ones are ambiguous. The vocabulary of economics is
not settled. Look up “capital” or “output” or “cash flow”, for example, in any
economic dictionary. It will show ranges of meanings, and appreciably different
ones from one dictionary to the next. I coped by defining as I went along, and would
have had to do the same even if this book were meant for economists only.
Otherwise the ambiguities would have left loopholes.
Definitions include:
Aims:
Capital:
Cash flow:
Ends:
Exhaust:
Flow:
Human capital:
Income:
Invested consumption:
Maximand rule:
Net transfer:
Intention to maximize the sum of current taste
satisfactions plus gift, plus growth in means of future
satisfactions and gift.
Means of aims; human plus physical capital; present
value of expected cash flows.
Capital passed out, in transfer or exhaust, less capital
inserted from outside.
Rationale of aims; biological imperative.
Termination of capital in taste satisfaction.
Any process measured in capital per unit time.
Present value of skill sets; capital whose outside
operating cost is exhausted in taste satisfaction; present
value of pay less invested consumption; present cost of
past invested consumption less pay.
Rights to output; equal to output.
Transfer into value of human capital.
All behavior is maximization of perceived risk-adjusted
output and return as a flow and a rate respectively.
Transfer out less transfer in.
Chapter 3: Foundations 1/11/16 18
Output:
Physical capital:
Present value rule:
Profit:
Pure consumption:
Rate:
Stock:
Tastes:
Total return rule (or total
return truism):
Transfer in:
Creation of wealth, or equivalently of capital of either
factor.
Capital whose outside operating cost does not satisfy
tastes.
Capital of either value is expected cash flow discounted
at our time preference rate.
Output of physical capital.
Same as exhaust.
Quantity measured as a flow over a stock, and
equivalently as a pure number over time.
Quantity measured in dollars alone. Same as capital.
Intentions whose satisfaction terminates capital in
exhaust.
Output equals capital growth plus cash flow.
Value inserted from outside. Same as new investment
from outside.
Transfer out:
Wage:
Work:
Value passed out and recovered fully in other assets
rather than exhausted.
Same as pay.
Output of human capital.
Summary
When I first thought these foundations through, maybe 25 years ago, I was just as
happy to see that they held so little originality. The vocabulary is about the same as
in Adam Smith, and the three fundamental theorems are well accepted. Any
composer knows that originality should be incidental. Our music says what we think
Chapter 3: Foundations 1/11/16 19
needs saying. If it does, that tends to mean that it is new to the current conversation.
It need not be new to the world.
All three fundamental theorems are part of the daily conversation of investors and
finance economists. They are not much on the screens of microeconomists and
macroeconomists. There may have been some originality in spelling out the implicit
axioms behind them, and in generalizing them into all capital including human
capital if we trust those axioms.
One of the mini-surprises was that gift appeared in my very first equation. Cash flow
at the scale of the total capital of the individual, where reinvestment cancels out,
simplifies to gift and exhaust alone. Obvious in hindsight, but surprising if we have
been taught that economics is all about numero uno. I think it is about adults giving
to the young to keep the generations turning.
That sets the theme of this book. Old ideas will find unfamiliar combinations and
applications. Those are originality enough. But so many little stretches of the tried
and true can be hard to track.
Economics needs a special and counterintuitive mindset. The guiding principle is the
analysis of the diamond ring. Economics means taking our minds off the physical
substrate. That goes to the corners of our eyes, not the focus. Capital is not people
and things. It is present value of foreseen cash flows. Output is the ripening of these
foreseen flows with time, and exhaust is the harvest eventually reaped. Economics
takes us through the looking glass to a place the same but different.
Chapter 3: Foundations 1/11/16 20
CHAPTER 4: MILL’S IDEA
Mill’s Paragraph
It always seemed obvious to me that growth is free. Survival costs investment in the
next generation, but growth costs nothing more. It seemed to me that innovation is
the human specialty, that we pay its cost every day as the cost of being human, and
that growth happens when genius or circumstance somehow gives it traction. I
spent most of my life assuming that all economists, but not politicians, thought the
same. I since learned that economists, following Solow, teach something close but
different. So I guessed that I had hit on something new.
I hadn’t. We read economic history to learn that our ideas are seldom original.
Thomas Malthus, contradicting his friend and rival David Ricardo, wrote something
like my or Mill’s free growth theory in 1820. Chapter 7 of his Principles 1 says this in
several ways. One example is
“When we have attained…increased and steady profits, we may then begin to
accumulate, and our accumulation will then be effectual. But if, instead of
saving from increased profits, we save from diminished expenditure; if, at the
very time that supply of commodities compared with the demand for them,
clearly admonishes us that the proportion of capital to revenue is already too
great, we go on saving to add still further of our capital, all general principles
concur in showing that we must of necessity be aggravating instead of
alleviating our distresses.”
John Rae renewed this theme in 1834. Book 1, Chapter 10 of his New Principles 2
includes
“If an improvement, for instance, in the art of baking bread were effected, by
which, with half the labor and fuel, equally good bread could be produced, it
would not benefit the bakers exclusively, but would be felt equally over the
whole society. The bakers would have a small additional profit, the whole
society would have bread for the product of somewhat less labor, and all who
1 Principles of Political Economy Considered with a View to their Practical Applications
2 Statement of some New Principles on the Subject of Political Economy
Chapter 4 Mill’s Idea 1/11/16 1
consumed bread, that is, every member of society, would from the same
outlay have somewhat larger returns. The whole series of instruments
owned by the society would be somewhat more productive, and would be
carried to an order of quicker returns.”
The clearest expression, and probably clearest even today, came from Mill in 1848.
He put it that output growth can precede and explain capital growth as well as the
reverse. Crediting Rae, he wrote:
There are other cases in which the term saving, with the associations usually
belonging to it, does not exactly fit the operation by which capital is
increased. If it were said, for instance, that the only way to accelerate the
increase of capital is by increase of saving, the idea would probably be
suggested of greater abstinence, and increased privation. But it is obvious
that whatever increases the productive power of labor creates an additional
fund to make savings from, and enables capital to be enlarged not only
without additional privation, but concurrently with an increase of personal
consumption. Nevertheless, there is here an increase of saving, in the
scientific sense. Though there is more consumed, there is also more spared.
There is a greater excess of production over consumption. It is consistent
with correctness to call this a greater saving. Though the term is not
unobjectionable, there is no other which is not liable to as great objections.
To consume less than is produced, is saving; and that is the process by which
capital is increased; not necessarily by consuming less, absolutely. We must
not allow ourselves to be so much the slaves of words, as to be unable to use
the word saving in this sense, without being in danger of forgetting that to
increase capital there is another way besides consuming less, namely, to
produce more.
The words “accelerate” and “concurrently” show that Mill understood calculus. His
autobiography says that he hadn’t really learned it from his father James, who had
bought a book and was trying to teach himself and the 13-year old son at the same
time. The son studied it in his later teens at school in France. He like me was writing
for everyone, and preferred to keep explicit math off the page. But the quote
reminds us that the only alternative in economics is implicit math in sentence form.
The paragraph implies the Y = C + I equation: output equals consumption plus
investment. I go a tad farther, starting one chapter ago, by offsetting my word
equations from the running text. These show equal signs and plus and minus and
Chapter 4 Mill’s Idea 1/11/16 2
division and multiplication signs, rather than keeping them inside the paragraph
and writing out such words as “equals” and “plus”. These word equations are
usually easy enough to read. My appendix will cover them and more in notation.
Mill’s equation may be as old as economics, although I haven’t found it put explicitly
before Keynes wrote it in his General Theory 1936. It is now foundational to national
accounts and macroeconomics (the art of balancing full employment with price
stability). I showed why I agree only if we add a couple of imaginary asterisks. We
have to mean total capital growth and pure consumption. Mill and tradition have
meant physical capital and all consumption.
That leaves me with something like the heuristic problem of Halliday and Resnick.
They started with Newton as something familiar and accessible and commonsensical.
I will follow suit. I will reason as if Mill’s equation were right. My own
argument is exactly the same if we remember the hidden asterisks. That saves us all
the trouble of going through it twice. Chapter 4 will restate it in terms of total
including human capital just to make sure.
It is an unsettling argument either way. It unsettled Solow. Chapter 2 showed why.
We are probably more comfortable to think of income as something known which
we can slice into consumption and saving slices as we like. Less of one would mean
that much more of the other. That would put us in charge. We can always consume
less by will power. If less consumption meant more growth, we could grow at will.
Keynes showed otherwise by invoking the old paradox of thrift. If everyone put
money in vaults instead of consuming, consumption would go down while money
piled up. But the added money would find less output to buy with it, as nothing new
was created to compensate for the drop in consumption. The value of the piled-up
money would vanish in inflation. Saving would equal investment in the end because
both disappeared. The Y = C + I equation shows the math. It say that less
Chapter 4 Mill’s Idea 1/11/16 3
consumption C means either more investment I or less output Y. It doesn’t say
which happens.
Investment, for Keynes, meant creation of new productive assets. He was right in
seeing that as the goal. But his analysis leaves too much outside. What I miss is a
variable for investment quality. Investments in new productive assets in 1929 or
2008 yielded negative return. Money in vaults did better.
I prefer an approach which takes our minds off the ultimate goal in new productive
assets. I drop all distinctions between saving and investment. Either word means
the other. What matters is its intended and realized return. That is the missing
quality variable. Notice that I don’t have to specify “risk-adjusted” return because
Keynes and I are describing only at the collective (national) scale. Risk of all
investments collectively is average risk. This can be implicit whenever I describe at
the collective scale.
Keynes’ analysis and equations appear in his General Theory. He was addressing the
world depression. A theme was that households do most saving, while businesses do
most investing. Banks collected the saving and made it available for business to
borrow and invest. But business lacked the “animal spirits” to take such a risk in a
slump. We saw the same story after 2008. Keynes’ proposal was for government to
do the borrowing and investing instead. That’s part of the “fiscal policy” I described
in Chapter 1. Here we tend to agree. That would explain his sense of urgency as to
new productive capital as the most direct way to put idle plant and workers back to
work.
I prefer to suspend judgment on what is a new productive asset and what isn’t. I
think my way of putting things is both simpler and subtler than Keynes’, although at
sacrifice of his explicit focus. Saving and investment, in my language, are the same
from the start. The maximand is return. Consumption foregone will translate into
Chapter 4 Mill’s Idea 1/11/16 4
capital growth insofar as rate of return actually realized matches the current norm.
Less return makes less growth than consumption sacrificed, and more makes more.
But collective return can be a surprise. Boom years and bust years arrive unforeseen.
The cost of investment in consumption given up, whether individually or collectively,
never agrees exactly with what it proves to be worth at market. Gunnar Myrdal, in
1939, coined the terms ex ante for the first and ex post for the second. The bucking
bronco describes the ex post picture overall.
Ex ante (at cost) and ex post (at market) investment agree when market-realized
return holds unchanged. Lower return means that ex post outcomes fell short of ex
ante cost and expectations. Higher return means the reverse. That gives the context
of Mill’s idea. And he clearly isn’t talking about growing or declining by random luck.
His prime mover is “whatever increase the productive power of labor.” He knew
that this meant innovative ideas. Can we dial them in as we like? All he says is that
they need cost nothing in consumption missed. Then how might that work?
Gross and Net Investment
Keynes, accepting the Y = I + C equation, defined saving S as gross income less
consumption C. I draw the impression that he implicitly defined output as creation
of economic value. So do I. He defined gross investment I as gross output less
consumption. Gross in both cases meant gross of depreciation. He knew that income
and output are equal, at all scales, since the first means rights to the second, and
gave both the symbol Y as I do. It followed that saving and investment are also
equal. The meaning was that actually realized saving, as distinct from consumption
restraint in hopes of saving, had to be realized in investment. This is the home truth
which I accept but prefer to rephrase.
I have traced Keynes’ argument and language on these points because I think it is
now generally accepted by Keynesian and anti-Keynesian and neo-Keynesian
schools alike. That’s why I think my own interpretation differs from a general
Chapter 4 Mill’s Idea 1/11/16 5
consensus rather than supports one school over another. I think it is the consensus
view, as well as Keynes’, that his “attempted saving” means gross saving (gross
income less consumption) not invested in new productive assets. That can be
written as
Keynesian attempted saving – transfer payments
= Keynesian net saving = Keynesian net investment,
at any scale.
I accept Keynes’ definition of transfer payments, and I recognize the importance of
his distinction of those from investment in new productive assets which put idle
plant and workers to work. My interpretation, even so, is that it is better to leave
them idle than to put them to work unproductively. Keynes made his opposite view
crystal-clear with his brilliant tongue-in-cheek parable of money buried in
mineshafts and idle workers hired to dig it up. He had a sense of theater as well as a
great mind. And he just might have been right. But I think my way of putting things
encompasses that possibility. His mineshaft scenario works if it somehow
maximizes return in the big picture.
My language differs from Keynes’ in several ways. I prefer Myrdal’s ex ante – ex post
dichotomy, published three years after the General Theory, to Keynes’ equivalent
attempted-realized one. Like Myrdal, and unlike Keynes, I apply it to investment as
well as saving. That’s why I treat them as synonymous. And I prefer to recognize
human capital explicitly. Keynes surely understood the concept. He was the star
pupil of Alfred Marshall’s later teaching career, unless he shared that distinction
with his lifelong personal friend and professional adversary Arthur Pigou, and
Marshall and Pigou both describe human capital in principle. Marshall wrote that he
neglected it as something outside what he saw as the main sequence ending with
consumption. Keynes could have agreed, or could have meant to provide for it
implicitly by defining output as investment plus consumption while realizing that
Chapter 4 Mill’s Idea 1/11/16 6
some consumption is investment in human capital. I said what I think this overlooks
(self-invested work) and what it forgets to exclude (recovered human depreciation).
My own way of putting things mightn’t strictly need the terms investment or saving
except to translate my ideas into the language we all know. That translation is
essential if I hope to be understood. It will first take account of the fact that Keynes
meant investment and saving as to physical capital only, with labor or human capital
to arrive exogenously as an outcome somehow of consumption. That led to the
Y = I + C equation
output = investment + consumption. (4.1)
Gross and net versions of (4.1) meant gross and net of depreciation. Thus
gross output = gross investment + consumption
(4.1a)
and
net output = net investment + consumption.
(4.1b)
In the General Theory, where (4.1) appears in his Chapter 6, (4.1) it means the gross
version unless otherwise specified. I prefer the opposite, and mean the net version
(4.1b) unless otherwise specified.
My ex ante investment corresponds to Keynes’ “intended saving” through
consumption restraint. My “depreciation investment”, or “depreciation plowback”,
means just enough ex ante investment to offset actual depreciation, not book
depreciation, of physical capital. I assume that we intuit roughly how much this is
when I say that optimum ex ante investment is depreciation plowback. Now let’s
consider how that could be true.
Chapter 4 Mill’s Idea 1/11/16 7
Growth Mechanics
Start with simplicity. Imagine a changeless world where people and things replicate
themselves exactly. Chapter 3 showed that in total capital terms including human
capital, although neither Mill nor Keynes used them, depreciation of both factors
together, net of transfers from one to the other, equals exhaust in taste satisfaction.
“Replacement investment,” or “depreciation investment,” is just enough to turn the
generations over as new (net) output makes up the loss to consumption exactly.
Ideas hold unchanged. That wouldn’t be too far from the truth for our million years
as homo erectus, or our millennia after as homo sapiens until some 50,000 years ago,
or our centuries in the dark ages after Rome fell. Most of the new norms we
innovated, although not all, eventually regressed to the old ones.
Next imagine growth of everything at a constant rate. Capital, consumption and
output all grow in constant proportion. Economists now call this “balanced” growth.
Mill had described that possibility in 1844. Balanced growth isn’t driven by
consumption restraint, as consumption never lags. And it isn’t driven by
productivity gain, meaning more output per unit capital, since output grows no
faster. What drives it?
Suppose first that there are still no new ideas. If we are pioneers in a new world or
empty niche, we might be able to increase numbers of exactly the same things and
skill sets until we reach niche limits. Then what would pay for capital growth in that
case? Zeno the Eleatic might insist that depreciation investment is never enough
because it chases a moving target. But depreciation moves just as fast. Identical
capital means identical in depreciation rates. That means the ratio of depreciation
(pure consumption) to capital. The two racers hold neck and neck indefinitely.
Depreciation investment is still enough, just as it was in the growthlessness before.
In balanced growth, as in standing still, it is the only need for of capital replacement.
Now comes a tougher problem. Niches in the real world are typically more or less
full. Here old ideas alone can’t bring growth. David Ricardo, Thomas Malthus and
Chapter 4 Mill’s Idea 1/11/16 8
Edward West had written in 1815 that in economies already developed, there isn’t
much room for more capital of the same kind. Its productivity disappears in capital
glut and diminishing returns. There could still be growth when some of the new
ideas would need only redeployment of existing kinds of capital, as in relocating
production nearer to the market or cutting out the middleman. This redeployment
was Solow’s “disembodied growth.” But growth after that have to come from capital
new in kind. Hourglasses might have to give place to pocket watches, or sailing ships
to steamships. Those were Solow’s “embodied” growth.
The apparent problem here is that novelty is expensive. There are blind alleys and
failure rates and learning curves that rote replication avoids. This is true somewhat
even in disembodied growth, where redeployment is already a step into the
unfamiliar. If depreciation investment is barely enough for balanced growth without
new ideas, how can it also pay for the failure rates and learning curves?
A tough question. And Mill was posing an even tougher one. The paragraph quoted
is clearly describing capital acceleration. Capital as he describes it is not only
innovating consistently as it keeps up with consumption, but picking up the pace,
and still taking the innovation costs in stride. Is that too much even for Achilles?
It is not. Charts and tables show that the kind of growth Mill describes has proved
the only kind in every country and period where tests are practical. It has proved
the only kind whether capital was growing faster or shrinking faster or anything
between. The growth bronco bucks, and the consumption rider stays on. This is
what clearly happens, or anyhow has happened so far, despite so many reasons to
think it is impossible. What would explain it?
First take the lesser puzzle. Balanced growth, where capital, output and
consumption all grow at the same constant rate, must make do with depreciation
investment. How can it in crowded niches where growth compels the costs of
innovation? Chapter 2 showed my inference that these are the costs of being human.
Chapter 4 Mill’s Idea 1/11/16 9
We were paying them as homo habilis two million years ago. The cost went up, but
the value of innovation just as much, when homo erectus arrived a little later. Both
rose again with the emergence of Ancestral Eve 200,000 years ago. Adaptation is the
human specialty. Its what gets us through the day. Innovation is adaptation that
happens to become new norms. It started leaving a record of embodied growth
about 50,000 years ago. That doubled pace about 400 years ago. The costs of being
human are the same failure rates and learning curves whether the payoff in
adaptation/innovation means faster gain in good times or slower decline in bad
ones. We row at a steady stroke, and gain against the shoreline when our new ideas
are particularly good ones and the current is right.
My idea, whether or not Mill’s, is that these costs might be about the same for
breakthroughs or meta-ideas or paradigm shifts as for modest upgrades, or even for
holding even in a world of daily surprises. Ideas trade in an inefficient market. Cost
is dissociated from value, and cause is desynchronized from effect, by the vagaries of
genius and the whim of circumstance.
Now the tougher puzzle. How can consumption keep up with capital even in
accelerations? That’s what Mill described, and that’s what happens. Can Achilles
catch the tortoise even when the tortoise speeds up? Put your money on Achilles.
Here it is Gunnar Myradal to the rescue. The apparent problem is that ex ante
depreciation investment is never enough in acceleration. But the charts and tables
show unanswerably that ex post depreciation investment is. We sow the first, but
reap the second. Plowback of depreciation investment is up to us. Growth is
whatever is added by genius or happenstance. The difference between market value
and cost is sometimes luck, which neither loses nor gains in the long run, but
sometimes imagination. Mother Nature and Gunnar Myrdal simultaneously say
“Shazam”, and convert new ideas into embodied or disembodied growth without
surcharge for the novelty.
Chapter 4 Mill’s Idea 1/11/16 10
That still leaves the mystery only half solved. How exogenous (sourced from
outside) are the genius and happenstance? Can we coax them along by policy? That
isn’t really my field. What seems reasonably clear is that growth flourishes in
secular free markets with solid infrastructure and rule of law. How to get those
things is the problem. I will suggest that the answers, whatever they are, will be
developed outside the usual marginalist perspective of supply and demand.
The Free Growth Equations
Now back to Mill’s argument. Notice first that he puts it all in the present tense.
Modern growth economists have preferred what I called the lagged flows method:
spikes in investment are compared to later ones in output. Mill here is substituting
what I called a concurrent rates method: he compares changes in consumption rate
to changes in capital growth rate at the same time. He writes that “whatever
increases the productive power of labor … enables capital to be enlarged …
concurrently with an increase of personal consumption.”
Let’s follow that. Mill’s root assumption is the Y = I + C equation in its net form
(4.1b). Put the ex post version as
output = growth + consumption, (4.2)
meaning net output, growth of physical capital and all consumption. The Y rule says
the same with the hidden asterisks after growth and consumption. So it will
continue for the rest of this discussion. (4.2) shows that less consumption implies
more growth, or less output, or some of both. Mill was asking which. To show how
to find out, first arrange (4.2) as
growth = output – consumption,
(4.2a)
again because terms can change sides if they change signs.
Chapter 4 Mill’s Idea 1/11/16 11
Mill and Keynes and tradition hold (4.2) and (4.2a) as logical certitudes which hold
constant over time. I agree if we imagine the asterisks. Constancy over time would
imply
change in growth = change in output – change in consumption. (4.3)
I take the trouble to derive this as a road I haven’t preferred to follow. I will reason
instead in rates rather than flows. Rates, or ratios of flows to capital, effectively
cancel capital from numerator and denominator. That frees them to show
comparison between smaller and larger economies among the eight I test. Mill’s idea,
or anyhow mine, is that the ratio of consumption to capital in all those countries can
hold constant. That is what the charts and tables show.
To follow that lead, divide (4.2a) by capital. This finds
growth
capital
= output
capital – consumption . (4.4)
capital
That can be put more compactly as
growth rate = capital productivity – consumption rate,
(4.4a)
where rate always means ratio to capital. That needs a caveat because consumption
rate in macro means ratio to output. Capital productivity in this sense is also called
rate of return.
For more compactness still, define
thrift rate = – consumption rate,
allowing (4.4a) to be restated as
Chapter 4 Mill’s Idea 1/11/16 12
growth rate = capital productivity + thrift rate.
(4.4b)
Notice that we must change the sign before “consumption rate” to find thrift. Change
downward in consumption rate is change upward in thrift rate, and conversely.
Further
change in growth rate = change in capital productivity
– change in consumption rate, (4.5)
by the same logic as with (4.3). Save space again by reexpressing (4.5) as
acceleration = productivity gain + thrift gain.
(4.5a)
Finally divide by acceleration to reach
1 =
productivity gain
acceleration
+
thrift gain
acceleration , (4.6)
if acceleration is nonzero. Reexpress as
1 = free growth index + thrift index, (4.6a)
where indexes are undefined if acceleration is zero.
I think this gets at what Mill meant, and anyhow what I mean. We both describe
acceleration as well as growth. One night think that his “whatever increases the
productive power of labor” is the opposite from my “change in capital productivity.”
But they are about the same. Better machines make their operators more productive
whether skills have changed or not.
Chapter 4 Mill’s Idea 1/11/16 13
(4.5) shows something about “balance” or the state where capital, consumption and
output grow at the same rate. It confirms the standard teaching that balance is
possible, although not compelled, when growth rate is constant. It also shows that
balance is impossible when growth rate changes. No one disputes that capital
productivity (output/capital) always leads, and consumption rate
(consumption/capital) always lags, in accelerations up and down. Output gets the
bad news first and the good news first. What the equations leave unspecified is
where capital itself joins the sequence. That is what the evidence in the charts and
tables tells us.
In the case where the free growth index equals one, for example, the above
equations show
thrift index =
thrift gain
acceleration = 0,
implying
– change in consumption rate
thrift gain = change in growth rate = 0, and
change in consumption rate = 0, or equivalently
consumption rate = consumption
capital
= constant, (4.7)
if acceleration is non-zero. (The reason for that qualifier is that zero acceleration
means zero change in growth rate, and division by zero is a no-no.)
In the opposite case where the thrift index is one, the same equations would show
free growth index =
productivity gain
acceleration
=
changein productivty rate
change in growth rate
= 0,
Chapter 4 Mill’s Idea 1/11/16 14
implying
productivity rate = output
capital = constant,
(4.7a)
assuming again that acceleration is nonzero.
This shows how to find the position of capital in the sequence led by output, and
how to test between free growth and thrift theories. The market-valued capital
denominator in (4.7) and (4.7a), and the consumption numerator in (4.7), can be
taken directly from national accounts data collected at the Piketty-Zucman website.
The output numerator in (4.7a) can be constructed as consumption plus current
change in market-valued capital. By (4.7), free growth theory (Mill’s idea) predicts a
roughly constant consumption/capital ratio, even in accelerations and decelerations
and reversals. Then capital acceleration would lag alongside consumption
acceleration while output led alone. Thrift theory makes the opposite prediction of a
roughly constant output/capital ratio, so that output and capital would lead
together while consumption lagged alone. There is no need to measure and test both
indexes, as either is defined as one less the other. My charts and tables track the free
growth index. They confirm free growth theory in all countries and periods.
Defining Free Growth and Thrift
(4.2) through (4.7a) defined the free growth and thrift indexes, but not free growth
or thrift themselves as flows. Since I will use those terms often, I’d better clear that
up now. Define
free acceleration = productivity gain = gain in rate of return,
thrift acceleration = thrift gain = drop in cash flow rate,
and
so that those sets of terms become interchangeable. Then (4.5a) can be put as
Chapter 4 Mill’s Idea 1/11/16 15
acceleration = free acceleration + thrift acceleration.
(4.5b)
Rates are flows divided by capital expressing them. Then define the two flows as
free growth = capital ∗ free acceleration, and (4.8)
thrift = capital ∗ thrift acceleration, giving (4.9)
growth = free growth + thrift. (4.10)
These equations apply equally in continuous or discrete-period time. In the latter,
they leave the periods of acceleration and growth unspecified. Marginal or current
free growth, as with the speed of a car, is the sum of free accelerations since some
past origin when growth was zero. So it is with current thrift. That need not place
the origin with Ancestral Eve. Surprising as it might seem in the growth age, zero
points appear to recur every few minutes at the longest. Online stock index numbers
reverse direction at least that often. They pass through zero each time. Debt claims
on the corporate sector figure to be less volatile, but equity (stock) ones outweigh
them. Then marginal free growth means accumulated free acceleration, or rise in
rate of return, since the last zero growth point no more than a few minutes ago
when return and cash flow were equal. Growth is free whenever cash flow rate rises
or holds steady.
The Charts and Tables
Mill lacked data to test whether growth tends to lead with output when it changes,
or to lag with consumption, or something else. So did all economists until national
accounts began reporting market-valued capital in 1990 or so, and reconstructing it
backward over a few decades before. The equations through (4.7) show how to test
from data in the Piketty-Zucman and Global Financial Data websites.
First I downloaded the Piketty-Zucman data for market-valued capital and
consumption for all countries and periods. I chose their “private wealth” data for the
Chapter 4 Mill’s Idea 1/11/16 16
former. I neglected “government wealth” net of national debt, which is small and
often negative, as I don’t feel that I understand it well enough. I took consumption as
the sum of personal consumption expenditure (PCE) and government consumption
expenditure (GCE). I also downloaded real stock market rates of growth, dividends
and return from the Global Financial Data website for the same years and countries.
Yearly change in capital in each country gave each year’s capital growth as a flow. I
added this to consumption to give what I call market-valued output. I said earlier
that Piketty and Zucman should logically have done the same. This gave the values
for (4.1) and (4.1a).
I then divided by year-end capital to give values for (4.3). I next found annual
changes in those three to give acceleration, productivity gain and thrift gain as
shown in (4.5) and (4.5a), and divided by acceleration to find the two indexes of
(4.6) and (4.6a).
The test from Global Financial Data took fewer steps. Stock market growth rate, rate
of return and dividend rate were downloaded directly. I took them as corresponding
respectively to growth rate, capital productivity and consumption rate in (3.3a). I
found their annual changes to find values for (3.4a), and again divided by
acceleration to reach (3.5a).
This allows tests of Mill’s idea from national accounts data for all eight nations
reported at the Piketty-Zucman website, and over their entire reporting periods
through 2010. (The website also reports for Spain, but only since 1993 and without
data for consumption.) In each year, for each country, change in capital growth rate
is compared to change in consumption rate (consumption/capital). If consumption
rate grows faster than capital growth rate while both grow, or declines faster if both
decline, the free growth index in that year is greater than one. If they change at the
same rate in the same direction it is one exactly. If both change in the same direction,
but consumption changes less, the free growth index is between zero and one. If
Chapter 4 Mill’s Idea 1/11/16 17
either grows while the other declines, the index is zero or less; zero if one grew as
much as the other declined, and less if the change in capital growth rate was larger
than the opposite one in consumption rate.
Interpreting the Charts and Tables
Now look again at the charts captioned “free growth index” in the appendix. I will
summarize them and all other charts and tables only briefly here, and save most
description for there. They cover all eight countries. Each chart covering free growth
tracks three separate versions of the free growth index labeled !
ϕ(K), !
ϕ(K T
) and
! ϕ(SM). The one I have discussed so far is ! ϕ(K). ! ϕ(K ) is a version including human
T
capital, and !
ϕ(SM)is taken from stock markets only. will be explained in the
! ϕ(K ) T
next chapter.
The powerful spikes both up and down in the free growth charts were described in
Chapter 2. Spikes tend to be explained by the fact that acceleration, the denominator
in both the free growth and the thrift index, is occasionally close to zero. Near-zero
denominators, whether above zero or below, can magnify mismeasurements. Some
charts report the free growth index every year, and show all the spikes. Others filter
out years where denominators fall below a chosen threshold, and spikes disappear
accordingly. Filtration is unbiased in that free growth index is corrected down as
often as up.
What jumps out from all those charts is that all versions of the free growth index ϕ
fluctuate around one. That means that the unshown thrift index fluctuates around
zero. We just saw that the thrift index will show as negative whenever the thrift
numerator and acceleration denominator disagree in sign, meaning that thrift gain
coincided with deceleration (negative acceleration) or conversely. Charts and tables
show that thrift gain, meaning drop in consumption rate, coincides as often with a
lower as a higher capital growth rate. Growth by thrift is a theoretical possibility
Chapter 4 Mill’s Idea 1/11/16 18
which doesn’t actually happen. The means of growth Mill describes in the paragraph
quoted is the only kind that appears in the record.
Evidence from Stock Markets
Market-valued capital, reported in national accounts since 1990 or so and
assembled at the convenient Piketty-Zucman website, is measured by a common
standard in principle. Measurement begins with stock markets. It should. The stock
market is the most exact source of economic information that I know. With due
reservations about connivance and “stale prices,” meaning outdated prices from
earlier days because the stock has not traded since, or anyhow not enough for
confidence, we know pretty well what markets think stocks are worth from tick to
tick.
We would know better if markets were perfectly efficient. Proof that they aren’t
shows in medium-term autocorrelation or trend. Autocorrelation (in price) is
tendency for markets to be up tomorrow if up today, and down if down. Trend is a
shorter word for the same. Perfect efficiency ought to show a “random walk” where
prices change captures all current news, news captures reality without optimistic or
pessimistic bias, and tomorrow’s price direction is as unpredictable as tomorrow’s
news. The only exception should be long-term uptrend with productivity gain
through innovation. In this case it is not surprise in the news that brings growth, but
gradual gain in present value as a foreseen better future is less discounted as it
draws nearer.
There is chicanery as well as inefficiency. Insiders, braving the legal risks, may take
advantage of outsiders. But it is not clear to me that insiders are likelier to be sellers
than buyers. National accounts follow prices of publicly traded shares collectively,
where some chicaneries should offset others.
Allowing for all this, I think national accounts are wise to accept stock prices as the
best measure of underlying assets. Intangibles such as patents or market advantages
Chapter 4 Mill’s Idea 1/11/16 19
are factored into share prices because they are realities that would be valued as
such by bidders for the assets themselves. It is a mistake, I think, to suppose that