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Chapter 7 Petty’s Idea 2/3/16 2
I confess that this book casts me as that little boy crashing the economic party, and
maybe the evolutionary biology one too, in trust that outsiders might have better
chances to spot the obvious unseen. What else was the pay rule? I derived it easily
from doctrines already accepted, I think, and anyhow hard to refute. Those were the
total return turism and Ben-Porath’s equation for human growth. The maximand
rule or deadweight loss rule would prove it as well. How could Becker have missed
that what holds for investment in job training by employers holds for any
investment by anyone in anything? How could students of the age-wage problem
have missed the obvious solution? Investment implies expected recovery with
interest, by the investor or a chosen donee, and recovery means recovery of
depreciation. I belabor this point because tradition dies hard, and naturally tends to
circle wagons under attack. I doubt that my surprise attack will meet the resistance
Darwin’s found. Darwin’s met resistance founded on faith. I took pains to show that
my version requires only selection for lineage survival, and that a benign Artificer
might ordain the same.
Evolutionary Biology and Hamilton’s Rule
Economics, meaning any quantitative rationale of choice, normally describes
humans and human choice. That goes for this book too. But some treatments of
economics including this one are meant to fit other creatures as well. My axioms
have kept that in mind. The mortal and reproducing population need not be human.
Much of the animal kingdom, I think, shows convergent tastes and predictions or
acts as if it did. The biological imperative is meant to apply to all. All, as I see it, own
capital of both factors. Even protozoans own (“monopolize”) the nutrients they
assimilate and the space they occupy. Humans are exceptional in their cultural
accumulations of learning and technology shown in our secular (lasting) growth.
But I did not make those features axioms.
I argued that economics tended to reason explicitly or implicitly from the biological
imperative, meaning what I call “ends” in lineage survival, from Petty through Smith
Chapter 7 Petty’s Idea 2/3/16 3
and Ricardo and Malthus and Mill, until the marginalist revolution shifted focus
from objectives to the mechanics in supply, demand and price. Bioeconomics awoke
a century later, largely it seems in response to the challenge of Hamilton’s rule. Now
I will look at it too.
My term “lineage survival” is unusual. It is meant not to take sides between “kin
selection” and “group selection.” The kin selection idea was another word for
Hamilton’s rule from his doctorial thesis in 1964. It said that genes encoding
investment in close kin encode investment in likeliest sharers of those genes, and
should tend to entrench and perpetuate themselves. His condition for investment
was r 〉 bc . r here meant relatedness: ½ for offspring or siblings, ¼ for nephews or
nieces or grandoffspring, and so forth. b meant benefit to the donee, and c meant
cost to the investor. The sign > means “greater than”. The cost and benefit were
measured in fitness itself, meaning chances to survive and breed. But that too meant
“inclusive fitness” where investing in kin counted as breeding when adjusted for
relatedness. The idea was that I give up some of my chances if I can increase yours
to my net genic advantage in the long run. Hamilton allowed for exceptions
including meiotic drive, which sometimes forecloses gene competition. His rule
prevailed because it made mostly good predictions. Humans and creatures in
general usually care for their own young first, if they have any, and for closely
related young if not.
Hamilton made it clear that cost c and benefit b in his hurdle rb > c respectively
meant fitness given up by the investor and fitness grained by the investee. He
further made it clear that fitness could be measured as R. A. Fisher’s “reproductive
value” V(x) published in 1930 and 1957. V(x) meant likelihood at age x of
reaching each successive age times expected offspring at that age. V(x), or Bob
Trivers’ “reproductive success” RS, which simplifies V(x) to expected remaining
offspring, is implicitly constant at the population scale unless there is population
growth (Fisher’s “Malthusian parameter”). For creatures other than us, the
Chapter 7 Petty’s Idea 2/3/16 4
parameter typically fluctuates around zero and group fitness holds about where it
started.
Hamilton’s rule, applied to diploids like us where closest relatedness r absent
inbreeding is ½, forbids investment where fitness gained (benefit) is less than twice
fitness given up (cost). I see no escape from the inference that fitness would double
with each generation, or more to account for cases where relatedness fell below ½. I
see no relief in an interpretation, say, that each successive generation cures this
imbalance by investing only half or less of its fitness and letting the rest lapse.
Fitness is likelihood of leaving descendants of equal fitness. It is not strictly
conserved, because likelihood is generally not identical to outcome. There is ex ante
and ex post fitness. But the ex ante kind is meaningless unless potency, in Aristotle’s
terms, is expected to converge to act. Hamilton’s rule should not have escaped this
critique for half a century. It clearly has merit, but needs some different expression.
Such a reformulation might treat rb/c as a maximand within practical constraints.
We can see how it might be by looking at the context. Darwin’s idea is a competition
for breeding success. This biological imperative is a powerful predictor in nature. It
predicts that traits are selected for successful reproduction to the exclusion of all
else. Evidence is impressive. “Semelparous” creatures who breed only once and do
not invest postpartum care, like salmon and soybeans, die within hours. An octopus
mother breeds only once, cares for her young a few weeks, and dies as they disperse.
Nature is on a tight budget. Resources wasted soon become resources lost to
thriftier lineages.
Hamilton saw this. He was right in stressing the role of competition among
individuals and individual heritable traits. Darwin did the same. One thing
Hamilton’s rule leaves out, which is not to claim that he overlooked it, is that traits
and their genes best at prioritizing self-replication might for that reason hurt
chances of achieving it. We know this happens. Human tradition everywhere resists
and punishes nepotism when it crosses a line. Jane Goodall reported the same for
Chapter 7 Petty’s Idea 2/3/16 5
her chimps at Gombe. I think I have seen it among the pack of dogs, led by my
father’s favorite “Sean”, at Sutton Place. That would count as one of the practical
constraints. Too little support for family over equally deserving others is seen as a
fault, and too much as another.
The reason is obvious. Jack’s ambitions for kin will eventually conflict with Zack’s,
just as with ambitions for food and nest sites and mating opportunities. Not
everyone’s firstborn can be king of the hill. Social creatures evolve agonistic rules to
settle such conflicts peacefully. Losers in mating tournaments, or in contests where
males display and females choose, usually survive to compete again next year. The
contest is in the group interest because the traits of strength and skill proved in the
winner will be those passed on. Our genes tell us to compete as best we can for the
sake of a fair test, and to stop when the verdict seems clear. And soon enough it does.
The quarterback tries his best for three downs to move the yardsticks, but trots to
the sidelines on fourth down for the sake of another chance later. If genes can
encode this farsighted strategy for those other kinds of competition, why not for
nepotistic competition too?
For decades, biologists wondered why genes need so much selecting in species long
established. Shouldn’t earlier contests have selected the fittest genes once and for all,
with no need for further ones but to screen out recent and harmful mutations?
Shouldn’t the best traits have become clear millennia ago? Why need males contest
in tournaments or beauty contests every breeding season, with mostly the same
contestants, when best genes ought to have proved themselves soon after the
species began? Then there would be no genetic diversity except for recent
mutations not yet screened out. Population genetists such as Fisher, J. B. S. Haldane
and Sewall Wright had written mathematical models showing that even the slightest
selection pressures should drive a gene to fixity, and its rivals to extinction, within a
few generations if selection favored it consistently. Their argument was Malthus’
insight: breeding success is geometric. Yet there is rich allelic diversity wherever we
look. There are some gene sites in some species where the most common allele
Chapter 7 Petty’s Idea 2/3/16 6
holds frequencies under ten percent, and those frequencies are constantly shifting.
The flux proves that losers are allowed mating opportunities too, though not as
much, and leave young to compete in the next generation.
Hamilton explained why that could make sense in a paper published with Marlene
Zuk in 1982. George Williams in 1976 and John Tooby in 1980 had argued that
fittest genes in one generation might not be fittest in the next if niche pressures
varied to counter current gene choices. Tooby had pointed to parasites and
pathogens, particularly single-cell ones whose life cycle runs less than an hour. They
could evolve new strains to outflank our old defenses and call for new ones.
Hamilton and Zuk continued this theme. They suggested that genes might have long
memories, put in human terms, and might have seen the same parasites and
pathogens pull such tricks before. If some individuals in the host population still
carried the antidote gene that worked the last time the same unexpected strain
arose, or something close enough to it, hosts collectively could weather the threat if
that antidote gene could be identified and spread fast enough. Then how? Hamilton
and Zuk proposed that what winning males display in contests of singing or
croaking or agility or symmetry, or bright colors in the right places, was possession
of the genes needed to counter the current strains of pathogens and parasites.
Losers in the same contests carried genes that had proved best against strains of the
past and might come back in the future. Nepotism practiced by winners would
speed up the spread of the current antidote. But losers carried genes that had
worked against other strains that might recur. A way had to be found to keep all
those potential antidotes somewhere in the medicine cabinet. Current losers had to
be saved for later. Gene diversity was the key to group survival in the long run. The
quarterback trots to the bench on fourth down because that is better for himself and
the team than being carried to the hospital. He realizes that other players are best
for punts or field goals or defense until he gets the ball again. Selection pressures do
not favor the same traits and genes every time.
Chapter 7 Petty’s Idea 2/3/16 7
Hamilton’s Parasite Theory
My take on Hamilton’s 1982 paper, which I consider his masterpiece, is a blend of
his thoughts, Bob Trivers’ from a decade before, Richard Alexander’s, and maybe
mine. Mine sees a population arranged in local “demes” which intrabreed in most
cases for best adaptation to local pressures including pathogens and parasites. A
local strain to which the local deme is adapted might spread to other demes which
are not. Hosts in the invaded demes become sick. Female ones there intuit the
degraded conditions, breed less often, and breed mostly females (mothers can
choose) because males with their now ill-adapted anti-parasite (histocampatability)
genes will find few willing mates. This begins the part from Trivers. I’ll come to
Alexander’s later.
Mothers in the source deme see an opposite picture. Conditions are not necessarily
better than before, but they are better than in the invaded demes. They intuit this,
breed more often, and breed mostly males. The males migrate to those invaded
demes, carrying histocompatibility genes pre-adapted to the invaders, and find
willing mates there if they can show the signs. The idea that mothers choose to
breed mostly males in prosperous conditions is the other half of Trivers’ idea. The
idea that the invading parasite and the males with antidote genes might tend to
originate from the same deme may be mine.
That presupposes that females can trust the signs. Nature makes sure they can. She
provides resistant males with hard-to-feign ones to prove it. This was one of
Hamilton’s key insights. His idea has been called the “truth in advertising” theory.
Symmetrical antlers, deep croaks, accurate songs and bright colors where they
should be tell the females whose genes can be trusted. Parasites and pathogens
would fake them in afflicted host males if they could. It seems they can’t.
Hamilton, I believe, had solved three nagging puzzles at once. Why does nature
waste resources on beauty displays that seem at first glance to hinder fitness? A
Chapter 7 Petty’s Idea 2/3/16 8
peacock’s tail feathers are an encumbrance in running from predators. And why give
the expensive displays mostly to males? Why do males exist at all in species where
they contribute genes but no care?
We just saw the answer to the first. Answers to the second two again build on an
insight of Trivers in 1973. Males produce cheap sperm carrying genes alone.
Females produce eggs packed with costly nutrients. A male can pass genes to many
descendants through many mates if they approve his signs. That speeds up the fight
against parasites. Nature evolved males and their self-promoting signs and their
contests for fastest spread of antidote genes to catch up to shifts in parasite load.
Where Do Losers Go?
A key point in the Hamilton-Zuk theory is that losers’ genes in the beauty contest are
typically not driven to extinction. They are driven to low frequencies until needed
again. Kin selection, up to a point, helps maintain genic diversity by preserving
current losers within the gene pool. Selection pressures punish and restrain kin
selection when it conflicts with preservation of other genes whose time will come
again. I met Hamilton at a conference in Squaw Valley, where Bob Trivers had
helped us attract him, and told him this reason why I thought his 1982 paper helped
complete and qualify his 1964 paper. He was the absent-minded professor to
perfection. Moody, distracted, profound. He smiled, a rare thing for him, and said
“It’s been a long search.”
This explains what I mean by lineage survival or fitness. Much of this book assumes
its maximization even among modern humans, who create our own urban
environments in place of the ancestral savanna for which we were adapted. And
much of economic history, although written in cities by city-dwellers, appears to
assume the same. Chapter 2 listed some examples. Let’s review them. There was
Petty’s of 1662. The similar equilibrium wage theories of Smith and Ricardo
expected pay to converge to the level maintaining and replacing the work force,
which is trusted to spend it on both. Malthus’ population principle in 1798 and 1801
Chapter 7 Petty’s Idea 2/3/16 9
added the mechanics. Nassau Senior made that principle his first axiom in his
Outline of 1836. The biological imperative lapsed from attention when the first
generation of marginalists, led by Jevons and Menger, with Walras soon to follow,
thought it unscientific to explain or justify tastes. It reemerged a century later in
bioeconomics, much of which looked for economic implications of Hamilton’s rule.
We will see how it might clarify pure consumption and the maximand.
Enlightened Kin Selection
Hamilton’s rule needs completion because the quarterback and his genes have
figured out that the bench is better than the hospital. What really happens, I think, is
a long-range example of Bob Trivers’ “reciprocal altruism” of 1971 as generalized by
Richard Alexander. Bob wrote that creatures might invest in non-kin if the
investment were expected to be repaid with interest. Alexander added that the
repayment could be to the investor’s kin with equal genetic benefit if Hamilton’s
hurdle rb > c were cleared from the investor’s perspective. The quarterback yields
to special teams on fourth down, and they to the defense until possession changes
again, for the best interests of each and all in the long run. The interest they receive
in turn for deferring to non-kin is the cost of maintaining themselves on the bench. It
does not accrue and compound because it is paid out continuously. It is an insurance
cost that each temporary winner dares not trim. Group selection is enlightened kin
selection.
Three or four decades ago, this much acknowledgement of group selection would
have met more resistance than I expect now. It shouldn’t have. Half the beauty of the
Hamilton-Zuc scenario is in explaining allelic diversity as a result of agonistic rather
than lethal competition. Zack and Jack and their genotypes are rivals now because
they are teammates in the big picture.
Kin selection is a help until it crosses the line and becomes a hindrance. Some
mothers in the source deme will carry higher frequencies of the antidote gene than
others. They will tend to be healthier, and so able to invest more energy in more
Chapter 7 Petty’s Idea 2/3/16 10
young. If all mothers invest preferentially in their own, or maximize Hamilton’s
standard rb > c , healthier mothers will produce more young with higher doses of
the antidote genes, while sicklier mothers will produce less with less. Here it is
females who compete to prove the same better genes that males just proved in the
tournaments or beauty contests.
The race against parasites speeds up again with Trivers’ fine insight about healthier
mothers choosing to dial up the ratio of sons to daughters (“primary sex ratio”), and
to expand the reproductive period at both ends with shorter birth spacing for more
male offspring still. (Some of this may be my idea rather than his.) Nature proves
best current genes twice. Fathers prove them by duking it out or strutting their stuff.
Mothers carrying the same best genes prove it by winning the breeding contest
against other mothers after.
The ex ante/ ex post distinction counts as much in biology as in economics. Here it
accelerates the selection process. Offspring carrying the antidote gene to meet
current parasites will generally not on that account cost more ex ante invested
consumption to raise. If they are males, who can turn that advantage into many
offspring, the ex post value of that same investment can be far higher. The converse
works for offspring lacking the gene. Their mothers can make the best of it by
producing females who will find breeding opportunities anyhow with mates
carrying the gene, since she knows which they are and males always have cheap
sperm to spare, and will so keep their own genes in the gene pool.
Parasites got the last laugh by killing Hamilton on research in Africa a few years
after I met him. I never knew well enough to call him Bill. Bob Trivers called him the
deepest thinker in the world. That couldn’t be wrong by much.
Parasites and Demes
Ernst Mayr, Bob Trivers’ doctoral advisor at Harvard, defined a deme as a race or
subpopulation that intrabreeds at least 95% of the time. I hypothesize that it does so,
Chapter 7 Petty’s Idea 2/3/16 11
in some cases, to maximize frequency of a histocompatibility gene which is an
antidote to the local strain of parasite or pathogen. This idea could complement the
Hamilton-Zuc parasite model nicely. It would give a safe home to which both gene
and parasite could retreat until their times come again.
Period of Production Theory
Back to economics. Chapter 4 mentioned John Rae as a contributor to what later
developed into Mill’s free growth theory. Rae’s book, published in 1834, also begins
what was called period of production theory. The idea was that production took
time, and that profit compensated the investor’s patience over the production
period. Senior, who had sent Rae’s book to Mill, adopted this idea in his own betterknown
Outline in 1836. Rae’s book itself found few readers, despite its warm
endorsement by Mill in his own magnus opus of 1848. Jevons adopted the idea from
Senior in 1871, and Boehm Bawerk from Senior and Jevons in his book of 1889.
Boehm Bawerk soon learned of Rae’s work, and dedicated later editions to him.
Period of production theory thrives today in the Austrian School, which had been
founded by Boehm Bawerk’s teacher Carl Menger in 1871. (Menger was the guy who
squabbled with Schmoller in Chapter 2.)
It has found little favor elsewhere. The period seemed impractical to define or
measure, and so gave little predictive value. Joseph Schumpeter, a student of Boehm
Bawerk who disagreed with him on this point, argued in 1911 that the period of
production is zero; capital is present continuously. Frank Knight, who had
anticipated Schultz in realizing that some consumption is investment in human
capital, argued as Schumpeter had.
But the theory is true by definition. Any rate is the inverse or reciprocal of a period.
The inverse of 4% per year is 25 years. Return is the ratio of net output to capital
producing it, meaning the rate of production, and its reciprocal is the period of
Chapter 7 Petty’s Idea 2/3/16 12
production. Where the critics were right was in finding a lack of clarity and
predictive value in the theory. Where does it lead? Rabbits and redwoods have
different periods of production, at first glance, but should nonetheless agree in
return if in risk. Jevons wrote that he meant production of the “wage fund” as a
whole, meaning the universe of consumer goods. But he pointed to wine and timber
as examples to help pin down the period. Boehm Bawerk picked nine years for no
reason I can see.
All went wrong by considering physical capital only. The factors blend into each
other; physical becomes human capital through invested consumption, and
conversely when human depreciation is recovered in products. The generation
length gives the replacement period for total capital if total capital is interpreted as
fitness and if all fitness of each generation is passed to the next.
Jevons and Boehm Bawerk assumed growthlessness for simplicity, and would have
realized that they were modeling only the replacement component in net output.
Boehm Bawerk’s contribution, anticipated by Petty, was his insight that time
preference rate explains rate of return by pricing the capital denominator, and not
the reverse. This had not been clear in Rae or Senior or Jevons. I give all four high
marks for a near miss. But they could have come closer. Remember that Senior’s
first axiom had been Malthus’ population principle. He and the others would also
have known of Petty’s human and total capital idea, which was occasionally revived
and critiqued. They didn’t quite connect the dots.
Next Generation Theory
Petty wrote A Treatise of Taxes in 1662. The whole title continues to about as many
words, counting ampersands, as pages in the book or pamphlet. His son tells us that
Petty dictated his books overnight to secretaries who slept by turns. It is easy to
believe that Petty didn’t need much sleep. He was a go-getter who had sailed to
Chapter 7 Petty’s Idea 2/3/16 13
Ireland as chief medical officer to Cromwell’s ironsides, stayed on to survey the Irish
land with which Cromwell would pay his troops, and then got Parliament’s approval
to invest in that high-risk land to make a fortune. It is rare for a man of practical gifts
to be a deep thinker too. Petty, like my father, was both. His Verbum Sapienti of 1664
was first to apply the ancient capitalization formula to both factors, meaning
workers as well as tradeable things, and so originated the concept of human capital
as present value. He applied this insight there and his Political Arithmetick in 1676,
and again in The Total Wealth of England in 1683, to measure the total wealth of
England including human capital. That makes him the father of national accounts.
But his greatest achievements, I think came in A Treatise of Taxes.
Chapter 4, paragraph 9 of that book begins with
19. Having found the Rent or value of the usus fructus per annum, the
question is, how many years purchase (as we usually say) is the Fee simple
naturally worth? If we say an infinite number, then an Acre of Land would be
equal in value to a thousand Acres of the same Land; which is absurd, an
infinity of unites being equal to an infinity of thousands.
Petty clearly recognizes that time preference, meaning our taste for impatience,
explains productivity, or ratio of output to capital, rather than the other way around.
This powerful and counterintuitive insight is usually credited to Boehm Bawerk in
1889, who showed that it is true for man-made things as well as land. The utility or
usus fructus being a given, we bid less for the land or other capital producing it if we
are less patient, and more if more. Bidding less for this denominator of rate of return
bids that rate itself up if the numerator is a given, and conversely. That’s why riskier
assets offer higher return. Petty’s reductio ad absurdam of a hypothesis of infinite
patience is obvious in hindsight, but may not have been written down before. Petty
continues:
Chapter 7 Petty’s Idea 2/3/16 14
Wherefore we must pitch upon some limited number, and that I apprehend
to be the number of years, which I conceive one man of fifty years old,
another of twenty eight, and another of seven years old, all being alive
together may be thought to live; that is to say, of a Grandfather, Father and
Childe; few men having reason to take care of more remote Posterity: for if a
man be a great Grandfather, he himself is so much nearer his end, so as there
are but three in a continual line of descent usually coexisting together; and as
some are Grandfathers at forty years, yet as many are not till above sixty, and
sic de eteteris.
20. Wherefore I pitch the number of years purchase, that any Land is
naturally worth, to be the ordinary extent of three such person their lives.
Now in England we esteem three lives equal to one and twenty years, and
consequently the value of Land, to be about the same number of years
purchase. Possibly if they thought themselves mistaken. . . .(as the observer
on the Bills of Mortality thinks they are. . .)
21. . . . But in other Countreys Lands are worth nearer thirty years purchase,
by reason of the better titles, more people, and perhaps truer opinion of the
value and duration of three lives.
23. One the other hand, Lands are worth fewer years purchase (as in
Ireland) . . . by reason of the frequent rebellions. . .”
The “other Countreys” could include France and especially Holland, then models of
prosperity. Petty had made his fortune in Irish mortgages, and knew the years
purchase there.
But the argument is a puzzle. There is a focus on longevity and mortality, as if the
generations are providing for old age. But Petty’s overlapping generations model
cannot be much like Paul Samuelson’s of three centuries later, where a generation of
productives leaves a nest egg for retirement. Samuelson’s productives are
replenished exogenously, with children left to the imagination. Why would Petty
have mentioned their ages? And retirement at age 50, as a norm, would have made
no sense to Petty or his readers. The grandfather will stay in harness.
Chapter 7 Petty’s Idea 2/3/16 15
The one and twenty years could mean remaining life expectancy at age 50. But Petty
could easily have spelled that out, or the implied 71 year terminus. He does spell out
the ages of the three generations. Their average difference in age rounds to 21
years.
Petty’s readers, like Smith’s and Ricardo’s after, would have taken it for granted that
each generation provides for the next. “Few men having reason to take care of more
remote posterity” would have registered in the context of that provision. “Posterity”
usually meant and means descendants.
His description, like mine, is incomplete. He may mean that life expectancy is also a
factor in calculating the years purchase. If so, he apparently leaves that thought to
be followed up later. There is also room to argue that the grandfather looks two
generations ahead, so that the years purchase becomes 42 years. But that would
give the usus fructus at 2.3%. All the rates Petty reports elsewhere in the tract are
much higher. One generation length is what he seems to apply. My reading is that
the grandfather provides for the grandson by passing all to the son.
Petty’s overlapping generation insight has been one of his least noticed, just as with
Mill’s on output growth preceding and explaining capital growth. I first read of
Petty’s idea in a collection of Lionel Robbins’ lectures at London School of
Economics delivered in 1979-1980, but published in 2000. I learned from these
lectures that Gustav Cassel had published the same idea in his The Nature and
Necessity of Interest in 1903. I hunted that down. Robbins misremembered in telling
his students that Cassel had arrived at the idea independently. In fact Cassel and
Robbins both quote the same excerpts from A Treatise of Taxes that I just did. Cassel
inferred that interest rates cannot stably be less than 2% per year.
Chapter 7 Petty’s Idea 2/3/16 16
I arrived at the same idea independently, anyhow, and published it in Social Science
Information in 1989. To date it is my only publication in a refereed journal, and
remains uncited as far as I know. Alan Rogers, a biologist at University of Utah,
published almost the same idea in 1994 1 and 1997 2 . Neither of us knew of Petty or
Cassel or each other. Both of Rogers’ two papers are included in my appendix.
Petty’s great idea has otherwise remained unnoticed as far as I know.
His idea in modern terms comes from the same ancient capitalization formula.
Sumerian temples knew how to evaluate land as well as mortgages and annuities by
discounting to present value. In the simplest case, where cash flow is expected to
hold constant forever, the logic begins with the definition
cash flow rate =
cash flow
capital
.
Algebra allows
capital =
cash flow
cash flow rate
. (7.1)
Years purchase, given those simplifying assumptions, meant
years purchase =
1
cash flow rate , (7.2)
1 The Evolution of Time Preference.
2 Evolution and Human Choice over Time.
Chapter 7 Petty’s Idea 2/3/16 17
Suppose for example that cash flow rate is known to be 4%. Using (7.2), we would
figure
years purchase =
1
4%/ year = year
4% = year
4 /100 = 100years = 25 years.
4
That allows (7.1) to be reexpressed as
capital = (cash flow) x (years purchase). (7.3)
Where cash flow and cash flow rate are assumed constant over time, they become
identical to profit and rate of return. Sumerians realized that return is the universal
maximand, three millennia before Turgot wrote that down, and that competition
tended to equalize it to a current market norm. Then it would also equal years
purchase.
Petty was searching for the rationale of years purchase, and found it in the
generation length. Petty’s idea I think, and mine anyhow, could begin with
capital = means of accomplishing goals= means of lineage survival= fitness. (7.4)
Nature’s way is transmission of all fitness, meaning total capital for humans, to the
next generation. Nature cares just as much for later generations, but trusts each
generation of immediate descendants to know best what their own immediate
descendants will need for that long-range goal. Each passes the baton and retires.
We invest everything in the next generaton precisely because we care about the
ones after. Hamilton’s rule reflects this reality. Grandoffspring are only ¼ related to
Chapter 7 Petty’s Idea 2/3/16 18
donors, while offspring are ½ related. Hamilton thus predicts grandoffspring to
receive investment only when benefit/cost ratio is double. My own analysis allows
more role for group selection, without saying how much, and shifts attention from
who benefits to when.
Petty’s idea, if I understand him, is
years purchase = generation length = 21years, (7.5)
which would give
cash flow rate
1
generation length = 1
21 years
= 4.7%/year. (7.6)
This would tally well enough with rates of return and interest rates as Petty knew
them.
I would adjust Petty’s estimate of the generational length. Petty’s primogeniture
model may have been true to law and custom for land inheritance, but it is not true
to biology. I prefer R. A. Fisher’s 3 method equal-weighting all births from first to last,
and equal-weighing ages of both parents at each birth. We have some evidence that
the maternal generation length in recent decades, by that method, has run near 26
years over recent decades. If fathers are five years older on average, Fisher’s method
would arrive at 28.5 years. Rogers found 28.9 years from other sources. Then (7.6)
would give
cash flow rate =
1
= 3.5%/year. (7.7)
28.5 years
3 The Genetical Theory of Natural Selection (1930).
Chapter 7 Petty’s Idea 2/3/16 19
All this has assumed has assumed constant cash flow indefinitely. That would imply
zero growth. Only under zero growth do output and rate of return simplify to cash
flow and cash flow rate.
Now let’s model growth in. I divide the Y rule by total capital, as in Chapter 4, to get
output
total capital
=
total capital growth
total capital
+
cash flow
total capital ,
or more compactly
rate of return = growth rate + cash flow rate. (7.8)
At the collective scale, cash flow rate simplifies to pure consumption rate. That
would be written
rate of return = growth rate + pure consumption rate, (7.9)
as in Chapter 4. Then (7.6) through (7.9) allow
rate of return = growth rate + 3.5%/year (7.10)
at the collective scale.
(7.10) would be wrong if growth rate were a function of cash flow rate. I said that
politicians, and even economists to a degree, teach that faster growth needs
consumption restraint first. That corresponds to cash flow restraint in (7.10). Free
Chapter 7 Petty’s Idea 2/3/16 20
growth theory says such restraint doesn’t happen. Data say the same. I apply the
same idea in next generation theory.
My 3.5% is a rough estimate. What counts is the generation length. The length was
probably higher, and the rate lower, before medicine and sanitation lowered
mortality rates, and let two or three births per couple meet the need for population
replenishment.
The cash flow or pure consumption rate modeled at 3.5% might also vary for
reasons other than changes in the generation length. My charts show the pure
consumption/total capital rate as higher in the middle part of the twentieth century
as people drained capital reserves to keep up consumption in times of world-wide
depression. I’ll say more about these reserves.
First Interpretation
Next generation theory says in effect that R. A. Fisher’s version of the generation
length, not Petty’s primogeniture version, gives the period of production of total
capital. We would miss the point if we focused on the period production of human
capital separately. Total capital is our means of lineage survival. This reinforces my
theme that human capital does not mean humans. It means skill sets priced at
present value of foreseen cash flow. Skill sets are not enough for lineage survival.
We also need things. We should not fall into the trap of surplus value theory, which
had been taught by communists for decades before Karl Marx joined their ranks, in
supposing that skills make things. It is only half the truth. Skills plus things make
skills plus things as the generations repeat.
Nor should we make the mistake of supposing that the generation length begins and
ends uniquely from birth to birth, so that the remaining period of production grows
shorter over adult life and the time discount rate steeper. The period of a cycle is the
same at any point. The young, simply by maturing, are already investing in their
Chapter 7 Petty’s Idea 2/3/16 21
counterparts in the next generation. Each cohort (same-age group) invests
effectively in its immediate descendent. Eight-year-olds are investing in the next
generation of eight-year-olds, and so to the end. That’s why Fisher’s version of the
generation length is best. It prioritizes each cohort and gender without judgment as
to which matter more. The period of production gives our patience horizon. The
horizon and its reciprocal, the pure consumption rate, both hold the same at any age.
Cash Flow and Risk
The maximand rule notes that time preference and return vary with risk. Return is
growth rate plus cash flow rate. Is variance with risk captured more in one of these
two components than the other?
We might intuit that riskier and higher-return assets grow faster on average, over
enough time for the bumps of risk to even out. But if that tended to be true, the
universe of assets would grow progressively riskier over the decades and centuries.
That is not my reading of history. My impression is that smoother and rockier
periods come and go without overall trend. In the world we know, then, it is cash
flow rate rather than growth rate that varies from asset to asset with risk.
For illustration, consider factor risk. I argued that human capital figures to be the
riskier and higher return factor because assets tend to reflect the risk appetites of
their owners. The young are more risk-tolerant, and own human capital
disproportionately. If this higher return were reflected in higher growth, rather than
in higher cash flow, the ratio of human to physical capital would tend to rise steadily
over the millennia. Most readings have tended to see it the other way around. I
myself favor the neutral assumption that the factors keep pace. Then cash flow rate
becomes higher for human than physical capital, with 3.5% the cap-weighted
average.
Chapter 7 Petty’s Idea 2/3/16 22
Consider also the history of corporate leverage. Equities are riskier because bond
interest is paid first. If equities grew faster, however, leverage would constantly
decline. That is not what we see.
This inferred concentration of risk premium in cash flow rate is convenient for
testing. Growth and return are two of the most closely followed variables in
economics. We have no direct measure of the pure consumption rate, or cash flow
rate at the collective scale. Nor have we any direct measure of growth and return to
total capital at any scale. But we have a good idea of average return and growth and
cash flow to securities and business assets. By the maximand rule, return to human
capital should be the same but for differences in risk. I model human capital as
somewhat riskier, for reasons just given, and human capital is the larger factor.
Then if I am right in placing the risk premium within the cash flow component of
return, and in estimating average-risk cash flow rate at 3.5%, cash-flow rate to the
business sector as a whole should be somewhat less.
Next generation theory predicts at the collective scale. Collective return is implicitly
average return, and that means average-risk return. My reading of history, which
rules out progressive growth of higher-risk assets at the expense of lower-risk ones,
simplifies that to average-risk cash flow plus whatever collective or average growth
happens to be at the moment.
Don’t Grandparents Invest?
Next generation theory assumes that each generation invests all its capital of both
factors in the next within the generation length. We expect it to do the same in turn.
We care about grandoffspring too, but serve them best by trusting and enabling
their parents only.
A first reaction is that this denies the obvious. Humans today, in advanced countries,
normally live to nearly three times the generation length. (3 x 28.5 = 85.5). Even
retirement at age 65 comes eight years after twice that length. And job number one
Chapter 7 Petty’s Idea 2/3/16 23
for grandparents seems to be helping take care of grandchildren. Doesn’t that falsify
next generation theory?
Note quite. Retirement typically means dependence on savings or subsidy. The
parental generation subsidizes both the young and the old. Retirees can be
interpreted to some extent as hired though willing caregivers paid for by parents.
That explains part. The rest, I think, is best explained as replenishing a capital
reserve. Nature builds up reserves in good times and depletes them in bad times. A
rise in longevity from what is normally needed for lineage survival is a rise in
human capital reserves. Human capital is the most versatile kind. We geezers have
lost a step. But we remember how it’s done. We particularly remember how
parenting and homemaking are done, since those change least with technology.
Julius Caesar’s nanny, with a few pointers, could probably fill in as a nanny today. If
the parental generation were pulled away to fight a war, or rebuild after a
catastrophe, we oldsters could keep up the home front.
Free growth theory, abundantly proved in the data, is essential to next generation
theory. What each generation invests in the next is all its fitness (total capital). All ex
post growth, up or down, is added or subtracted for free. Catastrophes and windfalls
are the random kind of free growth. Tech gain is the accumulating “secular” (of
ages) kind. I wouldn’t put it past nature to have learned that sustained growth
means rising risk. She could adjust with reserves. We may be selected (a nicer word
than programmed) to build human capital reserves intentionally, whether or not
seeing nature’s motives for the buildup as distinct from our own, when real wealth
doubles with every generation.
That intentional or ex ante part would mean investment in the reserve. It isn’t
targeted to the grandoffspring generation, because they aren’t expected to draw it
down unless needed. All the rest of the buildup of human capital reserves in lifespan
prolongation is best explained as random free growth if my interpretation holds
Chapter 7 Petty’s Idea 2/3/16 24
water. Next generation theory is not contradicted because it describes cash flows
only. It treats all growth at the collective scale as free and exogenous.
Testing Next Generation Theory
The proxies for the pure consumption rate (Schultz’ pure consumption over total
capital) in security markets would be dividend yield for equities, and interest for
debt claims. Ibbotson Associates’ SBII (2012), Chapter 4, shows average real
interest on U.S. corporate bonds as 3.0% over the period 1926-2011. Real corporate
dividend yield rate over the period can be estimated from the same source at about
2.9%. Jeremy Siegel’s Stocks for the Long Run (2002), Table 1-2, reports data
extending back to 1802. Real return over the period 1802 – 2001 is shown as
averaging 3.5% for long-term governments, and 2.9% for short-term governments.
Corporate bond returns would have run somewhat higher.
Global Financial Data shows stock market information for 95 countries. Data for U.K.,
U.S., Germany, Australia and France begin from 1701, 1801, 1870, 1883 and 1896
respectively. My charts and tables, and my website Free Growth and Other Surprises,
show this information along with evidence for free growth.
The eighteenth century is represented by U.K. alone. U.K. then showed real price
return, dividend yield and total return at 21.4%, 7.9% and 29.3%. Volatility of
dividend yield was exceptional. From 1801 forward, U.K. averages for these flows
were 2.2%, 4.2% and 6.4%. U.S. figures from 1801 forward were 2.9%, 5.3% and
8.3%. Global Financial Data also shows collective flows for Europe and the world
since 1926. Here the figures were 3.3%, 3.9% and 7.3% for Europe, and 3.5%, 3.8%
and 7.3% for the world.
Modeling of the pure consumption rate before the emergence of security markets
could refer to the history of interest rates alone. Interest is rate of return to senior
claims. Rate of return to any claim is realization by investors net of all expense.
Chapter 7 Petty’s Idea 2/3/16 25
Investors as to interest means lenders, not borrowers. Interest rates published
historically are rates borrowers are contracted to pay. Interest rates realized by
lenders are less for two reasons. There are friction costs of due diligence,
contracting and collection. Default costs, slight when times are good, can be
catastrophic when times are bad.
Homer and Sylla describe normal contracted rates, not realized rates net of those
costs, as 10% − 40% in Sumer and Babylonia, 6% − 18% in ancient Greece, 5% −
24% in Egypt, and 4% − 12+% in Rome and the Byzantine Empire. 4 After higher
rates in the dark ages, European mortgages and commercial loans found the range
7% − 25% in the thirteenth and fourteenth centuries. 5 The range settled down to
4% − 14% in the sixteenth century, 6 and to 3% − 10% by the seventeenth and
eighteenth 7 . The authors comment: 8 “…interest rates declined during much of the
later Middle Ages and Renaissance. The earliest short-term rates quoted were
somewhat higher than the last and highest of the western Roman Legal limits. They
were not too different from early Greek rates and were within the range of
Babylonian rates… The later Renaissance rates were well within the range of
modern rates and the lowest were far below modern rates in periods of credit
stringency.” Merchants of Venice in Shakespeare’s time and long before borrowed
from banks, not from Shylocks, and at rather lower cost than merchants of the
twentieth century.
Economics and Biology
Bioeconomics has meant economics informed by biology. I argued that this
describes much or all of classical economics from Petty through Mill, then lapsed
when the marginalists preferred to do without any explanations or justifications of
tastes, and revived a century later to explore Hamilton’s rule.
4 A History of Interest Rates, Rutgers, 1996, Table 4.
5 Ibid. Tables 6 and 7.
6 Ibid. Table 9.
7 Ibid. Tables 10 and 14.
8 Ibid. Chapter 10.
Chapter 7 Petty’s Idea 2/3/16 26
I too reason from biological axioms, and from much the same ones implicit or
explicit in the classical period. But I end up framing ideas of biology in the language
of economics rather than the opposite. I begin with
total capital = means of ends = means of replication = fitness,
where fitness is understood as a stock. The concomitant flow and rate would be
output (creation of fitness/total capital) and return (ratio of the two).
Free growth theory gave the inference
optimum ex ante output = optimum controllable output
= exact offset of pure consumption, at the collective scale.
Next generation theory specified the period of this exhaust and recovery as the
generation length.
Consider Hamilton’s rule in this context. All ex ante output, continuing steadily at
the generation rate, must be invested concurrently in the next generation or stored
for later investment within the deadline. It is the problem of Brewster’s millions.
Adults must invest or store as efficiently as practical (the maximand rule) before the
output means has slipped by. And the more stored instead, the more pressure to
invest later within the deadline. Time left for investment is another of the practical
constraints on maximization of rb/c.
What I sense is a watering down of Hamilton’s rule from what seemed logical
compulsion a few decades ago to something more like a target of opportunity. A
prediction maximizing rb/c has proved its value as a useful rule of thumb. I
suggested why some nepotism might be more adaptive than none in my review of
the Hamilton-Zuk parasite theory. It’s about giving all genes a fair but speedy trial.
Chapter 7 Petty’s Idea 2/3/16 27
The quarterback gets three downs, and the batter three strikes, before they go back
to the bench. Some nepotism directs healthier mothers to invest in more and
healthier offspring, and sicker ones conversely, long enough to demonstrate which
is really which. Males passing the test carry the signs to prove it. Females choose
them to spread the antidote gene to the whole population. Losing genes and losing
parasites retreat until their time comes again.
Summary
This chapter trades my wannabe economist hat for my wannabe biologist one.
Herbert Spencer called those fields the same at bottom. I never read Spencer, and
know him mostly from Bertrand Russell’s books on the history of philosophy.
Spencer rates a subchapter there. Yet he was an autodidact with less training in
either field than mine. He even had less training in philosophy than mine. He was a
philosopher all the same, by Russell’s tough standards, and knew that logic comes
first. Data eventually prove their worth when it’s time to test. The data I’ve found
fits net generation theory more or less. What I really have on, all the while, is my
wannabe philosopher hat.
Popperians make no sense. Are we supposed to find that a rose is not a rose? Or that
all reasoning from definition is as transparent as that example? Wiles’ proof of
Fermat’s last theorem ended a search that took some pretty bright minds three
centuries. My best guess would be that Popperians confuse the concepts of logic and
question-begging. They are opposite. Logic (reasoning from definition) means
taking out no more than you put in. Truism or tautology usually means obvious
examples of the same, but sometimes includes subtle ones too. Question-begging
means taking out what you never put in 9 .
9 Circularity is question-begging which claims to take out as inference what it put in as assumption.
Assumption that Socrates is a man and that all men are mortal does not confirm that Socrates is a
man. It confirms that Socrates is mortal if assumptions are sound.
Chapter 7 Petty’s Idea 2/3/16 28
Spencer’s “survival of the fittest’ doctrine would be a truism if we could prove the
theory of natural causality. We can’t by any means known to me. Science takes it as a
working assumption. So did Hume, and so do I. If God intervenes only a little, so that
laws of nature comes close to reality most of the time, we’re still in business.
My critique of Hamilton’s rule proposed that nepotism meets resistance when it
conflicts with nepotistic goals of others. I proposed a modus vivendi through
agonistic rules. Hamilton’s parasite theory with Zuk, written 18 years later, gives the
game plan.
Nepotism, meaning kin selection through Hamilton’s rule, is in the common interest
to a point. It speeds up proof of best genes to beat the current parasites by testing
female genes as well as male ones. Healthier mothers and sisters and aunts carry
more fitness to invest in more young. And females in most K-selected species,
including humans, perform most care of the offspring and siblings and nepotes
(nephews and nieces) that receive it 10 . Male competition alone does not determine
best current genes to nature’s satisfaction. Female breeding competition and
nepotistic investment help prove them farther.
All agonistic rules are about keeping the contest fair and deciding when proof is
enough. Long-term success against future as well as current parasites needs most
losers, not all, to go to the bench (low frequencies; source demes in my version)
rather than to extinction. Most losers survived to enter the contest because they
10 The burden is about 50-50 in pair-bonding birds. Fathers look to be the only caregivers in
territorial fish such as sticklebacks.
Chapter 7 Petty’s Idea 2/3/16 29
were winners once before. Their cost on the bench, or on the taxi squad, is good
insurance.
My version of Hamilton’s parasite theory patched in some of Trivers’ ideas. One was
that mothers intuiting self-health and good prospects should tend to breed higher
primary sex ratios and conversely. Their male offspring can then find willing mates
if health carries reliable signs as Hamilton proposed. Also the investment of
insurance cost by winners in maintaining losers on the bench can be interpreted as
Trivers’ reciprocal altruism to be recovered when winners now become losers later.
My discussion of grandparental investment let still more worms out of the can. It is
clear that humans in advanced economies today normally live to nearly three
generation lengths. I proposed that we are replenishing a total capital reserve,
meaning mainly a human capital one, when recovering from hard times in the world
wars and world depression. No one really knows.
Chapter 7 Petty’s Idea 2/3/16 30
CHAPTER 8: BANKS, MONEY AND MACROECONOMICS
Splitting up Banks
I started to write a book on banks and money a year ago. I stopped when I realized
that I don’t know enough about the subject. I have some experience and have done
some reading in those fields, but not enough to justify a whole book. A chapter, or
part of a chapter, is more like it.
Sumerian temples doubled as banks, mostly for agricultural loans to finance the next
crop. It is from their records, in clay tablets, that we know they understood
compound interest and the capitalization formula.
Deposit-and-lend banks as we know them today emerged in Venice and other
European cities in the twelfth and thirteenth centuries. Chapter 1 said that equity
investors cannot be attracted at leverage (deposit/equity) of less than 10:1, that
even one tenth so much leverage is unstable in high winds, and that we rebuild the
banking system after every systemic failure because we blamed the high winds
rather than the rickety structure.
I said that the solution is to split up banks as we know them into deposit banks
which invest in ETFs on the one side, and lending banks which raise funds from
investors rather than depositors on the other. These entities would have separate
stockholders, and would not interact unless incidentally.
A different kind of bank split-up has been urged since the 2008 crash. Repeal of the
Glass-Steagle act had allowed commercial (deposit-and-lend) banks to operate as
investment banks (brokerage firms). Many blamed the crash on that repeal, and on
investment bank innovations such as mortgage-backed securities. I think those
critics are looking in the wrong direction. The problem, as with most bank crashes
over the centuries, was overleverage encouraged by nearly costless deposits. The
solution is not to peel off brokerage operations from the mix, but to peel off deposits.
