Monday, July 15, 2013

The Puzzle of the Other Hockey Stick

I have been reading Dierdre’ McCloskey’s Bourgeouis Dignity, the second volume of a projected six volume project. Judging by the early chapters, the book contains three central theses:

1.    The graph of real per capita income over history is a hockey stick. For thousands of years, the overwhelming bulk of the world’s population lived at a real income equivalent to about three dollars a day. Over  the past two centuries, that increased roughly ten-fold averaged over the world population, twenty or thirty fold for developed countries, probably by a good deal more if one tries to allow for improvements in the quality of what was available to buy—electric lighting over candles, air conditioning over house fans. And the average continues to rise.

2.    Conventional material explanations of economic growth offered by economists with approaches ranging from Marx to the Chicago School cannot explain the size and speed of the change.

3.    The correct explanation is a change in attitude, the shift, first in North-west Europe and then increasingly in the rest of the world, from regarding “bourgeois” activities, trade, manufacturing, money making, as low status to regarding them as dignified and worthy of respect.

It’s an interesting thesis. The first part, so far as I can tell, is correct—we really are enormously better off than our ancestors. I am skeptical about the second part, not because I know what the right explanation is but because proving a negative is hard. Also, while the increase in material well being over two centuries is indeed enormous, it represents the cumulative effect of an average increase of less than two percent a year, which looks less startling and so easier to offer possible explanations for.

As for the third part, McCloskey is pretty clearly describing  a real and important change in attitudes—rich people no longer feel obliged to apologize for the fact that they made it in trade instead of inheriting it, and we no longer take it for granted that, having made a fortune in business, the only respectable thing to do with it is to use it to buy land and so buy your way into the landed elite. How much responsibility that change has for economic growth I do not know—but I am still in the early parts of the book.

I am struck, however, by a puzzle that McCloskey does not discuss in any detail—the long handle of the hockey stick. If, as she claims, real incomes were roughly constant for thousands of years, there must have been something keeping them that way, an equilibrating process that pushed incomes back down if some exogenous factor such as improving climate or the availability of new food crops was increasing it, and back up if some exogenous factor pushed it down.

The most plausible candidate for such a process was offered more than two hundred years ago by Thomas Malthus. His argument was not, as modern references sometimes imply, that population growth leads to catastrophe. It was rather that population growth made impossible any large sustained increase in the standard of living of the masses. The argument was simple and persuasive—and its implication strikingly inconsistent with what actually happened over the next two hundred years.

Malthus started with the observation that humans like sex, and sex produces babies. He concluded that, unless there were large costs to producing babies, population would increase at something close to the biological maximum, leading to an exponential growth rate high enough to overcome any plausible rate of increase in human productivity. Looking around him, he observed that  most people were poor enough so that the cost of supporting an additional child was a substantial burden. He concluded that if that was not the case, if, as Godwin and Condorcet, the authors he was responding to, expected, the future saw a sharp rise in the standard of living of the masses, making additional children only a minor burden, population would increase rapidly and the pressure of population against a fixed supply of land would push standards of living back down.

It’s an elegant argument and provides a plausible explanation for most of human history, but one that stopped working within the lifetime of its author. Why? What went wrong with Malthus’ model?

The answer cannot be simply that output increased, and kept increasing, fast enough to outweigh population growth, because if that had happened the population would eventually  have been growing at something close to the biological maximum, and although population in England during the 19th and 20th centuries did indeed increase, it did not increase nearly that fast.

One possibility is that Malthus overestimated the cost of holding down population growth. Implicit in his argument is the assumption that the only practical alternatives are having babies and not having sex. While modern contraceptive technology appeared too late to explain the first century or so of economic growth, contraception itself is a very old technology, in at least two forms. Coitus Interruptus, intercourse with withdrawal just before orgasm, is mentioned in the bible, discussed in medieval Islamic law, pretty clearly a known option for at least the past two thousand years and more. The rhythm method, refraining from intercourse during the woman’s fertile period, is a second low tech alternative, although it is less clear how far back the knowledge necessary to use it goes. And, of course, there are the various forms of non-vaginal intercourse.

Critics of the Catholic church’s stand on contraception sometimes blame it for large family sizes in poor Catholic countries. It occurred to me long ago that they were probably wrong. Rhythm is not as reliable a form of contraception as the pill, diaphragm, or IUD, but if the objective is only to have four children instead of eight, it does not have to be all that reliable. A mildly cynical defender of the Catholic doctrine might argue that it bans forms of contraception sufficiently reliable to make sinning—non-marital intercourse—safe, while permitting a form reliable enough to substantially reduce population growth.

Which brings me to an empirical question to which I do not know the answer, but someone else probably does: How effective are pre-modern forms of contraception? If a couple uses rhythm and withdrawal, does their birth rate go down from one child every two years to one child every twenty-five months, or does it go down to one child every five years? If the latter, then a central assumption of Malthus’ argument, the high cost of holding birth rates down, is wrong. That would explain why his prediction failed to hold through the 19th and 20th century but leaves us without an explanation of why it worked pretty well for millenia before that.

A second possibility is suggested by a modification of the argument introduced by Malthus’ friend David Ricardo, arguably the first great economic theorist. He argued that what level of income corresponded to the Malthusian population equilibrium depended on the tastes of the masses.The more luxurious the tastes of the working class, the higher the income level at which the cost of an additional child was no longer an adequate incentive to hold down the birth rate. Hence he concluded that the “friends of mankind” should wish that the workers have more luxurious tastes. Following out that argument, one might explain the rise of incomes over the past two centuries as a result of increases in the level of income that ordinary people considered acceptable. That would be a non-material explanation, although not the same as the one that McCloskey offers.

Like the previous possibility, that explains the past two centuries at the cost of failing to explain all of previous history. Standards of living have gone up and down at various points in the past. Why didn’t each increase result in a rise in expectations, ratcheting up the level of the Malthusian equilibrium?

Which brings me to a final possibility, and one that I think is consistent with at least the most obvious data. One of the assumptions that went into the Malthusian argument was the high cost of holding down birth rates. The other was the economic importance of land. Suppose we weaken the former assumption, for the reasons I have already suggested, and drop the latter.

Consider an economy in which land is a very important input, making per capita output very sensitive to population density. In such an economy, even a weak version of Malthus’ theory is sufficient to produce the Malthusian conclusion. If real incomes go up substantially population grows, even if at nothing like the biological maximum, and even a modest population growth is sufficient to push incomes back down.

Now introduce one change—technological progress that makes labor rather than land the key input. The logic of the situation is the same as before, but the magnitudes have changed. Rising income produces an increase in the birth rate, hence in population, but that exerts only a modest downward pressure on incomes—one that can be outweighed by technological improvement, better property rights, increased foreign trade, or any of a variety of other positive factors.

Forty some years ago, when population played the same role in public discourse that global warming now does—the looming catastrophe that could perhaps be prevented if only we took sufficiently strong measures against it—I did a simple calculation, designed to test the popular assumption that the reason poor countries were poor was overpopulation. I calculated population density across countries, and found the five most densely populated. Two were rich developed countries, Belgium and the Netherlands. Three were rapidly developing countries, Taiwan, South Korea, and Singapore. Hong Kong had about ten times the population density of Singapore, but I did not include it because it was not an independent country. I concluded that population density was probably not nearly as important a factor as generally supposed.

The reason, most spectacularly illustrated by the later history of Hong Kong, was that land in a modern economy is not all that important an input. I do not know enough economic history to say with any confidence just when the shift from land to labor as the most important input to production occurred, but it provides at least a possible explanation of the puzzle of McCloskey’s hockey stick, an explanation of both the long handle and the short, and steeply rising, blade.

Before ending I should say that although that particular puzzle is what has so far interested me most about the book, there is a great deal more there. McCloskey’s overall project, with which I am very much in sympathy, is a defense of the modern world, of capitalism very broadly defined, against its critics, left and right.


Power Child said...

You mention technological change that makes labor rather than land the key input. What about a technological change that makes land more accessible, usable, or habitable? Think about the parts of the world that civilizations covered 200 years ago, and then the parts they covered 150 years ago.

Richard Ober Hammer said...

I am suspicious of the hockey stick assertion, the part which claims that income per capita was relatively constant for hundreds or thousands of years before the industrial revolution.

This assertion is being repeated by many economists. For instance Robert Lucas makes the hockey stick assertion, assuming I understand him correctly, in Lectures on Economic Growth, 2002, (see Chapter 5, "The Industrial Revolution: Past and Future"). His data for 1750 and later may be respectable. But, get this, for the centuries before 1750 he tells, “Earlier production estimates are extrapolations based on the assumption that per capita incomes were equal to their 1750 levels in all earlier years.” I could not see that Lucas gave any source for this. If the hockey stick has any respectable basis, I hope to learn it.

I do not believe that the human race was stupid and incapable of improving itself before the industrial revolution. I continue to believe what I was taught while growing up, that life was improved by use of fire, domesticated animals, the wheel, and the printing press.

So what explains the appearance of the hockey stick? A better explanation might be that the assumptions made, to attribute per capita income to various populations in history, cannot be extrapolated onto a history in which different assets were valued.

About limits on population growth, I found a believable account in The Selfish Gene by Richard Dawkins. Dawkins told of birds which have mating territories. The population was limited by the number of mating territories. People have instincts like that too, I believe.

Chris H said...

I think you might be dismissing the Richardian theory a bit too quickly. It's certainly true that the past 200 years have been exceptional in terms of world growth, but there have been other periods of growth that seems to defy Malthusian limits as well. Jack Goldstone from UC Davis actually wrote an article on this subject (url here: just a note I do hate his clunky term for the opposite of a crisis but I lack a better word to replace his with). Early Qing China, the Dutch Golden Age, even the High Middle Ages managed to maintain population growth without per capita incomes falling to sustenance for decades or centuries (and in some cases even saw some rise in per capita income with population growth). Ricardo's theory nicely helps explain these periods, though weakening the importance of land can work as well (urbanization is a trend of most of these periods of significant growth).

It's also worth mentioning that the periods Goldstone examines do eventually falter, but the cause doesn't seem to be Malthusian as institutional decline seems to precede going back to Malthusian limits and slowing population growth.

kebko said...

I think Diedre has your answer. The explanation, via Robin Hanson:

Along with the acceptance of trade and accumulation was the breakdown of strong sharing rules among extended family. When your savings could be claimed by your cousins, it was locally advantageous to have more children, as it gave you more avenues to claims on family assets. Once the notion of individual accumulation gained traction, and you weren't expected to share, children were not advantageous.
This is still a major factor in poor areas today.
Mike Munger & Russ Roberts have a great podcast about how this is one of the ways that microfinance has been successful - as a backdoor way to save without having the savings claimed by family:

jdgalt said...

David: If McCloskey's theory is true, then I expect the same curves, when plotted in the future, to show that growth in each country pretty much stops, forever, when the environmental movement takes hold there. The central point of that movement is not really about protecting living things at all -- it is the idea that being rich, as we are, is not OK because the earth can't sustain that level of wealth for everybody.

(I believe it easily can -- in fact, rich countries put less stress on the ecosystem than poor ones, because we can afford cleanup measures. Compare our air and water with those in Shanghai or Mexico City, for instance. But the eco-belief is widespread and seems to render its holders as impervious to reason as would any religion. This, to me, is the most urgent reason to somehow create a really free country now.)

@kebko: I can't buy it. The reason people in the rich world have fewer children is simple: lower infant mortality. Before about 1870 there was no such thing as a pension plan, anywhere in the world; if you wanted to survive after you were too old to work, you had to have enough kids that at least one would survive and be able to support you when the time came. Cousins' claims had nothing to do with it.

Tim Worstall said...

A pet theory....and it is that, just a pet one, not something I'd like to have to prove.

We know about modern contraceptives that their provision only explains about 10% of the changes in actual fertility. The rest is from changes in desired fertility.

So, something changes desired fertility. My pet theory is that it is child mortality rates.

There's a cost to having children. There's also a cost to not having grandchildren (the genes die out etc). Therefore there's something of an optimisation problem going on. We need to be willing to bear the costs of having enough children in order not to bear the cost of no grandchildren.

If child mortality (or other mortality) rates decline then this changes that calculation.

I regard this as a pretty good description of modern changes in desired fertility....possibly with a generation lag. As people see that near all of those of the previous generation did indeed survive and then have children they're happy to forgo the costs of extra children secure that they'll still have grandchildren with only one or two kids of their own.

The problem with my pet theory in explaining the past is that I've absolutely no idea at all whether drops in mortality preceded the drops in fertility historically.

Patrick Sullivan said...

I think Tim Worstall's pet theory works pretty well. Mine is; Shakespeare. He, and lesser talents like Marlow and Jonson, gave the world a language that allowed the English speaking world a way of thinking about problems in a sophisticated way. A modern way.

Also, Shakespeare knew quite a bit of economics. For instance, in Henry VIII, Act 1, scene 2, he gives a near textbook description of the dead-weight loss of taxation. Which, as 'Vivian Darkbloom' once pointed out to me, he stole from Holinshed.

Glen Whitman said...

In addition to coitus interruptus, the rhythm method, and non-vaginal sex, they also had... condoms! I once saw a photo of a leather condom from Roman times. But the more common method was, I think, to take a section of sheep intestine and tie off one end. Probably not as effective as modern-day condoms, but it wouldn't have to be.

Unknown said...


I'm glad that David (my Harvard-Class-of-1964 classmate [50th Reunion next year, David!], and then rooming-house housemate---in the first year of grad school we lived down the hall from each other, but both of us were working so hard, David at physics, me at economics, that we barely saw each other!)is reading Bourgeois Dignity (2010). I invite you others do buy and read, too (especially buy!).
The book makes a pretty extensive, quantitative case that trade, exploitation, coal, markets couldn't explain a one-time hockey stick blade---until the ideological changes of the 17th and especially the 18th century (David expresses it well by noting that inherited wealth was long thought blameless compared with earned wealth, about which suspicion hung). Briefly, if the modern world is unique, as it is, then routine economics (except Austrian discovery) can't explain it, since other and older societies had all the material conditions put forward in he routine: property rights, trade, exploitation, coal, whatever. One has to be comparative and historical to test such a claim: theory won't do it, which is what is disappointing about "new" growth theory.
In the next volume, which will be the third and last (I've decided that six volumes would be lunacy), I develop the evidence for the hockey stick, in case you doubt the uniqueness of the modern world. (Put your orders in early to the U of Chicago Press, for a late 2014 pub!) I start of course with a Malthusian explanation for the handle. You can also explain the handle (I note there) with exploitation by elites and with density-causing-disease. But anyway, lacking modern liberty and dignity for ordinary people the frenetic innovation of the past 200 years couldn't get going, and most of our ancestors dragged along at $3 a day. Now worldwide we earn and spend $33 a day, and in the readily multiplying rich countries over $100 a day: a hockey stick indeed, and uniquely modern.
Regards, Deirdre

David Friedman said...

Not quite classmates--I was class of 1965. I look forward to the next volume, but first I have to finish this one.

Have you considered writing shorter books?

bruce said...

>the most effective method, I think, was to take a section of sheep intestine and tie off one end.

I remember that from Neal Stephenson's giant trilogy. Why didn't it catch on millenia ago?

Because when it did, the people it caught on with didn't breed.

Anonymous said...

>(except Austrian discovery)

Can you explain that for the non-economists?

Milhouse said...

Here's another, less plausible but more entertaining, explanation for why Malthus's theory worked for all of history, until shortly after he discovered it: it wore out.

Anonymous said...

Just a quick note on ancient chemical/hormonal contraceptives. This is from memory but about as far back as 3000BC there was a plant of the fennel family (now believed extinct, though its exact identity is not known, so who knows) that was widely prized throughout the mediterranean for its apparently highly effective contraceptive properties. Also there are many hints/reports from the Catholic church and its minions that other ancient cultures (Aztec, Mayan, Celts, Druids, etc...) were known to have highly effective plant based remedies (including contraceptives) as well, but the church so thoroughly destroyed what was left of those cultures (and in the case of the Maya, burned whole libraries) that we know even less -- but again the hints are tantalizing. Humans can be pretty smart -- even the ancient ones; unfortunately stupidity is the more common choice

David Friedman said...


I've seen the claim you mention but not the evidence for it, and find the story a bit suspicious--if it were that useful, it's hard to see how it could go extinct in a post agricultural revolution world.

On the other hand, rue is frequently claimed to be a natural abortafacient.

Instant Karma said...

I too loved "Dignity," while also sharing your reservations on the book's central thesis that the overiding factor in the modern breakthrough was attitudinal.

The way I view it is that prosperity can be oversimplified as creating more solutions on net than the world throws problems at us. As we accumulate more and better solutions, and learn to solve better, we become better off.

The problem though is that as people solve problems for themselves they often also create problems for others. There are positive sum games and human actions, but there are also zero and negative sum actions and interactions. Huge amounts of human action are zero sum in nature.

Using this framework, economic progress or lack thereof amounts to billions of steps forward summed against billions of steps backward (natural and human caused). I believe McCloskey underestimates the headwinds that push against progress. The first is the Malthusian curse, second, is active change resistance, especially by incumbents with something to lose from change or new competitors. The third headwind is zero sum, win/lose activities, coercive exploitation, theft, forced redistribution, etc. Finally, there are cultural headwinds such as those in the book and listed above.

Through most of history, the forces have balanced out with negative feedback. Prosperity leads to Malthusian pressure, attracts rent seekers and barbarians and promotes exploitation from within, without and above. Those with resources use them to solidify their position and suppress change and opportunity. Average daily income balanced around subsistence levels for all of history just about everywhere.

In those without strong states, the problems were more Malthusian and external. In stronger states the problem included a larger zero sum element from within and above.

In Northern Europe, we saw a constructive, competitive-cooperative arms race between integrated but autonomous states. Some of them stumbled upon the right blend of culture and institutions to solve problems on net faster than they were created. People became more prosperous at a rate eventually growing to about two percent a year. Good and bad ideas spread, previous leaders became laggards, but the vanguard moved somewhere else, from the Netherlands, to England to the US.

In the end we saw the institutional emergence of two killer apps -- two self amplifying positive sum games each supported by a classical liberal ideology: science, and then relatively free enterprise. These led to slow but steady cumulative improvements in standard of living as we for the first long term in history consistently solved problems at a faster net rate than they were created.

Milhouse said...

I've seen the claim you mention but not the evidence for it, and find the story a bit suspicious--if it were that useful, it's hard to see how it could go extinct in a post agricultural revolution world.

It's actually quite easy. It only grew in a relatively small area, and the agricultural tech of the day was certainly not up to identifying and replicating the necessary conditions elsewhere. That would leave it vulnerable to all sorts of disasters, from overharvesting or soil exhaustion to climate change.

Unknown said...


I don't know, technically speaking, how to reply to each comment, so this will have to do! David: Oh, yes; I think we established '65 vs. '64 in an earlier conversation! "Except Austrians": so-called "Austrian" economics takes the view that discovery, necessarily unpredictable and not routine like an investment, is crucial. That's my view. Instant Karma: try the next (and last!) volume I mention, which makes many of the points you make. As to short books, I have written many---one relevant one if If You're So Snmrt (1990). But I can't understand why readers complain about long books. Treat them as two or three short ones, eh?!


Deirdre McCloskey