Yes: Pre-Modern Economies Were Meaningfully “Malthusian” (Which Does Not Mean Incomes Were Stable); & BRIEFLY NOTED: For 2023-03-07 Tu

This is, of course, wonderful: a smart and thoughtful person disagreeing with me on the internet. He is, of course, wrong. But now I get to revisit my trains of thought, and explain why he is, in his turn wrong.

The Great Waves in Economic History

Introduction Economists often state that economic growth simply did not exist before recent times. The orthodox view that I was taught as an undergrad is that sustained economic growth began in the late 18th century. This view is articulated by economic historians like Clarke (2007). DeLong (2022) goes even further. He claims that modern economic growth …

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15 days ago · 6 likes · 1 comment · Rafael R. Guthmann

Rafael R. Guthmann: The Great Waves in Economic History: Malthusians are wrong: far from being stagnant, in western history, living standards had three “supercycles” of rise and fall of economic activity over the past 4,000 years…. DeLong (2022)… claims that modern economic growth only began in earnest in 1870, with the growth from 1770 to 1870 being very small in comparison, and that there was absolutely no growth in real incomes for ordinary people before 1770 (but he admits that living standards could have varied over pre-modern history for a tiny elite)…. This model of economic history is plain wrong…. Three major very-long-run economic cycles in the Western world that featured increasing incomes and then very long periods of decreasing incomes. These cycles of expansion and contraction lasted for several centuries…

The three cycles are (1) the Bronze Age Near East starting in -3000, followed by the late -1000s civilizational collapse; (2) the Classical and Hellenistic Greece plus Roman efflorescence from -700 to 150, followed by what I politely call the “Late-Antiquity Pause” from 150 to 700; and (3) the long mediæval and early modern ascent, followed by the industrial revolution and modern economic growth breakthrough.

The support is (1) the assertion that urbanization—even in cities as small as 5000—is closely correlated sith living standards an productivity levels, and (2) our guesses about the share of Europeans living in cities of 5000 or more:

Rafael says:

There is no evidence of any tendency for the rate of urbanization to stabilize around a level consistent with the Malthusian model’s “subsistence level.” Instead, the urbanization rate suggests that over the last three millennia of the history of Europe, there were long and sustained periods of economic progress and regression and that modern economic growth has been a dramatic acceleration compared to the pre-modern trend, instead of a complete break from it…

But what would we expect to see if we were, in fact, observing a Malthusian economy?

What is a Malthusian economy anyway? I write it down in four equations:

\(\frac{1}{y} \frac{dy}{dt} = g


\(\frac{1}{L} \frac{dL}{dt} = n\)

\(g = h – n/\gamma + \epsilon_1\)

\(n = \beta \left[ y/ y^{sub} – 1 \right] + \epsilon_2\)

The first and second equations are simply definitions: The first says that the proportional growth rate of living standards and productivity levels—the proportional growth rate of the output per worker y variable on the left-hand side—is equal to g, g for growth. The second says that the proportional growth rate of population and the labor force variable L, L for labor, on the right-hand side is equal to n, n for numbers.

The third and fourth equations are behavioral relationships: The third says that g—the proportional growth rate of living standards and productivity levels—on the left-hand side is equal to the proportional rate of growth h of human ideas about technology, minus the proportional rate of growth of population and the labor force n divided by a parameter ɣthat tells us how salient ideas about technology are in generating productivity vis-à-vis resource scarcity, plus a random shock term. It is human ingenuity versus resource scarcity. And resource scarcity is made more dire by population increases. The fourth says that the population growth rate variable n on the left-hand side will be such that population will grow if living standards y are above, and shrink if living standards are below, some “subsistence” level y^{sub}. It says that population will do so linearly, depending on a parameter βthat tells us how responsive fertility and mortality are to want and deprivation, plus a random shock term. Twice as big a gap between living standards and subsistence will produce twice as fast a population response, with the value of the β parameter calibrating how much. As people get poorer, fertility drops: women become sufficiently skinny that ovulation becomes hit-or-miss. And as people get poorer, mortality rises: it is not just that some people starve to death, it is that the malnourished have compromised immune systems, and malnourished children, especially, are easily carried off by the common cold.

This model captures three features of a pre-modern Malthusian economy:

  • There is (slow) progress in technology

  • A more prosperous society has higher population growth

  • Resource scarcity matters

What consequences do those features have? Well, let us set up a toy economy—a simulation—with these features, and only these features, and see how history evolves. Let us set h = 0.0005—5% growth in technology over a century. Let us set β= 0.25—if real living standards are 40% over “subsistence”, population grows at 1% per year, or doubles in three generations. And let us set ɣ = 2—ideas about technology are twice as salient as resources in generating productivity. And we also need to add a random term, an ε term, for plagues, bountiful harvests, mild winters in which babies do not die of pneumonia, and all the other non-systematic accidents that affect the growth of population. We do this in Python. Here is our first simulation run: the level of income per capita:

We see, in this simulation, a 500-year advance in civilization as measured by living standards, and then a sudden following crash into a dark age. There is then a 400-year period during which little appears to happen.

Would Rafael Guthman say of this that there “no evidence of any tendency… to stabilize around a level consistent with the Malthusian model’s ‘subsistence level’”? Would he point to it as strong evidence against the Malthusian economy hypothesis? Quite possibly. I would even say: probably. And yet there it is. There is nothing non-Malthusian going on here.

We find patterns even where there are no patterns—where there is only the random buffeting of the society by plague and good harvest.

Now, actually, I think there is much more going on with the Classical and Hellenistic Greek efflorescences, and with the Roman efflorescence, than just the random chances of plagues and good harvests.

But that more is happening than can be captured in my very simple model is not, I think, dispositive. A society can see considerable advances in average living standards and considerable increases in population without thereby ceasing to be Malthusian.

A society that acquires a substantial taste for luxuries—for expenditures on things that do not directly contribute to making women more fertile and children more likely to survive—will raise the average standard of living even in a Malthusian economy. So will customs, like late female first marriage or female infanticide, that will have the effect of diminishing reproduction. And the coming of a large commercial trade zone or an imperial peace—something that greatly increases the rewards of investing in tools and infrastructure and other forms of social, public, and private capital—will raise the average standard of living in the short run, and raise population in the long run, but note that it can take up to half a millennium for the long run to arrive.

So I regard Rafael’s figure as a striking illustration of how a Malthusian economy does not have to be stagnant. But it does not shake my confidence in the proposition that before 1870 the world economy was Malthusian. It does not shake my confidence in that at all.


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I confess I really do not know what to make of this:

Tim Burke: The News: It’s His Turn to Fail: ‘I don’t know what to say about political transitions in much of sub-Saharan Africa…. It’s hard to know what to say is that the political outcomes of most elections plainly do not reflect the political aspirations of the residents of many African democracies. That’s not unique to sub-Saharan Africa, mind you: it is just as hard to feel as if American politics has much to do with what national and regional majorities actually want in terms of governance outcomes…. Nigeria’s government is not so much one that needs to catch up to international norms as it is a window into the near-term international norm of paralysis, incompetency, corruption, insecurity and spasmodic authoritarianism that many nation-states are hurtling towards, the United States most prominently among them…. The successful people of most nations want from their failing states… something that works most of the time for most of the people. There is nothing harder to explain about our moment that this desire seems more remote with each passing day…

I understand how someone could claim that “most elections plainly do not reflect the political aspirations of the residents of many African democracies.” But that argument needs to be made—that the politicians the voters voted for are not, in fact, the politicians the voters would really, if they were fully infomred, want to have controlling the levers of power.

But to go on to claim that it is “just as hard to feel as if American politics has much to do with what national and regional majorities actually want in terms of governance outcomes…”?

To claim that all of the institutional frameworks for informing voters, counting votes, and getting people to organize and pressure and lobby for public policies is worth nothing?

To work to devalue the institutions and practices of really-existing democracy is an attitude that guarantees that one will be powerless.

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