Tuesday, March 25, 2014

Norman Borlaug always makes me appreciate the work of Thomas Malthus

It would have been Norman Borlaug's 100th birthday today. When I think about Borlaug it always makes me appreciate the work of Malthus. A lot of people find that odd, but I think it's because of the low quality of critiques of Malthus floating around.

What's frustrating about critiques of Malthus is that Malthus openly admits that the subsistence constraint is differentially binding because agriculture is differentially productive. He does have the famous base case model with arithmetic growth of food and geometric growth of population. And that's gripping for people, and the specification may be all wrong. But it served the useful purpose of being an equilibrium model (and an equilibrium model used by the rest of the classical economists, I should add). It also served the purpose of succinctly demolishing Condorcet and the utopians. Malthus insisted that you could not depend on the perfectibility of man. Man is an animal and the study of man needs to be tethered to that fact. We social scientists are studying a particularly goofy, creative, and eccentric primate that occupies a particular ecosystem, and those facts will govern the science of man. Moreover, when Malthus applies his model he talks about variations in preventative checks, positive checks, and agricultural productivity across different societies. I have not read much in his Principles of Political Economy outside of the stuff on general gluts, but I would be surprised if he denied technological progress there. So he is very clear that these parameters vary and change, but the fundamental point - and the point of having the rigidly parameterize arithmetic/geometric model - is that generally speaking man is constrained by the resources that sustain him.

Norman Borlaug matters precisely because Malthus was right on this point. If Malthus was wrong, Borlaug would not deserve his Nobel.

Accepting Malthus as one of the great political economists should really not be that hard. If you're willing to think in terms of early 18th century equivalents (i.e. - changing around what is the output and what is the input exactly), if you're willing to take logs, and if you squint a little, Malthus's model is basically the Solow model. Same sort of structure and same sort of equilibrium with the same sort of conclusion. Solow gets some abuse, sure, but nothing like the stupid sort of critiques that Malthus gets. Could you imagine someone offering "Solow is wrong because there's technological development" as a serious critique?

If you want to take the unified growth theory route and just label periods where subsistence constraints are binding as "Malthusian" and when they're not as "non-Malthusian" it makes perfect sense why you would use those sorts of labels. But don't try to pass off that labeling schema as history of economic thought.

What do we fault Solow for? Well we wish he endogenized a few things, chiefly technological growth. But even without that work, Mankiw, Romer, and Weil show that you can get a lot of mileage out of the Solow model. And of course "better" models cannibalize the Solow model for spare parts. The same could certainly be said for Malthus. It would be nice if he had more on technological growth. But don't confuse that case of "more research required" with the case that the model is useless or doesn't illustrate an important point. Anyway, my point here is that when Solow gets critiqued it makes for a quite edifying read. Not so with critiques of Malthus.


  1. Thomas R. Malthus will be remembered for striking a chord in intellectual history - not just for his theory of population, but also for being a precursor to J.M. Keynes. While one could argue over whether T.R. Malthus ought to be termed a "proto-Keynesian", there is no denying that he was a fine intellectual jouster for David Ricardo - and a good friend. On a somewhat related note...John Pullen has an article about more on the life of T.R. Malthus and his financial affairs that was recently published in the History of Economics Review, Volume 57, Winter 2013 edition. In case anyone is interested, please see the following link:


  2. I've argued, for as long as I can remember, that Malthus especially makes sense in the world in which he was writing, a world in which technological progress had been very, very slow, and in which increasing population growth apparently did lead to lower (average or median, it's not clear which) standards of living. So I never understood the "Wasn't Malthus stupid" sort of critique.

    And if people (Tyler Cowen, Robert Gordon come to mind) writing in the vein of the new secular stagnation are right, expect to see a resurgence of interest in Malthus. [I don't think they *are* right, but one never knows, do one? (As Fats Waller once said.)]

  3. Just to expand a little bit. The Maddison Project data attribute to Great Britain a real GDP per capita of $1703 in 1700 and $2097 in 1800. That's an average annual rate of growth of 0.2% per year, which means (essentially) that over a normal person's lifetime little or no improvement in the standard of living would be noticeable. (Incidentally, using the MP data from 1280, we get an average annual rate of growth of 0.2% between 1280 and 1800...) While Malthus would not have had this sort of data, he certainly had access to records and commentary which would suggest that little had happened to living standards over an extended time period.

  4. And, incidentally, according to the Wikipedia article on population in England, population grew from about 3,250,000 in 1100 to around 5,772,000 in 1751, an average annual growth rate of 0.09%...which might well have appeared to be indistinguishable from 0 to contemporary observers.

  5. " It also served the purpose of succinctly demolishing Condorcet and the utopians."

    Hmmm. Except it turned out that it was Condorcet (happily writing his optimistic utopian visions while sitting in a French prison waiting to be executed (or running from the authorities, can't recall)) who was right not Malthus. And he wasn't just "sort-of" right, he pretty much called. So... lots of people have read Malthus and his essay. But a lot fewer actually sat down and read the Condorcet (it's French, and it's not as rigorous and can't really be mathematized... except maybe for the "quantity-quality" trade off which then Becker and Co. reinvented a century and a half later. Yes, that's in Condorcet)

    I say this as someone who really likes Malthus, and his theory as it applies to the pre-IR world. But Condorcet did win that one.

  6. "but I would be surprised if he denied technological progress there."

    Malthus of course never denied technological progress - the point of the whole Essay is that income will stagnate *despite* technological progress. And as it turned out - one thing he was sort of "wrong" about - you could even have "geometric" technological progress (as long as it wasn't higher than the maximum possible birth rate) and Malthusian conclusions still hold.

    You can do a sort of hierarchical break down of how technology works in various economic "growth" models in terms of the effects of *levels* and *growth rates*:

    1. Take an endogenous growth model, like AK or anything with increasing returns to scale. Increasing the *level* of technology increases the *growth rate* of income (how an increase in the *growth rate* of technology affects *growth rate* of income depends on how you conceptualize "technology" vs. "capital" so it's sort of a weird question to ask. But basically an increase in the *growth rate* of technology will make the *growth rate* of income more exponential, like in Kremer's model)

    2. Step down to a Solow model with constant returns to scale. There an increase in the *growth rate* of technology increases the *growth rate* of per capita income. But an increase in the *level* of technology only increases the *level* of (steady state) per capita income, not the growth rate.

    3. Now Malthus with endogenous population, An increase in the *growth rate* of technology increases the *level* of (steady state) per capita income. An increase in the *level* of technology has no effect on the *level* of (steady state) per capita income.

    4. One step further down (though this is sort of my own ideas/stuff), resource-constrained Hunter-Gatherer economies. Not only does an increase in the *level* of technology does not increase the *level* of per capita income but can actually lower it via resource depletion and cause a collapse of the entire economy (like in the Brander-Taylor Easter Island model). An increase in the *growth rate* of technology is not even something you can consider.

    If this wasn't a blog comments section, you could put this in a little matrix/table, but basically as you move down from modern Endogenous Growth to Solow to Malthus to HG economies, the effects of *growth rates* translate into *level* effects then into nothing. What gets you an increase in *growth rate* in one model, only gets you an increase in *level* one step below, and what gets you an increase in *level* gets you nothing.

  7. I still have a lot of problems with this idea that Malthus' theory applies to pre-industrial society. I think disease and war controlled the population at least as much as agricultural productivity did. Take the Black Death for example, it too centuries for Europe to regain the population lost at that time. On the agricultural side, descriptions of farming before the agricultural revolution don't paint a picture of a very efficient system.

    1. I don't follow. Disease and war are both positive checks featured prominently in Malthus, aren't they?

    2. In the first edition. He got some (well deserved) flak for it so in the latter editions he emphasized the preventive checks and that actually became the lens through which we see Malthus today (more income = more babies = lower income). Big literature on the "European marriage pattern" etc.

      It was well deserved because it's pretty sketchy to try and attribute causality there. More people = more war? Maybe. More people = more disease? Yeah, sort of, once in awhile. You can well argue (even if you're sitting there arguing on the 18th century blogs) that, yes, sometimes these things are true, But it's easy to come up with counter examples and argue, as Condorcet did, that the general trend, despite one time shocks, is the opposite way. So Malthus in the end went with the preventive check. And modern analysis does tend to support that (Lee, Lee and Anderson, Crafts and Mills) though there's some sketchy things going on there as well.

      One big misunderstanding (well, there's actually quite a few) that one often encounters is that even people who understand Malthus' argument in qualitative terms often fail to get a grasp on the quantitative aspect. Malthus never said that these adjustments would take place over night. So even in a purely Malthusian world, with or without technological progress, the adjustment to it's long run equilibrium could take a very long time. But it would get there. It's a question about the speed of convergence. Which could be on the order of centuries.

    3. "I don't follow. Disease and war are both positive checks featured prominently in Malthus, aren't they"

      "It's a question about the speed of convergence. Which could be on the order of centuries."

      Yes, that's the problem. Malthus' system is one of those that's supposed to be an equilibrium system but for the equilibrium to appear we have to have certain conditions. Those conditions are not a proper part of the model. War doesn't correlate with population. Disease correlated with trade, if anything. So we end up with an equilibrium statement that's like "all other things being equal fat people should use more soap". To pick a more modern theory that's similar, in one of his books Fisher describes brilliantly the range of factors that control the demand for money, then he throws them all away and introduces a simple equilibrium model centred on a velocity that's set by the technicalities of banking.

      In the past I don't think any sort of Malthusian equilibrium was established, which is why I don't like this idea that Malthusian ideas describe the past accurately.

  8. "Those conditions are not a proper part of the model"

    Well, in the Essay itself they sort of are. Malthus posits certain relationships between mortality and income. And diminishing returns to labor. That gets you an "equilibrium" (steady state). Now, if a shock occurs, it might take long time to get back there, but given that it's an equilibrium (steady state), it will get there.

    The modern version of the Malthusian theory goes something like this:

    Per capita income: y=A*(L^-b), where A is productivity and 01 which suggests a problem). The usual estimate of a half life is 100 years.

    1. Yes, mortality, income and diminishing returns are all proper parts of the model, but war and disease aren't. Do you really think that in reality the shocks are rare enough that the equilibrium is ever reached? I'm doubtful about that.

      Also, there are institutional things to think about too. What if the institutions of land-ownership and use are setup for a situation where land isn't very scarce. How long does that take to change? Or should we consider it a constant?

    2. In my own view the Malthusian pressures operated through the birth rate, although I do have some doubts about that too, and the relationship between income, nutrition and susceptibility to disease. A good chunk of the adjustment mechanism might have been due to the effect of income on infant mortality - which, despite the fact that that it has the word "mortality" in there actually needs to be counted as (a negative) part of fertility. That's how it got to equilibrium.

      In my own view, the connection between war and income pressure is sketchy and something Malthus pulled out of thin air because he had some doubts as to whether the other mechanisms he posited were strong enough. So I agree with you there.

      With disease it sort of depends on whether you're talking about epidemics or just individuals succumbing to infections and the like. The first one, like war, is also sketchy. The second, somewhat plausible.

      You can look up Crafts and Mills 2009 "From Malthus to Solow: how did the Malthusian economy really evolve?" to see some estimates of how strong these forces were, at least in Britain, although as I alluded to above, there's one big glaring problem with those estimates (and likewise those of Anderson and Lee, which preceded C&M). (And it's a sort of problem that if I knew how to properly address, I'd be writing it up as a paper not a comment on a blog).

    3. Interesting I must read more about this in the future.

  9. Ugh, the math got screwed up by mark up. Anyway, there's a fully specified, precise model there.


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