Using the Malthusian model to measure technology


Jason Collins


March 27, 2013

Underlying much of Ashraf and Galor’s analysis of genetic diversity and economic development is a Malthusian model of the world. The Malthusian model, as the name suggests, originates in the work of Thomas Malthus (pictured). Malthus had the misfortune of providing an excellent description of the world across millennia, just at the point at which the model (apparently) lost much of its predictive power.

The Malthusian model rests on the assumption that any increase in income generates population growth. This ultimately prevents increases in technology from translating into increases in living standards. The greater resource productivity must now be  shared between more people. Of course, the reason people state that the Malthusian model no longer applies is that since 1800 many parts of the world have experienced substantial increases in per person income as population growth did not match technological progress.

The Malthusian model generates a couple of important predictions. First, any increase in productivity will generate population growth, not income growth. Secondly, differences in productivity between regions will be reflected in different population densities, not income differences.

This last point is important. It allows economists to use population density as a measure of technology and productivity in a Malthusian world. Since measuring technology is difficult but we have many measures of population density across time and societies, the Malthusian model provides a basis for conducting comparative economic analysis between countries and regions for times before 1800.

Ashraf and Galor use population density as a measure of technology for most of their analysis of genetic diversity and economic development, following a long line of economists who have done the same. But until recently, whether population density is a reasonable measure had not been properly tested.

In 2009, Ashraf and Galor published in the American Economic Review (ungated version here) an empirical examination of this hypothesis for the period 1 to 1500 CE (originating from Ashraf’s PhD thesis, as did the paper on genetic diversity and economic growth). The problem they faced was how to untangle population and technology when the two are so closely intertwined. Economists use the population density measure because technology is hard to measure and each flows directly into the other (more people leads to more ideas).

To untie the two, Ashraf and Galor use the timing of the onset of the Neolithic Revolution in different regions as a proxy for technology. The Neolithic Revolution occurred when populations moved from hunting and gathering to agricultural activities. If we accept Jared Diamond’s thesis that countries with favourable biogeographical factors gained a technological head start through the advent of agriculture that they maintain through to today, the timing of the Neolithic Revolution in different societies could be a proxy for technology and productivity.

Using this proxy, Ashraf and Galor found that, consistent with Malthusian theory, technology and productivity had a positive effect on population density, but no effect on per person income levels for the period 1 to 1500 CE. The result is robust to a range of controls including geographic and climactic factors, and holds when they use a more direct (but possibly less reliable) measure of technology.

There are two particularly interesting observations that Ashraf and Galor draw from their work. The first is that despite income stagnation, pre-Industrial times could be very dynamic. It is just that the Malthusian dynamics mask the effect of technological changes.

Secondly, their finding can be interpreted as supporting Jared Diamond’s hypothesis (or at least, it is not inconsistent with it). Those societies that first experienced the Neolithic Revolution had the highest population densities, suggesting a persistent advantage to an early start.

However, this support for the Malthusian model is not a ticket to use any population density data as a measure of technological progress. One of the more interesting points in the critique of Ashraf and Galor’s genetic diversity work published in Current Anthropology was the way some of the population density estimates used by Ashraf and Galor were developed.

McEvedy and Jones (1978:292) argue that the total population in Mexico in 1500 CE was no more than 5 million. They do so based on data from Rosenblat (1945, 1967), a source that uses problematic postconquest records. In fact, scholars contemporary with McEvedy and Jones (1978) proposed estimates in the 5–6 million range for the area corresponding only to the Aztec empire (e.g., Sanders and Price 1968). The Aztecs controlled a territory that covered no more than one quarter of contemporary Mexico and that excluded all of northwest Mexico and the Yucatan. Even while, at the time McEvedy and Jones (1978) were writing, other estimates for Mexico’s population were set at around 18–30 million (Cook and Borah 1971), McEvedy and Jones (1978: 272) discredit those estimates on the puzzling claim that they were not in line with those of other populations at “comparable levels of culture.”

Given that McEvedy and Jones are allowing the level of culture to colour their population estimates, those population estimates cannot be considered a sound basis for measuring technology. Population data shaped by the Malthusian model is not ideal to use as a measure of development. I don’t expect that changing the population density numbers substantially change Ashraf and Galor’s results (although the data is online if you want to check this), but we should use the numbers with some caution.

My posts on Ashraf and Galor’s paper on genetic diversity and economic growth are as follows:

  1. A summary of the paper methodology and findings

  2. Does genetic diversity increase innovation?

  3. Does genetic diversity increase conflict?

  4. Is genetic diversity a proxy for phenotypic diversity?

  5. Is population density a good measure of technological progress? (this post)

  6. What are the policy implications of the effects of genetic diversity on economic development?

  7. Should this paper have been published?

Earlier debate on this paper can also be found hereherehere and here.