What do we know about population and technological progress?

Bryan Caplan writes:

The more populous periods of human history–most obviously the last few centuries–clearly produced more scientific, technological, and cultural innovations than earlier, less populous periods. More populous countries today produce many more scientific, technological, and cultural innovations that less populous countries… Here’s a challenge for you: Name the most credible measure of idea production that isn’t at least moderately positively correlated with population.

Is this about the absolute number of ideas generated or ideas as a percentage contributor to economic growth?  If we are estimating the costs and benefits of greater population, or the future of economic growth rates, the latter is arguably the more important variable.  In any case, most plausible theories of economic growth imply that higher populations should lead to higher rates of ideas generation, as measured in terms of value.  Ideas are non-rival and can be enjoyed by the entire group, thus yielding a higher social rate of return.  There are also larger markets to pay for the ideas or award more fame to the inventors.

Here is a famous Michael Kremer paper arguing for a version of Caplan’s position.  That all said, it is far from obvious that Caplan is correct:

1. The measured rate of technological progress, as it contributes to gdp, seems to have peaked in the 1930s.  At that time total population, including the population of scientists, was much lower than today.  “Effective” total population was yet lower, given the backward nature of transportation and communications and trade at the time, compared to today.

2. A recent paper by Ashraf and Galor (it’s also worth reading for other reasons) concludes: “…population density in pre-industrial times was on average higher at latitudinal bands closer to the equator.”  Yet the countries closer to the equator did not end up being the drivers of industrial progress, even though they sometimes had higher rates of progress in agricultural times.  Northern Europe, with the exception of the Dutch Republic, was never the star for population density.  This paper also indicates that technology drives population growth — more than vice versa — and that “time elapsed since a region’s neolithic breakthrough” predicts later technological progress fairly well.

If you add an extra baby to most societies, ceteris paribus, the rate of expected idea generation does indeed go up in theory.  But how important a factor is that, compared to other influences on ideas generation?

Or: at very gross time scales (“the last few hundred years” vs. “the dark ages”) a positive relationship holds between population and ideas production, or at very gross numerical comparisons (“one million people” vs. “ten people”).  But viewed at finer granulations (by the way, the evidence in the Kremer paper is quite gross; e.g., pp. 710-712), the relationship isn’t nearly as strong as one might expect.  In the time series, it’s been largely a negative relationship for the last eighty years or so, as mentioned above.

What model might give you a positive relationship between population and innovation at grosser scales but not finer scales?  Let’s say there are various technological “platforms,” such as “fire,” “agriculture,” and “fossil fuels,” and maybe someday “uploads.”  At any point in time, growth rates depend on how much a region has exhausted the potential of its current platform.  This is largely independent of current population.  That said, larger population areas may have a greater chance of progressing to the next platform, so there is a long-term, gross correlation between population size and levels of technology.  Furthermore, if all regions have more or less exhausted the current platform, the larger region has a greater chance of leading the next breakthrough and thus being first to have the new and higher growth rate, even if most of the time it doesn’t have a higher growth rate for technological progress.  That view is hardly anti-population, but it explains why you will find screwy population-innovation correlations all over the place.  Finally, further breeding, as a recipe for progress, is an extreme lottery ticket and it only works at some special margins.


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