Population Growth and Technological Change: One Million B.C. to 1990

The paper combines two assumptions: that the nonrivalry of technology makes total research output increase with population, and that, per the Malthusian tradition, the level of technology limits the population that can be supported. As Arrow [1962] and Romer [1990] point out, “the cost of inventing a new technology is independent of the number of people who use it” (p. 681), so holding the share of resources devoted to research fixed, more people means proportionally more potential inventors and hence more total invention – even though, in the simple model, each individual’s own chance of inventing something is assumed independent of population. Kremer is explicit that this population-spurs-technology implication is standard in the endogenous-growth literature (citing Aghion and Howitt [1992] and Grossman and Helpman [1991]) but “is typically dismissed as empirically undesirable” (p. 681) – motivating the paper’s attempt to show it fits the long-run data.

Combining the research equation A/A = pg (growth in technology proportional to population) with the Malthusian population-determination equation p = (A/y)^(1/(1-α)) yields the prediction that the growth rate of population is itself proportional to the level of population (Section I, eqs. 3-5). Formally, taking logs of the population equation and differentiating, then substituting the research equation, gives p-dot/p = g/(1-α) · p. Kremer notes this implies “much faster than exponential” population growth, in contrast to a model with constant exogenous technological change (which implies no relationship between population level and its growth rate, hence ordinary exponential growth) or to biological logistic models of animal populations, in which the growth rate declines, not increases, with population.

Because technology diffuses between countries, even with a long lag, so a country’s own population does not determine the technology available to it once contact exists. “Belgium, for example, is rich not because it has invented a lot of technology, but because it has the human capital and social institutions that allow it to employ technology invented in other countries” (p. 686) – Belgium has access to the inventions of at least as many people as Zaire despite having fewer people itself. The model’s testable implication therefore concerns technologically separate populations (Section IV.B), not a cross-section of modern, interconnected economies.

Section II.A lets research productivity g equal ky^δ, so that total technological change increases with population if δ < 1/(1-α) and decreases with population if δ > 1/(1-α). With a generous estimate of 1-α (land’s share) around one-third, technological change would fall in response to an exogenous population increase only if each person’s chance of inventing something rose faster than the cube of income – which Kremer treats as implausible, concluding that low research productivity in some poor, populous countries (India, China) can coexist with the model’s long-run, time-series prediction that technological change rises with population, because in the model population growth is itself an endogenous response to technology, not an exogenous shock that depresses income. The cross-section relationship between population and research output is correspondingly ambiguous under this extension, even though the time-series prediction survives.

Following Jones [1992], Section II.B lets research output be A-dot = g p^λ A^φ, where φ < 1 captures diminishing contribution of the already-attained technology level to further research. Kremer shows that under this equation, exogenous population growth at rate n generates a steady-state technology growth rate of λn/(1-φ), and that matching the model to the Malthusian population-determination equation requires λ - (1-α)(1-φ) ≈ 1, i.e., the exponents must combine so that population growth remains roughly proportional to population. Because population growth rates “did not increase over the postwar period, and even declined a bit” (p. 689) while TFP growth stayed roughly constant, the φ<1 version is needed to reconcile the model with modern data – a pure φ=1 (Section I) specification would imply ever-accelerating technological change, which the twentieth century does not show.

If population adjusts to its Malthusian steady state at finite speed rather than instantaneously, per capita income rises gradually over time rather than staying constant, because technological change keeps outrunning population’s ability to catch up (formally, once gp/(1-α) exceeds n(y), population growth cannot keep pace with technological change).* Combined with the assumption – drawn from Schultz [1981], Becker [1981], Willis [1982], and Galor and Weil [1992] – that population growth eventually declines in income once income is high enough, this gradually rising income eventually produces a demographic transition and a decline in population growth. Kremer stresses that under this extension, “population growth rates will eventually decline,” not because of overpopulation, but “due… to increased income and declining fertility” (p. 699), which the model attributes to specific functional assumptions about fertility, not to the core nonrivalry/Malthusian mechanism breaking down.

Kremer regresses the population growth rate on the level of population using data assembled mainly from McEvedy and Jones [1978] (10,000 B.C. to 1900) and United Nations sources (1920 on), spanning homo erectus (one million years ago) to 1990, correcting for heteroskedasticity because period lengths are uneven. In the baseline heteroskedasticity-weighted specification, the coefficient on population is 0.524 (s.e. 0.0258) with an intercept insignificantly different from zero and R^2 = 0.92 (n = 37); restricting to the post-200-B.C. sample gives a similar coefficient (0.537, s.e. 0.0334). The population coefficient remains significant (using standard t-statistics on the heteroskedasticity-weighted regression) at all times after 4000 B.C., and survives even through the major negative population shocks of the Black Death and the Mongol conquests when the theoretically appropriate upper-tail Dickey-Fuller critical values are used. The result is robust to three alternative historical population data sets (Durand, Deevey, Clark) and to regional series for Europe, China, and India (Table V), each of which independently shows population significant in explaining its own growth rate.

The melting of polar ice caps around 10,000 B.C. flooded land bridges and nearly eliminated technological contact between the Old World, the Americas, mainland Australia, Tasmania, and Flinders Island, giving regions that started with similar technology and population proportional to land area a long, uncontaminated test of whether greater land area (and hence larger initial population) produces faster technological change. By 1500, just before Columbus’s voyage reestablished contact, “the region with the greatest land area, the Old World, had the highest technological level” (p. 709); “the Americas followed, with the agriculture, cities, and elaborate calendars of the Aztec and Mayan civilizations”; and “Mainland Australia was third, with a population of hunters and gatherers.” Tasmania, in turn, “lacked even such mainland Australian technologies as the boomerang, fire-making, the spear-thrower, polished stone tools, stone tools with handles, and bone tools.” Flinders Island – cut off roughly 8,700 years ago with only about 680 square kilometers of land – shows possible technological regress: its inhabitants “lost the ability to make bone tools, for example, which archaeological evidence shows they once possessed” before dying out, according to radiocarbon evidence, about 4,000 years after being cut off by rising seas. Kremer calculates that, under the null that technological change is independent of initial population, the probability that the four inhabited regions’ technology levels would rank in exactly this order by land area is only 1 in 24 (1 in 120 including Flinders Island). Quantitative calibration of equation (17) broadly reproduces the observed 1500 population densities for Tasmania and Australia but underpredicts the Americas relative to the Old World, a discrepancy Kremer attributes candidly to possible underestimation of 10,000 B.C. population, the inclusion of sub-Saharan Africa in the “Old World” bloc despite limited trans-Saharan contact, and land-quality differences.

Kremer is explicit that the model is designed to fit the historical record, not current cross-country data, and that its single-differential-equation (instantaneous adjustment) version is an approximation that “breaks down at high enough levels of population” (p. 694), requiring the fuller two-equation phase-diagram analysis for recent history. He also notes the data are “obviously subject to measurement error” (p. 681) but argues that i.i.d. measurement error biases the regression against finding the predicted relationship rather than toward it, and that the main systematic-bias risk – an implicit Malthusian model already built into McEvedy and Jones’s own data construction – would, if anything, favor a different (discontinuous, technology-shock-driven) null hypothesis rather than the paper’s continuous proportionality prediction.

Kremer contrasts his model of continuous acceleration with “models involving discontinuous breaks, such as multiple equilibria models in which the economy either stagnates or experiences steady state growth” (p. 712), arguing that such models “typically make few predictions about when the economy will be in each equilibrium” and that treating most of history as mere stagnation sits awkwardly with inventions such as “the wheel, Euclidean geometry, the plow, and the compass.” He calls it “ironic that growth theorists are building models with sharp breaks at a time when most development economists reject the notion of takeoff and many economic historians stress continuity rather than a discontinuous industrial revolution” (pp. 712-713), and flags for future research the need to model the demographic transition quantitatively and to allow for slow technological diffusion and stochastic shocks, which the present paper abstracts from.