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Population and development redux


The effects of population growth on long-term economic development are obviously important. This paper introduces new predictions from a general Malthus-Boserup model of population growth and ideas-based technological change. It also tests these predictions using numerous data sources, empirical specifications, and sample periods. Time series tests reveal that the empirical associations that hold true in the modern era are completely reversed in pre-modern samples. Inferences drawn from the pre-modern population growth of geographically isolated populations are also reversed when relevant controls are taken into account. While there is a clear break with Malthusian theory, in general, and especially outside of the modern era, there is no unequivocal evidence supporting Boserupian views. An alternative model consistent with transitional demographic patterns is briefly discussed.

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  1. Kuznets (1960) and Simon (1977) emphasized, but did not quantify, positive population externalities such as those advocated by endogenous growth theorists. Johnson (2000) and Jones (2005) also discussed population externalities in the production of knowledge in a long-term perspective. Pryor and Maurer (1982) and Lee (1988) are earlier syntheses of Malthus and Boserup with predictions that are similar to those of Kremer (1993). Curiously, the (positive) relationship between population growth and population size was first studied in the 1960s in the context of fatalistic “doomsday” models; see, e.g., von Foerster et al. (1960) and Umpleby (1987).

  2. This paper, however, is not a test for Malthusian dynamics. In contrast to Ashraf and Galor (2011), for example, the analysis does not focus exclusively on the pre-modern period. This paper, in fact, provides a clear illustration of the breakdown of Malthusian theory. This paper lacks direct data on technological differences across space and time. Comin et al. (2010) assembled a dataset on the adoption of technology during pre-modern times. The concluding section establishes consistency with their findings.

  3. The findings are also relevant due to the renewed interest in global environmental change and population externalities; see, e.g., Acemoglu et al. (2012), Baland and Robinson (2002), Bohn and Stuart (2015), Cohen (1995), Dasgupta (2000), and Lee and Miller (1990).

  4. Ravallion (2010) previously discussed the fragility of Kremer’s (1993) findings, but in a different context. Ravallion (2010) noted that Kremer’s (1993) model has a spacing implication: longer time periods between observations imply higher growth rates. Ravallion (2010) showed that the global data contradicts the spacing implication. The analysis presented here complements Ravallion (2010). For example, I examine different predictions and consider additional sources of data; specifically, data with evenly spaced observations.

  5. For example, it is not possible to separately test for “scale effects” (e.g., γ=1 and ϕ=0) and “market size effects” (e.g., γ<1 and ϕ<1). Madsen (2008) used patents and R&D data for OECD economies to examine Schumpeterian and semi-endogenous versions of the knowledge production function. These tests require data that is not available for pre-modern times. Madsen et al. (2010) implemented tests for the shape of the knowledge production function during the Industrial Revolution, with data that cannot be extended far back in time. See also Ang and Madsen (2011) for similar tests in high performing Asian economies.

  6. There are multiple alternative estimates of past population sizes including Clark (1967), Bairoch (1988), and more recently Maddison (2001). Caldwell and Schindlmayr (2002) discusses in detail the connections between these alternative estimates and the sources used here.

  7. There are very few alternatives sources to estimate the human population in the distant past; see, e.g., Hassan (1981). Deevey (1960) is a common source to most estimates. Deevey’s (1960, p. 195) estimates are available “from the inception of the hominid line one million years ago,” but his population data is so speculative that Deevey (1968, p. 248) himself remarked: “my own treatment of this, published some years ago in Scientific American, was not very professional.” Deevey’s (1960) data is especially problematic because it is biased toward accepting hypotheses (i) to (iii). I discuss this point in an Appendix not for publication.

  8. I re-scaled the growth rates so that all values of the normalized population growth rates are positive. The results are sensitive to the normalization I used. I do not present these results here, but as expected, ρ is an upper bound. I also considered a nonlinear OLS estimation of the model in the form of (4) but the estimates did not converge or were too sensitive to the initial guess to be of any value.

  9. An observation is considered high leverage if its leverage exceeds 4 /N.obs; see, Chatterjee and Hadi (1988, p. 100). All of Cook’s distances (D ) should be roughly equal. A relatively large Cook’s distance indicates an influential observation. I use the cut-off values based on D>F(0.5,2, N.obs −2); see, Chatterjee and Hadi (1988, p. 119). Influential observations are not necessarily outliers, but their inclusion is likely to influence the estimation of the regression coefficients. For example, because OLS minimizes square deviations, the estimates place a relatively heavy weight on atypical observations. I also computed the previous diagnostics for country data. Leverage and the Cook’s distance show a significant positive time trend. This indicates that recent observations are more influential than pre-modern observations.

  10. Focusing only on modern observations, an alternative way to examine the sensitivity of the results, agrees with the findings of Table 2. To save space, I only discuss the post-1600 estimates of Eq. 6 for the global data and the fixed effects regional estimates in McEvedy and Jones (1985), where more data is available. For the global data, β=7.52 (s.e. 0.70). For the fixed effects estimates, β=42.60 (s.e. 11.70). These estimates are positive, significant, and larger than the estimates for the entire sample. These results and Table 2 show that the strong positive relationship in the recent samples drives the results in Table 1.

  11. The number of domesticable plants and the number of animals are highly correlated in the sample (the correlation coefficient is 0.87). I included the continental axis of orientation from Hibbs and Olsson (2004) as an alternative specification. The results are similar to Panel B and are available upon request.

  12. Henrich (2004) proposed an analytical model of knowledge accumulation and diffusion much in line with Boserupian ideas and used demography to account for Tasmania’s technological conditions during pre-modern times. Read (2006) provides a critical assessment of Henrich’s (2004) theory and finds population to be a second-order influence. The analytical and empirical relationship between population/group size and cultural complexity in hunter-gather societies is the subject of a considerable literature in anthropology; see, e.g., Collard et al. (2013), Kline and Boyd (2010), and Read (2012). Existing empirical findings seem heavily constrained by small samples and by the fact that hunter-gatherers face different environments that require different technological adaptations and risk strategies.

  13. I also added dummy controls for the Black Death and the Mongol invasions to specification (5) in Table 5. The point estimates for these events are negative, but they do not alter the estimate of π 3.

  14. Population in 200 BC may be an inadequate proxy for the population size prior to the melting of the ice caps. In 200 BC, the large centers of agricultural production in Asia were consolidated and may have faced relatively stagnant conditions. Arable land may be a better proxy for the size of pre-treatment populations.

  15. For example, regressing ln[N i,t ] on ln[N i,t−1] in the full sample for McEvedy and Jones (1985) yields a fixed effects point estimate of 1.030 (s.e. 0.016). Since this point estimate exceeds one, the estimates suggest “divergence” across regions. For the reasons discussed in the previous section, this divergence appears to be a transitory event associated with the demographic transition.

  16. There are few alternative data sources for examining pre-modern conditions. Anthropological analyses of genetic diversity in current populations have been able to shed light on the demography of past populations; see, e.g., Relethford (2001, 2003). In economics, a growing literature has started using genetic information to examine current and past differences in economic development; see, e.g., Spolaore and Wacziarg (2009) and Ashraf and Galor (2013).


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I would like to thank two anonymous referees and the editor for many helpful suggestions. I would also like to thank Gary Becker, Michele Boldrin, David Carr, Robert Fogel, Kellie Forrester, Michael Gurven, Hyeok Jeong, Stephan Klasen, Gary Libecap, Peter Lindert, Bonnie Queen, Romain Wacziarg, Bruce Wyndick, as well as seminar participants from several different locations for their comments. I would especially like thank the late D. Gale Johnson for his many useful discussions on the role of population in the economy.

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Correspondence to Javier A. Birchenall.

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Birchenall, J.A. Population and development redux. J Popul Econ 29, 627–656 (2016).

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  • Population growth
  • Technological change
  • Malthus and Boserup

JEL Classification

  • J10
  • O40