غیر یکنواختی باروری در انباشت سرمایه انسانی و رشد اقتصادی

This paper investigates the relationship between per capita human capital investment and the fertility rate. In the first part of the article we analyze a theoretical model with endogenous birth rate in which we do not make any assumption on how fertility directly affects per capita human capital accumulation. The results obtained in this model are then compared with those of a more traditional setting where the birth rate is exogenous and in which the direct effect of this variable on per capita human capital investment is monotonically negative, a rather standard assumption within the available theoretical literature. By using non-parametric techniques, we document the presence of a strong non-monotonicity in the total effect that fertility plays on human capital accumulation, and hence on economic growth. The non-monotonic effect of fertility on human capital appears to hold empirically for OECD, as well as non-OECD countries.

The analysis of the impact of demographic change (population growth) on the growth rate of real per capita income represents an old, but still unsettled topic of research. Malthus (1798) was among the first to recognize that a higher population growth rate would ultimately in the very long-run have led to economic stagnation. According to his view, in a world in which economic resources are in fixed supply and technological progress is very slow or totally absent, the food-production activity would, sooner or later, have been overwhelmed by the pressures of a rapidly growing population. In this scenario, the available diet of each single individual in the population would have fallen below a given subsistence level, so leading to a fall of the productivity growth rate as well. 1 Unlike Malthus, proponents of the optimistic view 2 emphasize, instead, the positive effect that a larger population can exert on the rate of technological progress (an endogenous variable) and, thus, on economic growth: “…More people means more Isaac Newtons and therefore more ideas. More ideas, because of nonrivalry, mean more per capita income. Therefore, population growth, combined with the increasing returns to scale associated with ideas delivers sustained long-run growth” ( Jones, 2003, p. 505). 3 Besides the pessimistic and optimistic ones, there also exists another belief about the long-run effects of population growth on economic growth: the neutralist one. The advocates of this view claim that population growth has in general only little significant impact on economic growth and that such impact can be either positive, or negative, or else wholly inexistent ( Srinivasan, 1988 and Bloom et al., 2003). The pessimistic prediction of Malthus (1798) has fortunately never become reality. Nonetheless, it is now well known (Bloom et al., 2003 and United Nations, 2004) that, unlike the industrialized world, the less (and especially the least) developed regions of the planet are rapidly and increasingly gaining shares of the world population. Since these regions are those that actually exhibit the highest fertility and the lowest literacy and economic growth rates, the following question becomes of paramount importance in such a context: what is the effect that a further increase in the fertility rate (thus, in the population growth rate) may have on human capital accumulation and, through this channel, on sustained long-run economic growth? The main objective of the present paper is to tackle this issue from a theoretical as well as an empirical perspective. In order to achieve this objective we briefly present the main results of a simple benchmark model in which individuals can invest solely in human capital, the only input in the aggregate production function. We also assume that final output (aggregate GDP) can only be consumed, that the economy is closed (there is no international trade in goods and services and no international migration of people) and, finally, that there exists no governmental activity. Thus, in such an environment there is no room for physical capital investment. In this model the birth rate is exogenous, and moreover its direct effect on per-capita human capital investment (the so-called dilution effect) is taken as linear and monotonically negative. This is a rather standard assumption in the growth literature with human capital accumulation. The main prediction of the model is that the total impact of the population growth rate (the birth rate) on the rate of economic growth is, in general, monotonically negative as well. 4 Then, we extend the benchmark model by allowing for an endogenous birth rate, and by making no ex-ante specific assumption on the way this rate might affect directly per capita human capital investment. This modeling strategy is compatible with a situation in which the total impact of population growth on economic growth is non-monotonic, i.e. a situation where the growth-effect of higher fertility is, as a whole, different (in sign and in magnitude) across different groups of countries characterized by different birth rates. Kelley (1988, p. 1686) was among the first to admit that the relationship between population and economic growth rates is indeed non-monotonic.5 In the last section of the paper we go to the data. By using semi-parametric and fully non-parametric methods, our empirical investigation finds strong evidence against the exogeneity of the birth rate, as well as against the monotonicity of the total impact that the birth rate has on the rate of per capita human capital investment and economic growth (these are the two building-blocks on which the simple benchmark model is founded).6 Kalaitzidakis et al. (2001), using non-parametric techniques, were among the first to search empirically for a nonlinear effect of human capital accumulation on economic growth. In their paper, the authors split human capital by gender (male vs. female human capital) and by category (primary vs. tertiary education). They argue that the nonlinearities come especially from the distinction of human capital by gender (as a result of the discrimination between males and females in the labor market), and suggest that overall human capital investment has a negative impact on economic growth (due to the fact that, particularly in countries with low levels of human capital, acquiring skills is generally considered as a rent-seeking economic activity). In our paper, contrary to Kalaitzidakis et al. (2001), we search for possible non-monotonic effects of demographic factors (the birth rate) on economic growth. Starting from the idea that a change in the birth rate affects agents’ decision of how much to invest in per-capita human capital, and realizing that a higher birth rate leads to a faster depletion of available resources (so that investing in education becomes more costly), we claim that the relation between birth rate and per-capita human capital accumulation is non-monotonic. The presence of this non-monotonicity is, in turn, at the heart of the non-monotonicity in the relationship between birth rate and economic growth as well, and suggests that the opportunity cost of having children is different across countries with different birth rates. The article is organized as follows. In Section 2 we present the main assumptions and predictions of a simple (benchmark) model in which all the demographic components of population growth are taken as exogenous and summarized in a single parameter, n. This benchmark model represents a useful theoretical starting point and offers itself for comparison with a richer and more general model (Section 3) where the birth rate is endogenous. In Section 4, we empirically estimate the effect of the birth rate on human capital accumulation. According to this analysis, we first of all find strong evidence that the birth rate is endogenous. Moreover, we also observe that the impact of the birth rate on human capital accumulation at the individual level is non-monotonic, a result that is contrary to the monotonically negative relationship revealed by the simple benchmark model. The last section summarizes and concludes.

This paper has reassessed the long run correlation between demographic change and economic growth from an empirical, as well as a theoretical point of view. In order to accomplish this task, we focused on the fertility rate as our demographic variable of interest (the birth rate is, indeed, one of the most important demographic variables, as it affects directly population growth), and on human capital accumulation as the fundamental driver of sustained long run economic growth. While, from the empirical point of view, our motivation was to search for possible non-monotonic effects of the birth rate on human capital investment at the individual level, from the theoretical point of view our main objective was to analyze and characterize two completely different settings. The first is a simple model in which the birth rate is exogenous and affects monotonically and negatively per capita human capital accumulation (linear and negative dilution effect); the second, instead, is a model in which the birth rate is endogenous and the dilution effect can be either linear or nonlinear, and is potentially non-monotonic. Since countries experience different birth rates and have different economic performances, our major conjecture in building the second model was that the non-monotonic total impact of fertility on economic growth is indeed the consequence of its non-monotonic effect on per capita human capital investment. The benchmark model is strongly rejected by the data, according to which the birth rate is endogenous and, more importantly, there exist a strong non-monotonicity in the relationship between fertility rate and per capita human capital investment. Because of this evident non-monotonicity, our analysis can ultimately suggest, for any different value of n (and, hence, for any different country in the sample), the direction of the differential total effect of this demographic variable on economic growth. As a whole, our analysis implies that at low levels of the birth rate higher birth rates can surely have a positive growth-effect and that the main policy initiatives here should concentrate on easing the opportunity cost of having children. On the other hand, at high levels of the birth rate, a reduction in these rates can definitely contribute to boost per capita human capital accumulation and economic growth. This paper can be extended along different directions, three of which are listed here. The first would be to consider a human capital production technology different from the Lucas’ (1988), and more similar to the Mincer’s (1974) specification (see Bils and Klenow, 2000, Eq. (3), p. 1162). Secondly, in this article we treated human capital as the sole reproducible factor, entering the aggregate production function as the only input. Though, it is well known that economic agents (individuals and firms) do accumulate and produce by way of a variety of other factor-inputs (think of physical and technological capital, just to mention some notable examples). Building and testing a theory of endogenous fertility in which there is more than one reproducible factor-input and where there are non-monotonicities of the birth rate in the law of motion of one or all of these factor-inputs still remains at the top of future research agenda and, thus, represents a further possible extension of the present paper. Finally, there is also scope to develop a micro-founded model in which the non-monotonic effect of the birth rate on human capital accumulation decisions is derived from individual (rather than aggregate) behavior.