A stochastic model of mortality, fertility, and human capital investment
Introduction
Three major developments of the past century are the declines in mortality and fertility rates and the growth of educational investment. These events have occurred both in the developed countries and in the developing countries.1 The relationship between these three phenomena has nontrivial implications for economic growth.
Since increased life span implies a higher rate of return, declining child and youth mortality provides an important incentive to increase investment in the education of each child. Numerous researchers have emphasized that human capital accumulation is the prime engine for economic growth. They have not, however, rigorously investigated this particular mechanism through which increased survival chances promote growth by raising the human capital investment.
Historical and contemporary data show that mortality decline preceded the fertility decline in general.2 As a result, countries have experienced a phase of increasing population growth rates followed by a phase of declining rates. This whole phenomenon is known as “demographic transition” and has important implications for the process of economic growth. Lucas (2002) argues that demographic transition and industrial revolution are linked events and what is new about 1800 is not technological change by itself but the fact that fertility increases no longer translated improvements in technology into increases in population. Therefore, understanding the causes of the fertility transition is crucial in terms of past, present, and future economic growth.
One explanation of the fertility transition is the reduction in infant and child mortality.3 Previous literature models causality running from mortality to fertility as follows: if households are concerned about the number of surviving children, and if they desire a specific number of survivors, then a reduction in mortality may lead to a corresponding reduction in fertility. While this direct channel accounts for the significant portion of the reduction in fertility, it is an incomplete explanation since it cannot explain the reduction in the “net rate of reproduction” (NRR) and hence, the reduction in the population growth rate.4
Existing models of endogenous fertility, if they allow for mortality at all, do so in the context of certainty.5 High mortality is modeled as reducing the fraction of children who survive to adulthood. Thus, these models ignore the uncertainty about the number of surviving children that is present in a high-mortality environment. Uncertainty has been found to be important in a number of other areas of economics, and this paper illustrates that it is also critical in the context of survival of children. Indeed, it is shown that a model without uncertainty produces results at variance with the data.
The model here is built on the effects of mortality decline on the fertility and education decision of parents. If the marginal utility of a surviving child is convex in the number of survivors, then there will be a precautionary demand for children. Thus, parents are prudent in the sense of Kimball (1990). Since parents choose the number of births before they know how many children will survive, in a high mortality environment, they will increase the number of births beyond the number required to produce the desired number of survivors in expectation. As the mortality rate and thus, uncertainty fall, this precautionary demand decreases, and so does the NRR. Second, lower mortality increases a child's expected life span, which encourages investment in the child's human capital. The resources allocated to additional investment in education are freed by the reduction in fertility. Thus, parents find it optimal to move along a quality–quantity frontier, having fewer children and investing more resources in each one. The key result is that this quality–quantity trade-off is realized only if uncertainty is incorporated into individual's optimization problem.
As a result, this paper makes two novel contributions. The first is to establish the positive link between increased survival and human capital investment in an endogenous fertility framework. Some of the previous literature found that changes in mortality had no effect on the optimal amount of education. The second contribution is a proposed mechanism under which the relationship between the mortality decline and the fertility decline can be causal. Uncertainty about child survival gives rise to a precautionary demand for children. Thus, exogenous reductions in mortality lead to a decline in fertility and eventually in population growth. These two contributions indicate that relying on the causality from mortality to fertility to explain the fertility transition is not at odds with the view that the fertility decline is due to a quality–quantity trade-off. Increased child survival and the quality–quantity trade-off are complementary explanations, and together they tell a more complete story of the fertility decline.
The rest of the paper is structured as follows. Section 2 briefly presents the related literature. Section 3 introduces and solves the model under both certainty and uncertainty. Section 4 discusses the conclusion and extensions.
Section snippets
Empirical evidence and theoretical literature
Eckstein et al. (1998), in a study of Swedish fertility dynamics, show that the reduction in infant and child mortality is the most important factor explaining the fertility decline, while increases in the real wages can explain less than one-third of the fertility decline.6
There may be two different strategies at work that generate the fertility response.7
The model
Consider an OLG model, where individuals within a generation have identical preferences. Members of generation t live for two periods: in the first period of life (t−1), individuals consume a fraction of their parent's unit time endowment. In the beginning of the second period of life (t), individuals make a one-time fertility decision.
The preferences of the altruistic member of generation t are defined over second period's consumption, Ct, and the future income of the survivors, Ntwt+1ht+1,
Conclusion and extensions
Empirical studies show that there is a significant positive effect of human capital investment and a negative effect of fertility on economic development. Furthermore, researchers have found a positive correlation between life expectancy (or health proxies) and the rate of economic growth (Barro, 1997). However, there is not any study that provides direct evidence regarding the mechanism through which higher life expectancy promotes growth.
Based on these empirical findings, one such mechanism
Acknowledgements
I thank the referee, Oded Galor, Herschel Grossman, Harl Ryder, David Weil, and participants at numerous seminars and conferences for valuable comments and suggestions.
References (34)
- et al.
Mortality decline, human capital investment and economic growth
Journal of Development Economics
(2000) - Azariadis, C., Drazen, A., 1991. Demographic Transition in a Dual Economy. UCLA working...
Determinants of Economic Growth: A Cross-Country Empirical Study
(1997)Altruism in the family and selfishness in the market place
Economica
(1981)- et al.
A reformulation of the economic theory of fertility
Quarterly Journal of Economics
(1988) - et al.
Human capital, fertility and economic growth
Journal of Political Economy
(1990) Fertility response to child mortality: micro data from Israel
Journal of Political Economy
(1976)Social classes, demographic transition and economic growth
European Economic Review
(2001)Toward a restatement of demographic transition theory
Population and Development Review
(1976)The decline of fertility in Europe since the eighteenth century as a chapter in human demographic history
Statistical Inference
Demographic transition, income distribution, and economic growth
Journal of Economic Growth
Intergenerational trade, longevity, intrafamily transfers and economic growth
Journal of Political Economy
Infant mortality and the fertility transition: macro evidence from Europe and new findings from Prussia
The gender gap, fertility, and growth
American Economic Review
From Malthusian stagnation to modern growth
American Economic Review
Cited by (156)
Air pollution and online lender behavior: Evidence from Chinese peer-to-peer lending
2024, Journal of Behavioral and Experimental FinanceChina's demographic transition: A quantitative analysis
2023, European Economic ReviewChild mortality, child labor, fertility, and demographics
2023, Economic ModellingChild survival and contraception choice: Theory and evidence
2023, Journal of MacroeconomicsFinancial sector development and growth volatility: An international study
2020, International Review of Economics and FinanceChange and persistence in the age of Modernization: Saint-Germain-d'Anxure, 1730–1895
2020, Explorations in Economic History