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Timing of childbearing and economic growth

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Abstract

This paper incorporates the timing of childbearing into a growth model with endogenous fertility. It analyzes a model in which individuals' human capital stock depends positively on their education and parental human capital and in which producing and raising children and acquiring human capital are time intensive. The model highlights how changes in the human capital stock interact with individuals' timing of childbearing in affecting the evolution of the economy. It shows that increases in the human capital stock raise the opportunity cost of having children while young and induce individuals to delay childbearing. That, in turn, accelerates human capital accumulation in the future. The model also demonstrates that early childbearing may lead to a development trap with low human capital.

Introduction

The link between economic development, educational attainment and fertility yields one of the most well-documented empirical regularities in economics and demographics: As economies develop, fertility rates fall, the level of educational attainment and the average age of childbearing increase (Table 1).1 While the economic growth and development literature has focused more on the interaction between fertility and long-run economic performance (see, for example, Becker et al., 1990; Galor and Weil, 1996), some microeconometric studies, such as Olsen and Farkas (1989) and Ribar (1994), have found evidence that adolescent childbearing and school completion are jointly and endogenously determined. This paper incorporates the timing of childbearing — as part of individuals' fertility decisions — into an economic growth model. In doing so, it demonstrates the mutually reinforcing effects of economic growth on delayed childbearing and delayed childbearing on growth.

In the nineteenth century, Thomas Malthus made the pioneering theoretical contribution on fertility and economic growth. His model predicts that death rates fall and fertility rises when incomes exceed the equilibrium per capita income. However, empirical evidence has revealed that fertility rates and economic development were negatively related during the past century and a half. It has also provided strong support for educational investment as a determinant of economic growth. See, for example, Barro (1991) and Mankiw et al. (1992).

Accordingly, economists have developed theoretical models that incorporate the interactions among fertility, educational investment and economic growth. Becker and Barro (1988) construct a model with a dynastic utility function in which the discount rate on future consumption is higher the more children a person has. According to their model, technological progress leads to lower fertility and higher consumption. Becker et al. (1990) consider a model in which human capital investment exhibits increasing returns, at least up to a point, and individuals' discount rate of future generations' utility is identical to the one developed by Becker and Barro (1988). They demonstrate that families have fewer children and educate each child more in economies with higher human capital levels. They also show that high fertility leads to slower economic growth. The important feature of these models is the specific nature in which the discount factor of parents depends on the number of their offspring. Sundstrom and David (1988) and Azariadis and Drazen (1990) explain the negative relation between fertility and economic development by individuals' desire to provide for their old age. In these models, increases in the wage rate improve the bargaining power of children with their parents and reduce parents' perceived value of having children. Galor and Weil (1996) present a model in which household fertility is determined by the relative wages of men and women. They consider a production function where capital is more complementary to women's labor input than it is to men's. Thus, increases in capital per worker raise women's relative wages and reduce fertility by increasing the cost of children more than household income.

This paper differs from existing related work in three main aspects: First, it provides an explanation for the well-documented empirical relation between economic development and timing of childbearing. In existing work, this relation arises implicitly and only as a by-product of individuals' fertility decisions (i.e., in any given period, if individuals face a trade-off between work and producing and rearing children, the fact that they have fewer children due to a higher opportunity cost implies that they also delay childbearing provided that individuals allocate the latter part of the period to producing and rearing children). Second, unlike existing work that has mostly emphasized time taken away from employment as the main opportunity cost of having children (see Birdsall, 1988 for a review), this paper includes time diverted from education as well as employment as part of the opportunity cost. Thus, it shows that delayed childbearing and higher levels of educational attainment are consequences of increases in the opportunity cost associated with time taken away from education relative to that associated with time taken away from employment. And third, the model presented below highlights how the human capital stock interacts with individuals' timing of childbearing in determining the evolution of the economy. It demonstrates that human capital accumulation raises the cost of having children while young relative to lifetime wage income. As a result, individuals delay childbearing and spend more time acquiring education when they are young. Since delayed childbearing, in turn, leads to higher future human capital levels, the model identifies the importance of the positive feedback between human capital accumulation and delayed childbearing in economic development.

In what follows, a three-period overlapping generations model — in which individuals receive utility from consumption in the last period and from the total number of their offspring — is considered. In the model, individuals are young and reared in the first period; they devote time to education and producing and rearing children in the second period; and they work, consume and produce and rear children in the last period. By assumption, accumulating human capital and producing and rearing children are time intensive. An important feature of the model is that human capital accumulation depends positively on the time spent on education and the parental human capital stock, which are assumed to be complements in human capital formation.2

In this setup, individuals' most productive time in acquiring human capital and having children coincide. Therefore, when individuals are young, they face a trade-off between getting educated and having children. Moreover, producing and rearing children in the second period becomes more costly with increases in parental human capital. In response, individuals devote more time to education and delay having children. Thus, as parental human capital increases, the fertility rate of young women declines while that of older women who are in the labor force increases. Nonetheless, since the effect of substitution of time to education from childbearing in the second period (due to higher parental human capital) always dominates the effect of higher income on the number of children individuals choose to have in the last period, total fertility declines as the economy evolves.

The model described below also shows that multiple steady-state regimes, where the initial stock of human capital of each country will determine the evolution of its economy, may exist. More specifically, countries that start out with a low initial human capital stock could converge to a development trap in which individuals are less educated and bear more children early. In contrast, those countries that start with a higher value of the initial human capital stock could converge to a steady-state in which individuals are more educated and have fewer children later.3

The remainder of the paper is organized as follows: Section 2describes the technology of production and the behavior of individuals. Section 3discusses the evolution of the economy. And, Section 4concludes.

Section snippets

Production

Consider a small open economy that operates in a perfectly competitive world in which economic activity extends over an infinite discrete time. The output of the economy is a single homogeneous good produced by a CRS production function that uses physical and human capital as input. The output produced at time t, Yt, is given byYt=F(Kt,Ht)=Htf(kt);kt≡Kt/Htwhere Kt and Ht, respectively, denote the quantities of physical and human capital employed in production at time t. The production function f

The evolution of the economy

The evolution of this economy, and, in particular, the evolution of the stock of human capital, {ht}t=0, is governed by an autonomous, non-linear, first-order difference equation. The evolution of the human capital stock, {ht}t=0, in turn, determines the evolutions of the amount of time allocated to education, {et}t=0, the number of children individuals choose to have in the second and third periods and in total, {nt}t=0, {nt+1}t=0, nT=nt+nt+1, and of per capital income, {yt}t=0. We

Conclusion

In providing an explanation for the well-documented negative relation between economic growth, development and fertility, existing work in the literature emphasizes time diverted from employment as the main opportunity cost of having children, and stresses that increases in the return to human capital make more educated individuals' time too valuable to care for children. Nonetheless, to the extent that individuals' most productive periods in having children and acquiring human capital

Acknowledgements

For useful comments and suggestions, I am indebted to two anonymous referees, the editor, Pranab Bardhan, John Fernald, Michael Gibson, Ann Owen, and David N. Weil. Of course, remaining errors are all my own. This paper represents the views of the author and should not be interpreted as reflecting those of the Board of Governors of the Federal Reserve System or other members of its staff.

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