باروری، انباشت سرمایه انسانی، و سیستم بازنشستگی

This paper provides a unified treatment of externalities associated with fertility and human capital accumulation within pay-as-you-go pension systems. It considers an overlapping generations model in which every generation consists of high earners and low earners with the proportion of types being determined endogenously. The number of children is deterministically chosen but the children's future ability is in part stochastic, in part determined by the family background, and in part through education. In addition to the customary externality source associated with a change in average fertility rate, this setup highlights another externality source. This is due to the effect of a parent's choice of number and educational attainment of his children on the proportion of high-ability individuals in the steady state. Our other results include: (i) Investments in education of high- and low-ability parents must be subsidized; (ii) direct child subsidies to one or both parent types can be negative; i.e., they can be taxes; (iii) net subsidies to children (direct child subsidies plus education subsidies) to at least one type of parents must be positive; (iv) parents who have a higher number of children should invest less in their education.

One of the most pressing problems facing the economies of the industrialized world is the fiscal solvency of their pay-as-you-go (PAYGO) social security systems.1 An important contributing factor to this problem has been the recent drastic fertility declines in Western Europe and Japan. What truly determines fertility, and what accounts for the observed evolution in fertility behavior, are still open questions. What is clear, however, is that, faced with a PAYGO social security system, parents do not have the right incentives to choose a fertility rate that is optimal. In such systems, each person's fertility decision affects the economy's population growth rate and with it everybody's pension benefits. Specifically, an increase in the rate of population growth increases the number of future workers who will have to support a retired person. No individual, however, takes this impact into account and that leads to a decentralized equilibrium outcome with too few children.2 The above problem is exacerbated by another externality associated with the “quality” of children, and their human capital accumulation, through the education decisions of parents. The rate of return of a pay-as-you-go system depends not just on the fertility rate, but also on productivity growth. The more productive the children, the higher will be their ability to produce and to pay taxes. This reinforces the public good nature of a family's child-rearing activities.3 Most of the literature has thus far treated the quality and quantity issues separately; or else have lumped the investments in quantity and quality together as if one decision determines both.4 A basic shortcoming of this approach is that it cannot distinguish between child subsidies, which correct externalities emanating from fertility decisions, and education subsidies which correct for externalities due to investing in education. This lack of distinction becomes more of a serious problem when the two types of externalities interact as they often do. To be sure, there are a number of studies in the literature that distinguish between quantity and quality decisions and study them both in one unified framework. Peters (1995) is an early example of this. In his model, both fertility and education choices are made deterministically. The main shortcomings of his approach are the deterministic nature of both quantity and quality decisions, and the lack of any heterogeneity among parents. Cigno et al. (2003) also allow for both fertility and quality. Fertility is fully deterministic, but children's quality, which Cigno et al. define in terms of “lifetime tax contributions”, is in part random and in part determined through actions of parents. The limitations of their study come from the static nature of their model, in looking at the decisions of the initial parent only, and their not allowing for heterogeneity among parents. Cigno and Luporini (2003), while building on Cigno et al. (2003), allow for parents’ heterogeneity in terms of their ability to influence their children's probability of success in life.5 However, their model remains static in nature as they too do not go beyond the decisions of the initial parents. In Meier and Wrede (2008) both fertility and types are partly stochastic and partly determined by investments. The limitation of their model comes from their ignoring the impact of fertility and education investments on the distribution of types in the economy. But this induced change in the distribution of types constitutes an important component of fertility and education externalities.6 The current paper addresses the quantity and quality questions in an overlapping generations model with high- and low-ability individuals. The unique feature of our study is its endogenous determination of the distribution of types. Specifically, we allow for this distribution to be affected by both education and fertility decisions. This framework gives rise to three sources of externality. First, there is the customary externality associated with the change in average fertility—the intergenerational transfer effect. It arises from the fertility decisions of parents. This source of externality disappears if the pension system is a pre-funded one. The second source of externality emanates from decisions that change the distribution of types even if average fertility is kept constant. It arises from both education decisions and fertility decisions. Its unique feature is that it does not depend on the institution of social security and exists for pre-funded systems as well. The third source of externality is due to interaction between average fertility and the distribution of types. It too arises from both education decisions and fertility decisions. It is different from the second externality source in that it exists because of the PAYGO institution and disappears if one moves to a pre-funded system. It is also different from the first externality source because it will not exist if the distribution of types were immutable. One distinguishing element between quantity and quality decisions is that of timing. One decides on the number of children quite early; the quality of children, i.e. their future earning capacity, is determined much later. We incorporate this timing sequence in our two-period overlapping generations model by assuming a sequential decision making process: At the end of the first-period, the young decide on starting a family and having children first and then on the extent of their children's education. We assume that parents choose the number of their children deterministically. It is true that the actual number of children in a family does not necessarily coincide with the number that parents initially intended to have.7 However, this choice is intrinsically more deterministic and less susceptible to random and other shocks than determining the quality of one's children. As to the quality, it is unrealistic to expect that one can determine the future earning abilities of one's children in a deterministic fashion simply by investing in their education and training. We assume that quality is determined by three factors. One is random; the second is due to education; and the third is pre-determined by one's “genes” and family background. Nevertheless all children of a particular parent turn out to be either of high- or of low-ability. Finally, we study the properties of an optimal pension system assuming that intergenerational transfer of resources occur only through the PAYGO scheme. This simplifies the analysis drastically by allowing us to ignore the issues relating to the choice between PAYGO and fully- or partially-funded pension systems. The determinants of this choice are multi-dimensional and, given our focus on endogenous fertility and education, any attempt to address this choice is bound to be inadequate.

In discussing PAYGO pension plans, models with endogenous fertility have emphasized the positive externality that each person's fertility decision bestows on everybody by increasing everybody's pension benefits through a higher population growth rate. This type of externality, it has been argued, may be internalized through child subsidies. Similarly, models with endogenous human capital formation have emphasized the positive externality of investing in education of one's children (because parents cannot expropriate the children's extra earnings due to parents’ education expenditures). The same argument has been put forward in cases when parents build their own human capital which they subsequently pass on to their children. These types of externalities may be internalized through education subsidies. In this paper, we have combined the different externality sources to learn what their interactions teach us about the combination of child and education subsidies one must use to internalize them both. We have also been concerned with the question of heterogeneity of parents and how this may come into play in connection with externality-correcting policies. This is particularly relevant when child and education subsidies change the distribution of parent types. To this end, the paper has modeled endogenous fertility and human capital formation in an overlapping generations framework wherein every generation consists of high earners and low earners with the proportion of types being determined endogenously. We have found, among other results, that: (1)Investing in education of children by either type of parents increases the proportion of high-ability children in the economy and bestows a positive externality on everybody else. This externality has two components, one of which is specific to PAYGO pension plans. (2)Increasing the fertility rate of one type of parents increase the proportion of high-ability children in the economy and bestows a positive externality on everybody else. An increase in the fertility rate of the other type reduces the proportion of high-ability children and imposes a negative externality on everybody else. (3)The ambiguity in determining which parents impose a positive externality, and which ones a negative externality, by having more children is due to the fact that the type who has more children invests less in education. (4)Direct child subsidies and education subsidies both reduce the cost of raising children. Thus a subsidy to education is also a subsidy to fertility. The difference is that the education subsidy lowers the share of education cost in the fertility subsidy. On the other hand, a subsidy to children is “neutral” between the two sources of costs. (5)Investments in education of high- and low-ability parents must always be subsidized because they entail positive externalities. (6)Direct child subsidies to one or both parent types can be negative; i.e., they can be taxes. (7) Net subsidies to children of a particular parent type (direct child subsidies plus education subsidies) must be set equal to the net externalities associated with increasing the fertility rate of that type. Net child subsidies to at least one type of parents must be positive; net child subsidies to the other type can be positive or negative. As a final observation, we remind our readers that our study has been conducted in a first-best environment. Although the main thrust of our observations should carry over to second-best environments wherein educational investments and/or types are not publicly observable, other interesting issues would also surface. We have left the examination of these other issues to a subsequent paper.