فرزندان وابسته و پدر و مادر سالمند: آموزش کمک های مالی و تامین اجتماعی در یک اقتصاد افزایش سن

In the last few decades in the United States birth rates have declined and longevity has risen while productivity growth has slowed. Given such changes, the increasing burden of funding programs for the elderly is likely to shift resources away from the young and toward the elderly. This paper uses an overlapping generations framework to examine the effects of tax policies on an aging economy. We find that if the quality of the education system is sufficiently high then raising the education tax rate and subsequently lowering the social security tax rate enhances growth and welfare.

The demographic profile of the United States is undergoing profound change. Birth rates are falling and longevity is increasing. As a result the elderly are projected to comprise an increasing proportion of the population. This has led to an increasing focus on issues relevant to the welfare of the elderly, such as social security. Meeting the demands of an aging population may, at the same time, reduce resources allocated to the young, such as education expenditures. In this paper we extend Pecchenino and Utendorf (1999) to examine the interconnections between funding for programs benefiting the elderly, represented by social security, and funding for programs benefiting the young, represented by public education. We utilize a Diamond (1965) style overlapping generations model to analyze possible intergenerational linkages. In our model, growth, along the transition or balanced-growth paths, is endogenously fueled by individuals' investments in both physical capital, to fund their retirements, and human capital, to fund their children's education, and by the government's investment in human capital via public education expenditures. Individuals face uncertainty over their longevity. All old agents receive social security benefits, which are funded in a pay-as-you-go manner. We examine how policies aimed at a specific target group, e.g. the elderly or the young, affect current and future welfare of the economy as a whole. Our model is similar in construct to Kaganovich and Zilcha (1999), which also examines the effects of the public funding of social security and education on economic growth. They, as we, find that shifting tax revenues from social security benefits to education can be welfare improving. We, however, take the constraints of the social security system (that benefits are determined as a replacement rate on wages, so benefits determine taxes) explicitly into account in our analysis. In addition, we assume that the government, effectively, faces two budget constraints: a social security constraint and an education constraint, rather than the unified constraint with the explicit tradeoff (more for social security implies less for education) assumed by Kaganovich and Zilcha. Further, our model incorporates uncertainty over the length of life as well as population growth, allowing us to analyze the demographic transition, an important issue absent from their analysis.2 The connection between social security and education is also central to a model sketched in Mulligan and Sala-i-Martin (1999). In this model social security is an explicit return when old on investments made in the human capital of the young and is a formalization of the observation found in Pogue and Sgontz (1977) and Becker and Murphy (1988) that social security is a dividend paid to the old for investing in the human capital of the current workers when they were young. Our model does not make this political linkage since in practice social security is a federal program while education is by and large a local program. Our model differs from many models of social security (see, for example, Diamond (1977), Imrohoroglu et al. (1995) among others) in that these models ignore child welfare when assessing the effects of various social security programs. Other work, while neither ignoring children nor education, makes expenditures on children exogenous, as in Wildasin (1991), or claims that human capital formation is independent of direct expenditures on children so that parents' decisions concerning their children's education are not important to the analysis, as in Sala-i-Martin (1996). In still other work education decisions are central to the analysis, as in Glomm and Ravikumar (1992), while abstracting from any spillovers of these decisions on the utility of the aged. In our model the interactions between social security programs and expenditures on children's education play a central role through the effects of education on individual and aggregate productivity. We model education as being utility enhancing for parents and productivity enhancing for the individual and society. Given our assumption of representative individuals we exclude the possibility of education as a signal, as in Spence (1974). We instead concentrate on the effects of the quality of education on individual and social welfare where middle-aged individuals value education for their children's sake and these children are rewarded by a higher market return for their labor. That the quality of education a child gets matters, both in terms of the market return to schooling and parental utility, is supported by empirical studies such as Hanushek (1986), Card and Krueger (1992), Ehrenberg et al. (1991), and Altonji and Dunn (1996) and by the casual empiricism that parents often relocate to “good” school districts. Because education is productivity enhancing, it provides the impetus for growth in our model. This connection between education and growth has its roots in the work of Shultz (1961) and the more recent theoretical work of Lucas (1988), Rebelo (1991) and others who, building on Schultz's insight, suggest that human capital formation as evidenced by educational attainment is an important ingredient in explaining economic growth. This theoretical position is supported empirically by Barro and Lee's (1993) analysis. Hanushek and Kim (1995) extend this analysis, providing evidence that not only does the amount of schooling matter but so does the quality of that schooling. Since education may be growth inducing the failure to adequately provide for and educate children may lead to slower growth or economic decline. Our model allows us to explore this possibility. Analysis of our model yields the following results. Increases in the social security replacement rate (and hence tax rate) leads to reductions in steady-state physical and human capital accumulation, and output or the rate of balanced growth while the opposite may be true for increases in the education tax rate. Increases in life expectancy increase capital accumulation, and steady-state output or the rate of balanced growth if the positive longevity effect overwhelms the negative tax and bequest effects. These results suggest that there is the potential for Pareto-improving changes in tax policy. Using a balanced-growth version of the model we show that in an aging economy if the efficiency of public expenditures on education is sufficiently high increasing public expenditures on education is both growth and welfare enhancing. Thus, shifting public resources toward the young may benefit all generations.

As a population ages there is increasing pressure to shift resources away from programs directly benefiting the young (education) and toward those directly benefiting the elderly (social security). The results of this paper indicate that such policies may be shortsighted. Because of the productivity enhancing effects of education and the saving reducing effects of social security, growth and welfare can both be increased by increasing the resources dedicated to educating the young. The key determinant of whether dedicating more resources to the young is growth enhancing is the quality of the education system, measured by the effectiveness of government expenditures on education. When the efficiency of public education expenditures is low the productivity gains from an increase in spending are slight and do not offset the reduction in social security benefits from the expenditure switching policy for the initial generations. The key determinants of whether dedicating more resources to the young is welfare enhancing in all periods are the quality of the education system and the degree of intergenerational altruism. Because the efficiency of government expenditures on education is linked with the growth rate of the economy it affects consumption and hence welfare. In an economy that places little or no importance on the young, policies that shift public resources toward the young will result in initial declines in welfare as the first effects of such policies are to raise the consumption of the young while reducing that of the middle aged. Moreover, while in this paper the education tax rate is exogenous, this tax rate is likely linked to the weight that society places on the education of its youth. Thus, in economies with low levels of altruism, aging is more likely to lead to decreases rather than increases in taxes to fund education. Such a policy will raise consumption of the current generation of workers and thus current welfare to the detriment of future generations.