امنیت اجتماعی مطلوب در مدل سلسله ای با اثرات جانبی سرمایه انسانی، باروری و رشد درونزا

In this paper we investigate the optimal scale of pay-as-you-go social security in a dynastic family model with human capital externalities, fertility and endogenous growth. Human capital externalities reduce the return to human capital investment and hence lead to under-investment in human capital and over-reproduction of the population. If the taste for the number of children is sufficiently weak relative to the taste for the welfare of children, social security can be welfare enhancing by reducing fertility and raising human capital investment per child.

In this paper we investigate the implication of human capital externalities for optimal pay-as-you-go (PAYG) social security in a dynastic family model with two types of capital and with endogenous fertility. Human capital accumulation has been recognized as a key factor for earnings; see, e.g., some related studies in the survey article of Lemieux (2006). Yet, the outcome of human capital accumulation for children is under the influence of parental factors as well as social factors outside their families (i.e. external to families). According to empirical evidence by Solon (1999), about half of children's earnings are correlated with their parental earnings. This evidence suggests that non-parental factors or human capital externalities may be quantitatively substantial in the formation of one's human capital. Indeed, some empirical studies find evidence on human capital externalities in the determination of individuals' earnings through channels such as ethnic groups, neighborhoods, work places, or state funding of schools; see, e.g., Borjas, 1992, Borjas, 1994 and Borjas, 1995, Rauch (1993), Davies (2002) and Moretti, 2004a and Moretti, 2004b. For example, according to the studies of Borjas, the earnings of children are affected significantly not only by the earnings of their parents, but also by the mean earnings of the ethnic group in the parents' generation through ethnic neighborhoods in the United States. Also, Moretti (2004b) finds evidence on the effects of human capital externalities on individuals' earnings in manufacturing establishments across cities in the United States. The existence of human capital externalities found in the literature implies that the private rate of return to human capital investment should be lower than the social rate of return. This tends to engender underinvestment in human capital and thus may have strong policy implications for optimal social security. As important family decisions according to the well known trade-off between the quality and quantity of children in Becker and Lewis (1973), human capital investment and fertility have been found to be responsive to social security and thus serve as channels through which social security affects economic growth and population growth in Zhang (1995). Using cross-country data for the period 1960–2000, Zhang and Zhang (2004) investigate the effect of social security on growth and growth determinants (savings, human capital investment, and fertility).1 Their empirical analysis allows for feedback from growth to social security and treats growth, fertility, human capital investment and savings as endogenous variables using the IV estimation method. They also allow for country-specific fixed effects in a panel regression. They find that the ratio of social security benefits to GDP has a positive effect on human capital investment and a negative effect on fertility, as suggested in Fig. 1 and Fig. 2 that plot secondary school enrolment and fertility respectively against the ratio of social security benefits to GDP in 70 countries of market economies. It is thus interesting to extend this line of research to explore the welfare implication and the optimal scale of social security in a dynastic family model with both human capital and fertility. This task is highly relevant today when many countries have been debating on whether PAYG social security should be reformed.While most studies on social security focus on its implication for capital accumulation, few have paid close attention to its welfare implication. Among them, Cooley and Soares (1999) have used a majority voting mechanism to justify why social security receives a majority support once it is already in place, although their model does not explain why it was instituted in the first place. Also, Zhang and Zhang (2007) have considered optimal social security with investment externalities in the final production sector in an extended neoclassical growth model without sustainable growth. However, having ignored human capital accumulation, these models do not capture the interaction between social security on the one hand and the trade-off between the quality and quantity of children on the other. The inclusion of human capital investment can be highly relevant in the analysis of optimal social security. On the one hand, the payroll tax for social security reduces the after-tax wage rate or the after-tax rate of return on human capital investment, thereby tending to reduce human capital investment. Thus, considering human capital investment in the analysis may make it more likely for social security to reduce welfare. On the other hand, when social security reduces fertility, human capital investment per child may rise via the trade-off between the quantity and quality of children. Because of these opposing forces, social security may engender a welfare gain only when the human capital externality causes fertility to be above its first-best level and causes human capital investment per child to be below its first-best level. If social security does improve welfare, it is also interesting in theory and relevant in practice to gauge the size of the optimal social security tax rate numerically for plausible parameterizations and compare it to the observed social security payroll tax rates in the real world. The rest of the paper proceeds as follows. The next section introduces the model. 3 and 4 determine the equilibrium solution and derive the results. Section 5 concludes.

In this paper we have examined the welfare implication of social security by incorporating life-cycle savings, bequests, human capital investment and fertility in a dynastic family model. In achieving this, we have overcome difficulties in tracking down the entire equilibrium path of capital accumulation and deriving an explicit solution for the welfare level with both human and physical capital. We have shown analytically that scaling up PAYG social security improves welfare when there are externalities under the same condition it reduces fertility and raises capital intensity, until reaching an optimal tax rate. Quantitatively, for an externality in the range of ε from ε = 0.85 to ε = 0.7, our model can generate optimal social security contribution rates in a range of 12%–22%. This is very much in line with the actual range of the contribution rates in many industrial countries. In terms of the underlying driving forces, our results hinge on assumptions of altruistic intergenerational transfers, human capital spillovers and endogenous fertility. Whether the results in this paper are useful contributions depends on whether these assumptions are plausible. Among them, the assumption of endogenous fertility follows the Beckerian approach. As a necessary condition for PAYG social security programs to mitigate the efficiency loss of the human capital externality, the negative response of fertility to social security is consistent with empirical evidence in some existing studies such as Cigno and Rosati (1992) and Zhang and Zhang (2004). The human capital externality works through the trade-off between the number and the quality of children, implying a below optimal level of human capital investment per child and an above optimal level of fertility. This differs from the implication of the investment externality explored in Zhang and Zhang (2007) that leads to suboptimal investment in physical capital and suboptimal fertility. Both types of externalities have received some supporting empirical evidence in the literature; their relative significance is an empirical task and awaits future research. If both externalities are present at the same time, we expect the results to remain similar qualitatively in the sense that they render a welfare improving role for unfunded social security. However, the results may differ quantitatively because of their different impacts on human capital accumulation, physical capital accumulation and fertility. Among these driving forces, the assumption of altruistic intergenerational transfers in dynastic families is more controversial since there are different views and evidence with regard to the existence or the form of altruism among family members in different generations. Though the related literature is inconclusive, some of the existing empirical studies have found supporting evidence for intergenerational altruism. Such a combination of these factors has not been used in the welfare analysis of social security, to the best of our knowledge. Thus, our results are complementary to Cooley and Soares (1999) that justifies why PAYG social security receives a majority support once it has already been put in place in an overlapping-generations model with selfish agents. Unlike their results, our model can also explain why social security has been instituted in many countries in the first place. While we focus on social security in this paper, there are other fiscal instruments that can also mitigate the efficiency loss of the human capital externality. These additional instruments include subsidies on education investment and taxes on the number of children. Since the competitive solution differs from the social planner's solution in two dimensions in our paper (fertility and human capital investment), using the conventional education subsidy alone cannot eliminate the efficiency loss of the human capital externality to reach the social planner allocation. Moreover, taxes on the number of children have hardly been practiced in Western countries. In fact, poor families with many children have often been provided with financial assistance from social programs, which can be traced back to the early 19th century in England (see, e.g., Boyer, 1989). Population aging in the last several decades has created financial pressure on maintaining a balanced budget for PAYG social security programs in many countries. Different proposals for social security reform have emerged. Some of them aim at replacing pay-as-you-go social security with compulsory retirement savings in individual accounts. For instance, there was a failed referendum in New Zealand in 1997 calling for establishing a compulsory individually-based retirement savings scheme, which was regarded as a substitute for its public pension. The policy implication of our analysis in this paper is a call for caution against reform plans that abandon pay-as-you-go social security or reduce its scale significantly. In developed countries, population aging has been driven by two factors: below-replacement fertility rates and falling mortality rates. Our present paper abstracts from the second factor. For population aging driven by a permanent decline in fertility (caused by factors other than social security), our numerical results suggest that little change in the optimal contribution rate for PAYG social security may be made in the presence of the human capital externality. Indeed, many reform proposals try to keep the contribution rates at today's level and only change the “design” of the pension system such as strengthening the funded component or weakening the intragenerational redistribution. According to Zhang (1995), however, an inframarginal funded pension component is neutral if the benefit is linked to one's own contribution, whereas it has a positive effect on fertility and negative effects on human capital investment and growth if the benefit is independent of one's own contribution. In either case of the relationship between pension benefits and contributions for an individual, the funded component is not useful to mitigate the efficiency loss caused by human capital externalities in this model. Finally, reducing intragenerational redistribution makes social security benefits more dependent on one's own contribution. According to Zhang and Zhang (2003), this stronger linkage of benefits to contributions at an individual level makes it more likely for PAYG social security to raise human capital investment and the growth rate and reduce fertility. Therefore, reducing intragenerational redistribution is likely to make PAYG social security more effective in mitigating the efficiency loss of the human capital externality.