امنیت اجتماعی مطلوب در مدل سلسله ای با اثرات جانبی سرمایه گذاری و حاصلخیزی درونی
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|24189||2007||23 صفحه PDF||سفارش دهید||11280 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Journal of Economic Dynamics and Control, Volume 31, Issue 11, November 2007, Pages 3545–3567
This paper studies optimal pay-as-you-go social security with investment externalities, positive bequests and endogenous fertility. With an investment externality, a competitive solution without social security suffers from under-investment in capital and over-reproduction of population. We show the existence of time-consistent optimal social security that improves welfare by reducing fertility and increasing capital intensity. We also illustrate numerically that a small degree of this externality can justify the observed high ratios of social security spending to GDP.
Pay-as-you-go social security (PAYG) has been practiced in many countries in the last several decades. In industrial nations, for example, payroll tax rates for social security range from 10% to 20% or higher; see the United States Department of Health and Human Services (1999). At the same time, PAYG social security has attracted a great deal of attention in the literature. While most studies of social security have focused on how it affects capital accumulation, much less attention has been paid to how it affects social welfare. Existing studies of the welfare consequence of social security differ between models with or without altruistic bequests. Without such bequests, social security reduces life-cycle saving and its welfare implication hinges on some form of market failure or on the fact that the competitive solution in the life-cycle model with overlapping generations is typically second-best.1 In the life-cycle model, social security can improve welfare by mitigating the problem of over-accumulation of capital (e.g. Diamond, 1965), or it can emerge from a political equilibrium among different age groups with conflicting interests (e.g. Cooley and Soares, 1999). In a dynastic-family model, by contrast, social security is well known to be neutral concerning households’ consumption–saving decision (Barro, 1974), because a rise in social security transfers from workers to the elderly can be fully offset by increasing bequests from parents to children.2 Moreover, when fertility is endogenously chosen by parents, the rise in the bequest cost of having a child caused by social security reduces fertility and hence raises capital per worker (e.g. Becker and Barro, 1988 and Zhang, 1995). However, the welfare implication of such changes caused by social security remains unclear. In this situation, social security can increase the level, or the growth rate, of per capita output by reducing fertility. Indeed, there is empirical evidence in Zhang and Zhang (2004) and others indicating that social security has a negative effect on fertility and a positive effect on the growth rate of per capita income.3 It is therefore relevant and interesting to explore whether PAYG social security can be justified in terms of welfare when altruistic bequests are operative and fertility is endogenous. In this paper, we examine the welfare implication of PAYG social security with altruistic bequests and endogenous fertility in a dynastic model of capital accumulation. As in the literature, scaling up PAYG social security has no effect on the saving rate in a dynastic model when altruistic parents respond by leaving more bequests to their children to offset the resultant increase in the future tax burden. However, a rise in the tax rate for social security has opposing effects on fertility. On the one hand, by increasing the bequest cost of having a child, the tax rise tends to reduce fertility. On the other hand, by reducing the after-tax wage rate, the tax rise reduces the opportunity cost of spending time rearing a child and thus tends to raise fertility. In addition, if the amount of social security benefits depends on an individual's earnings, the tax rise implies a higher replacement rate that retains a balanced budget of social security. By raising the replacement rate, the tax rise raises the opportunity cost of spending time rearing a child and thus tends to reduce fertility. Given the same saving rate, any change in fertility due to the tax rise must affect capital intensity in an opposite direction. The net effect of scaling up social security on fertility (capital intensity) is found to be negative (positive) if the taste for the welfare, relative to the number, of children is strong enough. The opposite movements in fertility and capital intensity influence welfare differently. A fall in fertility reduces welfare as the number of children enters utility, while a rise in capital intensity raises labor productivity and hence raises welfare. The net welfare effect of social security depends on the strength of an investment externality in the model.4 Given this investment externality, private rates of return on investment are lower than the social rate. As a result, competitive solutions without government intervention would suffer from under-investment in capital compared to the social planner's solution. This under-investment in capital lowers the marginal product of labor from its socially optimal level (the opportunity cost of spending time rearing a child), thereby inducing parents to have too many children. We show the existence of time-consistent optimal social security that improves welfare by reducing fertility and increasing capital intensity.5 We also illustrate numerically that a small degree of the externality can justify the observed high ratios of social security spending to GDP. Exploring ideal public policy to deal with the under-investment arising from the investment externality has become an important issue in economic analysis in recent years (e.g. Devarajan et al., 1998 and Turnovsky, 2000). A typical result in this literature is to subsidize private investment rather than publicly provide such investment. Our result in this paper indicates that social security can also be an attractive policy instrument to promote per capita accumulation by lowering fertility, because developing countries that have little social security typically have too many children and too little capital per capita. In particular, the mechanism in our analysis differs from the standard infinitely lived representative agent model used in the related literature in that we incorporate life-cycle savings into a dynastic-family model and treat fertility as an endogenous variable. In order to fully characterize the underlying dynamics in this complex model, it is necessary that the tax rate, fertility and proportional allocations of output are constant over time. To deliver this, we assume log preferences and a Cobb–Douglas production function, which are rather standard in the literature on economic growth. We can then solve for the welfare level that applies not only in the steady state but also in the transitional path. With the solution for the welfare level, we can assess the welfare implication of social security. The remainder of this paper proceeds as follows. The next section introduces the model. Section 3 characterizes the equilibrium and derives the solution for the welfare level. Section 4 provides the main results. Section 5 discusses the extension to include leisure. The last section concludes.
نتیجه گیری انگلیسی
In this paper we have examined the welfare implication of social security by incorporating life-cycle savings, bequests, and fertility in a dynastic model. It is the first such welfare analysis in this type of model whereby life-cycle and dynastic-family decisions are determined together. To achieve this, we overcame the difficulty in tracking down the entire equilibrium path of capital accumulation and deriving an explicit solution for the welfare level. We have shown that scaling up social security improves welfare under the same condition it reduces fertility and raises capital intensity, until reaching an optimal tax rate. We have also shown that the optimal tax rate is time consistent in the sense that the current generations have no incentive to deviate from it when expecting future generations to follow it. In terms of underlying driving forces, our results emerge from the combination of altruistic bequests, learning-by-doing spillovers and endogenous fertility. Such a combination has not been used in dealing with the justification of social security. Thus, our results are complementary to Cooley and Soares (1999) that justifies social security in an overlapping generations model with selfish agents. We say this partly because, as some observers would argue, altruistic bequests may not be operative in some families. Quantitatively, we have also illustrated that realistic social security tax rates can be justified in this simple model. For rather weak externalities, the optimal tax rates for social security are found to range from 10% to 20%. However, our results would be over-stated if they were taken to reflect the full picture of the functioning of social security in reality. Nevertheless, they do highlight the importance of the investment externality and endogenous fertility in the welfare assessment of unfunded social security. Acknowledgment We would like to thank Peter N. Ireland (the Editor) and one anonymous referee for their helpful comments and suggestions. We are responsible for any remaining errors or omissions. Jie Zhang gratefully acknowledges the financial support of a research Grant on economic growth in an aging population by National University of Singapore (Ref. no. R-122-000-084-101).