امنیت اجتماعی و تقسیم خطر

In this paper we identify conditions under which the introduction of a pay-as-you-go social security system is ex ante Pareto-improving in a stochastic OLG economy with capital accumulation and land. We argue that these conditions are consistent with realistic specifications of the parameters of the economy. In our model financial markets are complete and competitive equilibria interim Pareto efficient. Therefore, a welfare improvement can only be obtained if agentsʼ welfare is evaluated ex ante, and arises from an improvement in intergenerational risk sharing. We also examine the optimal size of a given social security system as well as its optimal reform.

The pay-as-you-go social security system in the US was introduced as a tool to mitigate the effects of economic crises. In a special message to Congress accompanying the draft of the social security bill President Roosevelt said “No one can guarantee this country against the dangers of future depressions, but we can reduce those dangers. ...we can provide the m eans of mitigating their results. This plan for economic security is at once a measure of prevention and a measure of alleviation.” (see e.g. Kennedy [14, p. 270]). In this paper we examine to what extent enhanced intergenerational risk sharing through a pay-as-you-go social security can alleviate the conse- quences of economic downturns. This idea dates back to at least Enders and Lapan [9]. More recently, it is used as an argument against privatization of social security. For example, Shiller [18] writes “If risk management is to be really effective, it is most important that it help out in the most desperate situations, and this is what the US government’s social security, financed with income taxes, does.” To properly evaluate whether a social security system allows to improve risk-sharing it is important to specify the welfare criterion that is used (and hence the market failures social se- curity may address). If agents’ utility is evaluated at an interim stage, conditionally on the state at their birth, an improvement can only be obtained if some financial markets are missing, or the economy is dynamically inefficient. While one might argue that in reality crucial markets are missing (in particular annuity markets and markets for securities that pay contingent on id- iosyncratic shocks), this source of inefficiency is not specific to economies with overlapping generations and other insurance schemes could be introduced which are Pareto-improving (in particular new financial assets, fully funded annuities, etc.). Hence the presence of some miss- ing markets might provide a justification for some government intervention but does not directly point to social security as an ideal instrument. Using an interim welfare criterion, several authors have examined the potential benefits of pay-as-you-go social security systems in realistically cal- ibrated, dynamically efficient economies with missing markets (see e.g. Imrohoroglu et al. [13] or Krueger and Kubler [16]). They find that the negative effects of social security on the capi- tal stock and wages clearly outweigh, quantitatively, any positive risk sharing effects of such a system. However, if agents’ welfare is evaluated at an ex ante stage competitive equilibria in stochas- tic overlapping generation models are generally suboptimal, even when markets are complete, because agents are unable to trade to insure against the realization of the uncertainty at their birth. There must then be some transfers between generations which improve intergenerational risk sharing and constitute a Pareto-improvement. It is then particularly of interest to investigate under what conditions a pay-as-you-go social security system (or, more generally, one-sided transfers from the young to the old) is Pareto-improving according to an ex ante welfare cri- terion in economies where equilibria are interim Pareto efficient. In these economies the only possible source of an improvement is the imperfection in intergenerational risk sharing due to the limitations on trading imposed by the demographic structure. In this paper we consider a class of overlapping generations economies where markets are complete, there is capital accumulation and land, an infinitely lived asset used in the production process together with labor and capital. The presence of land together with the completeness of markets ensure that competitive equilibria are interim Pareto efficient. We show that, for a wide range of realistic specifications of the parameters of the economy, a pay-as-you-go so- cial security system is ex ante Pareto improving and we demonstrate that the effects on the equilibrium price of land play a crucial role in enhancing the welfare benefits of social secu- rity We consider two period overlapping generations economies with a single 1 agent per gener- ation and stochastic shocks to aggregate production, and analyze three different pay-as-you-go systems: a defined contribution system, where transfers from the young are proportional to their income level, a defined benefits system, where transfers from the young to the old are state in- dependent, and an ideal system, where any state contingent transfer from the young to the old is allowed. We decompose the effects of a social security scheme into: i) a direct transfer from the young to the old (the one prescribed by the scheme), ii) an indirect transfer (which may have positive or negative sign) induced by the general equilibrium effects of social security on the stock of capital, and hence on equilibrium wages and return to capital, and on the price of long lived assets, iii) a change in the level of total resources available for consumption (due to the change in the stock of capital). We analyze first these various effects in isolation. This allows us to identify several conditions (primarily on the covariance between the shocks affecting the agents when young and old, on their risk aversion, and on the stochastic properties of the production shocks) under which these different components of the effects of a social security scheme have a positive effect on welfare. We find that for the direct transfer effect prescribed by a defined benefits social security system to be Pareto-improving, we need 2 consumption (and hence income) of the old agents to be pos- itively correlated with the consumption of the young and, at the same time, to exhibit a higher variability. A weaker condition suffices for an ideal system to be improving. Next, we consider the general equilibrium effect given by the changes in the price of long- lived assets. We find that the price of land tends to decrease as a result of the introduction of social security, so that we have an indirect transfer from young to old agents of negative sign, which in interim efficient economies has typically a positive effect on the welfare of future gener- ations. On this basis, we show that the presence of long-lived assets improves the case for social security, making the conditions for such policy to be welfare improving less stringent. Finally we examine the other general equilibrium effects, due to changes in capital accumulation and hence equilibrium wages and interest rates. The introduction of social security in dynamically efficient economies tends to crowd out the investment in capital and hence to lower output level. Further- more, the stochastic structure of the production shocks determine the correlation between wages, affecting the income when young, and return to capital, affecting the income when old. While we are able to identify some conditions on the properties of the production shocks under which the indirect effect of various social security schemes due to changes in capital accumulation is welfare improving, when combined with the direct effect, we show that in general it is rather difficult to find a rationale of pay-as-you-go social security in models with capital accumulation but without land. On this basis, we proceed then to examine the equilibria of the class of economies considered, where all these effects are combined together. In this case we solve for equilibria numerically and show that for economies with somewhat realistic parameter specifications the introduction of a defined contributions as well as that of a defined benefits social security system is welfare improving. These welfare changes are also decomposed into the various effects identified in the previous sections and the qualitative analysis carried out there proves helpful in gaining a better understanding of our results. We find that, while the general equilibrium effect of social security on the equilibrium level of the stock of capital tends to decrease welfare, this effect is more than compensated by the effect of the change in the price of land. The sign (and size) of the direct effect is then crucial for determining if a (defined benefits or defined contributions) social security scheme is Pareto-improving. As argued above, this direct effect is positive if the consumption when old is positively correlated, but sufficiently more volatile, with the consumption when young. These findings are in accord with our previous qualitative analysis, which then helps us in gaining some understanding into the welfare effects of social security. In our analysis we assume that labor is supplied inelastically. Hence our analysis abstracts form another important general equilibrium effect of social security and the labor supply distortions resulting from such scheme might be substantial. In this set-up we also analyze the optimal size of the social security system and evaluate the benefits of reforming an existing social security system to improve its risk-sharing properties. We find that the welfare gains that can be obtained by reforming a pay-as-you-go defined con- tributions system making social security contributions state contingent are much larger, in the environment considered, than those resulting from the introduction of the pay-as-you-go system. Such a finding is in line with Shiller [19]’s observation that, the US system’s risk sharing poten- tials seem limited in that the young’s transfers to the current old do not depend on the wealth of the young relative to that of the old. Starting with Gordon and Varian [12] several papers have examined the scope for a pay-as- you-go social security system under an ex ante welfare criterion. Shiller [19], Ball and Mankiw [2] and de Menil et al. [8] approach this question by using a partial equilibrium analysis in that in their model there is no capital accumulation and no land, and agents have access to a risky storage technology. As argued in this paper, the general equilibrium effects induced by social security play a very important role in a proper assessment of the benefits of costs and benefits of social security. Bohn [3] (see also Olovsson [17]) compares the competitive equilibria with and without social security for a realistically calibrated version of an economy with capital accumulation. He shows that it is difficult to make an argument in favor of social security in such set-up. This result, how- ever, depends crucially on the fact that Bohn abstracts from the presence of long-lived assets and restricts his attention to a specific form of production shocks, which implies the possibilities for intergenerational risk sharing are rather limited. We should also point out that, without control- ling for the fact that competitive equilibria without social security are interim efficient it is not possible to properly argue that any welfare gain is due to the improvements in intergenerational risk sharing induced by social security. Imrohoroglu et al. [13] and Krueger and Kubler [16] consider realistically calibrated models with agents that live for many periods. They consider a different welfare criterion (interim and not ex ante as in this paper) and consider the case where financial markets are incomplete rather than complete. In [13] as in this paper, land plays an important role. However, in their paper there are no stochastic shocks to depreciation. Our theoretical analysis shows the importance of these shocks. [16] has stochastic depreciation shocks but does not have land. Under the ex ante welfare criterion, the presence of land is critical for achieving possible Pareto-improvements via social security, at least in our setup with two-period lived agents. The results obtained in these papers on the welfare benefits of a pay-as-you-go social security system are then rather different from the ones found here. Another distinctive feature of our work with respect to these and most other papers is our attempt to characterize some properties of an optimal social security scheme.The effects of other forms of fiscal policy interventions on intergenerational risk sharing ac- cording to an ex ante welfare criterion have been studied by various authors. Gale [11] analyzes the efficient design of public debt, while Smetters [20] examines the role of capital taxation. The paper is organized as follows. In Section 2 we describe the class of economies and the various types of social security systems considered, and give conditions for interim and ex ante optimality. Section 3 examines the direct effects of such systems and Section 4 the equilibrium effects due to changes in the price of land and in capital accumulation. In Section 5 we analyze the interaction among all the effects of the alternative social security schemes for the class of economies under consideration. In Section 6 we examine within the same framework the optimal size of a social security system as well as the optimal design of such system and assess the welfare gains of reforming an existing system.

The idea that a pay-as-you-go social security system can lead to enhanced intergenerational risk sharing has been formalized in various papers (see the literature review in the introduction). However, it is also well known that the general equilibrium effects of social security lead to lower capital formation and hence lower consumption for future generations if the economy is dynamically efficient. In most quantitative studies this second effect seems to overcompensate any beneficial effects of enhanced risk sharing. We show that the presence of a durable good like land as an additional factor of production mitigates the crowding out effect and that intergenerational risk-sharing provides a normative justification of a pay-as-you-go social security system even if one takes into account the effects on the capital stock and equilibrium prices and if markets are complete. It is crucial to note that in our framework social security is only desirable under an ex ante welfare criterion: in the economies considered competitive equilibria are in fact always interim efficient, the only possibility for an improvement is then due to agents’ inability to trade before their birth, which prevents the attainment of efficient intergenerational risk sharing. 19 We also show that the welfare gains from an optimal design of a social security, where contribution rates and benefits are state contingent, can be quite large. Of course, our results should be interpreted cautiously: our model is missing many impor- tant ingredients, in particular, endogenous labor supply, population growth and technological progress and since it is a two period model, a proper calibration to the data turns out to be not possible.