تعیین کمیت خطربه اشتراک گذاری سود رفاهی تامین اجتماعی

The welfare effects of intergenerational risk sharing through a pay-as-you-go social security system that is efficiently indexed to wages or interest rates are quantified. Comparing steady states, there are large welfare gains of being born into an economy with efficient risk sharing as compared to the current U.S. system. Efficient policy involves an increasingly risky net of tax income over the life cycle. When adjustment to steady state is taken into account, the welfare gains largely turn negative. The results are also compared and contrasted to the first best allocation.

How should aggregate productivity risk be allocated between taxpayers and retirees in a pay-as-you-go (PAYGO) social security system? This question is motivated by the fact that overlapping generations (OLG) models are known to be inefficient in an ex ante sense, stemming from the inability of the unborn to insure themselves. 1 With standard CRRA preferences and Cobb–Douglas technology, the laissez-faire allocation of risk is inefficient by imposing too little productivity risk on retirees and too much on future generations. 2 A PAYGO system has the potential of correcting these inefficiencies, due to the inherent intergenerational link found by current pension payments being immediately transferred to retirees. More precisely, productivity risk can be transferred between taxpayers and retirees by allowing benefits to respond to macroeconomic shocks. When the economy is hit by a shock, the government can keep the social security budget in balance by adjusting benefits or contributions (or, naturally, by a combination thereof). In the former case, exposure to productivity risk is amplified for retirees and, in the latter case, for taxpayers. Using the PAYGO system to transfer productivity risk between these two groups is thus straightforward.3 In the current U.S. social security system, an element of intergenerational risk sharing is found in the mechanism of wage-indexed benefits, implying that benefits respond to younger generations’ income.4 In this paper, a three-period overlapping generations model is used to analyze the importance of intergenerational risk sharing in social security. Specifically, the model features Epstein and Zin preferences, aggregate uncertainty, endogenous production and a PAYGO system characterized by simple schemes, where benefits are indexed to the aggregate wage rate or the return to capital.5 A search algorithm then searches for the coefficients of the schemes that maximize the expected lifetime utility of a newborn agent. Finally, outcomes are compared to the current U.S. system and the social optimum. The allocation of risk in social security is found to have a large influence on the economy. The first section of the analysis abstracts from transitions and finds welfare gains of being born into an economy with efficient wage indexation of up to 15% of the per-period consumption, as compared to the U.S. system. The efficient risk policy, which features highly volatile benefits in combination with highly procyclical taxes, ensures that agents are well insured when they enter the economy (as young). Highly volatile benefits then imply that agents’ risk exposure is increasing over the life cycle. Given this structure, workers hold more capital to hedge their coming volatile benefits, which significantly reduces the crowding out effect of the unfunded system.6 The main point from the analysis in the first section is that the risk structure should be predictable, known in advance and that agents should be given time to prepare. The efficient policy then has important general equilibrium effects and, in fact, the major part of the welfare gains associated with improved risk sharing in the first section is found to be general equilibrium effects.7 Unexpected transitions are taken into account in the second part of the analysis. Here, the net present values of the welfare gains are computed and mostly found to be largely negative.8 Even though all generations but the first two are better off, the loss for particularly the first generation (the middle-aged) is so large that it outweighs the positive gains for future generations. To determine the economic causes for these losses, the welfare effects for the first two generations are decomposed into three components. The first concerns the level and volatility of agents’ consumption at the beginning of the transition. Procyclical taxes stabilize current income, implying a positive effect, but future income also becomes more volatile. This leads agents (endogenously) to increase their precautionary savings, which reduces the level of current consumption. The net effect is negative for the middle-aged, implying that the level effect outweighs the volatility effect. The second effect comes from the interest rate. The higher capital stock associated with the new risk allocation implies a lower rate of return in the model, which also contributes negatively to the welfare gains. Third, policy affects the level and volatility of future consumption. However, which of these two effects that dominates depends on whether agents can short-sell assets. Finally, the transitions to the command optimum constitute Pareto improvements. However, since the simple schemes considered in the paper fail to produce Pareto improvements, a question for further research is to analyze whether the schemes can be improved in a simple way to yield Pareto improvements.

The allocation of risk in social security is found to have a large influence on the economy. The first section of the analysis abstracts from transitions and finds large welfare gains of being born into an economy with efficient intergenerational risk sharing as compared to the U.S. system. The efficient risk policy features strongly procyclical taxes in combination with highly volatile benefits and ensures that agents are well insured when they enter the economy. Highly volatile benefits imply an increasingly risky net of tax income over the life cycle. More generally, agents should be given time to prepare for risk. This strengthens the precautionary savings motive and reduces the crowding out effect of the unfunded system. Welfare effects turn largely negative when transitions are taken into account in the second section. It is mainly the first generation in the transition that is substantially worse off, but also the second tends to lose. The welfare effects for these generations are decomposed into three components that all are found to be important. The transitions to the command optimum constitute Pareto improvements, but the simple schemes considered in the paper fail to produce Pareto improvements. The implementation of the first best seems to require the schemes to also depend on the consumption histories of the agents alive in a given period. Unfortunately, that problem is complicated by the fact that the state space then becomes large. An important question for future research is then whether the simple social security schemes considered in the paper could be improved in a simple way to yield Pareto improvements. A first step could be to evaluate whether the inclusion of the consumption history of the old is sufficient to generate Pareto improvements.