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When markets are incomplete, social security can partially insure against idiosyncratic and aggregate risks. We incorporate both risks into an analytically tractable model with two overlapping generations and demonstrate that they interact over the life-cycle. The interactions appear even though the two risks are orthogonal and they amplify the welfare consequences of introducing social security. On the one hand, the interactions increase the welfare benefits from insurance. On the other hand, they can in- or decrease the welfare costs from crowding out of capital formation. This ambiguous effect on crowding out means that the net effect of these two channels is positive, hence the interactions of risks increase the total welfare benefits of social security.
When markets are incomplete, social security can partially insure against idiosyncratic and aggregate risks. We incorporate both risks into an analytically tractable model with two overlapping generations. We derive the equilibrium dynamics in closed form and show that joint presence of both risks leads to over-proportional risk exposure for households. This implies that the whole benefit from insurance through social security is greater than the sum of the benefits from insurance against each of the two risks in isolation. We measure this through interaction effects which appear even though the two risks are orthogonal by construction. While the interactions unambiguously increase the welfare benefits from insurance, they can in- or decrease the welfare costs from crowding out of capital formation. The net effect depends on the relative strengths of the opposing forces.
We propose a unified framework to measure the effects of different reforms of the pension system on retirement ages and macroeconomic indicators in the face of demographic change. A rich overlapping generations (OLG) model is built and endogenous retirement decisions are explicitly modeled within a public pension system. Heterogeneity with respect to consumption preferences, wage profiles, and survival rates is embedded in the model. Besides the expected direct effects of these reforms on the behavior of households, we observe that feedback effects do occur. Results suggest that individual retirement decisions are strongly influenced by numerous incentives produced by the pension system and macroeconomic variables, such as the statutory eligibility age, adjustment rates, the presence of a replacement rate, and interest rates. Those decisions, in turn, have several impacts on the macro-economy which can create feedback cycles working through equilibrium effects on interest rates and wages. Taken together, these reform scenarios have strong implications for the sustainability of pension systems. Because of the rich nature of our unified model framework, we are able to rank the reform proposals according to several individual and macroeconomic measures, thereby providing important support for policy recommendations on pension systems.