Social Security in an Analytically Tractable Overlapping Generations Model with Aggregate and Idiosyncratic Risk
SAFE Working Paper No. 71
35 Pages Posted: 29 Oct 2014 Last revised: 16 Apr 2015
Date Written: April 13, 2015
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.
Keywords: social security, idiosyncratic risk, aggregate risk, welfare, insurance, crowding out
JEL Classification: C68, E27, E62, G12, H55
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