International Tax and Public Finance

, Volume 22, Issue 4, pp 579–603 | Cite as

Social security in an analytically tractable overlapping generations model with aggregate and idiosyncratic risks

  • Daniel Harenberg
  • Alexander Ludwig


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 the joint presence of both risks leads to overproportional 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 increase or decrease the welfare costs from crowding-out of capital formation. The net effect depends on the relative strengths of the opposing forces.


Social security Idiosyncratic risk Aggregate risk Welfare Insurance 

JEL Classification

C68 E27 E62 G12 H55 



Daniel Harenberg gratefully acknowledges financial support of the Sonderforschungsbereich SFB 884 (German National Research Foundation), and of Swiss Re. Alex Ludwig gratefully acknowledges research support from the Research Center SAFE, funded by the State of Hessen initiative for research LOEWE and financial support by the German National Research Foundation under SPP 1578.

Supplementary material

10797_2015_9368_MOESM1_ESM.pdf (100 kb)
Supplementary material 1 (pdf 99 KB)


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.ETH ZürichZürichSwitzerland
  2. 2.SAFE, CMR, and MEAGoethe University FrankfurtFrankfurt am MainGermany

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