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Optimal Social Insurance: Insights from a Continuous-Time Stochastic Setup

Pedro G. Rodrigues
Publication Year 
JEL Code 
C61 - Optimization Techniques; Programming Models; Dynamic Analysis
H55 - Social Security and Public Pensions
This paper focuses on the determinants of the optimal level of social insurance, thus contributing to explain its cross-country variation. In a continuous-time stochastic endogenous growth setup, it is a form of public insurance against idiosyncratic shocks affecting the income, as well as the dependency ratio of an individual household. Such shocks include, for example, illness, disability, unemployment, or changes in the number of infants and elderly in care. We conclude that a higher average dependency ratio and a higher covariance between technological and dependency shocks both decrease the optimal amount of social insurance. In addition, a higher variance of technological shocks does not affect optimal decisions, while a higher variance of dependency shocks increases optimal social insurance, provided the covariance between technological and dependency shocks is not very negative.
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