Social security, economic growth, and social welfare in an overlapping generation model with idiosyncratic TFP shock and heterogeneous workers

This paper develops an overlapping generation model of endogenous growth by incorporating an idiosyncratic productivity shock and heterogeneous individual labor productivity. The idiosyncratic shock generates ex-post inequalities, whereas workers’ heterogeneity generates ex-ante inequalities. Social security programs might improve social welfare by providing insurance for risks not covered by private annuities and redistribution for inequalities. The equilibrium growth rate achieved under a pay-as-you-go pension system is lower than the growth rate achieved under the fully funded pension systems because the pay-as-you-go pension system hinders capital accumulation. However, a pay-as-you-go pension with additional benefits for savings enhances capital accumulation by incentivizing people to save. If the degree of relative risk aversion is sufficiently low, then the equilibrium growth rate under the modified unfunded pension system exceeds that under the funded pension system. In terms of social welfare within the Rawlsian welfare function, if people are highly risk-averse and therefore strongly inequality-averse, a pay-as-you-go system with no savings credit outperforms a fully funded system. By contrast, pay-as-you-go with savings credit is preferred if people have low risk aversion leading to weak inequality aversion.