Optimal risk sharing and incentive provision in social security systems*

Abstract

Should workers or retirees bear the risk of economic growth? We show that efficient risk-sharing depends on how incentive provision – through consumption dispersion – affects the marginal value of resources, and how retirement promises back-load incentive provision. We use statistics for these two forces to show that perfect risk-sharing is optimal when the utility from consumption is logarithmic or when aggregate productivity growth is i.i.d. When neither condition holds, deviations from perfect risk sharing increase welfare. These deviations are, however, small due to the failure of a consumption-based stochastic discount factor (SDF) to price consumption growth. An augmented model that matches asset price behavior yields quantitatively relevant deviations from perfect risk-sharing.