We study the effects on the macroeconomic equilibrium, the wealth distribution, and welfare of adverse selection in private annuity markets in a closed economy inhabited by overlapping generations of heterogeneous agents who are distinguished by their health status. If an agent’s health type is private information there will be a pooling equilibrium in the private annuity market. We also study the implications for the macro-economy and welfare of a social security system with mandatory contributions that are constant across health types. These social annuities are immune to adverse selection and therefore offer a higher rate of return than private annuities do. However, they have a negative effect on the steady-state capital intensity and welfare. The positive effect of a fair pooled rate of return on a fixed part of savings and a higher return on capital in equilibrium is outweighed by the negative consequences of increased adverse selection in the private annuity market and a lower wage rate.