Adverse Selection in the Annuity Market and the Role for Social Security

This paper studies the role of social security in providing annuity insurance. I calculate the welfare cost of adverse selection in the annuity market using a life cycle model in which individuals have private information about their mortality. I calibrate the model to the current U.S. social security replacement ratio, fraction of annuitized wealth and mortality heterogeneity in the Health and Retirement Study. My findings are as follows. First, in the absence of social security, individuals (on average) maintain about the same fraction of annuitized wealth as they do in the presence of social security, despite the fact that prices in the market are actuarially unfair. As a result, the welfare loss of abolishing social security is only 0.15 percent (in terms of consumption). Second, there is an ex ante gain of 0.51 percent from implementing the ex ante efficient allocations, which comes from redistributing resources from high mortality types to low mortality types. Individuals with high mortality (who will die soon and do not have demand for longevity insurance) incur large welfare losses from mandatory participation. These losses offset the benefits of providing insurance to low mortality types, leaving the overall ex ante welfare gain small.