Much of the extensive empirical literature on insurance markets has focused on whether adverse selection can be detected. Once detected, however, there has been little attempt to quantify its welfare cost or to assess whether and what potential government interventions may reduce these costs. To do so, we develop a model of annuity contract choice and estimate it using data from the U.K. annuity market. The model allows for private information about mortality risk as well as heterogeneity in preferences over different contract options. We focus on the choice of length of guarantee among individuals who are required to buy annuities. The results suggest that asymmetric information along the guarantee margin reduces welfare relative to a first‐best symmetric information benchmark by about £127 million per year or about 2 percent of annuitized wealth. We also find that by requiring that individuals choose the longest guarantee period allowed, mandates could achieve the first‐best allocation. However, we estimate that other mandated guarantee lengths would have detrimental effects on welfare. Since determining the optimal mandate is empirically difficult, our findings suggest that achieving welfare gains through mandatory social insurance may be harder in practice than simple theory may suggest.