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 importance. We start by showing theoretically that the efficiency cost of adverse selection cannot be inferred from reduced form evidence of how "adversely selected" an insurance market appears to be. Instead, an explicit model of insurance contract choice is required. We develop and estimate such a model in the context of the U.K. annuity market. The model allows for private information about risk type (mortality) 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 annual premiums. We also find that government mandates, the canonical solution to adverse selection problems, do not necessarily improve on the asymmetric information equilibrium. Depending on the contract mandated, mandates could reduce welfare by as much as £107 million annually, or increase it by as much as £127 million. Since determining which mandates would be welfare improving is empirically difficult, our findings suggest that achieving welfare gains through mandatory social insurance may be harder in practice than simple theory may suggest.