We study the demand response to non-linear price schedules using data on insurance contracts and prescription drug purchases in Medicare Part D. We exploit the kink in individuals' budget set created by the famous "donut hole," where insurance becomes discontinuously much less generous on the margin, to provide descriptive evidence of the drug purchase response to a price increase. We then specify and estimate a simple dynamic model of drug use that allows us to quantify the spending response along the entire non-linear budget set. We use the model for counterfactual analysis of the increase in spending from "filling" the donut hole, as will be required by 2020 under the Affordable Care Act. In our baseline model, which considers spending decisions within a single year, we estimate that "filling" the donut hole will increase annual drug spending by about $150, or about 8 percent. About one-quarter of this spending increase reflects "anticipatory" behavior, coming from beneficiaries whose spending prior to the policy change would leave them short of reaching the donut hole. We also present descriptive evidence of cross-year substitution of spending by individuals who reach the kink, which motivates a simple extension to our baseline model that allows - in a highly stylized way - for individuals to engage in such cross year substitution. Our estimates from this extension suggest that a large share of the $150 drug spending increase could be attributed to cross-year substitution, and the net increase could be as little as $45 per year.

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.

We use employee-level panel data from a single firm to explore the possibility that individuals may select insurance coverage in part based on their anticipated behavioral ("moral hazard") response to insurance, a phenomenon we label "selection on moral hazard." Using a model of plan choice and medical utilization, we present evidence of heterogeneous moral hazard as well as selection on it, and explore some of its implications. For example, we show that, at least in our context, abstracting from selection on moral hazard could lead to over-estimates of the spending reduction associated with introducing a high-deductible health insurance option.