I propose a model of insurance demand where non-monetary attributes determine which plans an individual considers, and monetary attributes determine an individual's expected utility. This approach reconciles the classic view of insurance as purely financial with the empirical finding that choice is driven by additional attributes. I estimate the model using Medicare Part D data, allowing for unobserved heterogeneity in consideration and preferences. I find the former plays a crucial role: more than 90% of individuals consider 5 or fewer plans, approximately lO°lo of the menu. Additionally, estimates of risk preferences are comparable to existing studies of similar stakes.

We propose a robust method of discrete choice analysis when agents' choice sets are unobserved. Our core model assumes nothing about agents' choice sets apart from their minimum size. Importantly, it leaves unrestricted the dependence, conditional on observables, between choice sets and preferences. We first characterize the sharp identification region of the model's parameters by a finite set of conditional moment inequalities. We then apply our theoretical findings to learn about households' risk preferences and choice sets from data on their deductible choices in auto collision insurance. We find that the data can be explained by expected utility theory with low levels of risk aversion and heterogeneous non‐singleton choice sets, and that more than three in four households require limited choice sets to explain their deductible choices. We also provide simulation evidence on the computational tractability of our method in applications with larger feasible sets or higher‐dimensional unobserved heterogeneity.