This paper is concerned with learning decision-makers’ preferences using data on observed choices from a finite set of risky alternatives. We propose a discrete choice model with unobserved heterogeneity in consideration sets and in standard risk aversion. We obtain sufficient conditions for the model’s semi-nonparametric point identification, including in cases where consideration depends on preferences and on some of the exogenous variables. Our method yields an estimator that is easy to compute and is applicable in markets with large choice sets. We illustrate its properties using a dataset on property insurance purchases.

We survey the literature on estimating risk preferences using field data. We concentrate our attention on studies in which risk preferences are the focal object and estimating their structure is the core enterprise. We review a number of models of risk preferences—including both expected utility (EU) theory and non-EU models—that have been estimated using field data, and we highlight issues related to identification and estimation of such models using field data. We then survey the literature, giving separate treatment to research that uses individual-level data (e.g., property-insurance data) and research that uses aggregate data (e.g., betting-market data). We conclude by discussing directions for future research.

Using a unique dataset, we test whether households' deductible choices in auto and home insurance reflect stable risk preferences. Our test relies on a structural model that assumes households are objective expected utility maximizers and claims are generated by household-coverage specific Poisson processes. We find that the hypothesis of stable risk preferences is rejected by the data. Our analysis suggests that many households exhibit greater risk aversion in their home deductible choices than their auto deductible choices. Our results are robust to several alternative modeling assumptions.

We outline a strategy for distinguishing rank-dependent probability weighting from systematic risk misperceptions in field data. Our strategy relies on singling out a field environment with two key properties: (i) the objects of choice are money lotteries with more than two outcomes; and (ii) the ranking of outcomes differs across lotteries. We first present an abstract model of risky choice that elucidates the identification problem and our strategy. The model has numerous applications, including insurance choices and gambling. We then consider the application of insurance deductible choices and illustrate our strategy using simulated data.

We use data on insurance deductible choices to estimate a structural model of risky choice that incorporates “standard” risk aversion (diminishing marginal utility for wealth) and probability distortions. We find that probability distortions—characterized by substantial overweighting of small probabilities and only mild insensitivity to probability changes—play an important role in explaining the aversion to risk manifested in deductible choices. This finding is robust to allowing for observed and unobserved heterogeneity in preferences. We demonstrate that neither Kőszegi-Rabin loss aversion alone nor Gul disappointment aversion alone can explain our estimated probability distortions, signifying a key role for probability weighting.

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.