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 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.