Estimating Risk Preferences from Deductible Choice

We use a large data set of deductible choices in auto insurance contracts to estimate the distribution of risk preferences in our sample. To do so, we develop a structural econometric model, which accounts for adverse selection by allowing for unobserved heterogeneity in both risk (probability of an accident) and risk aversion. Ex-post claim information separately identifies the marginal distribution of risk, while the joint distribution of risk and risk aversion is identified by the deductible choice. We find that individuals in our sample have on average an estimated absolute risk aversion which is higher than other estimates found in the literature. Using annual income as a measure of wealth, we find an average two-digit coefficient of relative risk aversion. We also find that women tend to be more risk averse than men, that proxies for income and wealth are positively related to absolute risk aversion, that unobserved heterogeneity in risk preferences is higher relative to that of risk, and that unobserved risk is positively correlated with unobserved risk aversion. Finally, we use our results for counterfactual exercises that assess the profitability of insurance contracts under various assumptions.