Empirical Identification of Behavioral Choice Models under Risk

The generalized expected utility literature typically assumes an absence of judgment bias in the individual perception of probabilities when inferring risk preferences. This assumption is in disagreement with many other studies that document such bias. We show that models of preference anomalies are mathematically equivalent to models of perception anomalies when estimating perceptions and/or preferences based on observable risky choice data. Empirical models admitting both involve multiplicative functions of common variables and are discernible only by assuming specifications that arbitrarily separate the two. This inability to separately identify preferences and probability perceptions is not readily solved by experimental means. Vastly different combinations of preference and perception modifications fit behavioral data identically, implying that Arrow-Pratt risk aversion estimates are arbitrary. In contrast, the risk premium and certainty equivalent are identifiable without unverifiable and untestable separating assumptions, and provide sufficient statistics for policy and welfare analysis regardless.