Bayesian Identification: A Theory for State-Dependent Utilities

We provide a revealed preference methodology for identifying beliefs and utilities that can vary across states. A notion of comparative informativeness is introduced that is weaker than the standard Blackwell ranking. We show that beliefs and state-dependent utilities can be identified using stochastic choice from two informational treatments, where one is strictly more informative than another. Moreover, if the signal structure is known, then stochastic choice from a single treatment is enough for identification. These results illustrate novel identification methodologies unique to stochastic choice. Applications include identifying biases in job hiring, loan approvals, and medical advice.