Identification and inference in discrete choice models with imperfect information

We study identification of preferences in a single-agent, static, discrete choice model where the decision maker may be imperfectly informed about the utility generated by the available alternatives. We impose no restrictions on the information frictions the decision maker may face and impose weak assumptions on how the decision maker deals with the uncertainty induced by those frictions. We leverage on the notion of one-player Bayes Correlated Equilibrium in Bergemann and Morris (2016) to provide a tractable characterisation of the identified set and discuss inference. We use our methodology and data on the 2017 UK general election to estimate a spatial model of voting under weak assumptions on the information that voters have about the returns to voting. We find that the assumptions on the information environment can drive the interpretation of voter preferences. Counterfactual exercises quantify the consequences of imperfect information in politics.