Identification in discrete choice models with imperfect information

We study identification of preferences in static single-agent discrete choice models where decision makers may be imperfectly informed about the state of the world. We leverage the notion of one-player Bayes Correlated Equilibrium by Bergemann and Morris (2016) to provide a tractable characterization of the sharp identified set. We develop a procedure to practically construct the sharp identified set when the state of the world is continuous following a sieve approach, and provide sharp bounds on counterfactual outcomes of interest. We use our methodology and data on the 2017 UK general election to estimate a spatial voting model under weak assumptions on agents' information about the returns to voting. Counterfactual exercises quantify the consequences of imperfect information on the well-being of voters and parties.