We state conditions under which choice data suffice to identify preferences when consumers may not be fully informed about attributes of goods. Our approach can be used to test for full information, forecast how consumers will respond to information, and conduct welfare analysis when consumers are imperfectly informed. In a lab experiment, we successfully forecast the average response to new information when consumers engage in costly search. In data from Expedia, our method identifies which attribute was not immediately visible to consumers in search results and allows us to compute the value of additional information.