Random Choice and Private Information

We consider an agent who chooses an option after receiving some private information. This information, however, is unobserved by an analyst, so from the latter's perspective, choice is probabilistic or random . We provide a theory in which information can be fully identified from random choice. In addition, the analyst can perform the following inferences even when information is unobservable: (1) directly compute ex ante valuations of menus from random choice and vice versa, (2) assess which agent has better information by using choice dispersion as a measure of informativeness, (3) determine if the agent's beliefs about information are dynamically consistent, and (4) test to see if these beliefs are well‐calibrated or rational.