Random Choice and Private Information

Abstract

We consider an agent who chooses an option after receiving some private informa- tion. This information, however, is unobserved by an analyst, so from the latter’s per- spective, 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 fol- lowing 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) de- termine if the agent’s beliefs about information are dynamically consistent, and (4) test to see if these beliefs are well-calibrated or rational.