Dynamic Discrete Choice Models with Incomplete Data: Sharp Identification

In many empirical studies, the states that are relevant for economic agents to make decisions may not be included in the data to which researchers have access. This problem often arises in the context of monotone industries. In this paper, we develop the sharp identified sets of structural parameters and counterfactuals for dynamic discrete choice models when empirical data do not cover realizations of relevant states. We use simulation studies to confirm the theoretical property of the sharpness. Applying the proposed method to the annual Toyo Keizai database, we study the behaviors of Japanese firms on foreign direct investments in China without observing the future states after Chinese economy slows down.