Estimation and inference in games of incomplete information with unobserved heterogeneity and large state space

Building on the sequential identification result of Aguirregabiria and Mira (2019), this paper develops estimation and inference procedures for static games of incomplete information with payoff‐relevant unobserved heterogeneity and multiple equilibria. With payoff‐relevant unobserved heterogeneity, sequential estimation and inference face two main challenges: the matching‐types problem and a large number of matchings. We tackle the matching‐types problem by constructing a new minimum‐distance criterion for the correct matching and the payoff function with both correct and incorrect "moments." To handle large numbers of matchings, we propose a novel and computationally fast multistep moment selection procedure. We show that asymptotically, it achieves a time complexity that is linear in the number of "moments" when the occurrence of multiple equilibria does not depend on the number of "moments." Based on this procedure, we construct a consistent estimator of the payoff function, an asymptotically uniformly valid and easy‐to‐implement test for linear hypotheses on the payoff function, and a consistent method to group payoff functions according to the unobserved heterogeneity. Extensive simulations demonstrate the finite sample efficacy of our procedures.