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

• 成果类型: Article
• 署名作者: Fan, Yanqin; Jiang, Shuo; Shi, Xuetao
• 署名单位: University of Washington; University of Washington Seattle; Xiamen University; University of Sydney
• 刊物名称: QUANTITATIVE ECONOMICS
• ISSN/ISSBN: 1759-7323
• DOI: 10.3982/QE2169
• 发表日期: 2024
• 页码: 893-938
• 关键词: Matching-types problem; minimum-distance characterization; multistep moment selection procedure; time complexity; C12; C13; C57

摘要

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.