Quantitative Economics

Journal Of The Econometric Society

Edited by: Stéphane Bonhomme • Print ISSN: 1759-7323 • Online ISSN: 1759-7331

Quantitative Economics: Nov, 2024, Volume 15, Issue 4

Estimation and Inference in Games of Incomplete Information with Unobserved Heterogeneity and Large State Space

https://doi.org/10.3982/QE2169
p. 893-938

Yanqin Fan|Shuo Jiang|Xuetao Shi

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.


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Supplemental Material

Supplement to "Estimation and Inference in Games of Incomplete Information with Unobserved Heterogeneity and Large State Space"

Yanqin Fan, Shuo Jiang, and Xuetao Shi

This document provides proofs and additional details for the results in the authors’ paper: “Estimation and Inference in Games of Incomplete Information with Unobserved Heterogeneity and Large State Space”. Appendix B collects the proofs. Appendix C collects illustration of Xiao (2018)’s CCP estimator and discussion on Step-2 identification in the General Game. Appendix D provides more details on the games used in the simulation.

Supplement to "Estimation and Inference in Games of Incomplete Information with Unobserved Heterogeneity and Large State Space"

Yanqin Fan, Shuo Jiang, and Xuetao Shi

The replication package for this paper is available at https://doi.org/10.5281/zenodo.13318751. The Journal checked the data and codes included in the package for their ability to reproduce the results in the paper and approved online appendices. Given the highly demanding nature of the algorithms, the reproducibility checks were run on a simplified version of the code, which is also available in the replication package.