{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T09:08:51Z","timestamp":1765357731780,"version":"3.28.0"},"reference-count":42,"publisher":"The Econometric Society","issue":"4","license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/legalcode"}],"funder":[{"DOI":"10.13039\/501100002338","name":"Ministry of Education of the People's Republic of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002338","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013314","name":"Higher Education Discipline Innovation Project","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100013314","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QE"],"abstract":"<jats:p>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\u2010relevant unobserved heterogeneity and multiple equilibria. With payoff\u2010relevant unobserved heterogeneity, sequential estimation and inference face two main challenges: \n            <jats:italic>the matching\u2010types problem<\/jats:italic> and \n            <jats:italic>a large number of matchings<\/jats:italic>. We tackle the matching\u2010types problem by constructing a new minimum\u2010distance criterion for the correct matching and the payoff function with both correct and incorrect \u201cmoments.\u201d 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 \u201cmoments\u201d when the occurrence of multiple equilibria does not depend on the number of \u201cmoments.\u201d Based on this procedure, we construct a consistent estimator of the payoff function, an asymptotically uniformly valid and easy\u2010to\u2010implement 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.\n          <\/jats:p>","DOI":"10.3982\/qe2169","type":"journal-article","created":{"date-parts":[[2024,11,15]],"date-time":"2024-11-15T09:48:52Z","timestamp":1731664132000},"page":"893-938","source":"Crossref","is-referenced-by-count":2,"title":["Estimation and inference in games of incomplete information with unobserved heterogeneity and large state space"],"prefix":"10.3982","volume":"15","author":[{"given":"Yanqin","family":"Fan","sequence":"first","affiliation":[{"name":"Department of Economics, University of Washington"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuo","family":"Jiang","sequence":"additional","affiliation":[{"name":"MOE Key Lab of Econometrics, WISE, Department of Statistics and Data Science at School of Economics, Xiamen 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