{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T05:52:44Z","timestamp":1783489964491,"version":"3.55.0"},"reference-count":19,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2020,6,25]],"date-time":"2020-06-25T00:00:00Z","timestamp":1593043200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,5,22]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study the first-order asymptotic properties of a class of estimators of the structural parameters in dynamic discrete choice games. We consider $K$-stage policy iteration (PI) estimators, where $K$ denotes the number of PIs employed in the estimation. This class nests several estimators proposed in the literature. By considering a \u201cpseudo likelihood\u201d criterion function, our estimator becomes the $K$-pseudo maximum likelihood (PML) estimator in Aguirregabiria and Mira (2002, 2007). By considering a \u201cminimum distance\u201d criterion function, it defines a new $K$-minimum distance (MD) estimator, which is an iterative version of the estimators in Pesendorfer and Schmidt-Dengler (2008) and Pakes et al. (2007). First, we establish that the $K$-PML estimator is consistent and asymptotically normal for any $K \\in \\mathbb{N}$. This complements findings in Aguirregabiria and Mira (2007), who focus on $K=1$ and $K$ large enough to induce convergence of the estimator. Furthermore, we show under certain conditions that the asymptotic variance of the $K$-PML estimator can exhibit arbitrary patterns as a function of $K$. Second, we establish that the $K$-MD estimator is consistent and asymptotically normal for any $K \\in \\mathbb{N}$. For a specific weight matrix, the $K$-MD estimator has the same asymptotic distribution as the $K$-PML estimator. Our main result provides an optimal sequence of weight matrices for the $K$-MD estimator and shows that the optimally weighted $K$-MD estimator has an asymptotic distribution that is invariant to $K$. The invariance result is especially unexpected given the findings in Aguirregabiria and Mira (2007) for $K$-PML estimators. Our main result implies two new corollaries about the optimal $1$-MD estimator (derived by Pesendorfer and Schmidt-Dengler (2008)). First, the optimal $1$-MD estimator is efficient in the class of $K$-MD estimators for all $K \\in \\mathbb{N}$. In other words, additional PIs do not provide first-order efficiency gains relative to the optimal $1$-MD estimator. Second, the optimal $1$-MD estimator is more or equally efficient than any $K$-PML estimator for all $K \\in \\mathbb{N}$. Finally, the Appendix provides appropriate conditions under which the optimal $1$-MD estimator is efficient among regular estimators.<\/jats:p>","DOI":"10.1093\/restud\/rdaa032","type":"journal-article","created":{"date-parts":[[2020,6,18]],"date-time":"2020-06-18T11:17:32Z","timestamp":1592479052000},"page":"1031-1073","source":"Crossref","is-referenced-by-count":6,"title":["On the Iterated Estimation of Dynamic Discrete Choice Games"],"prefix":"10.1093","volume":"88","author":[{"given":"Federico A","family":"Bugni","sequence":"first","affiliation":[{"name":"Duke University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jackson","family":"Bunting","sequence":"additional","affiliation":[{"name":"Duke 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