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Hence, the distribution of the unobserved heterogeneity can be recovered by means of a Fourier transformation without imposing a distributional assumption on the CRE specification. We subsequently construct a semiparametric family of average likelihood functions of observables by combining the conditional distribution of the model and the recovered distribution of the unobserved heterogeneity, and show that the parameters in the nonlinear panel data model and in the CRE specification are identifiable. Based on the identification result, we propose a sieve maximum likelihood estimator. Compared with the conventional parametric CRE approaches, the advantage of our method is that it is not subject to misspecification on the distribution of the CRE. Furthermore, we show that the average partial effects are identifiable and extend our results to dynamic nonlinear panel data models.<\/jats:p>","DOI":"10.1017\/s0266466620000481","type":"journal-article","created":{"date-parts":[[2021,1,25]],"date-time":"2021-01-25T08:57:22Z","timestamp":1611565042000},"page":"1075-1099","source":"Crossref","is-referenced-by-count":1,"title":["NONLINEAR PANEL DATA MODELS WITH DISTRIBUTION-FREE CORRELATED RANDOM EFFECTS"],"prefix":"10.1017","volume":"37","author":[{"given":"Yu-Chin","family":"Hsu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ji-Liang","family":"Shiu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2021,1,25]]},"reference":[{"key":"S0266466620000481_r13","doi-asserted-by":"publisher","DOI":"10.1198\/jbes.2009.07219"},{"key":"S0266466620000481_r31","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2012.01.033"},{"key":"S0266466620000481_r40","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1978.10480103"},{"key":"S0266466620000481_r32","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00139"},{"key":"S0266466620000481_r38","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2012.05.023"},{"key":"S0266466620000481_r16","doi-asserted-by":"crossref","first-page":"159","DOI":"10.3982\/ECTA8419","article-title":"Binary response models for panel data: Identification and information","volume":"78","author":"Chamberlain","year":"2010","journal-title":"Econometrica"},{"key":"S0266466620000481_r18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2013.10.002"},{"key":"S0266466620000481_r22","unstructured":"Evdokimov, K. 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