{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T21:08:05Z","timestamp":1791493685776,"version":"4.3.4"},"reference-count":19,"publisher":"The Econometric Society","issue":"2","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ECTA"],"abstract":"<jats:p>We study discrete panel data methods where unobserved heterogeneity is revealed in a first step, in environments where population heterogeneity is not discrete. We focus on \n            <jats:italic>two\u2010step grouped fixed\u2010effects<\/jats:italic> (GFE) estimators, where individuals are first classified into groups using \n            <jats:italic>kmeans<\/jats:italic> clustering, and the model is then estimated allowing for group\u2010specific heterogeneity. Our framework relies on two key properties: heterogeneity is a function\u2014possibly nonlinear and time\u2010varying\u2014of a low\u2010dimensional continuous latent type, and informative moments are available for classification. We illustrate the method in a model of wages and labor market participation, and in a probit model with time\u2010varying heterogeneity. We derive asymptotic expansions of two\u2010step GFE estimators as the number of groups grows with the two dimensions of the panel. We propose a data\u2010driven rule for the number of groups, and discuss bias reduction and inference.\n          <\/jats:p>","DOI":"10.3982\/ecta15238","type":"journal-article","created":{"date-parts":[[2022,3,17]],"date-time":"2022-03-17T06:12:45Z","timestamp":1647497565000},"page":"625-643","source":"Crossref","is-referenced-by-count":109,"title":["Discretizing Unobserved Heterogeneity"],"prefix":"10.3982","volume":"90","author":[{"given":"St\u00e9phane","family":"Bonhomme","sequence":"first","affiliation":[{"name":"Kenneth C. Griffin Department of Economics, University of Chicago"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thibaut","family":"Lamadon","sequence":"additional","affiliation":[{"name":"Kenneth C. Griffin Department of Economics, University of Chicago"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elena","family":"Manresa","sequence":"additional","affiliation":[{"name":"Department of Economics, New York University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2022]]},"reference":[{"key":"ecta200371-bib-0001","volume-title":"Advances in Economics and Econometrics, Ninth World Congress","author":"Arellano","year":"2007"},{"key":"ecta200371-bib-0002","doi-asserted-by":"crossref","first-page":"1229","DOI":"10.3982\/ECTA6135","volume":"77","author":"Bai","year":"2009","journal-title":"Econometrica"},{"issue":"3","key":"ecta200371-bib-0003","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.3982\/ECTA11319","volume":"83","author":"Bonhomme","year":"2015","journal-title":"Econometrica"},{"key":"ecta200371-bib-0004","doi-asserted-by":"crossref","unstructured":"Bonhomme, S., T. Lamadon, and E. Manresa (2017): \u201cDiscretizing Unobserved Heterogeneity,\u201d Becker Friedman Working Paper No. 2019-16.","DOI":"10.2139\/ssrn.3333452"},{"issue":"3","key":"ecta200371-bib-0005","doi-asserted-by":"crossref","first-page":"699","DOI":"10.3982\/ECTA15722","volume":"87","author":"Bonhomme","year":"2019","journal-title":"Econometrica"},{"key":"ecta200371-bib-0006","doi-asserted-by":"crossref","unstructured":"Bonhomme, S., T. Lamadon, and E. Manresa (2022): \u201cSupplement to \u2018Discretizing Unobserved Heterogeneity\u2019,\u201d Econometrica Supplemental Material, 90, https:\/\/doi.org\/10.3982\/ECTA15238.","DOI":"10.3982\/ECTA15238"},{"key":"ecta200371-bib-0007","unstructured":"Buchinsky, M., J. Hahn, and J. Hotz (2005): \u201cCluster Analysis: A Tool for Preliminary Structural Analysis,\u201d Unpublished manuscript."},{"key":"ecta200371-bib-0008","unstructured":"Chen, M., I. Fern\u00e1ndez-Val, and M. Weidner (2021): \u201cNonlinear Panel Models With Interactive Effects,\u201d Journal of Econometrics (forthcoming)."},{"issue":"3","key":"ecta200371-bib-0009","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1093\/restud\/rdv007","volume":"82","author":"Dhaene","year":"2015","journal-title":"Review of Economic Studies"},{"key":"ecta200371-bib-0010","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.jeconom.2015.12.014","volume":"196","author":"Fern\u00e1ndez-Val","year":"2016","journal-title":"Journal of Econometrics"},{"issue":"6","key":"ecta200371-bib-0011","doi-asserted-by":"crossref","first-page":"2624","DOI":"10.1214\/15-AOS1354","volume":"43","author":"Gao","year":"2015","journal-title":"Annals of Statistics"},{"issue":"2","key":"ecta200371-bib-0012","doi-asserted-by":"crossref","first-page":"874","DOI":"10.1214\/aop\/1023481010","volume":"30","author":"Graf","year":"2002","journal-title":"Annals of Probability"},{"issue":"6","key":"ecta200371-bib-0013","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1017\/S0266466611000028","volume":"27","author":"Hahn","year":"2011","journal-title":"Econometric Theory"},{"issue":"3","key":"ecta200371-bib-0014","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1017\/S0266466609990132","volume":"26","author":"Hahn","year":"2010","journal-title":"Econometric Theory"},{"key":"ecta200371-bib-0015","doi-asserted-by":"crossref","first-page":"1295","DOI":"10.1111\/j.1468-0262.2004.00533.x","volume":"72","author":"Hahn","year":"2004","journal-title":"Econometrica"},{"issue":"2","key":"ecta200371-bib-0016","doi-asserted-by":"crossref","first-page":"271","DOI":"10.2307\/1911491","volume":"52","author":"Heckman","year":"1984","journal-title":"Econometrica"},{"issue":"3","key":"ecta200371-bib-0017","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1086\/262080","volume":"105","author":"Keane","year":"1997","journal-title":"Journal of Political Economy"},{"issue":"1","key":"ecta200371-bib-0018","doi-asserted-by":"crossref","first-page":"211","DOI":"10.3982\/ECTA4657","volume":"79","author":"Kennan","year":"2011","journal-title":"Econometrica"},{"issue":"1","key":"ecta200371-bib-0019","doi-asserted-by":"crossref","first-page":"44","DOI":"10.2307\/1235460","volume":"43","author":"Mundlak","year":"1961","journal-title":"Journal of Farm Economics"}],"container-title":["Econometrica"],"original-title":[],"language":"en","deposited":{"date-parts":[[2022,3,17]],"date-time":"2022-03-17T06:15:19Z","timestamp":1647497719000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.econometricsociety.org\/doi\/10.3982\/ECTA15238"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"references-count":19,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022]]}},"alternative-id":["10.3982\/ECTA15238"],"URL":"https:\/\/doi.org\/10.3982\/ecta15238","relation":{},"ISSN":["0012-9682"],"issn-type":[{"value":"0012-9682","type":"print"}],"subject":[],"published":{"date-parts":[[2022]]}}}