{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T14:47:11Z","timestamp":1769525231682,"version":"3.49.0"},"reference-count":50,"publisher":"The Econometric Society","issue":"2","license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QE"],"abstract":"<jats:p>In this paper, I study identification of a nonseparable model with endogeneity arising due to unobserved heterogeneity. Identification relies on the availability of binary proxies that can be used to control for the unobserved heterogeneity. I show that the model is identified in the limit as the number of proxies increases. The argument does not require an instrumental variable that is excluded from the outcome equation nor does it require the support of the unobserved heterogeneity to be finite. I then propose a nonparametric estimator that is consistent as the number of proxies increases with the sample size. I also show that, for a fixed number of proxies, nontrivial bounds on objects of interest can be obtained. Finally, I study two real data applications that illustrate computation of the bounds and estimation with a large number of items.<\/jats:p>","DOI":"10.3982\/qe674","type":"journal-article","created":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T13:09:22Z","timestamp":1557234562000},"page":"527-563","source":"Crossref","is-referenced-by-count":7,"title":["Identification of a nonseparable model under endogeneity using binary proxies for unobserved heterogeneity"],"prefix":"10.3982","volume":"10","author":[{"given":"Benjamin","family":"Williams","sequence":"first","affiliation":[{"name":"Department of Economics, George Washington University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2359","published-online":{"date-parts":[[2019]]},"reference":[{"key":"quan12183-bib-0001","doi-asserted-by":"crossref","DOI":"10.1016\/B978-0-444-53444-6.00001-8","volume-title":"Handbook of the Economics of Education","volume":"4","author":"Almlund","year":"2011"},{"key":"quan12183-bib-0002","doi-asserted-by":"crossref","first-page":"233","DOI":"10.3982\/ECTA12723","volume":"85","author":"Belloni","year":"2017","journal-title":"Econometrica"},{"key":"quan12183-bib-0003","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.1162\/qjec.2007.122.4.1351","volume":"122","author":"Bloom","year":"2007","journal-title":"The Quarterly Journal of Economics"},{"key":"quan12183-bib-0004","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1017\/CBO9780511610257.011","volume-title":"Advances in Economics and Econometrics: Theory and Applications","author":"Blundell","year":"2003"},{"key":"quan12183-bib-0005","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1111\/1468-2354.t01-1-00074","volume":"44","author":"Carneiro","year":"2003","journal-title":"International Economic Review"},{"key":"quan12183-bib-0006","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1257\/jel.49.4.901","volume":"49","author":"Chen","year":"2011","journal-title":"Journal of Economic Literature"},{"key":"quan12183-bib-0007","doi-asserted-by":"crossref","first-page":"535","DOI":"10.3982\/ECTA8405","volume":"81","author":"Chernozhukov","year":"2013","journal-title":"Econometrica"},{"key":"quan12183-bib-0008","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1017\/S0003055404001194","volume":"98","author":"Clinton","year":"2004","journal-title":"American Political Science Review"},{"key":"quan12183-bib-0009","doi-asserted-by":"crossref","first-page":"883","DOI":"10.3982\/ECTA6551","volume":"78","author":"Cunha","year":"2010","journal-title":"Econometrica"},{"key":"quan12183-bib-0010","first-page":"251","volume":"4","author":"Finetti","year":"1931","journal-title":"Atti della R. 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