{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T11:12:02Z","timestamp":1790680322866,"version":"4.1.0"},"reference-count":27,"publisher":"The Econometric Society","issue":"3","funder":[{"DOI":"10.13039\/100006734","name":"Princeton University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006734","id-type":"DOI","asserted-by":"publisher"}]},{"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>It is well understood that classical sample selection models are not semiparametrically identified without exclusion restrictions. Lee (2009) developed bounds for the parameters in a model that nests the semiparametric sample selection model. These bounds can be wide. In this paper, we investigate bounds that impose the full structure of a sample selection model with errors that are independent of the explanatory variables but have unknown distribution. The additional structure can significantly reduce the identified set for the parameters of interest. Specifically, we construct the identified set for the parameter vector of interest. It is a one\u2010dimensional line segment in the parameter space, and we demonstrate that this line segment can be short in practice. We show that the identified set is sharp when the model is correct and empty when there exist no parameter values that make the sample selection model consistent with the data. We also provide non\u2010sharp bounds under the assumption that the model is correct. These are easier to compute and associated with lower statistical uncertainty than the sharp bounds. Throughout the paper, we illustrate our approach by estimating a standard sample selection model for wages.<\/jats:p>","DOI":"10.3982\/ecta16481","type":"journal-article","created":{"date-parts":[[2020,5,7]],"date-time":"2020-05-07T11:57:12Z","timestamp":1588852632000},"page":"1007-1029","source":"Crossref","is-referenced-by-count":31,"title":["Selection Without Exclusion"],"prefix":"10.3982","volume":"88","author":[{"given":"Bo E.","family":"Honor\u00e9","sequence":"first","affiliation":[{"name":"Department of Economics, Princeton University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luojia","family":"Hu","sequence":"additional","affiliation":[{"name":"Economic Research Department, Federal Reserve Bank of Chicago"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2020]]},"reference":[{"issue":"1-2","key":"ecta200116-bib-0001","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0304-4076(93)90111-H","volume":"58","author":"Ahn","year":"1993","journal-title":"Journal of Econometrics"},{"issue":"3","key":"ecta200116-bib-0002","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1111\/1467-937X.00055","volume":"65","author":"Andrews","year":"1998","journal-title":"The Review of Economic Studies"},{"key":"ecta200116-bib-0003","doi-asserted-by":"crossref","unstructured":"Barrow, L., and C. E. Rouse (2017): \u201cFinancial Incentives and Educational Investment: The Impact of Performance-Based Scholarships on Student Time Use,\u201d Education Finance and Policy.","DOI":"10.1162\/edfp_a_00228"},{"issue":"2","key":"ecta200116-bib-0004","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1111\/j.1468-0262.2006.00750.x","volume":"75","author":"Blundell","year":"2007","journal-title":"Econometrica"},{"key":"ecta200116-bib-0005","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1017\/9781108227223.009","volume-title":"Advances in Economics and Econometrics: Eleventh World Congress","volume":"2","author":"Canay","year":"2017"},{"issue":"2","key":"ecta200116-bib-0006","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0304-4076(86)90038-2","volume":"32","author":"Chamberlain","year":"1986","journal-title":"Journal of Econometrics"},{"issue":"1","key":"ecta200116-bib-0007","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1111\/1467-937X.00236","volume":"70","author":"Das","year":"2003","journal-title":"The Review of Economic Studies"},{"key":"ecta200116-bib-0008","series-title":"Cambridge Series in Statistical and Probabilistic Mathematics","doi-asserted-by":"crossref","DOI":"10.1017\/9781108591034","volume-title":"Probability: Theory and Examples","author":"Durrett","year":"2019","edition":"fith"},{"issue":"2","key":"ecta200116-bib-0009","doi-asserted-by":"crossref","first-page":"561","DOI":"10.3982\/QE328","volume":"7","author":"Escanciano","year":"2016","journal-title":"Quantitative Economics"},{"issue":"1","key":"ecta200116-bib-0010","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1086\/344801","volume":"111","author":"Haile","year":"2003","journal-title":"Journal of Political Economy"},{"key":"ecta200116-bib-0011","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/0304-4076(87)90030-3","volume":"35","author":"Han","year":"1987","journal-title":"Journal of Econometrics"},{"issue":"4","key":"ecta200116-bib-0012","first-page":"475","volume":"5","author":"Heckman","year":"1976","journal-title":"Annals of Economic and Social Measurement"},{"issue":"1","key":"ecta200116-bib-0013","doi-asserted-by":"crossref","first-page":"153","DOI":"10.2307\/1912352","volume":"47","author":"Heckman","year":"1979","journal-title":"Econometrica"},{"issue":"2","key":"ecta200116-bib-0014","first-page":"313","volume":"80","author":"Heckman","year":"1990","journal-title":"The American Economic Review"},{"key":"ecta200116-bib-0015","doi-asserted-by":"crossref","unstructured":"Honor\u00e9, B. E., and L. Hu (2020): \u201cSupplement to \u2018Selection Without Exclusion\u2019,\u201d Econometrica Supplemental Material, 88, https:\/\/doi.org\/10.3982\/ECTA16481.","DOI":"10.3982\/ECTA16481"},{"issue":"6","key":"ecta200116-bib-0016","doi-asserted-by":"crossref","first-page":"1675","DOI":"10.1111\/j.1468-0262.2006.00722.x","volume":"74","author":"Honor\u00e9","year":"2006","journal-title":"Econometrica"},{"issue":"5","key":"ecta200116-bib-0017","doi-asserted-by":"crossref","first-page":"2043","DOI":"10.3982\/ECTA11974","volume":"83","author":"Kitagawa","year":"2015","journal-title":"Econometrica"},{"issue":"468","key":"ecta200116-bib-0018","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/1468-0297.00586","volume":"111","author":"Krueger","year":"2001","journal-title":"The Economic Journal"},{"issue":"3","key":"ecta200116-bib-0019","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1111\/j.1467-937X.2009.00536.x","volume":"76","author":"Lee","year":"2009","journal-title":"The Review of Economic Studies"},{"issue":"3","key":"ecta200116-bib-0020","doi-asserted-by":"crossref","first-page":"343","DOI":"10.2307\/145818","volume":"24","author":"Manski","year":"1989","journal-title":"The Journal of Human Resources"},{"issue":"2","key":"ecta200116-bib-0021","first-page":"319","volume":"80","author":"Manski","year":"1990","journal-title":"The American Economic Review"},{"issue":"2","key":"ecta200116-bib-0022","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1111\/1468-0262.00294","volume":"70","author":"Manski","year":"2002","journal-title":"Econometrica"},{"issue":"4","key":"ecta200116-bib-0023","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1002\/jae.1006","volume":"23","author":"Mora","year":"2008","journal-title":"Journal of Applied Econometrics"},{"issue":"1","key":"ecta200116-bib-0024","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1111\/j.2044-8317.1990.tb00930.x","volume":"43","author":"Muth\u00e9n","year":"1990","journal-title":"British Journal of Mathematical and Statistical Psychology"},{"key":"ecta200116-bib-0025","unstructured":"Powell, J. L. (1987): \u201cSemiparametric Estimation of Bivariate Latent Models,\u201d Working Paper no. 8704, Social Systems Research Institute, University of Wisconsin\u2013Madison."},{"key":"ecta200116-bib-0026","series-title":"Handbooks in Economics","doi-asserted-by":"crossref","first-page":"2443","DOI":"10.1016\/S1573-4412(05)80010-8","volume-title":"Handbook of Econometrics","volume":"4","author":"Powell","year":"1994"},{"issue":"4","key":"ecta200116-bib-0027","doi-asserted-by":"crossref","first-page":"931","DOI":"10.2307\/1912705","volume":"56","author":"Robinson","year":"1988","journal-title":"Econometrica"}],"container-title":["Econometrica"],"original-title":[],"language":"en","deposited":{"date-parts":[[2020,5,7]],"date-time":"2020-05-07T11:59:48Z","timestamp":1588852788000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.econometricsociety.org\/doi\/10.3982\/ECTA16481"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"references-count":27,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020]]}},"alternative-id":["10.3982\/ECTA16481"],"URL":"https:\/\/doi.org\/10.3982\/ecta16481","relation":{},"ISSN":["0012-9682"],"issn-type":[{"value":"0012-9682","type":"print"}],"subject":[],"published":{"date-parts":[[2020]]}}}