{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T18:26:19Z","timestamp":1777573579937,"version":"3.51.4"},"reference-count":40,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2020,6,1]],"date-time":"2020-06-01T00:00:00Z","timestamp":1590969600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100000155","name":"SSHRC","doi-asserted-by":"publisher","award":["435-2016-0045"],"award-info":[{"award-number":["435-2016-0045"]}],"id":[{"id":"10.13039\/501100000155","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"NNSFC","doi-asserted-by":"publisher","award":["71991475"],"award-info":[{"award-number":["71991475"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Humanities and Social Sciences Funds of the Mninistry of Education of\n        China","award":["20YJA790047"],"award-info":[{"award-number":["20YJA790047"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,9,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>In this paper, we propose a novel method to identify the conditional average treatment effect partial derivative (CATE-PD) in an environment in which the treatment is endogenous, the treatment effect is heterogeneous, the candidate 'instrumental variables' can be correlated with latent errors, and the treatment selection does not need to be (weakly) monotone. We show that CATE-PD is point-identified under mild conditions if two-way exclusion restrictions exist: (a) an outcome-exclusive variable, which affects the treatment but is excluded from the potential outcome equation, and (b) a treatment-exclusive variable, which affects the potential outcome but is excluded from the selection equation. We also propose an asymptotically normal two-step estimator and illustrate our method by investigating how the return to education varies across regions at different levels of development in China.<\/jats:p>","DOI":"10.1093\/ectj\/utaa013","type":"journal-article","created":{"date-parts":[[2020,6,1]],"date-time":"2020-06-01T12:10:01Z","timestamp":1591013401000},"page":"345-362","source":"Crossref","is-referenced-by-count":6,"title":["Two-way exclusion restrictions in models with heterogeneous treatment\n     effects"],"prefix":"10.1093","volume":"23","author":[{"given":"Shenglong","family":"Liu","sequence":"first","affiliation":[{"name":"School of Public Policy and Management, Tsinghua University , 30 Shuangqing Rd, Haidian District, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ismael","family":"Mourifi\u00e9","sequence":"additional","affiliation":[{"name":"Department of Economics, University of Toronto , 150 St. George Street, Toronto ON M5S 3G7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanyuan","family":"Wan","sequence":"additional","affiliation":[{"name":"Department of Economics, University of Toronto ,150 St. George Street, Toronto ON M5S 3G7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,6,1]]},"reference":[{"issue":"3","key":"2022072305482193800_bib1","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1111\/1467-937X.00055","article-title":"Semiparametric estimation of the intercept of a\n      sample selection model","volume":"65","author":"Andrews","year":"1998","journal-title":"Review of Economic Studies"},{"key":"2022072305482193800_bib2","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1086\/687599","article-title":"School entry, educational attainment, and quarter of\n      birth: a cautionary tale of a local average treatment effect","volume":"10","author":"Barua","year":"2016","journal-title":"Journal of Human Capital"},{"issue":"4","key":"2022072305482193800_bib1_1001_1592673412787","doi-asserted-by":"crossref","first-page":"720","DOI":"10.2307\/2109413","article-title":"Sheepskin effects in the returns to education: An\n      examination of women and minorities","volume":"73","author":"Belman","year":"1991","journal-title":"The Review of Economics and\n      Statistics"},{"key":"2022072305482193800_bib4","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1111\/j.1468-0262.2005.00570.x","article-title":"An IV model of quantile treatment\n      effects","volume":"73","author":"Chernozhukov","year":"2005","journal-title":"Econometrica"},{"key":"2022072305482193800_bib5","doi-asserted-by":"crossref","first-page":"1525","DOI":"10.1111\/j.1468-0262.2005.00628.x","article-title":"Nonparametric identification under\n      discrete variation","volume":"73","author":"Chesher","year":"2005","journal-title":"Econometrica"},{"key":"2022072305482193800_bib8","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.jeconom.2013.01.005","article-title":"Inference on an extended Roy model, with an\n      application to schooling decisions in France","volume":"174","author":"D'Haultf\u0153uille","year":"2013","journal-title":"Journal of\n      Econometrics"},{"key":"2022072305482193800_bib6","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/j.jeconom.2004.02.001","article-title":"Instrumental variables estimators of\n      nonparametric models with discrete endogenous regressors","volume":"124","author":"Das","year":"2005","journal-title":"Journal of Econometrics"},{"key":"2022072305482193800_bib7","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1111\/1467-937X.00236","article-title":"Nonparametric estimation of sample selection\n      models","volume":"70","author":"Das","year":"2003","journal-title":"Review of Economic Studies"},{"issue":"2","key":"2022072305482193800_bib3","doi-asserted-by":"crossref","first-page":"367","DOI":"10.3982\/QE601","article-title":"Tolerating defiance? 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