{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T06:55:01Z","timestamp":1791442501295,"version":"4.3.3"},"reference-count":24,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2021,11,29]],"date-time":"2021-11-29T00:00:00Z","timestamp":1638144000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,8,24]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>Multi-dimensional heterogeneity and endogeneity are important features of models with multiple treatments. We consider a heterogeneous coefficients model where the outcome is a linear combination of dummy treatment variables, with each variable representing a different kind of treatment. We use control variables to give necessary and sufficient conditions for identification of average treatment effects. With mutually exclusive treatments we find that, provided the heterogeneous coefficients are mean independent from treatments given the controls, a simple identification condition is that the generalized propensity scores (Imbens, 2000) be bounded away from zero and that their sum be bounded away from one, with probability one. Our analysis extends to distributional and quantile treatment effects, as well as corresponding treatment effects on the treated. These results generalize the classical identification result of Rosenbaum &amp; Rubin (1983) for binary treatments.<\/jats:p>","DOI":"10.1093\/biomet\/asab060","type":"journal-article","created":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T20:56:32Z","timestamp":1637700992000},"page":"865-872","source":"Crossref","is-referenced-by-count":5,"title":["Heterogeneous coefficients, control variables and identification of multiple treatment effects"],"prefix":"10.1093","volume":"109","author":[{"given":"W K","family":"Newey","sequence":"first","affiliation":[{"name":"Department of Economics, Massachusetts Institute of Technology , 50 Memorial Drive, Cambridge, Massachusetts 02139, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S","family":"Stouli","sequence":"additional","affiliation":[{"name":"School of Economics, University of Bristol, The Priory Road Complex , Priory Road, Clifton BS8 1TU, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2021,11,29]]},"reference":[{"key":"2022082420280860500_B1","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1080\/07350015.2019.1660664","article-title":"Multivalued treatments and decomposition analysis: An application to the WIA program","volume":"39","author":"Ao,","year":"2021","journal-title":"J. Bus. Econ. Statist."},{"key":"2022082420280860500_B2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1257\/jep.31.2.3","article-title":"The state of applied econometrics: causality and policy evaluation","volume":"31","author":"Athey,","year":"2017","journal-title":"J. Econ. Perspect."},{"key":"2022082420280860500_B3","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s00181-009-0322-6","article-title":"Endogenous product versus process innovation and a firm\u2019s propensity to export","volume":"44","author":"Becker,","year":"2013","journal-title":"Empirical Econ."},{"key":"2022082420280860500_B4","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1017\/CBO9780511610257.011","article-title":"Endogeneity in nonparametric and semiparametric regression models","volume":"1","author":"Blundell,","year":"2003","journal-title":"Advances in Economics and Econometrics"},{"key":"2022082420280860500_B5","doi-asserted-by":"crossref","first-page":"635","DOI":"10.2307\/2297609","article-title":"Hypothesis testing in unidentified models","volume":"53","author":"Breusch,","year":"1986","journal-title":"Rev. Econ. Studies"},{"key":"2022082420280860500_B6","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.jeconom.2009.09.023","article-title":"Efficient semiparametric estimation of multi-valued treatment effects under ignorability","volume":"155","author":"Cattaneo,","year":"2010","journal-title":"J. Economet."},{"key":"2022082420280860500_B7","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1016\/S1573-4412(84)02014-6","article-title":"Panel data","volume":"2","author":"Chamberlain,","year":"1984","journal-title":"Handbook of Econometrics"},{"key":"2022082420280860500_B8","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1002\/sim.4168","article-title":"Generalized propensity score for estimating the average treatment effect of multiple treatments","volume":"30","author":"Feng,","year":"2012","journal-title":"Statist. Med."},{"key":"2022082420280860500_B9","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1111\/j.0950-0804.2004.00001.x","article-title":"Programme evaluation with multiple treatments","volume":"18","author":"Fr\u00f6lich,","year":"2004","journal-title":"J. Econ. Surveys"},{"key":"2022082420280860500_B10","doi-asserted-by":"crossref","DOI":"10.3386\/w25234","article-title":"Semiparametrically efficient estimation of the average linear regression function","author":"Graham,","year":"2018"},{"key":"2022082420280860500_B11","doi-asserted-by":"crossref","first-page":"854","DOI":"10.1198\/016214504000001187","article-title":"Causal inference with general treatment regimes: generalizing the propensity score","volume":"99","author":"Imai,","year":"2004","journal-title":"J. Am. Statist. Assoc."},{"key":"2022082420280860500_B12","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1093\/biomet\/87.3.706","article-title":"The role of the propensity score in estimating dose-response functions","volume":"87","author":"Imbens,","year":"2000","journal-title":"Biometrika"},{"key":"2022082420280860500_B13","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.3982\/ECTA7108","article-title":"Identification and estimation of triangular simultaneous equations models without additivity","volume":"77","author":"Imbens,","year":"2009","journal-title":"Econometrica"},{"key":"2022082420280860500_B14","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/978-3-642-57615-7_3","article-title":"Identification and estimation of causal effects of multiple treatments under the conditional independence assumption","author":"Lechner,","year":"2001","journal-title":"Econometric Evaluation of Labour Market Policies"},{"key":"2022082420280860500_B15","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1162\/003465302317411488","article-title":"Program heterogeneity and propensity score matching: an application to the evaluation of active labor market policies","volume":"84","author":"Lechner,","year":"2002","journal-title":"Rev. Econ. Statist."},{"key":"2022082420280860500_B16","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.jeconom.2020.07.027","article-title":"Control variables, discrete instruments, and identification of structural functions","volume":"222","author":"Newey,","year":"2021","journal-title":"J. Economet."},{"key":"2022082420280860500_B17","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1080\/02664763.2018.1523375","article-title":"Performance evaluation of propensity score methods for estimating average treatment effects with multi-level treatments","volume":"46","author":"Nian,","year":"2019","journal-title":"J. Appl. Statist."},{"key":"2022082420280860500_B18","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511803161","author":"Pearl,","year":"2009","journal-title":"Causality"},{"key":"2022082420280860500_B19","doi-asserted-by":"crossref","first-page":"e0246631","DOI":"10.1371\/journal.pone.0246631","article-title":"A review of methods for addressing components of interventions in meta-analysis","volume":"16","author":"Petropoulou,","year":"2021","journal-title":"PloS One"},{"key":"2022082420280860500_B20","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1093\/biomet\/70.1.41","article-title":"The central role of the propensity score in observational studies for causal effects","volume":"70","author":"Rosenbaum,","year":"1983","journal-title":"Biometrika"},{"key":"2022082420280860500_B21","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1037\/h0037350","article-title":"Estimating causal effects of treatments in randomized and nonrandomized studies","volume":"66","author":"Rubin,","year":"1974","journal-title":"J. Educ. Psychol."},{"key":"2022082420280860500_B22","article-title":"Modelling network interference with multi-valued treatments: the causal effect of immigration policy on crime rates","author":"Tort\u00fa,","year":"2020"},{"key":"2022082420280860500_B23","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1002\/jae.2386","article-title":"Doubly robust estimation of causal effects with multivalued treatments: an application to the returns to schooling","volume":"30","author":"Uysal,","year":"2015","journal-title":"J. Appl. Economet."},{"key":"2022082420280860500_B24","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1017\/CBO9780511614491.004","article-title":"Unobserved heterogeneity and the estimation of average partial effects","author":"Wooldridge,","year":"2005","journal-title":"Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg"}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asab060\/42310156\/asab060.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/109\/3\/865\/45512187\/asab060.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/109\/3\/865\/45512187\/asab060.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,24]],"date-time":"2022-08-24T20:28:59Z","timestamp":1661372939000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/109\/3\/865\/6446028"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,29]]},"references-count":24,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,11,29]]},"published-print":{"date-parts":[[2022,8,24]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asab060","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2022,9,1]]},"published":{"date-parts":[[2021,11,29]]}}}