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This paper proposes an analysis of the asymptotic distributions of the limited information maximum likelihood (LIML) estimator and plug-in statistics when potential instruments are omitted. Our results provide several new insights and extensions of earlier studies. We show that the exclusion of instruments can eliminate the first-stage, thus weakening identification and invalidating the plug-in subset inference. However, when instrument omission does not affect LIML consistency, it preserves the plug-in subset test validity, although LIML is no longer asymptotically efficient. Unlike the instrumental variable (IV) estimator, the LIML estimator of the identified linear combination of the nuisance parameter is not asymptotically a Gaussian mixture, even without instrument exclusion.<\/jats:p>","DOI":"10.1017\/s0266466614000462","type":"journal-article","created":{"date-parts":[[2014,11,17]],"date-time":"2014-11-17T10:16:06Z","timestamp":1416219366000},"page":"1192-1228","source":"Crossref","is-referenced-by-count":4,"title":["SUBSET HYPOTHESES TESTING AND INSTRUMENT EXCLUSION IN THE LINEAR IV REGRESSION"],"prefix":"10.1017","volume":"31","author":[{"given":"Firmin Doko","family":"Tchatoka","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,11,17]]},"reference":[{"key":"S0266466614000462_ref10","doi-asserted-by":"publisher","DOI":"10.1111\/ectj.12021"},{"key":"S0266466614000462_ref13","doi-asserted-by":"publisher","DOI":"10.1198\/jbes.2009.08283"},{"key":"S0266466614000462_ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2009.01.013"},{"key":"S0266466614000462_ref49","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00151"},{"key":"S0266466614000462_ref50","doi-asserted-by":"publisher","DOI":"10.1198\/073500102288618658"},{"key":"S0266466614000462_ref42","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0084.2004.00095.x"},{"key":"S0266466614000462_ref41","unstructured":"Malcomson J. & Mavroeidis S. 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