{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,20]],"date-time":"2023-08-20T05:18:55Z","timestamp":1692508735036},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,4,1]],"date-time":"2009-04-01T00:00:00Z","timestamp":1238544000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2009,4]]},"abstract":"<jats:p>For the problem of testing the hypothesis that all <jats:italic>m<\/jats:italic> coefficients of the right-hand-side endogenous variables in an instrumental variables (IV) regression are zero, the likelihood ratio (LR) test can, if the reduced form covariance matrix is known, be rendered similar by a conditioning argument. To exploit this fact requires knowledge of the relevant conditional cumulative distribution function (c.d.f.) of the LR statistic, but the statistic is a function of the smallest characteristic root of an (<jats:italic>m<\/jats:italic> + 1)-square matrix and is therefore analytically difficult to deal with when <jats:italic>m<\/jats:italic> &gt; 1. We show in this paper that an iterative conditioning argument used by Hillier (2009) and Andrews, Moreira, and Stock (2007 <jats:italic>Journal of Econometrics<\/jats:italic> 139, 116\u2013132) to evaluate the c.d.f. in the case <jats:italic>m<\/jats:italic> = 1 can be generalized to the case of arbitrary <jats:italic>m<\/jats:italic>. This means that we can completely bypass the difficulty of dealing with the smallest characteristic root. Analytic results are obtained for the case <jats:italic>m<\/jats:italic> = 2, and a simple and efficient simulation approach to evaluating the c.d.f. is suggested for larger values of <jats:italic>m<\/jats:italic>.<\/jats:p>","DOI":"10.1017\/s0266466608090105","type":"journal-article","created":{"date-parts":[[2009,1,29]],"date-time":"2009-01-29T04:12:35Z","timestamp":1233202355000},"page":"305-335","source":"Crossref","is-referenced-by-count":2,"title":["ON THE CONDITIONAL LIKELIHOOD RATIO TEST FOR SEVERAL PARAMETERS IN IV REGRESSION"],"prefix":"10.1017","volume":"25","author":[{"given":"Grant","family":"Hillier","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,4,1]]},"reference":[{"key":"S0266466608090105_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2006.06.007"},{"key":"S0266466608090105_ref10","doi-asserted-by":"publisher","DOI":"10.2307\/2171753"},{"key":"S0266466608090105_ref9","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316559"},{"key":"S0266466608090105_ref4","volume-title":"Methods of Mathematical Physics","volume":"vol. 1","author":"Courant","year":"1953"},{"key":"S0266466608090105_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004114"},{"key":"S0266466608090105_ref2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2006.00680.x"},{"key":"S0266466608090105_ref6","article-title":"Exact properties of the conditional likelihood ratio test in an IV regression","volume":"25","author":"Hillier","year":"2006","journal-title":"Econometric Theory"},{"key":"S0266466608090105_ref1","volume-title":"Handbook of Mathematical Functions","author":"Abramowitz","year":"1972"},{"key":"S0266466608090105_ref8","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00438"},{"key":"S0266466608090105_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2006.06.010"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466608090105","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,8]],"date-time":"2019-04-08T16:32:09Z","timestamp":1554741129000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466608090105\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4]]},"references-count":10,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2009,4]]}},"alternative-id":["S0266466608090105"],"URL":"https:\/\/doi.org\/10.1017\/s0266466608090105","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4]]}}}