{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T02:26:16Z","timestamp":1792808776704,"version":"4.5.0"},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T00:00:00Z","timestamp":1744675200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2026,6]]},"abstract":"<jats:p>\n                    This article extends the validity of the conditional likelihood ratio (CLR) test developed by Moreira (2003,\n                    <jats:italic>Econometrica<\/jats:italic>\n                    71(4), 1027-\u20131048) to instrumental variable regression models with unknown homoskedastic error variance and many weak instruments. We argue that the conventional CLR test with estimated error variance loses exact similarity and is asymptotically invalid in this setting. We propose a modified critical value function for the likelihood ratio (LR) statistic with estimated error variance, and prove that our modified test achieves asymptotic validity under many weak instruments asymptotics. Our critical value function is constructed by representing the LR using four statistics, instead of two as in Moreira (2003,\n                    <jats:italic>Econometrica<\/jats:italic>\n                    71(4), 1027-\u20131048). A simulation study illustrates the desirable finite sample properties of our test.\n                  <\/jats:p>","DOI":"10.1017\/s0266466625000088","type":"journal-article","created":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T03:41:46Z","timestamp":1744688506000},"page":"604-630","source":"Crossref","is-referenced-by-count":2,"title":["CONDITIONAL LIKELIHOOD RATIO TEST WITH MANY WEAK INSTRUMENTS"],"prefix":"10.1017","volume":"42","author":[{"given":"Sreevidya","family":"Ayyar","sequence":"first","affiliation":[{"name":"London School of Economics"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yukitoshi","family":"Matsushita","sequence":"additional","affiliation":[{"name":"Hitotsubashi University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Taisuke","family":"Otsu","sequence":"additional","affiliation":[{"name":"London School of Economics"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2025,4,15]]},"reference":[{"key":"S0266466625000088_r3","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2006.00680.x"},{"key":"S0266466625000088_r1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2012.00383.x"},{"key":"S0266466625000088_r19","doi-asserted-by":"crossref","first-page":"687","DOI":"10.3982\/ECTA6224","article-title":"Generalized method of moments with many weak moment conditions","volume":"77","author":"Newey","year":"2009","journal-title":"Econometrica"},{"key":"S0266466625000088_r16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2014.03.012"},{"key":"S0266466625000088_r13","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00353"},{"key":"S0266466625000088_r23","doi-asserted-by":"publisher","DOI":"10.2307\/2171753"},{"key":"S0266466625000088_r5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2006.05.012"},{"key":"S0266466625000088_r24","doi-asserted-by":"crossref","unstructured":"Stock, J. H. , & Yogo, M. (2005). Testing for weak instruments in linear IV regression. In D. W. K. Andrews & J. H. Stock (Eds.), Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg (pp. 80\u2013108). 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