{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T20:03:47Z","timestamp":1792008227860,"version":"4.4.0"},"reference-count":40,"publisher":"The Econometric Society","issue":"4","license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QE"],"abstract":"<jats:p>This paper introduces a new identification\u2010 and singularity\u2010robust conditional quasi\u2010likelihood ratio (SR\u2010CQLR) test and a new identification\u2010 and singularity\u2010robust Anderson and Rubin (1949) (SR\u2010AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is required is that the moment functions and their derivatives have 2\u2009+\u2009\n            <jats:italic>\u03b3<\/jats:italic> bounded moments for some \n            <jats:italic>\u03b3<\/jats:italic>\u2009&gt;\u20090. No conditions are placed on the expected Jacobian of the moment functions, on the eigenvalues of the variance matrix of the moment functions, or on the eigenvalues of the expected outer product of the (vectorized) orthogonalized sample Jacobian of the moment functions.\n          <\/jats:p>\n          <jats:p>The SR\u2010CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi\u2010strong identification (for all \n            <jats:italic>k<\/jats:italic>\u2009\u2265\u2009\n            <jats:italic>p<\/jats:italic>, where \n            <jats:italic>k<\/jats:italic> and \n            <jats:italic>p<\/jats:italic> are the numbers of moment conditions and parameters, respectively). The SR\u2010CQLR test reduces asymptotically to Moreira's CLR test when \n            <jats:italic>p<\/jats:italic>\u2009=\u20091 in the homoskedastic linear IV model. The same is true for \n            <jats:italic>p<\/jats:italic>\u2009\u2265\u20092 in most, but not all, identification scenarios.\n          <\/jats:p>\n          <jats:p>We also introduce versions of the SR\u2010CQLR and SR\u2010AR tests for subvector hypotheses and show that they have correct asymptotic size under the assumption that the parameters not under test are strongly identified. The subvector SR\u2010CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi\u2010strong identification.<\/jats:p>","DOI":"10.3982\/qe1219","type":"journal-article","created":{"date-parts":[[2019,11,21]],"date-time":"2019-11-21T14:04:39Z","timestamp":1574345079000},"page":"1703-1746","source":"Crossref","is-referenced-by-count":24,"title":["Identification\u2010 and singularity\u2010robust inference for moment condition models"],"prefix":"10.3982","volume":"10","author":[{"given":"Donald W. 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