{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T16:17:29Z","timestamp":1776356249859,"version":"3.51.2"},"reference-count":47,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2023,9,18]],"date-time":"2023-09-18T00:00:00Z","timestamp":1694995200000},"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":[[2024,8]]},"abstract":"<jats:p>This paper analyses aspects of generalized method of moments (GMM) inference in moment equality models in settings where standard regularity conditions may break down. Explicit analytic formulations for the asymptotic distributions of estimable functions of the GMM estimator and statistics based on the GMM criterion function are derived under relatively mild assumptions. The moment Jacobian is allowed to be rank deficient, so first order identification may fail, the values of the Jacobian singular values are not constrained, thereby allowing for varying levels of identification strength, the long-run variance of the moment conditions can be singular, and the GMM criterion function weighting matrix may also be chosen sub-optimally. The large-sample properties are derived without imposing a specific structure on the functional form of the moment conditions. Closed-form expressions for the distributions are presented that can be evaluated using standard software without recourse to bootstrap or simulation methods. The practical operation of the results is illustrated via examples involving instrumental variables estimation of a structural equation with endogenous regressors and a common CH features model.<\/jats:p>","DOI":"10.1017\/s0266466623000221","type":"journal-article","created":{"date-parts":[[2023,9,18]],"date-time":"2023-09-18T09:19:54Z","timestamp":1695028794000},"page":"875-925","source":"Crossref","is-referenced-by-count":1,"title":["ON GMM INFERENCE: PARTIAL IDENTIFICATION, IDENTIFICATION STRENGTH, AND NONSTANDARD ASYMPTOTICS"],"prefix":"10.1017","volume":"40","author":[{"given":"Donald S.","family":"Poskitt","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2023,9,18]]},"reference":[{"key":"S0266466623000221_r23","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2005.00610.x"},{"key":"S0266466623000221_r25","volume-title":"Elementary Classical Analysis","author":"Marsden","year":"1974"},{"key":"S0266466623000221_r1","volume-title":"Topics on Analysis in Metric Spaces","author":"Ambrisio","year":"2004"},{"key":"S0266466623000221_r9","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2005.00632.x"},{"key":"S0266466623000221_r6","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2009.00279.x"},{"key":"S0266466623000221_r16","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466605050371"},{"key":"S0266466623000221_r17","doi-asserted-by":"publisher","DOI":"10.1257\/000282803321946912"},{"key":"S0266466623000221_r32","first-page":"461","volume-title":"Essays in Honor of Aman Ullah","volume":"36","author":"Phillips","year":"2016"},{"key":"S0266466623000221_r40","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1065705118"},{"key":"S0266466623000221_r4","doi-asserted-by":"publisher","DOI":"10.3982\/QE1219"},{"key":"S0266466623000221_r41","doi-asserted-by":"publisher","DOI":"10.2307\/2171753"},{"key":"S0266466623000221_r42","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00151"},{"key":"S0266466623000221_r43","doi-asserted-by":"publisher","DOI":"10.1198\/073500102288618658"},{"key":"S0266466623000221_r12","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600007519"},{"key":"S0266466623000221_r39","doi-asserted-by":"publisher","DOI":"10.2307\/1907619"},{"key":"S0266466623000221_r27","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(85)90154-X"},{"key":"S0266466623000221_r29","unstructured":"Pagan, A. & Robertson, J. (1997) GMM and Its Problems. Discussion paper, Australia National University."},{"key":"S0266466623000221_r36","first-page":"277","article-title":"Convergence of generalized inverses with applications to asymptotic hypothesis testing","volume":"46","author":"Puri","year":"1984","journal-title":"Sankhya: The Indian Journal of Statistics, Series A"},{"key":"S0266466623000221_r13","doi-asserted-by":"crossref","first-page":"2561","DOI":"10.3982\/ECTA10082","article-title":"Testing for common conditionally heteroskedastic factors","volume":"81","author":"Dovonon","year":"2013","journal-title":"Econometrica"},{"key":"S0266466623000221_r37","volume-title":"Generalized Inverse of Matrices and its Applications","author":"Rao","year":"1971"},{"key":"S0266466623000221_r19","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2006.00652.x"},{"key":"S0266466623000221_r21","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1080\/07350015.1996.10524656","article-title":"Finite sample properties of some alternative GMM estimators","volume":"14","author":"Hansen","year":"1996","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466623000221_r14","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1080\/07350015.1993.10509966","article-title":"Testing for common features","volume":"11","author":"Engle","year":"1993","journal-title":"Journal of Buisiness and Economic Statistics"},{"key":"S0266466623000221_r2","doi-asserted-by":"publisher","DOI":"10.2307\/2171944"},{"key":"S0266466623000221_r44","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511614491.006"},{"key":"S0266466623000221_r26","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2014.05.016"},{"key":"S0266466623000221_r33","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511625848.006"},{"key":"S0266466623000221_r47","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1080\/07350015.1986.10509537","article-title":"Statistical properties of generalized method-of-moments estimators of structural parameters obtained from financial market data","volume":"4","author":"Tauchen","year":"1986","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466623000221_r22","volume-title":"Continuous Univariate Distributions","volume":"2","author":"Johnson","year":"1995"},{"key":"S0266466623000221_r11","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(92)90032-M"},{"key":"S0266466623000221_r45","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2004.02.005"},{"key":"S0266466623000221_r8","doi-asserted-by":"publisher","DOI":"10.1080\/07474930903451599"},{"key":"S0266466623000221_r5","first-page":"122","volume-title":"Advances in Economics and Econometrics: Theory and Applications, Ninth World Congress, vol. III","author":"Andrews","year":"2007"},{"key":"S0266466623000221_r31","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466606060439"},{"key":"S0266466623000221_r24","doi-asserted-by":"publisher","DOI":"10.1017\/S026646661700024X"},{"key":"S0266466623000221_r3","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466616000347"},{"key":"S0266466623000221_r15","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1080\/07350015.1993.10509966","article-title":"Common volatility in international equity markets","volume":"11","author":"Engle","year":"1993","journal-title":"Journal of Business and Economic Statistics"},{"key":"S0266466623000221_r28","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":"S0266466623000221_r30","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600012408"},{"key":"S0266466623000221_r35","volume-title":"Inference in the Presence of Weak Instruments: A Selected Survey","volume":"6.1","author":"Poskitt","year":"2013"},{"key":"S0266466623000221_r46","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466603192055"},{"key":"S0266466623000221_r10","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2007.00794.x"},{"key":"S0266466623000221_r18","volume-title":"Generalized Method of Moments","author":"Hall","year":"2005"},{"key":"S0266466623000221_r20","doi-asserted-by":"publisher","DOI":"10.2307\/1912775"},{"key":"S0266466623000221_r38","doi-asserted-by":"publisher","DOI":"10.2307\/1913267"},{"key":"S0266466623000221_r34","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2008.00268.x"},{"key":"S0266466623000221_r7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2015.09.021"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466623000221","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,28]],"date-time":"2024-10-28T07:46:41Z","timestamp":1730101601000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466623000221\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,18]]},"references-count":47,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,8]]}},"alternative-id":["S0266466623000221"],"URL":"https:\/\/doi.org\/10.1017\/s0266466623000221","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,18]]}}}