{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T04:48:04Z","timestamp":1774414084211,"version":"3.50.1"},"reference-count":41,"publisher":"The Econometric Society","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ECTA"],"abstract":"<jats:p>This paper studies optimal decision rules, including estimators and tests, for weakly identified GMM models. We derive the limit experiment for weakly identified GMM, and propose a theoretically\u2010motivated class of priors which give rise to quasi\u2010Bayes decision rules as a limiting case. Together with results in the previous literature, this establishes desirable properties for the quasi\u2010Bayes approach regardless of model identification status, and we recommend quasi\u2010Bayes for settings where identification is a concern. We further propose weighted average power\u2010optimal identification\u2010robust frequentist tests and confidence sets, and prove a Bernstein\u2010von Mises\u2010type result for the quasi\u2010Bayes posterior under weak identification.<\/jats:p>","DOI":"10.3982\/ecta18678","type":"journal-article","created":{"date-parts":[[2022,3,17]],"date-time":"2022-03-17T06:12:45Z","timestamp":1647497565000},"page":"715-748","source":"Crossref","is-referenced-by-count":14,"title":["Optimal Decision Rules for Weak GMM"],"prefix":"10.3982","volume":"90","author":[{"given":"Isaiah","family":"Andrews","sequence":"first","affiliation":[{"name":"Department of Economics, Harvard University"},{"name":"NBER"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anna","family":"Mikusheva","sequence":"additional","affiliation":[{"name":"Department of Economics, MIT"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2359","published-online":{"date-parts":[[2022]]},"reference":[{"key":"ecta200386-bib-0001","volume-title":"Random Fields and Geometry","author":"Adler","year":"2007"},{"issue":"3","key":"ecta200386-bib-0002","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1111\/j.1468-0262.2006.00680.x","volume":"74","author":"Andrews","year":"2006","journal-title":"Econometrica"},{"issue":"4","key":"ecta200386-bib-0003","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.3982\/ECTA12868","volume":"84","author":"Andrews","year":"2016","journal-title":"Econometrica"},{"key":"ecta200386-bib-0004","doi-asserted-by":"crossref","unstructured":"Andrews, I., and A. Mikusheva (2022): \u201cSupplement to \u2018Optimal Decision Rules for Weak GMM\u2019,\u201d Econometrica Supplemental Material, 90, https:\/\/doi.org\/10.3982\/ECTA18678.","DOI":"10.3982\/ECTA18678"},{"key":"ecta200386-bib-0005","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9096-9","volume-title":"Reproducing Kernel Hilbert Spaces in Probability and Statistics","author":"Berlinet","year":"2004"},{"key":"ecta200386-bib-0006","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1111\/rssb.12294","volume":"81","author":"Bornn","year":"2019","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"ecta200386-bib-0007","doi-asserted-by":"crossref","DOI":"10.1214\/lnms\/1215466757","volume-title":"Fundamentals of Statistical Exponential Families With Applications in Statistical Decision Theory","author":"Brown","year":"1986"},{"key":"ecta200386-bib-0008","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1198\/073500102288618711","volume":"21","author":"Chamberlain","year":"2003","journal-title":"Journal of Business and Economic Statistics"},{"issue":"6","key":"ecta200386-bib-0009","doi-asserted-by":"crossref","first-page":"1965","DOI":"10.3982\/ECTA14525","volume":"86","author":"Chen","year":"2018","journal-title":"Econometrica"},{"issue":"1","key":"ecta200386-bib-0010","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1111\/j.1468-0262.2005.00570.x","volume":"73","author":"Chernozhukov","year":"2005","journal-title":"Econometrica"},{"issue":"2","key":"ecta200386-bib-0011","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/S0304-4076(03)00100-3","volume":"115","author":"Chernozhukov","year":"2003","journal-title":"Journal of Econometrics"},{"key":"ecta200386-bib-0012","doi-asserted-by":"crossref","unstructured":"Chernozhukov, V., C. Hansen, and M. Jansson (2006): \u201cFinite Sample Inference for Quantile Regression Models,\u201d Unpublished Manuscript.","DOI":"10.2139\/ssrn.880467"},{"issue":"2","key":"ecta200386-bib-0013","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.jeconom.2009.01.004","volume":"152","author":"Chernozhukov","year":"2009","journal-title":"Journal of Econometrics"},{"issue":"1","key":"ecta200386-bib-0014","doi-asserted-by":"crossref","first-page":"584","DOI":"10.1214\/19-AOS1829","volume":"48","author":"Cox","year":"2020","journal-title":"Annals of Statistics"},{"issue":"2","key":"ecta200386-bib-0015","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1080\/07350015.2019.1668799","volume":"39","author":"Florens","year":"2021","journal-title":"Journal of Business and Economic Statistics"},{"issue":"2","key":"ecta200386-bib-0016","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1093\/jjfinec\/nbv007","volume":"14","author":"Gallant","year":"2016","journal-title":"Journal of Financial Econometrics"},{"issue":"1","key":"ecta200386-bib-0017","doi-asserted-by":"crossref","first-page":"75","DOI":"10.2307\/2556036","volume":"26","author":"Graddy","year":"1995","journal-title":"Rand Journal of Economics"},{"issue":"4","key":"ecta200386-bib-0018","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1017\/S0266466605050371","volume":"21","author":"Guggenberger","year":"2005","journal-title":"Econometric Theory"},{"issue":"3","key":"ecta200386-bib-0019","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.3982\/QE989","volume":"10","author":"Han","year":"2019","journal-title":"Quantitative Economics"},{"issue":"5","key":"ecta200386-bib-0020","doi-asserted-by":"crossref","first-page":"1683","DOI":"10.3982\/ECTA6630","volume":"77","author":"Hirano","year":"2009","journal-title":"Econometrica"},{"issue":"2","key":"ecta200386-bib-0021","doi-asserted-by":"crossref","first-page":"733","DOI":"10.3982\/ECTA16413","volume":"89","author":"Kaji","year":"2021","journal-title":"Econometrica"},{"key":"ecta200386-bib-0022","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/S0304-4076(01)00119-1","volume":"107","author":"Kim","year":"2002","journal-title":"Journal of Econometrics"},{"issue":"7","key":"ecta200386-bib-0023","doi-asserted-by":"crossref","first-page":"1183","DOI":"10.1002\/jae.2398","volume":"29","author":"Kleibergen","year":"2014","journal-title":"Journal of Applied Econometrics"},{"issue":"2","key":"ecta200386-bib-0024","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1093\/biomet\/90.2.319","volume":"90","author":"Lazar","year":"2003","journal-title":"Biometrika"},{"key":"ecta200386-bib-0025","volume-title":"Asymptotic Theory of Statistical Inference","author":"Le Cam","year":"1986"},{"key":"ecta200386-bib-0026","series-title":"Springer Texts in Statistics","volume-title":"Theory of Point Estimation","author":"Lehman","year":"1998"},{"issue":"1","key":"ecta200386-bib-0027","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1214\/09-AOS714","volume":"38","author":"Liao","year":"2010","journal-title":"Annals of Statistics"},{"issue":"2","key":"ecta200386-bib-0028","doi-asserted-by":"crossref","first-page":"755","DOI":"10.3982\/ECTA8360","volume":"80","author":"Moon","year":"2012","journal-title":"Econometrica"},{"issue":"2","key":"ecta200386-bib-0029","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1016\/j.jeconom.2019.04.038","volume":"213","author":"Moreira","year":"2019","journal-title":"Journal of Econometrics"},{"key":"ecta200386-bib-0030","unstructured":"Moreira, M., and G. Ridder (2017): \u201cOptimal Invariant Tests in an Instrumental Variables Regression With Heteroskedastic and Autocorrelated Errors,\u201d Unpublished Manuscript, https:\/\/arxiv.org\/abs\/1705.00231."},{"issue":"2","key":"ecta200386-bib-0031","doi-asserted-by":"crossref","first-page":"395","DOI":"10.3982\/ECTA7793","volume":"79","author":"Mueller","year":"2011","journal-title":"Econometrica"},{"issue":"3","key":"ecta200386-bib-0032","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1214\/aos\/1056562461","volume":"31","author":"Neal","year":"2003","journal-title":"Annals of Statistics"},{"key":"ecta200386-bib-0033","series-title":"Seminaire Math. Sup.","volume-title":"Processus AIeatoires Gaussiens","author":"Neveu","year":"1968"},{"issue":"1","key":"ecta200386-bib-0034","first-page":"35","volume":"1","author":"Parzen","year":"1962","journal-title":"J. SIAM Control, Ser. A."},{"key":"ecta200386-bib-0035","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1093\/biomet\/92.1.31","volume":"92","author":"Schennach","year":"2005","journal-title":"Biometrika"},{"key":"ecta200386-bib-0036","unstructured":"Shin, M. (2015): \u201cBayesian GMM,\u201d Dissertation Chapter, University of Pennsylvania."},{"key":"ecta200386-bib-0037","series-title":"De Gruyter Studies in Mathematics","doi-asserted-by":"crossref","DOI":"10.1515\/9783110850826","volume-title":"Mathematical Theory of Statistics: Statistical Experiments and Asymptotic Decision Theory","volume":"7","author":"Strasser","year":"1985"},{"issue":"1","key":"ecta200386-bib-0038","doi-asserted-by":"crossref","first-page":"97","DOI":"10.2307\/1403577","volume":"59","author":"Van der Vaart","year":"1991","journal-title":"International Statistical Review"},{"key":"ecta200386-bib-0039","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511802256","volume-title":"Asymptotic Statistics","author":"Van der Vaart","year":"1998"},{"key":"ecta200386-bib-0040","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1214\/074921708000000156","volume-title":"Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta","author":"Van der Vaart","year":"2008"},{"key":"ecta200386-bib-0041","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2545-2","volume-title":"Weak Convergence and Empirical Processes","author":"Van der Vaart","year":"1996"}],"container-title":["Econometrica"],"original-title":[],"language":"en","deposited":{"date-parts":[[2023,11,18]],"date-time":"2023-11-18T22:51:07Z","timestamp":1700347867000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.econometricsociety.org\/doi\/10.3982\/ECTA18678"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"references-count":41,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022]]}},"alternative-id":["10.3982\/ECTA18678"],"URL":"https:\/\/doi.org\/10.3982\/ecta18678","relation":{},"ISSN":["0012-9682"],"issn-type":[{"value":"0012-9682","type":"print"}],"subject":[],"published":{"date-parts":[[2022]]}}}