{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T22:51:20Z","timestamp":1789426280571,"version":"build-2803163510"},"reference-count":55,"publisher":"The Econometric Society","issue":"1","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/legalcode"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QE"],"abstract":"<jats:p>We propose the double robust Lagrange multiplier (DRLM) statistic for testing hypotheses specified on the minimizer of the population continuous updating objective function. The (bounding) \n            <jats:italic>\u03c7<\/jats:italic>\n            <jats:sup>2<\/jats:sup> limiting distribution of the DRLM statistic is robust to both misspecification and weak identification, hence its name. The minimizer is the so\u2010called pseudo\u2010true value, which equals the true value of the structural parameter under correct specification. To emphasize its importance for applied work where misspecification and weak identification are common, we use the DRLM test to analyze: the risk premia in Adrian et al. (2014) and He et al. (2017); the structural parameters in a nonlinear asset pricing model with constant relative risk aversion.\n          <\/jats:p>","DOI":"10.3982\/qe2347","type":"journal-article","created":{"date-parts":[[2025,1,23]],"date-time":"2025-01-23T11:10:12Z","timestamp":1737630612000},"page":"295-327","source":"Crossref","is-referenced-by-count":5,"title":["Double robust inference for continuous updating GMM"],"prefix":"10.3982","volume":"16","author":[{"given":"Frank","family":"Kleibergen","sequence":"first","affiliation":[{"name":"Amsterdam School of Economics, University of Amsterdam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhaoguo","family":"Zhan","sequence":"additional","affiliation":[{"name":"Coles College of Business, Kennesaw State University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2025]]},"reference":[{"key":"quan200359-bib-0001","doi-asserted-by":"crossref","first-page":"2557","DOI":"10.1111\/jofi.12189","volume":"69","author":"Adrian","year":"2014","journal-title":"Journal of Finance"},{"key":"quan200359-bib-0002","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1214\/aoms\/1177729752","volume":"21","author":"Anderson","year":"1949","journal-title":"Annals of Mathematical Statistics"},{"key":"quan200359-bib-0003","doi-asserted-by":"crossref","first-page":"2153","DOI":"10.3982\/ECTA9456","volume":"80","author":"Andrews","year":"2012","journal-title":"Econometrica"},{"key":"quan200359-bib-0004","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"},{"key":"quan200359-bib-0005","doi-asserted-by":"crossref","first-page":"2155","DOI":"10.3982\/ECTA12407","volume":"84","author":"Andrews","year":"2016","journal-title":"Econometrica"},{"issue":"1","key":"quan200359-bib-0006","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/j.jeconom.2018.12.017","volume":"211","author":"Andrews","year":"2019","journal-title":"Journal of Econometrics"},{"key":"quan200359-bib-0007","doi-asserted-by":"crossref","first-page":"1249","DOI":"10.3982\/ECTA12030","volume":"84","author":"Andrews","year":"2016","journal-title":"Econometrica"},{"key":"quan200359-bib-0008","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.3982\/ECTA12868","volume":"84","author":"Andrews","year":"2016","journal-title":"Econometrica"},{"key":"quan200359-bib-0009","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1146\/annurev-economics-080218-025643","volume":"11","author":"Andrews","year":"2019","journal-title":"Annual Review of Economics"},{"key":"quan200359-bib-0010","doi-asserted-by":"crossref","first-page":"892","DOI":"10.1093\/restud\/rds044","volume":"80","author":"Beaulieu","year":"2013","journal-title":"Review of Economic Studies"},{"key":"quan200359-bib-0011","first-page":"201","volume-title":"Aspects of Labour Market Behaviour: Essays in Honor of John Vanderkamp","author":"Card","year":"1995"},{"issue":"2","key":"quan200359-bib-0012","doi-asserted-by":"crossref","first-page":"685","DOI":"10.3982\/ECTA18506","volume":"90","author":"Cheng","year":"2022","journal-title":"Econometrica"},{"key":"quan200359-bib-0013","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.2307\/2171740","volume":"65","author":"Dufour","year":"1997","journal-title":"Econometrica"},{"key":"quan200359-bib-0014","doi-asserted-by":"crossref","first-page":"937","DOI":"10.2307\/1913778","volume":"57","author":"Epstein","year":"1989","journal-title":"Econometrica"},{"key":"quan200359-bib-0015","unstructured":"Evdokimov, Kirill and Michal Kolesar \u201cInference in instrumental variables analysis with heterogeneous treatment effects.\u201d 2018. 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