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We show that the relevant moment selection procedure of Hall et al. (2007, <jats:italic>Journal of Econometrics<\/jats:italic> 138, 488\u2013512) is inconsistent in this setting as it does not explicitly account for the rate of convergence of parameter estimation of the candidate models which may vary. We introduce a new moment selection procedure based on a criterion that automatically accounts for both the convergence rate of the candidate model\u2019s parameter estimate and the entropy of the estimator\u2019s asymptotic distribution. The benchmark estimator that we consider is the two-step efficient generalized method of moments estimator, which is known to be efficient in this framework as well. A family of penalization functions is introduced that guarantees the consistency of the selection procedure. The finite-sample performance of the proposed method is assessed through Monte Carlo simulations.<\/jats:p>","DOI":"10.1017\/s0266466622000640","type":"journal-article","created":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T11:34:11Z","timestamp":1673868851000},"page":"1003-1064","source":"Crossref","is-referenced-by-count":2,"title":["RELEVANT MOMENT SELECTION UNDER MIXED IDENTIFICATION STRENGTH"],"prefix":"10.1017","volume":"40","author":[{"given":"Prosper","family":"Dovonon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Firmin","family":"Doko Tchatoka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Aguessy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2023,1,16]]},"reference":[{"key":"S0266466622000640_r23","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1765(01)00622-X"},{"key":"S0266466622000640_r26","doi-asserted-by":"publisher","DOI":"10.1081\/ETC-120024752"},{"key":"S0266466622000640_r36","doi-asserted-by":"publisher","DOI":"10.1006\/jmva.1997.1688"},{"key":"S0266466622000640_r17","doi-asserted-by":"publisher","DOI":"10.1080\/07474938.2019.1701809"},{"key":"S0266466622000640_r33","doi-asserted-by":"publisher","DOI":"10.2307\/2171753"},{"key":"S0266466622000640_r34","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511614491.006"},{"key":"S0266466622000640_r24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2006.05.006"},{"key":"S0266466622000640_r21","unstructured":"Dovonon, P. and Renault, E. 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