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We establish two asymptotic equivalence results based on the Bernstein\u2013von Mises (BvM) theorem by introducing a new formulation of the moment restriction model. First, the limiting posterior distribution of the BEL is the same as that of a parametric Bayesian method that uses the likelihood of a least favorable model of the moment restriction model. Second, the limiting posterior distribution is also the same as that of a semiparametric Bayesian method that places priors on both a finite-dimensional parameter of interest and an infinite-dimensional nuisance parameter. Because parametric and semiparametric Bayesian methods are legitimate Bayesian procedures, the equivalence results provide a large sample justification for the BEL as a Bayesian inference method. Moreover, the BvM theorem provides a frequentist justification for BEL posterior inference.<\/jats:p>","DOI":"10.1017\/s0266466622000603","type":"journal-article","created":{"date-parts":[[2022,12,5]],"date-time":"2022-12-05T09:39:50Z","timestamp":1670233190000},"page":"926-956","source":"Crossref","is-referenced-by-count":1,"title":["LARGE SAMPLE JUSTIFICATIONS FOR THE BAYESIAN EMPIRICAL LIKELIHOOD"],"prefix":"10.1017","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8757-1655","authenticated-orcid":false,"given":"Naoya","family":"Sueishi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2022,12,5]]},"reference":[{"key":"S0266466622000603_r40","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176325370"},{"key":"S0266466622000603_r42","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345338"},{"key":"S0266466622000603_r49","doi-asserted-by":"publisher","DOI":"10.1016\/j.econlet.2012.12.024"},{"key":"S0266466622000603_r8","unstructured":"Chae, M. 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