{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T07:04:22Z","timestamp":1791356662356,"version":"4.3.1"},"reference-count":38,"publisher":"The Econometric Society","issue":"2","license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/legalcode"}],"funder":[{"DOI":"10.13039\/501100000155","name":"Social Sciences and Humanities Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000155","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QE"],"abstract":"<jats:p>In many set\u2010identified models, it is difficult to obtain a tractable characterization of the identified set. Therefore, researchers often rely on nonsharp identification conditions, and empirical results are often based on an outer set of the identified set. This practice is often viewed as conservative yet valid because an outer set is always a superset of the identified set. However, this paper shows that when the model is refuted by the data, two sets of nonsharp identification conditions derived from the same model could lead to disjoint outer sets and conflicting empirical results. We provide a sufficient condition for the existence of such discordancy, which covers models characterized by conditional moment inequalities and the Artstein (1983) inequalities. We also derive sufficient conditions for the nonexistence of discordant submodels, therefore providing a class of models for which constructing outer sets cannot lead to misleading interpretations. In the case of discordancy, we follow Masten and Poirier (2021) by developing a method to salvage misspecified models, but unlike them, we focus on discrete relaxations. We consider all minimum relaxations of a refuted model that restores data consistency. We find that the union of the identified sets of these minimum relaxations is robust to detectable misspecifications and has an intuitive empirical interpretation.<\/jats:p>","DOI":"10.3982\/qe1960","type":"journal-article","created":{"date-parts":[[2024,4,25]],"date-time":"2024-04-25T12:22:43Z","timestamp":1714047763000},"page":"331-379","source":"Crossref","is-referenced-by-count":5,"title":["Discordant relaxations of misspecified models"],"prefix":"10.3982","volume":"15","author":[{"given":"Lixiong","family":"Li","sequence":"first","affiliation":[{"name":"Department of Economics, Johns Hopkins University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D\u00e9sir\u00e9","family":"K\u00e9dagni","sequence":"additional","affiliation":[{"name":"Department of Economics, The University of North Carolina at Chapel Hill"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Isma\u00ebl","family":"Mourifi\u00e9","sequence":"additional","affiliation":[{"name":"Department of Economics, University of Toronto"},{"name":"Department of Economics, Washington University in St. Louis"},{"name":"NBER"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2024]]},"reference":[{"key":"quan200324-bib-0001","unstructured":"Allen, Roy and John Rehbeck (2020), \u201cSatisficing, aggregation, and quasilinear utility.\u201d Available at SSRN 3180302."},{"issue":"1","key":"quan200324-bib-0002","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1093\/restud\/rdad033","volume":"91","author":"Andrews","year":"2024","journal-title":"Review of Economic Studies"},{"issue":"2","key":"quan200324-bib-0003","doi-asserted-by":"crossref","first-page":"609","DOI":"10.3982\/ECTA9370","volume":"81","author":"Andrews","year":"2013","journal-title":"Econometrica"},{"key":"quan200324-bib-0004","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/BF02762891","volume":"46","author":"Artstein","year":"1983","journal-title":"Israel Journal of Mathematics"},{"issue":"1","key":"quan200324-bib-0005","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1017\/S0266466615000250","volume":"33","author":"Aucejo","year":"2017","journal-title":"Econometric Theory"},{"issue":"4","key":"quan200324-bib-0006","doi-asserted-by":"crossref","first-page":"1724","DOI":"10.1093\/restud\/rdac061","volume":"90","author":"Berry","year":"2023","journal-title":"The Review of Economic Studies"},{"key":"quan200324-bib-0007","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1111\/j.1468-0262.2006.00750.x","volume":"75","author":"Blundell","year":"2007","journal-title":"Econometrica"},{"issue":"4","key":"quan200324-bib-0008","doi-asserted-by":"crossref","first-page":"1741","DOI":"10.3982\/ECTA9604","volume":"80","author":"Bugni","year":"2012","journal-title":"Econometrica"},{"key":"quan200324-bib-0009","unstructured":"Bureau of Labor Statistics, U.S. Department of Labor (2019), \u201cNational longitudinal survey of youth 1979 cohort, 1979\u20132016 (rounds 1\u201327).\u201d Produced and distributed by the Center for Human Resource Research (CHRR), The Ohio State University, Columbus, OH. https:\/\/www.nlsinfo.org\/content\/cohorts\/nlsy79."},{"issue":"4","key":"quan200324-bib-0010","doi-asserted-by":"crossref","first-page":"1050","DOI":"10.3368\/jhr.53.4.1015.7483R1","volume":"53","author":"Chen","year":"2018","journal-title":"Journal of Human Resources"},{"issue":"1","key":"quan200324-bib-0011","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1177\/1536867X1501500103","volume":"15","author":"Chernozhukov","year":"2015","journal-title":"Stata Journal"},{"issue":"2","key":"quan200324-bib-0012","doi-asserted-by":"crossref","first-page":"667","DOI":"10.3982\/ECTA8718","volume":"81","author":"Chernozhukov","year":"2013","journal-title":"Econometrica"},{"key":"quan200324-bib-0013","unstructured":"Chesher, Andrew and Adam M. 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