{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T17:51:41Z","timestamp":1785779501664,"version":"3.56.0"},"reference-count":41,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,11,13]],"date-time":"2014-11-13T00:00:00Z","timestamp":1415836800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2016,2]]},"abstract":"<jats:p>This paper considers the problem of coverage of the elements of the identified set in a class of partially identified econometric models with a prespecified probability. In order to conduct inference in partially identified econometric models defined by moment (in)equalities, the literature has proposed three methods: bootstrap, subsampling, and asymptotic approximation. The objective of this paper is to compare these methods in terms of the rate at which they achieve the desired coverage level, i.e., in terms of the rate at which the<jats:italic>error in the coverage probability<\/jats:italic>(ECP) converges to zero.<\/jats:p><jats:p>Under certain conditions, we show that the ECP of the bootstrap and the ECP of the asymptotic approximation converge to zero at the same rate, which is a faster rate than that of the ECP of subsampling methods. As a consequence, under these conditions, the bootstrap and the asymptotic approximation produce inference that is more precise than subsampling. A Monte Carlo simulation study confirms that these results are relevant in finite samples.<\/jats:p>","DOI":"10.1017\/s0266466614000826","type":"journal-article","created":{"date-parts":[[2014,11,13]],"date-time":"2014-11-13T03:35:19Z","timestamp":1415849719000},"page":"187-242","source":"Crossref","is-referenced-by-count":11,"title":["COMPARISON OF INFERENTIAL METHODS IN PARTIALLY IDENTIFIED MODELS IN TERMS OF ERROR IN COVERAGE PROBABILITY"],"prefix":"10.1017","volume":"32","author":[{"given":"Federico A.","family":"Bugni","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,11,13]]},"reference":[{"key":"S0266466614000826_ref31","unstructured":"Kim K . (2008) Set Estimation and Inference with Models Characterized by Conditional Moment Inequalities. Mimeo, Michigan State University."},{"key":"S0266466614000826_ref20","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2007.00794.x"},{"key":"S0266466614000826_ref7","unstructured":"Armstrong T.B . (2012) Asymptotically Exact Inference in Conditional Moment Inequality Models. Mimeo, Yale University."},{"key":"S0266466614000826_ref29","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2004.00555.x"},{"key":"S0266466614000826_ref14","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176345637"},{"key":"S0266466614000826_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2009.11.009"},{"key":"S0266466614000826_ref27","doi-asserted-by":"crossref","first-page":"3159","DOI":"10.1016\/S1573-4412(01)05005-X","volume-title":"Handbook of Econometrics","volume":"4","author":"Horowitz","year":"2001"},{"key":"S0266466614000826_ref26","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4384-7"},{"key":"S0266466614000826_ref38","doi-asserted-by":"crossref","first-page":"1979","DOI":"10.3982\/ECTA11011","article-title":"A practical two-step method for testing moment inequalities","volume":"82","author":"Romano","year":"2014","journal-title":"Econometrica"},{"key":"S0266466614000826_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466608090257"},{"key":"S0266466614000826_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/0047-259X(85)90084-3"},{"key":"S0266466614000826_ref40","first-page":"299","article-title":"More on confidence intervals for partially identified parameters","volume":"77","author":"Stoye","year":"2009","journal-title":"Econometrica"},{"key":"S0266466614000826_ref23","volume-title":"Local Properties of Distributions of Stochastic Functionals","volume":"173","author":"Davydov","year":"1995"},{"key":"S0266466614000826_ref15","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.3982\/ECTA7637","article-title":"Set identified linear models","volume":"80","author":"Bontemps","year":"2012","journal-title":"Econometrica"},{"key":"S0266466614000826_ref16","doi-asserted-by":"crossref","first-page":"735","DOI":"10.3982\/ECTA8056","article-title":"Bootstrap inference in partially identified models defined by moment inequalities: Coverage of the identified set","volume":"78","author":"Bugni","year":"2010","journal-title":"Econometrica"},{"key":"S0266466614000826_ref11","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1988.10478649"},{"key":"S0266466614000826_ref13","volume-title":"Normal Approximation and Asymptotic Expansions","author":"Bhattacharya","year":"1976"},{"key":"S0266466614000826_ref12","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2008.00859.x"},{"key":"S0266466614000826_ref35","unstructured":"Ponomareva M . (2010) Inference in Models Defined by Conditional Moment Inequalities with Continuous Covariates. Mimeo, Northern Illinois University."},{"key":"S0266466614000826_ref41","doi-asserted-by":"publisher","DOI":"10.1111\/1467-937X.00240"},{"key":"S0266466614000826_ref4","doi-asserted-by":"crossref","first-page":"2805","DOI":"10.3982\/ECTA8166","article-title":"Inference for parameters defined by moment inequalities: A recommended moment selection procedure","volume":"80","author":"Andrews","year":"2012","journal-title":"Econometrica"},{"key":"S0266466614000826_ref6","doi-asserted-by":"crossref","first-page":"119","DOI":"10.3982\/ECTA7502","article-title":"Inference for parameters defined by moment inequalities using generalized moment selection","volume":"78","author":"Andrews","year":"2010","journal-title":"Econometrica"},{"key":"S0266466614000826_ref34","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1554-7"},{"key":"S0266466614000826_ref10","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/74.3.457"},{"key":"S0266466614000826_ref2","doi-asserted-by":"crossref","unstructured":"Andrews D.W.K. , Berry S. , & Jia-Barwick P. (2004) Confidence Regions for Parameters in Discrete Games with Multiple Equilibria with an Application to Discount Chain Store Location. Mimeo, Yale University and M.I.T.","DOI":"10.2139\/ssrn.3417207"},{"key":"S0266466614000826_ref30","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346079"},{"key":"S0266466614000826_ref21","doi-asserted-by":"crossref","first-page":"667","DOI":"10.3982\/ECTA8718","article-title":"Intersection bounds: Estimation and inference","volume":"81","author":"Chernozhukov","year":"2013","journal-title":"Econometrica"},{"key":"S0266466614000826_ref22","doi-asserted-by":"crossref","unstructured":"Chetverikov D . (2012) Adaptive Test of Conditional Moment Inequalities. Mimeo, MIT.","DOI":"10.1920\/wp.cem.2012.3612"},{"key":"S0266466614000826_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2014.04.021"},{"key":"S0266466614000826_ref24","doi-asserted-by":"crossref","unstructured":"Galichon A. & Henry M. (2006) Inference in Incomplete Models. Mimeo, Ecole Polytechnique, Paris - Department of Economic Sciences and Pennsylvania State University.","DOI":"10.2139\/ssrn.886907"},{"key":"S0266466614000826_ref32","volume-title":"Identification Problems in the Social Sciences","author":"Manski","year":"1995"},{"key":"S0266466614000826_ref28","doi-asserted-by":"publisher","DOI":"10.1006\/jmva.2001.2031"},{"key":"S0266466614000826_ref39","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2008.08.001"},{"key":"S0266466614000826_ref36","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2008.03.015"},{"key":"S0266466614000826_ref1","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00114"},{"key":"S0266466614000826_ref37","doi-asserted-by":"crossref","first-page":"169","DOI":"10.3982\/ECTA6706","article-title":"Inference for the identified set in partially identified econometric models","volume":"78","author":"Romano","year":"2010","journal-title":"Econometrica"},{"key":"S0266466614000826_ref5","doi-asserted-by":"crossref","first-page":"609","DOI":"10.3982\/ECTA9370","article-title":"Inference based on conditional moment inequalities","volume":"81","author":"Andrews","year":"2013","journal-title":"Econometrica"},{"key":"S0266466614000826_ref33","doi-asserted-by":"publisher","DOI":"10.1920\/wp.cem.2007.1607"},{"key":"S0266466614000826_ref17","unstructured":"Bugni F.A . (2014) Supplemental Material to \u201cComparison of inferential methods in partially identified models in terms of error in coverage probability\u201d. Accepted for electronic publication in Econometric Theory on August 11, 2014."},{"key":"S0266466614000826_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2013.07.001"},{"key":"S0266466614000826_ref18","doi-asserted-by":"crossref","first-page":"1741","DOI":"10.3982\/ECTA9604","article-title":"Distortions of asymptotic confidence size in locally misspecified moment inequality models","volume":"80","author":"Bugni","year":"2012","journal-title":"Econometrica"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466614000826","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,17]],"date-time":"2019-08-17T05:03:55Z","timestamp":1566018235000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466614000826\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,13]]},"references-count":41,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,2]]}},"alternative-id":["S0266466614000826"],"URL":"https:\/\/doi.org\/10.1017\/s0266466614000826","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,11,13]]}}}