{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T08:48:27Z","timestamp":1785746907585,"version":"3.56.0"},"reference-count":28,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T00:00:00Z","timestamp":1755561600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2026,8]]},"abstract":"\n This article studies the identification of complete economic models with testable assumptions. We start with a local average treatment effect (\n \n \n \n L<\/mml:mi>\n A<\/mml:mi>\n T<\/mml:mi>\n E<\/mml:mi>\n <\/mml:math>\n $LATE$<\/jats:tex-math>\n \n upper L upper A upper T upper E<\/jats:alt-text>\n <\/jats:inline-graphic>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n ) model where the \u201cNo Defiers,\u201d the independent IV assumption, and the exclusion restrictions can be jointly refuted by some data distributions. We propose two relaxed assumptions that are not refutable, with one assumption focusing on relaxing the \u201cNo Defiers\u201d assumption while the other relaxes the independent IV assumption. The identified set of\n \n \n \n L<\/mml:mi>\n A<\/mml:mi>\n T<\/mml:mi>\n E<\/mml:mi>\n <\/mml:math>\n $LATE$<\/jats:tex-math>\n \n upper L upper A upper T upper E<\/jats:alt-text>\n <\/jats:inline-graphic>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n under either of the two relaxed assumptions coincides with the classical\n \n \n \n L<\/mml:mi>\n A<\/mml:mi>\n T<\/mml:mi>\n E<\/mml:mi>\n <\/mml:math>\n $LATE$<\/jats:tex-math>\n \n upper L upper A upper T upper E<\/jats:alt-text>\n <\/jats:inline-graphic>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n Wald ratio expression whenever the original assumption is not refuted by the observed data distribution. We propose an estimator for the identified\n \n \n \n L<\/mml:mi>\n A<\/mml:mi>\n T<\/mml:mi>\n E<\/mml:mi>\n <\/mml:math>\n $LATE$<\/jats:tex-math>\n \n upper L upper A upper T upper E<\/jats:alt-text>\n <\/jats:inline-graphic>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n and derive the estimator\u2019s limit distribution. We then develop a general method to relax a refutable assumption\n A<\/jats:italic>\n . This relaxation method requires finding a function that measures the deviation of an econometric structure from the original assumption\n A<\/jats:italic>\n , and a relaxed assumption\n \n \n \n \n \n A<\/mml:mi>\n ~<\/mml:mo>\n <\/mml:mover>\n <\/mml:mrow>\n <\/mml:math>\n $\\tilde {A}$<\/jats:tex-math>\n \n upper A overtilde<\/jats:alt-text>\n <\/jats:inline-graphic>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is constructed using this measure of deviation. We characterize a condition to ensure the identified sets under\n \n \n \n \n \n A<\/mml:mi>\n ~<\/mml:mo>\n <\/mml:mover>\n <\/mml:mrow>\n <\/mml:math>\n $\\tilde {A}$<\/jats:tex-math>\n \n upper A overtilde<\/jats:alt-text>\n <\/jats:inline-graphic>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n and\n A<\/jats:italic>\n coincide whenever\n A<\/jats:italic>\n is not refuted by the observed data distribution and discuss the criteria to choose among different relaxed assumptions.\n <\/jats:p>","DOI":"10.1017\/s0266466625100108","type":"journal-article","created":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T06:42:17Z","timestamp":1755585737000},"page":"950-995","source":"Crossref","is-referenced-by-count":0,"title":["EXTENDING ECONOMIC MODELS WITH TESTABLE ASSUMPTIONS: THEORY AND APPLICATIONS"],"prefix":"10.1017","volume":"42","author":[{"given":"Moyu","family":"Liao","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0384j8v12","id-type":"ROR","asserted-by":"publisher"}],"name":"The University of Sydney"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2025,8,19]]},"reference":[{"key":"S0266466625100108_r6","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA17232"},{"key":"S0266466625100108_r12","doi-asserted-by":"crossref","first-page":"1769","DOI":"10.3982\/ECTA8681","article-title":"Impossibility results for nondifferentiable functionals","volume":"80","author":"Hirano","year":"2012","journal-title":"Econometrica"},{"key":"S0266466625100108_r19","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729837"},{"key":"S0266466625100108_r14","doi-asserted-by":"publisher","DOI":"10.2307\/2951620"},{"key":"S0266466625100108_r5","doi-asserted-by":"publisher","DOI":"10.3386\/w4483"},{"key":"S0266466625100108_r24","doi-asserted-by":"publisher","DOI":"10.1162\/REST_a_00622"},{"key":"S0266466625100108_r10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jet.2006.06.010"},{"key":"S0266466625100108_r7","doi-asserted-by":"publisher","DOI":"10.1093\/ectj\/utad013"},{"key":"S0266466625100108_r16","doi-asserted-by":"publisher","DOI":"10.2139\/ssrn.3388373"},{"key":"S0266466625100108_r8","doi-asserted-by":"publisher","DOI":"10.3982\/QE601"},{"key":"S0266466625100108_r15","doi-asserted-by":"publisher","DOI":"10.2307\/1913714"},{"key":"S0266466625100108_r17","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA11974"},{"key":"S0266466625100108_r18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2021.03.006"},{"key":"S0266466625100108_r21","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00144"},{"key":"S0266466625100108_r13","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466618000439"},{"key":"S0266466625100108_r3","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(91)90032-9"},{"key":"S0266466625100108_r25","doi-asserted-by":"publisher","DOI":"10.4324\/9780203994627"},{"key":"S0266466625100108_r1","doi-asserted-by":"publisher","DOI":"10.1198\/073500108000000105"},{"key":"S0266466625100108_r2","doi-asserted-by":"publisher","DOI":"10.3982\/QE1930"},{"key":"S0266466625100108_r27","doi-asserted-by":"publisher","DOI":"10.1037\/h0037350"},{"key":"S0266466625100108_r11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jet.2004.12.006"},{"key":"S0266466625100108_r23","doi-asserted-by":"publisher","DOI":"10.1086\/708724"},{"key":"S0266466625100108_r22","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA17969"},{"key":"S0266466625100108_r20","doi-asserted-by":"crossref","unstructured":"Liao, M. (2024). Robust Bayesian method for refutable models. Working Paper. arXiv preprint, arXiv:2401.04512.","DOI":"10.2139\/ssrn.5450128"},{"key":"S0266466625100108_r4","doi-asserted-by":"publisher","DOI":"10.2307\/2297609"},{"key":"S0266466625100108_r26","doi-asserted-by":"publisher","DOI":"10.1093\/oxfordjournals.oep.a041827"},{"key":"S0266466625100108_r9","doi-asserted-by":"publisher","DOI":"10.1093\/restud\/rdr008"},{"key":"S0266466625100108_r28","doi-asserted-by":"publisher","DOI":"10.1111\/1467-937X.00240"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466625100108","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T08:33:47Z","timestamp":1785746027000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466625100108\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,19]]},"references-count":28,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,8]]}},"alternative-id":["S0266466625100108"],"URL":"https:\/\/doi.org\/10.1017\/s0266466625100108","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,19]]}}}