{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:22:52Z","timestamp":1759638172418},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2020,10,30]],"date-time":"2020-10-30T00:00:00Z","timestamp":1604016000000},"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":[[2021,8]]},"abstract":"<jats:p>In this study, we explore the partial identification of nonseparable models with continuous endogenous and binary instrumental variables. We show that the structural function is partially identified when it is monotone or concave in the explanatory variable. D\u2019Haultf\u0153uille and F\u00e9vrier (2015, <jats:italic>Econometrica<\/jats:italic> 83(3), 1199\u20131210) and Torgovitsky (2015, <jats:italic>Econometrica<\/jats:italic> 83(3), 1185\u20131197) prove the point identification of the structural function under a key assumption that the conditional distribution functions of the endogenous variable for different values of the instrumental variables have intersections. We demonstrate that, even if this assumption does not hold, monotonicity and concavity provide identification power. Point identification is achieved when the structural function is flat or linear with respect to the explanatory variable over a given interval. We compute the bounds using real data and show that our bounds are informative.<\/jats:p>","DOI":"10.1017\/s0266466620000353","type":"journal-article","created":{"date-parts":[[2020,10,30]],"date-time":"2020-10-30T07:20:40Z","timestamp":1604042440000},"page":"817-848","source":"Crossref","is-referenced-by-count":3,"title":["PARTIAL IDENTIFICATION OF NONSEPARABLE MODELS USING BINARY INSTRUMENTS"],"prefix":"10.1017","volume":"37","author":[{"given":"Takuya","family":"Ishihara","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2020,10,30]]},"reference":[{"key":"S0266466620000353_r18","doi-asserted-by":"publisher","DOI":"10.2307\/2171738"},{"key":"S0266466620000353_r9","doi-asserted-by":"publisher","DOI":"10.1002\/jae.1132"},{"key":"S0266466620000353_r5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2006.06.003"},{"key":"S0266466620000353_r12","doi-asserted-by":"publisher","DOI":"10.1111\/j.1468-0262.2007.00801.x"},{"key":"S0266466620000353_r11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2011.06.015"},{"key":"S0266466620000353_r23","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA9984"},{"key":"S0266466620000353_r17","first-page":"247","article-title":"Cash transfers, behavioral changes, and cognitive development in early childhood: Evidence from a randomized experiment","volume":"4","author":"Macours","year":"2012","journal-title":"American Economic Journal: Applied Economics"},{"key":"S0266466620000353_r21","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00037"},{"key":"S0266466620000353_r10","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2008.00273.x"},{"key":"S0266466620000353_r16","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466610000460"},{"key":"S0266466620000353_r8","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.3982\/ECTA5317","article-title":"Identification of treatment effects using control functions in models with continuous, endogenous treatment and heterogeneous effects","volume":"76","author":"Florens","year":"2008","journal-title":"Econometrica"},{"key":"S0266466620000353_r13","doi-asserted-by":"publisher","DOI":"10.2307\/2951620"},{"key":"S0266466620000353_r4","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00454"},{"key":"S0266466620000353_r19","doi-asserted-by":"publisher","DOI":"10.1162\/REST_a_00603"},{"key":"S0266466620000353_r7","doi-asserted-by":"publisher","DOI":"10.1920\/wp.cem.2013.4013"},{"key":"S0266466620000353_r6","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA10038"},{"key":"S0266466620000353_r2","doi-asserted-by":"publisher","DOI":"10.1257\/aer.103.3.563"},{"key":"S0266466620000353_r15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2009.02.011"},{"key":"S0266466620000353_r14","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.3982\/ECTA7108","article-title":"Identification and estimation of triangular simultaneous equations models without additivity","volume":"77","author":"Imbens","year":"2009","journal-title":"Econometrica"},{"key":"S0266466620000353_r22","doi-asserted-by":"publisher","DOI":"10.3982\/QE268"},{"key":"S0266466620000353_r20","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0262.00452"},{"key":"S0266466620000353_r1","doi-asserted-by":"publisher","DOI":"10.2307\/2937954"},{"key":"S0266466620000353_r3","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466620000213"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0266466620000353","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,19]],"date-time":"2021-08-19T08:31:14Z","timestamp":1629361874000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0266466620000353\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,30]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,8]]}},"alternative-id":["S0266466620000353"],"URL":"https:\/\/doi.org\/10.1017\/s0266466620000353","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,30]]}}}