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There is special attention to a widely employed semiparametric shape restriction, which requires the threshold-crossing function to be a monotone function of a linear index involving the observable explanatory variables. The restriction brings great computational benefits, allowing calculation of the identified set of index coefficients without calculating the nonparametrically specified threshold function. With the restriction in place, the methods of the paper can be applied to produce identified sets in a class of binary response models with mismeasured explanatory variables.<\/jats:p>","DOI":"10.1017\/s0266466612000321","type":"journal-article","created":{"date-parts":[[2012,7,30]],"date-time":"2012-07-30T08:52:41Z","timestamp":1343638361000},"page":"231-266","source":"Crossref","is-referenced-by-count":12,"title":["SEMIPARAMETRIC STRUCTURAL MODELS OF BINARY RESPONSE: SHAPE RESTRICTIONS AND PARTIAL IDENTIFICATION"],"prefix":"10.1017","volume":"29","author":[{"given":"Andrew","family":"Chesher","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2012,7,30]]},"reference":[{"key":"S0266466612000321_ref30","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1111\/j.1468-0262.2007.00767.x","article-title":"Dummy endogenous variables in weakly separable models","volume":"75","author":"Vytlacil","year":"2007","journal-title":"Econometrica"},{"key":"S0266466612000321_ref6","doi-asserted-by":"crossref","first-page":"1525","DOI":"10.1111\/j.1468-0262.2005.00628.x","article-title":"Nonparametric identification under discrete variation","volume":"73","author":"Chesher","year":"2005","journal-title":"Econometrica"},{"key":"S0266466612000321_ref8","doi-asserted-by":"crossref","first-page":"575","DOI":"10.3982\/ECTA7315","article-title":"Instrumental variable models for discrete outcomes","volume":"78","author":"Chesher","year":"2010","journal-title":"Econometrica"},{"key":"S0266466612000321_ref25","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/0304-4076(88)90063-2","article-title":"Limited information estimators and exogeneity tests for simultaneous probit models","volume":"39","author":"Rivers","year":"1988","journal-title":"Journal of Econometrics"},{"key":"S0266466612000321_ref14","volume-title":"LIMDEP 9.0 Reference Guide","author":"Greene","year":"2007"},{"key":"S0266466612000321_ref18","first-page":"313","article-title":"Varieties of selection bias","volume":"80","author":"Heckman","year":"1990","journal-title":"American Economic Review"},{"key":"S0266466612000321_ref4","unstructured":"Chernozhukov, V. , Lee, S. , & Rosen, A. 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