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Equivalence with IV is established for a semiparametric family of control function estimators and shown to hold at interior solutions for a class of maximum likelihood estimators. Our results suggest differences between structural and IV estimates often stem from disagreements about the target parameter rather than from functional form assumptions per se. In cases where equivalence fails, reporting structural estimates of LATE alongside IV provides a simple means of assessing the credibility of structural extrapolation exercises.<\/jats:p>","DOI":"10.3982\/ecta15444","type":"journal-article","created":{"date-parts":[[2019,3,26]],"date-time":"2019-03-26T04:27:16Z","timestamp":1553574436000},"page":"677-696","source":"Crossref","is-referenced-by-count":43,"title":["On Heckits, LATE, and Numerical Equivalence"],"prefix":"10.3982","volume":"87","author":[{"given":"Patrick","family":"Kline","sequence":"first","affiliation":[{"name":"Department of Economics, UC Berkeley"},{"name":"NBER"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christopher R.","family":"Walters","sequence":"additional","affiliation":[{"name":"Department of Economics, UC Berkeley"},{"name":"NBER"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2019]]},"reference":[{"key":"ecta12429-bib-0001","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1198\/016214502753479419","volume":"97","author":"Abadie","year":"2002","journal-title":"Journal of the American Statistical Association"},{"key":"ecta12429-bib-0002","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/S0304-4076(02)00201-4","volume":"113","author":"Abadie","year":"2003","journal-title":"Journal of Econometrics"},{"key":"ecta12429-bib-0003","doi-asserted-by":"crossref","first-page":"C52","DOI":"10.1111\/j.0013-0133.2003.00195.x","volume":"114","author":"Angrist","year":"2004","journal-title":"The Economic Journal"},{"key":"ecta12429-bib-0004","doi-asserted-by":"crossref","DOI":"10.1515\/9781400829828","volume-title":"Mostly Harmless Econometrics: An Empiricist's Companion","author":"Angrist","year":"2009"},{"key":"ecta12429-bib-0005","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1257\/jep.24.2.3","volume":"24","author":"Angrist","year":"2010","journal-title":"Journal of Economic Perspectives"},{"key":"ecta12429-bib-0006","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1080\/01621459.1996.10476902","volume":"91","author":"Angrist","year":"1996","journal-title":"Journal of the American Statistical Association"},{"key":"ecta12429-bib-0007","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1080\/01621459.1997.10474074","volume":"92","author":"Balke","year":"1997","journal-title":"Journal of the American Statistical Association"},{"key":"ecta12429-bib-0008","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1016\/j.jeconom.2007.05.006","volume":"142","author":"Battistin","year":"2008","journal-title":"Journal of Econometrics"},{"key":"ecta12429-bib-0009","unstructured":"Bertanha, M., and G. 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