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However, when participation is also misreported, the IV estimand may become a nonconvex combination of local average treatment effects that fails to satisfy even a minimal condition for being causal. The aim of our paper is to generalize the MR\u2010LATE approach. This is an alternative IV estimand that is more robust in cases of noncompliance and nondifferential misclassification of the treatment variable. Our generalization is threefold: First, we incorporate discrete and multiple\u2010discrete instrument(s); second, we consider the use of instrument(s) under a weaker, partial monotonicity condition; third, we provide a general inferential procedure. Under relatively stringent assumptions, MR\u2010LATE is either identical to the IV estimand or less biased than the na\u00efve IV estimand. Under less stringent assumptions, the MR\u2010LATE estimand can identify the sign of the IV estimand. We conclude with the use of a dedicated Stata command, <jats:styled-content>ivreg2m,<\/jats:styled-content> to assess the return on education in the United Kingdom.<\/jats:p>","DOI":"10.1002\/jae.3079","type":"journal-article","created":{"date-parts":[[2024,6,29]],"date-time":"2024-06-29T10:16:16Z","timestamp":1719656176000},"page":"1123-1148","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Identifying program benefits when participation is misreported"],"prefix":"10.1002","volume":"39","author":[{"given":"Denni","family":"Tommasi","sequence":"first","affiliation":[{"name":"University of Bologna, IZA and CDES  Bologna Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lina","family":"Zhang","sequence":"additional","affiliation":[{"name":"University of Amsterdam and Tinbergen Institute  Amsterdam The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2024,6,29]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(02)00201-4"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA7133"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/obes.12581"},{"key":"e_1_2_9_5_1","unstructured":"Acerenza S. 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