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We show certain causal parameters are identified in these models if and only if a version of the kappa of Abadie (2003) exists. Our identification results are constructive in yielding estimating moment conditions. Focusing on a leading special case, we develop asymptotically normal estimators based on a doubly robust version of these moment conditions.<\/jats:p>","DOI":"10.3982\/ecta23174","type":"journal-article","created":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T13:05:52Z","timestamp":1784207152000},"page":"1095-1133","source":"Crossref","is-referenced-by-count":0,"title":["Identification in Instrumental Variables Models: The Central Role of Abadie's Kappa"],"prefix":"10.3982","volume":"94","author":[{"given":"Manu","family":"Navjeevan","sequence":"first","affiliation":[{"name":"Department of Economics, TAMU"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rodrigo","family":"Pinto","sequence":"additional","affiliation":[{"name":"Department of Economics, USF"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andres","family":"Santos","sequence":"additional","affiliation":[{"name":"Department of Economics, 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