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Instrumental Variable Models for Discrete Outcomes
Author(s) -
Chesher Andrew
Publication year - 2010
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta7315
Subject(s) - instrumental variable , nonparametric statistics , outcome (game theory) , quantile , discrete choice , identification (biology) , parametric statistics , set (abstract data type) , mathematics , variable (mathematics) , econometrics , binary number , point (geometry) , parametric model , mathematical optimization , computer science , statistics , mathematical economics , mathematical analysis , botany , geometry , arithmetic , biology , programming language
Single equation instrumental variable models for discrete outcomes are shown to be set identifying, not point identifying, for the structural functions that deliver the values of the discrete outcome. Bounds on identified sets are derived for a general nonparametric model and sharp set identification is demonstrated in the binary outcome case. Point identification is typically not achieved by imposing parametric restrictions. The extent of an identified set varies with the strength and support of instruments, and typically shrinks as the support of a discrete outcome grows. The paper extends the analysis of structural quantile functions with endogenous arguments to cases in which there are discrete outcomes.