A condition for the identification of multivariate models with binary instruments

Florian F. Gunsilius

Journal of Econometrics, 2023, vol. 235, issue 1, 220-238

Abstract: This article introduces an empirical condition for the nonparametric point-identification of multivariate instrumental variable models with continuous endogenous variables using binary instruments. Verifying this condition can confirm point-identification in settings in which traditional approaches are not applicable. In particular, it shows that nonlinear instrumental variable models with general heterogeneity can be point-identified with only a binary instrument. This generalizes existing identification results which either restrict the unobserved heterogeneity substantially or require the instrument to have a large support. The main assumption on the instrumental variable model is cyclic monotonicity of its first stage, a multivariate generalization of the classical rank-invariance assumption for univariate models. Asymptotic convergence results for the empirical observable distributions are derived that allow to check the condition in practice. The identification rests on a fixed-set convergence result of cyclically monotone maps between quasi-concave functions.

Keywords: Cyclic monotonicity; Fixed set iteration; Instrumental variable; Nonseparable model; Optimal transportation (search for similar items in EconPapers)
JEL-codes: C01 C14 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:235:y:2023:i:1:p:220-238

DOI: 10.1016/j.jeconom.2022.04.003

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