A condition for the identification of multivariate models with binary instruments

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.