Identification and Estimation of Nonseparable Models with Multivalued Endogeneity and a Binary Instrument
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In this paper, I show that a nonseparable model where the endogenous variable is multivalued can be point-identified even when the instrument (IV) is only binary. Though the order condition generally fails in this case, I show that exogenous covariates are able to generate enough moment equations to restore the order condition as if enlarging the IV's support under very general selection mechanisms for the endogenous variable. No restrictions are imposed on the way these covariates enter the model, such as separability or monotonicity. Further, after the order condition is fulfilled, I provide a new sufficient condition that is weaker than the existing results for the global uniqueness of the solution to the nonlinear system of equations. Based on the identification result, I propose a sieves estimator and uniform consistency and pointwise asymptotic normality are established under simple low-level conditions. A Monte Carlo experiment is conducted to examine its performance.
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