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 .
Models with a discrete endogenous variable are typically underidentified when the instrument takes on too few values. This paper presents a new method that matches pairs of covariates and instruments to restore point identification in this scenario in a triangular model. The model consists of a structural function for a continuous outcome and a selection model for the discrete endogenous variable. The structural outcome function must be continuous and monotonic in a scalar disturbance, but it can be nonseparable. The selection model allows for unrestricted heterogeneity. Global identification is obtained under weak conditions. The paper also provides estimators of the structural outcome function. Two empirical examples of the return to education and selection into Head Start illustrate the value and limitations of the method .
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In this paper, I show that a nonseparable model where the endogenous variable is multivalued can be point-identified even
Models with a discrete endogenous variable are typically underidentified
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(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
takes on too few values. This paper presents a new method that matches pairs of covariates and instruments to restore point identification in this scenario in a triangular model. The model consists of a structural function for a continuous outcome and a selection model for the discrete
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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 structural outcome function must be continuous and monotonic in a scalar disturbance, but it can be nonseparable. The selection model allows for unrestricted heterogeneity. Global identification is obtained under weak conditions. The paper also provides estimators of the structural outcome function. Two empirical examples of the return to education and selection into Head Start illustrate the value and limitations of
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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
method