NONPARAMETRIC ESTIMATION OF SEMIPARAMETRIC TRANSFORMATION MODELS

Abstract

In this paper we develop a nonparametric estimation technique for semiparametric transformation models of the form: H ( Y ) = φ ( Z ) + X ′ β + U where H , φ are unknown functions, β is an unknown finite-dimensional parameter vector and the variables ( Y , Z ) are endogenous. Identification of the model and asymptotic properties of the estimator are analyzed under the mean independence assumption between the error term and the instruments. We show that the estimators are consistent, and a $\sqrt N$ -convergence rate and asymptotic normality for $\hat \beta$ can be attained. The simulations demonstrate that our nonparametric estimates fit the data well.