Nonparametric Estimation of Semiparametric Transformation Models

In this paper we develop a nonparametric estimation technique for semiparametric transformation models of the form: H(Y ) = φ(Z) + Xβ + U where H, φ and β are unknown 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 √ N -convergence rate for β-hat can be attained. The simulations demonstrate that our nonparametric estimates fits the data well.