Estimation of a Partially Linear Regression in Triangular Systems

We propose kernel-based estimators for the components of a partially linear regression in a triangular system where endogenous regressors appear both in the linear and nonparametric components of the regression. Compared with other estimators currently available in the literature, e.g. the sieve estimators proposed in Ai and Chen (2003) or Otsu (2011), our estimators have explicit functional form and are much easier to implement. They rely on a set of assumptions introduced by Newey et al. (1999) that characterize what has become known as the “control function†approach for endogeneity in regression. We explore conditional moment restrictions that make this model suitable for additive regression estimation as in Kim et al. (1999) and Manzan and Zerom (2005). We establish consistency and √n asymptotic normality of the estimator for the parameters in the linear component of the model, give a uniform rate of convergence, and establish the asymptotic normality for the estimator of the nonparametric component. In addition, for statistical inference, a consistent estimator for the covariance of the limiting distribution of the parametric estimator is provided. A small Monte Carlo study sheds light on the finite sample performance of our estimators and an empirical application illustrates their use.