Semiparametric Estimation of Partially Varying-Coefficient

This paper studies a new class of semiparametric dynamic panel data models, in which some coefficients are allowed to depend on some informative variables and some regressors can be endogenous. To estimate both parametric and nonparametric coefficients, a three-stage semiparametric estimation method is proposed. The nonparametric GMM is proposed to estimate all coefficients firstly and the average method is used to obtain the root-N consistent estimator of parametric coefficients. At the last stage, the estimator of varying coefficients is obtained by plugging the parametric estimator into the model. The consistency and asymptotic normality of both estimators are derived, and furthermore, the efficient estimation of parametric coefficients is discussed. Monte Carlo simulations verify the theoretical results and demonstrate that our estimators work well even in a finite sample.