Semiparametric Estimation of Partially Linear Dynamic Panel Data Models with Fixed Effects∗

In this paper, we study a partially linear dynamic panel data model with fixed effects, where either exogenous or endogenous variables or both enter the linear part, and the lagged dependent variable together with some other exogenous variables enter the nonparametric part. Two types of estimation methods are proposed for the first differenced model. One is composed of a semiparametric GMM estimator for the finite dimensional parameter  and a local polynomial estimator for the infinite dimensional parameter  based on the empirical solutions to Fredholm integral equations of the second kind, and the other is a sieve IV estimate of the parametric and nonparametric components jointly. We study the asymptotic properties for these two types of estimates when the number of individuals  tends to ∞ and the time period  is fixed. We also propose a specification test for the linearity of the nonparametric component based on a weighted square distance between the parametric estimate under the linear restriction and the semiparametric estimate under the alternative. Monte Carlo simulations suggest that the proposed estimators and tests perform well in finite samples. We apply our new model to study the relationship between economic growth, intellectual property right (IPR) protection and initial economic condition, and detect significant nonlinear dynamic structure.