Efficient Estimation and Variable Selection in Dynamic Panel Data Partially Linear Varying Coefficient Models with Incidental Parameter

This paper is concerned with the statistical inference of partially linear varying coefficient dynamic panel data model with incidental parameter, including efficient estimation of the parametric and nonparametric components and consistent determination of the lagged order. For the parametric component, we propose an efficient semiparametric generalized method-of-moments (GMM) estimator and establish its asymptotic normality. For the nonparametric component, B-spline series approximation is employed to estimate the unknown coefficient functions, which are shown to achieve the optimal nonparametric convergence rate. A consistent estimator of the variance of error component is also constructed. In addition, by using the smooth-threshold GMM estimating equations, we propose a variable selection method to identify the significant order of lagged terms automatically and remove the irrelevant regressors by setting their coefficient to zeros. As a result, it can consistently determine the true lagged order and specify the significant exogenous variables. Further studies show that the resulting estimator has the same asymptotic properties as if the true lagged order and significant regressors were known prior, i.e., achieving the oracle property. Numerical experiments are conducted to evaluate the finite sample performance of our procedures. An example of application is also illustrated.