Semiparametric estimation of a principal functional coefficient panel data model with cross-sectional dependence and its application to cigarette demand

In this paper, we consider the estimation of functional coefficient panel data models with cross-sectional dependence. Borrowing the principal component structure, the functional coefficient panel data models can be transformed into a semiparametric panel data model. Combining the local linear dummy variable technique and profile least squares method, we develop a semiparametric profile method to estimate the coefficient functions. A gradient-descent iterative algorithm is employed to enhance computation speed and estimation accuracy. The main results show that the resulting parameter estimator enjoys asymptotic normality with a $\sqrt{NT}$ convergence rate and the nonparametric estimator is asymptotically normal with a nonparametric convergence rate $\sqrt{NTh}$ when both the number of cross-sectional units $N$ and the length of time series $T$ go to infinity, under some regularity conditions. Monte Carlo simulations are carried out to evaluate the proposed methods, and an application to cigarette demand is investigated for illustration.