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

• Published in: Journal of statistical planning and inference Vol. 236; p. 106244
• Main Authors: Zhao, Yan-Yong, Ge, Ling-Ling, Zhang, Kong-Sheng
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2025
• Subjects: Cross-sectional dependence; Functional coefficients; Panel data; Principal component structure; Principal component structure; 62G08; Functional coefficients; Panel data; Cross-sectional dependence; 62H12; 62J10
• ISSN: 0378-3758
• DOI: 10.1016/j.jspi.2024.106244

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 NT convergence rate and the nonparametric estimator is asymptotically normal with a nonparametric convergence rate 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. •Analyze functional coefficient panel data models with cross-sectional dependence.•Develop a semiparametric profile method to estimate coefficient functions.•Develop a gradient-descent iterative algorithm to enhance estimation accuracy.•Asymptotic properties under some regular conditions are established.