Abstract: We propose a varying-coefficient panel-data model with unobservable multiple interactive fixed effects that are correlated with the regressors. We approximate each coefficient function using B-splines, and propose a robust nonlinear iteration scheme based on the least squares method to estimate the coefficient functions of interest. We also establish the asymptotic theory of the resulting estimators under certain regularity assumptions, including the consistency, convergence rate, and asymptotic distributions. To construct the pointwise confidence intervals for the coefficient functions, we propose a residual-based block bootstrap method that reduces the computational burden and avoids accumulative errors. We extend our proposed procedure to partially linear varying-coefficient panel-data models with unobservable multiple interactive fixed effects, and examine the problem of constant coefficients versus function coefficients. Simulation studies and a real-data analysis are used to assess the performance of the proposed methods.

Key words and phrases: Bootstrap, B-spline, hypothesis testing, interactive fixed effect, panel data, partially linear varying-coefficient model, varying-coefficient model.