A Varying-Coefficient Panel Data Model with Fixed Effects: Theory and an Application to U.S. Commercial Banks

In this paper, we propose a panel data semiparametric varying-coefficient model in which covariates (variables affecting the coefficients) are purely categorical. This model has two features: first, fixed effects are included to allow for correlation between individual unobserved heterogeneity and the regressors; second, it allows for cross-sectional dependence through a general spatial error dependence structure. We derive a semiparametric estimator for our model by using a modified within transformation, and then show the asymptotic and finite properties for this estimator. Finally, we illustrate our model by analysing the effects of state-level banking regulations on the returns to scale of commercial banks in the U.S. Our empirical results suggest that returns to scale is higher in more regulated states than in less regulated states.