Varying-coefficient spatial dynamic panel data models with fixed effects: Theory and application

This paper considers a varying-coefficient spatial dynamic panel data model with fixed effects. We show that a two-point approximation method poses a potential weak identification problem. We propose a robust modified estimator to address this issue. Our two-step estimation procedure incorporates both linear and quadratic moment conditions. We also extend our analysis to a partially linear varying-coefficient model and develop a consistent test for this specification. We establish the asymptotic properties of the proposed estimators. Simulations indicate that our estimators and the test statistic perform well in finite samples. We apply the partially linear varying-coefficient model to study how the sales of liquor producers respond to those of neighboring competitors in China. We find spatial dependence among liquor producers and show that the spatial effects vary with competition intensity.