Varying-coefficient panel data models with nonstationarity and partially observed factor structure

In this article, we study a varying-coefficient panel data model with both nonstationarity and partially observed factor structure. Two approaches are proposed. The first approach proposed in the main text considers a sieve based method to estimate the unknown coefficients as well as the factors and loading functions simultaneously, while the second approach proposed in the online supplementary document involving the principal component analysis provides an alternative estimation method. We establish asymptotic properties for them, compare the asymptotic efficiency of the two estimation methods and examine the theoretical findings through extensive Monte Carlo simulations. In an empirical study, we use our newly proposed model and the first method to study the returns to scale of large U.S. commercial banks, where some overlooked modeling issues in the literature of production econometrics are addressed. Supplementary materials for this article are available online.