Varying-coefficient panel data models with partially observed factor structure

In this paper, we study a varying-coefficient panel data model with nonstationarity, wherein a factor structure is adopted to capture different effects of time invariant variables over time. The methodology employed in this paper fills a gap of dealing with the mixed I(1)/I(0) regressors and factors in the literature. For comparison purposes, we consider the scenarios where the factors are either observable or unobservable, respectively. We propose an estimation method for both the unknown coefficient functions involved and the unknown factors before we establish the corresponding theory. We then evaluate the finite-sample performance of the proposed estimation theory through extensive Monte Carlo simulations. In an empirical study, we use our newly proposed model and method to study the returns to scale of large commercial banks in the U.S.. Some overlooked modelling issues in the literature of production econometrics are addressed.