Estimating interaction effects with panel data

Abstract: This paper analyzes how interaction effects can be consistently estimated under economically plausible assumptions in linear panel models with a fixed $T$-dimension. We advocate for a \emph{correlated interaction term estimator} (CITE) and show that it is consistent under conditions that are not sufficient for consistency of the interaction term estimator that is most common in applied econometric work. Our paper discusses the empirical content of these conditions, shows that standard inference procedures can be applied to CITE, and analyzes consistency, relative efficiency, inference, and their finite sample properties in a simulation study. In an empirical application, we test whether labor displacement effects of robots are stronger in countries at higher income levels. The results are in line with our theoretical and simulation results and indicate that standard interaction term estimation underestimates the importance of a country's income level in the relationship between robots and employment and may prematurely reject a null hypothesis about interaction effects in the presence of misspecification.