Treatment Effects in Interactive Fixed Effects Models

This paper considers identifying and estimating the Average Treatment Effect on the Treated (ATT) in interactive fixed effects models. We focus on the case where there is a single unobserved time-invariant variable whose effect is allowed to change over time, though we also allow for time fixed effects and unobserved individual-level heterogeneity. The models that we consider in this paper generalize many commonly used models in the treatment effects literature including difference in differences and individual-specific linear trend models. Unlike the majority of the literature on interactive fixed effects models, we do not require the number of time periods to go to infinity to consistently estimate the ATT. Our main identification result relies on having the effect of some time invariant covariate (e.g., race or sex) not vary over time. Using our approach, we show that the ATT can be identified with as few as three time periods and with panel or repeated cross sections data.