Treatment Effects in Interactive Fixed Effects Models with a Small Number of Time Periods

This paper considers identifying and estimating the Average Treatment Effect on the Treated (ATT) when untreated potential outcomes are generated by an interactive fixed effects model. That is, in addition to time-period and individual fixed effects, we consider the case where there is an unobserved time invariant variable whose effect on untreated potential outcomes may change over time and which can therefore cause outcomes (in the absence of participating in the treatment) to follow different paths for the treated group relative to the untreated group. 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.