Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects
57 Pages Posted: 24 Mar 2018 Last revised: 3 May 2018
Date Written: April 25, 2018
Around 20% of all empirical articles published by the American Economic Review between 2010 and 2012 estimate treatment effects using linear regressions with time and group fixed effects. In a model where the effect of the treatment is constant across groups and over time, such two-way fixed effects regressions identify the treatment effect of interest under the standard ``common trends'' assumption. But these regressions have not been analyzed yet allowing for treatment effect heterogeneity. We study two commonly used two-way fixed effects regressions. We start by showing that without assuming constant treatment effects, those regressions identify weighted sums of the average treatment effects in each group and period, where some weights may be negative. The weights can be estimated, and can help researchers assess whether their results are robust to heterogeneous treatment effects across groups and periods. When some weights are negative, their estimates may not even have the same sign as the true average treatment effect if treatment effects are heterogenous. We then propose another estimator that does not rely on any treatment effect homogeneity assumption. We revisit two empirical articles that have estimated two-way fixed effects regressions. In both cases, around half of the weights attached to those regressions are negative. In one application, our new estimator is of a different sign than the first two-way fixed effects estimator we study, and significantly different from the second one.
Keywords: Fixed Effects, First Difference, Differences-in-Differences, Heterogeneous Treatment Effects
JEL Classification: C21, C26
Suggested Citation: Suggested Citation