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Double fixed effects estimators with heterogeneous treatment effects
Clement de Chaisemartin, Xavier D'Haultfoeuille
Abstract: Around 20% of all empirical papers 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 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 show that under two alternative sets of assumptions, such regressions identify weighted sums of 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 many weights are negative, their estimates may not even have the same sign as the true average treatment effect if treatment effects are heterogenous. We also propose another estimator of the treatment effect that does not rely on any homogeneity assumption. Finally, we estimate the weights in two applications and find that in both cases, around half of the average treatment effects receive a negative weight.