Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects

Abstract

Linear regressions with period and group fixed effects are widely used to estimate treatment effects. We show that they estimate weighted sums of the average treatment effects (ATE ) in each group and period, with weights that may be negative. Due to the negative weights, the linear regression coefficient may for instance be negative while all the ATEs are positive. We propose another estimator that solves this issue. In the two applications we revisit, it is significantly different from the linear regression estimator. (JEL C21, C23, D72, J31, J51, L82)

Fuzzy differences-in-differences with Stata

“… 6. de Chaisemartin and D’Haultfœuille (2018a) obtain the same result on slightly different estimands and without assuming G ⫫ T . Under this additional condition, their estimands are equal to the Wald DID and Wald TC considered here.…”

“…Theorem 2 below shows that under our previous conditions plus assumption 8, the three estimands point identify Δ. This theorem is proved for the Wald DID and Wald TC in de Chaisemartin and D’Haultfœuille (2018a) and can be proved along the same lines for the Wald CIC. 6…”

“…Researchers then estimate treatment effects via linear regressions, including time and group fixed effects. de Chaisemartin and D’Haultfœuille (2018a) show that around 19% of all empirical articles published by the American Economic Review between 2010 and 2012 use this research design. They also show that these regressions are extensions of the Wald DID to multiple periods and groups and that they identify weighted averages of LATEs with possibly many negative weights.…”

On the effects of COVID-19 safer-at-home policies on social distancing, car crashes and pollution

“…Recent research on two-way fixed-effects (TWFE) estimators, which are usually motivated as difference-in-differences with multiple time periods, has identified issues that arise in the presence of heterogeneous treatment effects across groups or time ( Callaway and Sant’Anna (Forthcoming) ; De Chaisemartin and d’Haultfoeuille (2020) ; Goodman-Bacon and Marcus (2020) ). Using the twowayfeweights Stata package detailed in De Chaisemartin and d’Haultfoeuille (2020) , we document that 44% of the naive average treatments on the treated for pollution are assigned negative weights, indicating the need to reexamine our results using an alternative estimator. We use the alternative estimators provided by Callaway and Sant’Anna (Forthcoming) ; Callaway and Sant’Anna (2020) that are most appropriate for the staggered adoption of safer-at-home policies in our sample.…”

Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects

“…de Chaisemartin and D'Haultfoeuille (2020) show that with one treatment in the regression, under a parallel trends assumption TWFE regressions identify a weighted sum of the treatment effects of treated (g, t) cells, with potentially negative weights. Because of the negative weights, the treatment coefficient in such regressions may be, say, negative, even if the treatment effect is strictly positive in every (g, t) cell.…”