Working Paper: NBER ID: w25904
Authors: Clément de Chaisemartin; Xavier Dhaultfoeuille
Abstract: Linear regressions with period and group fixed effects are widely used to estimate treatment effects. We show that they identify 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 estimand may for instance be negative while all the ATEs are positive. In two articles that have used those regressions, half of the weights are negative. We propose another estimator that solves this issue. In one of the articles we revisit, it is of a different sign than the linear regression estimator.
Keywords: Two-way fixed effects; Heterogeneous treatment effects; Average treatment effects
JEL Codes: C21; C23
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| average treatment effect (ATE) identified by traditional FE estimator (f_e) (C51) | misleading conclusions (G41) |
| heterogeneous treatment effects (C21) | misleading conclusions (G41) |
| negative weights (C46) | misleading conclusions about treatment effects (C90) |
| average treatment effect (ATE) identified by traditional FE estimator (f_e) (C51) | negative value (D46) |
| small ratio of f_e to standard deviation of weights (C46) | concerns regarding validity of f_e (C52) |
| new estimator (C51) | average treatment effect across all cells where treatment changes (C22) |
| new estimator differs in sign and magnitude from traditional FE estimator (C51) | implications for applied researchers using two-way fixed effects regressions (C23) |