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)
We study treatment-effect estimation using panel data. The treatment may be nonbinary, nonabsorbing, and the outcome may be affected by the treatment lags. We make parallel-trends assumptions, but do not restrict treatment effect heterogeneity, unlike commonly-used two-wayfixed-effects regressions. We propose reduced-form event-study estimators of the effect of being exposed to a weakly higher treatment dose for periods. We also propose normalized event-study estimators, that estimate a weighted average of the effects of the current treatment and its lags. Finally, we show that the reduced-form estimators can be combined into an economically interpretable cost-benefit ratio.
Boarding schools substitute school to home, but little is known on the effects this substitution produces on students. We present results of an experiment in which seats in a boarding school for disadvantaged students were randomly allocated. Boarders enjoy better studying conditions than control students. However, they start outperforming control students in mathematics only two years after admission, and this effect mostly comes from strong students. After one year, levels of well-being are lower among boarders, but in their second year, students adjust: well-being catches-up. This suggests that substituting school to home is disruptive: only strong students benefit from the boarding school, once they have managed to adapt to their new environment.
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