Event studies are frequently used to estimate average treatment effects on the treated (ATT). In estimating the ATT, researchers commonly use fixed effects models that implicitly assume constant treatmenteffects across cohorts . We show that this is not an innocuous assumption. In fixed effect models where the sole regressor is treatment status, the OLS coefficient is a non-convex average of the heterogeneous cohort-specific ATTs. When regressors containing lags and leads of treatment are added, the OLS coefficient corresponding to a given lead or lag picks up spurious terms consisting of treatment effects from other periods . Therefore, estimates from these commonly used models are not causally interpretable . We propose alternative estimators that identify certain convex averages of the cohort-specific ATTs, hence allowing for causal interpretation even under heterogeneous treatment effects. To illustrate the empirical content of our results, we show that the fixed effects estimators and our proposed estimators differ substantially in an application to the economic consequences of hospitalization .
To estimate the dynamic effects of an absorbing treatment, researchers often use two-way fixed effects regressions that include leads and lags of the treatment . We show that in settings with variation in treatment timing across units, the coefficient on a given lead or lag can be contaminated by effects from other periods , and apparent pretrends can arise solely from treatment effects heterogeneity . We propose an alternative estimator that is free of contamination, and illustrate the relative shortcomings of two-way fixed effects regressions with leads and lags through an empirical application .
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Event studies are frequently used to estimate average treatment effects on the treated (ATT). In estimating the ATT, researchers commonly use fixed effects models that implicitly assume constant treatmenteffects across cohorts
To estimate the dynamic effects of an absorbing treatment, researchers often use two-way fixed effects regressions that include leads and lags of the treatment
R
this is not an innocuous assumption. In fixed effect models where the sole regressor is treatment status, the OLS coefficient is a non-convex average of the heterogeneous cohort-specific ATTs. When regressors containing lags and leads of treatment are added, the OLS coefficient corresponding to a
in settings with variation in treatment timing across units, the coefficient on a
R
picks up spurious terms consisting of treatment
can be contaminated by
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. Therefore, estimates from these commonly used models are not causally interpretable
, and apparent pretrends can arise solely from treatment effects heterogeneity
R
alternative estimators that identify certain convex averages of the cohort-specific ATTs, hence allowing for causal interpretation even under heterogeneous treatment effects. To illustrate the empirical content of our results, we show that the fixed effects estimators and our proposed estimators differ substantially in an application to the economic consequences of hospitalization
an alternative estimator that is free of contamination, and illustrate the relative shortcomings of two-way fixed effects regressions with leads and lags through an empirical application