Revisiting Event Study Designs

Abstract

A broad empirical literature uses “event study” research designs for treatment effect estimation, a setting in which all units in the panel receive treatment but at random times. We make four novel points about identification and estimation of causal effects in this setting and show their practical relevance. First, we show that in the presence of unit and time fixed effects, it is impossible to identify the linear component of the path of pre-trends and dynamic treatment effects. Second, we propose graphical and statistical tests for pre-trends. Third, we consider commonly-used “static” regressions, with a treatment dummy instead of a full set of leads and lags around the treatment event, and we show that OLS does not recover a reasonable weighted average of the treatment effects: long-run effects are weighted negatively, and we introduce different estimators robust to this issue. Fourth, we show that equivalent problems of under-identification and negative weighting arise in difference-in-differences settings when the control group is allowed to be on a different time trend or in the presence of unit-specific time trends. We show the practical relevance of these issues in a series of examples from the existing literature. We focus on the estimation of the marginal propensity to consume out of tax rebates: according to our preferred specification, the marginal propensity to consume is much lower than (about half of) the main estimates in the literature. The main message for practitioners is that because of identification issues and negative weighting in event study designs, results from common specifications are likely to seem non-robust. These problems can be alleviated in a principled way by using parametric and semi-parametric estimators and tests.