A Local Projections Approach to Difference-in-Differences Event Studies

Abstract

Many of the challenges in the estimation of dynamic heterogeneous treatment effects can be resolved with local projection (LP) estimators of the sort used in applied macroeconometrics. This approach provides a convenient alternative to the more complicated solutions proposed in the recent literature on Difference in-Differences (DiD). The key is to combine LPs with a flexible ‘clean control’ condition to define appropriate sets of treated and control units. Our proposed LP-DiD estimator is clear, simple, easy and fast to compute, and it is transparent and flexible in its handling of treated and control units. Moreover, it is quite general, including in its ability to control for pre-treatment values of the outcome and of other time-varying covariates. The LP-DiD estimator does not suffer from the negative weighting problem, and indeed can be implemented with any weighting scheme the investigator desires. Simulations demonstrate the good performance of the LP-DiD estimator in common settings. Two recent empirical applications illustrate how LP-DiD addresses the bias of conventional fixed effects estimators, leading to potentially different results.