Difference-in-Differences Estimators of Intertemporal Treatment Effects

TL;DR

This paper develops new difference-in-differences estimators for panel data that handle complex treatment dynamics and compare them to traditional fixed-effects methods, highlighting potential biases.

Contribution

It introduces event-study estimators for non-binary, lagged treatments and analyzes biases in standard two-way fixed-effects regressions.

Findings

Proposed estimators effectively capture intertemporal treatment effects.

Standard fixed-effects regressions can be biased with heterogeneous effects.

Local-projection regressions are biased even with homogeneous effects.

Abstract

We study treatment-effect estimation using panel data. The treatment may be non-binary, non-absorbing, and the outcome may be affected by treatment lags. We make a parallel-trends assumption, and propose event-study estimators of the effect of being exposed to a weakly higher treatment dose for $\ell$ periods. We also propose normalized estimators, that estimate a weighted average of the effects of the current treatment and its lags. We also analyze commonly-used two-way fixed-effects regressions. Unlike our estimators, they can be biased in the presence of heterogeneous treatment effects. A local-projection version of those regressions is biased even with homogeneous effects.