A Joint Analysis of Sensitivity to Anticipation and Parallel Trends Violations

TL;DR

This paper develops a method to assess the robustness of difference-in-differences estimates by jointly analyzing violations of parallel trends and no anticipation assumptions, providing sharp bounds on treatment effects.

Contribution

It introduces a new framework for sensitivity analysis that relaxes both key assumptions simultaneously using observed pre-trends, offering sharper bounds and more robust conclusions.

Findings

Bounds on treatment effects under assumption violations

Joint analysis reduces uncertainty compared to separate violations

Application demonstrates practical utility of the method

Abstract

Two key identifying assumptions used to justify difference-in-differences are parallel trends and no anticipation, yet both may fail in practice. I propose a class of assumptions on anticipation and derive closed-form, sharp bounds on the average treatment effect on the treated while simultaneously relaxing parallel trends. Deviations from both assumptions are jointly disciplined using observed pre-trends. When some anticipation is imposed, the identified set under joint deviations can be shorter than under parallel trends violations alone. These bounds inform a sensitivity analysis assessing the robustness of qualitative conclusions to anticipation and parallel trends violations. I illustrate with an empirical application.