A Joint Analysis of Sensitivity to Anticipation and Parallel Trends Violations
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 that constitute deviations from no anticipation and derive closed-form, sharp bounds for several common treatment effect parameters 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. For settings with a clean announcement window, I develop a benchmarking procedure to calibrate which values of the anticipation sensitivity parameters are most relevant for assessing robustness, making the practical interpretation of the multidimensional sensitivity analysis closer to that of a familiar one-dimensional sensitivity analysis. I illustrate with two empirical applications.