Sensitivity Analysis for Treatment Effects in Difference-in-Differences Models using Riesz Representation

Abstract: Difference-in-differences (DiD) is one of the most popular approaches for empirical research in economics, political science, and beyond. Identification in these models is based on the conditional parallel trends assumption: In the absence of treatment, the average outcome of the treated and untreated group are assumed to evolve in parallel over time, conditional on pre-treatment covariates. We introduce a novel approach to sensitivity analysis for DiD models that assesses the robustness of DiD estimates to violations of this assumption due to unobservable confounders, allowing researchers to transparently assess and communicate the credibility of their causal estimation results. Our method focuses on estimation by Double Machine Learning and extends previous work on sensitivity analysis based on Riesz Representation in cross-sectional settings. We establish asymptotic bounds for point estimates and confidence intervals in the canonical $2\times2$ setting and group-time causal parameters in settings with staggered treatment adoption. Our approach makes it possible to relate the formulation of parallel trends violation to empirical evidence from (1) pre-testing, (2) covariate benchmarking and (3) standard reporting statistics and visualizations. We provide extensive simulation experiments demonstrating the validity of our sensitivity approach and diagnostics and apply our approach to two empirical applications.