Primary Submission Category: Sensitivity Analysis
Applying Robustness of an Inference to Replacement (RIR) as the Sensitivity Test of Difference-in-Differences Estimator
Authors: Xuesen Cheng,
Presenting Author: Xuesen Cheng*
The validity of the Difference-in-Differences (DID) estimator is affected by (1) violations of the parallel trend assumption, (2) other sources of bias in OLS estimation, and (3) the low power of parallel trend tests, which often fail to detect violations even when they exist. Robustness of an Inference to Replacement (RIR), introduced by Frank et al. (2013, 2021), provides a powerful framework for sensitivity analysis. This paper applies conditional RIR for interaction term to compute threshold values, it can be explained as that the estimated effect can be nullified or reduced below a threshold by replacing RIR*100% of the post-treatment observations from treated to the untreated status. The paper proposes PseudoRIR as a sensitivity test for the conditional parallel trend assumption, assessing its stability. This serves as an important complement to traditional parallel trend tests with low power. Additionally, this paper applies RIR to evaluate the robustness of DID estimates against potential biases. The paper also introduces HonestRIR to account for violations of the parallel trend assumption, following the approach from Ramabachan & Roth (2022). This method produces an interval of HonestRIR adjusted for trend deviations, enhancing the robustness assessment of DID estimates. Finally, the paper extends the proposed sensitivity tests to staggered DID settings and provides an application based on the framework of Callaway & Sant’Anna (2021).