Primary Submission Category: Sensitivity Analysis
Pseudo-RIR for Interpreting Low-Power Pre-Trend Tests in Difference-in-Difference Estimator
Authors: Xuesen Cheng,
Presenting Author: Xuesen Cheng*
Difference-in-difference (DiD) estimators often check identifying assumptions by testing for “pre-trends.” A common example is an event-study specification, where researchers test whether lead coefficients are jointly zero. However, standard pre-trend tests can have low power, and conditioning on “passing” a pretest can lead to misleading reassurance and distorted inference.
This paper proposes Pseudo-RIR to make a “passed” pre-trend test more interpretable. The idea builds on Robustness of an Inference to Replacement (RIR). When a pre-trend test does not reject, Pseudo-RIR quantifies how large a fraction of the pre-treatment treated observations would need to be increased by the threshold amount for the parallel trends test to become significant (fail to pass). This converts nonrejection into a concrete robustness statement: “How fragile is the absence of detected pre-trends?”
The study then shows—using broad simulation evidence across realistic DiD settings—how Pseudo-RIR maps into the power of common pre-trend tests under serial correlation, limited pre-periods, clustering, and different forms of trend violations. The paper offers a systematic sensitivity analysis plan: (i) report Pseudo-RIR whenever pre-trend tests “passed”; (ii) when Pseudo-RIR indicates meaningful risk, complement with partial-identification style sensitivity analysis under bounded trend deviations (like Honest DiD); and (iii) summarize robustness for the main estimation effect with an RIR-style index