Nothing to See Here? A Non‐Inferiority Approach to Parallel Trends
Alyssa Bilinski, Laura A. Hatfield · 2026 · 102 citationsRead the paper
Difference-in-differences is a popular method for observational health policy evaluation. It relies on a causal assumption that in the absence of intervention, treatment groups' outcomes would have evolved in parallel to those of comparison groups. Researchers frequently look for parallel trends in the pre-intervention period to bolster confidence in this assumption. The popular "parallel trends test" evaluates a null hypothesis of parallel trends and, failing to find evidence against the null, concludes that the assumption holds. This tightly controls the probability of falsely concluding that trends are not parallel, but may have low power to detect non-parallel trends. When used as a screening step, it can also introduce bias in treatment effect estimates. We propose a non-inferiority/equivalence approach that tightly controls the probability of missing large violations of parallel trends, measured on the scale of the treatment effect. Our framework nests several common use cases, including linear trend tests and event studies. We show that our approach may induce no or minimal bias when used as a screening step under commonly assumed error structures and, absent violations, can offer a higher-power alternative to testing treatment effects in more flexible models. We illustrate our ideas by reconsidering a study of the impact of the Affordable Care Act's dependent coverage provision.
What the full text shows
Working prototype- Non-inferiority tests strictly controlled Type I error for violations exceeding the threshold. — <5% probability of passing when violation was 50% TX80 and threshold was 20% TX80 (Simulation study with 60 units, T=25 time points)
- Non-inferiority tests showed high power to rule out large violations. — 88-100% power to rule out violations > |5| (ACA dependent coverage provision empirical simulation)
- Non-inferiority tests showed low-to-moderate power for smaller violations. — 21-60% power to rule out violations > 2.1 (ACA dependent coverage provision empirical simulation)
- Conditioning on passing a non-inferiority test induces minimal bias in reduced model estimators under independent errors. — <=1% incremental bias (Independent errors simulation)
- Conditioning on passing a non-inferiority test induces substantial bias in expanded model estimators. — 8-157% bias range (Independent, heteroskedastic errors simulation)
- Conditioning on passing a non-inferiority test induces moderate bias in reduced model estimators with autocorrelated errors. — 0 to -2% (linear models) and -3 to -9% (event study models) of TX80 (AR(1), rho=0.2 error structure simulation)
- Setup
- Simulation: 60 units, 25 time points, 100,000 replications. Empirical: SIPP data on US health insurance coverage (Aug 2008 - Nov 2011).
- How
- The authors developed a non-inferiority/equivalence framework to test the parallel trends assumption in difference-in-differences models by comparing reduced and expanded model treatment effects. They validated this via a simulation study with varying error structures and a re-analysis of ACA dependent coverage data.
- Limitations
- Test-induced bias occurs in reduced models when errors are autocorrelated over time. · Power to detect violations is highly dependent on the chosen threshold strictness.
Summarized by Gemma 4 from the open-access full text · 13 Oct 2026. Read it