Thomas Leavitt
arXiv 16 Sep 2026 · Statistics — Methodology
arXiv:2609.19081 · PDF · Extracted main text
In the canonical Difference-in-Differences design, the control group's post-treatment change serves as an imputation of the treated group's counterfactual change in the same period, an imputation justified by parallel trends. However, differences in group composition can produce between-group differences in how outcomes would evolve over time, rendering this imputation vulnerable to confounding. An alternative imputation -- such as one based on the treated group's pre-treatment change -- avoids such between-group confounding but introduces the risk of confounding from within-group temporal shifts. Ideally, both imputations, each vulnerable to different sources of confounding, would have concordant values, thereby yielding the same causal conclusions. When the imputations are discordant, conclusions under parallel trends hinge more critically on that assumption since alternative imputations would point to different results. Yet in these scenarios, existing pretrends-based sensitivity analyses can show low sensitivity because they ignore post-treatment deviations from pretrends in the control group. This paper therefore proposes a discordance-based sensitivity model in which parallel pretrends are necessary but not sufficient for low sensitivity. I formally justify this model in terms of the expected distance between the ATT under parallel trends and under alternative assumptions, weighted by the joint plausibility of those assumptions. I then provide a decision-theoretic rationale for benchmarking violations of parallel trends using the worst-case discordance between the parallel trends imputation and alternative imputations. Finally, I apply both pretrends- and discordance-based sensitivity models to assess how a labor supply shock influenced electoral support for apartheid-era policies in South Africa, showing how the two approaches yield different results.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Ashesh Rambachan and Jonathan Roth (2023) A more credible approach to parallel trends | 1.000 | 6 | 4 | 100% |
| 2 | Laurence Wilse-Samson (2013) Structural change and democratization: Evidence from rural apartheid | 0.693 | 7 | 1 | 100% |
| 3 | Ting Ye, Luke Keele, Raiden Hasegawa, and Dylan S Small (2024) A negative correlation strategy for bracketing in difference-in-differences | 0.644 | 2 | 2 | 100% |
| 4 | Roger L. Berger and Jason C. Hsu (1996) Bioequivalence trials, intersection-union tests and equivalence confidence sets | 0.585 | 3 | 1 | 100% |
| 5 | Thomas Leavitt and Laura A Hatfield (2025) Averaged prediction models (APM): Identifying causal effects in controlled pre-post settings with application to gun policy self | 0.511 | 2 | 1 | 100% |
| 6 | Joshua D. Angrist and Jörn-Steffen Pischke (2008) Mostly Harmless Econometrics: An Empiricist's Companion | 0.405 | 1 | 1 | 100% |
| 7 | Brantly Callaway and Pedro H. C. Sant'Anna (2021) Difference-in-differences with multiple time periods | 0.405 | 1 | 1 | 100% |
| 8 | William G Cochran (1965) The planning of observational studies of human populations | 0.405 | 1 | 1 | 100% |
| 9 | William G. Cochran (1972) Observational studies | 0.405 | 1 | 1 | 100% |
| 10 | Peter L. Cohen, Matt A. Olson, and Colin B. Fogarty (2020) Multivariate one-sided testing in matched observational studies as an adversarial game | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 36 scored citations.