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Synthetic Parallel Trends

Yiqi Liu

arXiv 8 Nov 2025 · Econometrics

arXiv:2511.05870 · PDF · Extracted main text

Abstract

Popular empirical strategies for policy evaluation in the panel data literature -- including difference-in-differences (DID), synthetic control (SC) methods, and their variants -- rely on key identifying assumptions that can be expressed through a specific choice of weights $ω$ relating pre-treatment trends to the counterfactual outcome. While each choice of $ω$ may be defensible in empirical contexts that motivate a particular method, it relies on fundamentally untestable and often fragile assumptions. I develop an identification framework that allows for all weights satisfying a Synthetic Parallel Trends assumption: the treated unit's trend is parallel to a weighted combination of control units' trends for a general class of weights. The framework nests these existing methods as special cases and is by construction robust to violations of their respective assumptions. I construct a valid confidence set for the identified set of the treatment effect, which admits a linear programming representation with estimated coefficients and nuisance parameters that are profiled out. In simulations where the assumptions underlying DID or SC-based methods are violated, the proposed confidence set remains robust and attains nominal coverage, while existing methods suffer severe undercoverage.

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55
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Arkhangelsky, Dmitry and Athey, Susan and Hirshberg, David A and Imb… (2021) Synthetic difference-in-differences1.000335100%
2Abadie, Alberto and Diamond, Alexis and Hainmueller, Jens (2010) Synthetic control methods for comparative case studies: Estimating the effect of California’s tobacco control program1.000224100%
3Fang, Zheng and Santos, Andres (2019) Inference on directionally differentiable functions1.00073100%
4Imbens, Guido W and Viviano, Davide (2023) Identification and Inference for Synthetic Controls with Confounding0.92843100%
5Rambachan, Ashesh and Roth, Jonathan (2023) A more credible approach to parallel trends0.87492100%
6Ban, Kyunghoon and Kédagni, Désiré (2023) Robust Difference-in-differences Models0.73732100%
7Cox, Gregory and Shi, Xiaoxia and Shimizu, Yuya (2025) Testing Inequalities Linear in Nuisance Parameters0.73732100%
8Freyberger, Joachim and Horowitz, Joel L (2015) Identification and shape restrictions in nonparametric instrumental variables estimation0.73732100%
9Gafarov, Bulat (2025) Simple subvector inference on sharp identified set in affine models0.73732100%
10Goff, Leonard and Mbakop, Eric (2025) Inference on the value of a linear program0.73732100%

Showing the top 10 of 55 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Inference for Linear Systems with Unknown Coefficients0.87452
22510.261060.51121
3Beyond Parallel Trends: An Identification-Strategy-Robust Approach to Causal Inference with Panel Data0.40511
4Robust Inference for Weighted Estimands0.40511