Satarupa Bhattacharjee, Bing Li, Lingzhou Xue
arXiv 20 Jun 2026 · Statistics — Methodology
arXiv:2606.21840 · PDF · DOI · OpenAlex · Extracted main text
We develop a novel distributional Difference-in-Differences (DiD) framework to capture treatment heterogeneity across outcome distributions. By leveraging optimal transport, we use the control group to estimate the untreated distributional drift from the pre- to post-treatment period and apply it to the treated group's pre-treatment baseline, constructing a counterfactual distribution under the assumption of no treatment effect. We frame the null hypothesis as a distributional equality between the transported counterfactual distribution and the observed treated post-treatment distribution, and test it using a maximum mean discrepancy statistic in a reproducing kernel Hilbert space (RKHS). The resulting nonparametric omnibus test is sensitive to changes in location, scale, shape, and tail behavior. Under the null, we derive the asymptotic Gaussian quadratic-form limit of the test statistic, while under local alternatives, we provide a unified characterization of power that establishes its Pitman local power and moderate-deviation consistency. Our theory reveals how detectability is shaped by the interaction between transport-induced drift and RKHS geometry. Simulations and an application to the Card--Krueger minimum-wage data demonstrate that the proposed method identifies key distributional treatment effects missed by classical mean-based DiD.
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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 | Gretton, Arthur and Borgwardt, Karsten M and Rasch, Malte J and Schö… (2012) A kernel two-sample test | 0.644 | 2 | 2 | 100% |
| 2 | Card, David and Krueger, Alan B (1994) Minimum wages and employment: A case study of the fast-food industry in New Jersey and Pennsylvania | 0.511 | 2 | 1 | 100% |
| 3 | Torous, William and Gunsilius, Florian and Rigollet, Philippe (2024) An optimal transport approach to estimating causal effects via nonlinear difference-in-differences | 0.511 | 2 | 1 | 100% |
| 4 | van der Vaart, Aad W. and Wellner, Jon A (1996) Weak Convergence and Empirical Processes | 0.511 | 2 | 1 | 100% |
| 5 | Athey, Susan and Imbens, Guido W (2006) Identification and Inference in Nonlinear Difference-in-Differences Models | 0.405 | 1 | 1 | 100% |
| 6 | Callaway, Brantly and Sant’Anna, Pedro H. C (2021) Difference-in-Differences with Multiple Time Periods | 0.405 | 1 | 1 | 100% |
| 7 | Goodman-Bacon, Andrew (2021) Difference-in-Differences with Variation in Treatment Timing | 0.405 | 1 | 1 | 100% |
| 8 | Imhof, J. P (1961) Computing the Distribution of Quadratic Forms in Normal Variables | 0.405 | 1 | 1 | 100% |
| 9 | Sriperumbudur, B. and Gretton, Arthur and Fukumizu, Kenji and Schölk… (2010) Hilbert Space Embeddings and Metrics on Probability Measures | 0.405 | 1 | 1 | 100% |
| 10 | Sun, Liyang and Abraham, Sarah (2021) Estimating dynamic treatment effects in event studies with heterogeneous treatment effects | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 39 scored citations.