Takahiro Hoshino, Makoto Nakakita
arXiv 9 Jul 2026 · Econometrics
arXiv:2607.08324 · PDF · DOI · OpenAlex · Extracted main text
Synthetic difference-in-differences is widely used to estimate treatment effects for many treated groups against a common donor pool. When the same donors are reused across groups, the group-specific estimates are cross-sectionally dependent, and plug-in second moments overstate effect heterogeneity. We develop finite-population inference for heterogeneity in many-group synthetic difference-in-differences: the projection of realized group effects on observed group covariates, the projected group-effect curve, the between-group variance, and the explained share. The theory combines a modular first-stage representation, a joint covariance kernel for donor sharing and block dependence, analytic and leave-out corrections for second moments, and calibrated omnibus and directed tests under explicit exchangeability or fit-matching conditions. In an American Community Survey application to the Affordable Care Act Medicaid expansion, whose estimand is the incremental effect of expansion status, pre-expansion uninsured rates explain much of the state-level effect variation on the percentage-point scale, household split-samples validate the decomposition, and donor sharing materially increases the standard error for the average effect. In a county-level Clean Air Act application, groupwise estimates are noisy, but a pre-specified projection on baseline fine-particulate pollution reveals a sign-stable directed component under state and division block covariance; placebo analyses attribute part of the raw gradient to regional convergence.
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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 | Abadie, A., Diamond, A., & Hainmueller, J (2010) Synthetic control methods for comparative case studies | 0.843 | 4 | 3 | 75% |
| 2 | Kline, P., Saggio, R., & S lvsten, M (2020) Leave-out estimation of variance components | 0.843 | 4 | 3 | 75% |
| 3 | Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., & Wage… (2021) Synthetic difference-in-differences | 0.794 | 6 | 4 | 50% |
| 4 | Dube, A., & Zipperer, B (2015) Pooling multiple case studies using synthetic controls: An application to minimum wage policies | 0.644 | 2 | 2 | 100% |
| 5 | Abadie, A., Athey, S., Imbens, G. W., & Wooldridge, J. M (2020) Sampling-based versus design-based uncertainty in regression analysis | 0.511 | 2 | 2 | 50% |
| 6 | Abadie, A., Athey, S., Imbens, G. W., & Wooldridge, J. M (2023) When should you adjust standard errors for clustering? | 0.511 | 2 | 2 | 50% |
| 7 | Armstrong, T. B., Kolesár, M., & Plagborg-M ller, M (2022) Robust empirical Bayes confidence intervals | 0.511 | 2 | 2 | 50% |
| 8 | Bloom, H. S., Raudenbush, S. W., Weiss, M. J., & Porter, K (2017) Using multisite experiments to study cross-site variation in treatment effects | 0.511 | 2 | 2 | 50% |
| 9 | Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C… (2018) Double/debiased machine learning for treatment and structural parameters | 0.511 | 2 | 2 | 50% |
| 10 | Ignatiadis, N., & Wager, S (2022) Confidence intervals for nonparametric empirical Bayes analysis (with discussion) | 0.511 | 2 | 2 | 50% |
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