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Distributional Synthetic Controls

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  • F. F. Gunsilius

Abstract

The method of synthetic controls is a fundamental tool for evaluating causal effects of policy changes in settings with observational data. In many settings where it is applicable, researchers want to identify causal effects of policy changes on a treated unit at an aggregate level while having access to data at a finer granularity. This article proposes an extension of the synthetic controls estimator that takes advantage of this additional structure and provides nonparametric estimates of the heterogeneity within the aggregate unit. The idea is to replicate the quantile function associated with the treated unit by a weighted average of quantile functions of the control units. This estimator relies on the same mathematical theory as the changes‐in‐changes estimator and can be applied in both repeated cross‐sections and panel data with as little as a single pre‐treatment period. It also provides a unique counterfactual quantile function for any type of distribution.

Suggested Citation

  • F. F. Gunsilius, 2023. "Distributional Synthetic Controls," Econometrica, Econometric Society, vol. 91(3), pages 1105-1117, May.
    • Handle: RePEc:wly:emetrp:v:91:y:2023:i:3:p:1105-1117
    DOI: 10.3982/ECTA18260
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Masahiro Kato & Akari Ohda, 2023. "Asymptotically Unbiased Synthetic Control Methods by Moment Matching," Papers 2307.11127, arXiv.org, revised Nov 2025.
    2. Daisuke Kurisu & Yuta Okamoto & Taisuke Otsu, 2026. "Lee Bounds for Random Objects," Papers 2601.09453, arXiv.org.
    3. Tadao Hoshino, 2024. "Functional Spatial Autoregressive Models," Papers 2402.14763, arXiv.org, revised Oct 2024.
    4. Yihong Xu & Li Zheng, 2025. "Quantile Treatment Effects in High Dimensional Panel Data," Papers 2504.00785, arXiv.org, revised Jun 2025.
    5. Florian F Gunsilius, 2025. "A primer on optimal transport for causal inference with observational data," Papers 2503.07811, arXiv.org, revised Mar 2025.
    6. Xinran Liu, 2026. "Recovering Counterfactual Distributions via Wasserstein GANs," Papers 2601.17296, arXiv.org.
    7. David Van Dijcke & Kaspar Wuthrich, 2026. "IV regression with distribution-valued outcomes," Papers 2605.28749, arXiv.org.
    8. Maciej Berk{e}sewicz, 2023. "Survey calibration for causal inference: a simple method to balance covariate distributions," Papers 2310.11969, arXiv.org, revised Mar 2024.
    9. Songnian Chen & Junlong Feng, 2023. "Group-Heterogeneous Changes-in-Changes and Distributional Synthetic Controls," Papers 2307.15313, arXiv.org, revised Feb 2026.
    10. Lu Zhang & Xiaomeng Zhang & Xinyu Zhang, 2024. "Asymptotic Properties of the Distributional Synthetic Controls," Papers 2405.00953, arXiv.org, revised May 2026.
    11. Brantly Callaway & Derek Dyal & Pedro H. C. Sant'Anna & Emmanuel S. Tsyawo, 2025. "Beyond Parallel Trends: An Identification-Strategy-Robust Approach to Causal Inference with Panel Data," Papers 2511.21977, arXiv.org.
    12. Gedefaw Abebe Abiye & Serge Svizzero & Daregot Berihun, 2025. "The impact of home-grown economic reform intervention on crop productivity in Ethiopia," Humanities and Social Sciences Communications, Palgrave Macmillan, vol. 12(1), pages 1-20, December.
    13. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.
    14. Taehyeon Koo & Zijian Guo, 2025. "Distributionally Robust Synthetic Control: Ensuring Robustness Against Highly Correlated Controls and Weight Shifts," Papers 2511.02632, arXiv.org, revised Jan 2026.
    15. Christian Alemán-Pericón & Alexander Ludwig & Christopher Busch & Raül Santaeulàlia-Llopis, 2022. "A Stage-Based Identification of Policy Effects," Working Papers 1369, Barcelona School of Economics.
    16. Florian Gunsilius & David Van Dijcke, 2025. "disco: Distributional Synthetic Controls," Papers 2501.07550, arXiv.org, revised Jan 2025.
    17. Undral Byambadalai & Tomu Hirata & Tatsushi Oka & Shota Yasui, 2025. "Beyond the Average: Distributional Causal Inference under Imperfect Compliance," Papers 2509.15594, arXiv.org, revised Oct 2025.
    18. Ratzanyel Rinc'on & Kyungchul Song, 2025. "Causal Inference with Groupwise Matching," Papers 2510.26106, arXiv.org, revised Mar 2026.
    19. Yixiao Sun & Haitian Xie & Yuhang Zhang, 2025. "Difference-in-Differences Meets Synthetic Control: Doubly Robust Identification and Estimation," Papers 2503.11375, arXiv.org, revised Sep 2025.
    20. Lihua Lei & Timothy Sudijono, 2024. "Inference for Synthetic Controls via Refined Placebo Tests," Papers 2401.07152, arXiv.org, revised Apr 2025.
    21. Kyle Schindl & Larry Wasserman, 2026. "Distributional Discontinuity Design," Papers 2602.19290, arXiv.org.

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