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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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    8. Alberto Abadie, 2021. "Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects," Journal of Economic Literature, American Economic Association, vol. 59(2), pages 391-425, June.
    9. Abadie, Alberto & Diamond, Alexis & Hainmueller, Jens, 2010. "Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 493-505.
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    Cited by:

    1. Masahiro Kato & Akari Ohda & Masaaki Imaizumi, 2023. "Asymptotically Unbiased Synthetic Control Methods by Distribution Matching," Papers 2307.11127, arXiv.org, revised May 2024.
    2. Tadao Hoshino, 2024. "Functional Spatial Autoregressive Models," Papers 2402.14763, arXiv.org, revised Oct 2024.
    3. 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.
    4. Songnian Chen & Junlong Feng, 2023. "Group-Heterogeneous Changes-in-Changes and Distributional Synthetic Controls," Papers 2307.15313, arXiv.org.
    5. Lu Zhang & Xiaomeng Zhang & Xinyu Zhang, 2024. "Asymptotic Properties of the Distributional Synthetic Controls," Papers 2405.00953, arXiv.org, revised Aug 2024.
    6. Christian Alemán & Christopher Busch & Alexander Ludwig & Raül Santaeulàlia-Llopis, 2022. "A Stage-Based Identification of Policy Effects," Working Papers 1369, Barcelona School of Economics.
    7. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.
    8. Lihua Lei & Timothy Sudijono, 2024. "Inference for Synthetic Controls via Refined Placebo Tests," Papers 2401.07152, arXiv.org, revised Apr 2024.

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