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Prediction Intervals for Synthetic Control Methods

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  • Matias D. Cattaneo
  • Yingjie Feng
  • Rocio Titiunik

Abstract

Uncertainty quantification is a fundamental problem in the analysis and interpretation of synthetic control (SC) methods. We develop conditional prediction intervals in the SC framework, and provide conditions under which these intervals offer finite-sample probability guarantees. Our method allows for covariate adjustment and nonstationary data. The construction begins by noting that the statistical uncertainty of the SC prediction is governed by two distinct sources of randomness: one coming from the construction of the (likely misspecified) SC weights in the pretreatment period, and the other coming from the unobservable stochastic error in the post-treatment period when the treatment effect is analyzed. Accordingly, our proposed prediction intervals are constructed taking into account both sources of randomness. For implementation, we propose a simulation-based approach along with finite-sample-based probability bound arguments, naturally leading to principled sensitivity analysis methods. We illustrate the numerical performance of our methods using empirical applications and a small simulation study. Python, R and Stata software packages implementing our methodology are available. Supplementary materials for this article are available online.

Suggested Citation

  • Matias D. Cattaneo & Yingjie Feng & Rocio Titiunik, 2021. "Prediction Intervals for Synthetic Control Methods," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1865-1880, October.
  • Handle: RePEc:taf:jnlasa:v:116:y:2021:i:536:p:1865-1880
    DOI: 10.1080/01621459.2021.1979561
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    References listed on IDEAS

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    1. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Fernández-Val, Iván, 2019. "Conditional quantile processes based on series or many regressors," Journal of Econometrics, Elsevier, vol. 213(1), pages 4-29.
    2. 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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    4. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    5. Horiuchi, Yusaku & Mayerson, Asher, 2015. "The Opportunity Cost of Conflict: Statistically Comparing Israel and Synthetic Israel," Political Science Research and Methods, Cambridge University Press, vol. 3(3), pages 609-618, September.
    6. Alberto Abadie & Javier Gardeazabal, 2003. "The Economic Costs of Conflict: A Case Study of the Basque Country," American Economic Review, American Economic Association, vol. 93(1), pages 113-132, March.
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    Cited by:

    1. Masahiro Kato & Akari Ohda & Masaaki Imaizumi & Kenichiro McAlinn, 2023. "Synthetic Control Methods by Density Matching under Implicit Endogeneity," Papers 2307.11127, arXiv.org, revised Jul 2023.
    2. Roy Cerqueti & Raffaella Coppier & Alessandro Girardi & Marco Ventura, 2022. "The sooner the better: lives saved by the lockdown during the COVID-19 outbreak. The case of Italy [Using synthetic controls: Feasibility, data requirements, and methodological aspects]," The Econometrics Journal, Royal Economic Society, vol. 25(1), pages 46-70.
    3. Emery Thomas J. & Kovac Mitja & Spruk Rok, 2023. "Estimating the Effects of Political Instability in Nascent Democracies," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 243(6), pages 599-642, December.
    4. Dennis Shen & Peng Ding & Jasjeet Sekhon & Bin Yu, 2022. "Same Root Different Leaves: Time Series and Cross-Sectional Methods in Panel Data," Papers 2207.14481, arXiv.org, revised Oct 2022.
    5. Guillaume Allaire Pouliot & Zhen Xie, 2022. "Degrees of Freedom and Information Criteria for the Synthetic Control Method," Papers 2207.02943, arXiv.org.
    6. Manuel Funke & Moritz Schularick & Christoph Trebesch, 2020. "Populist Leaders and the Economy," ECONtribute Discussion Papers Series 036, University of Bonn and University of Cologne, Germany.
    7. Matias D. Cattaneo & Yingjie Feng & Filippo Palomba & Rocio Titiunik, 2022. "Uncertainty Quantification in Synthetic Controls with Staggered Treatment Adoption," Papers 2210.05026, arXiv.org, revised Sep 2023.
    8. Matias D. Cattaneo & Yingjie Feng & Filippo Palomba & Rocio Titiunik, 2022. "scpi: Uncertainty Quantification for Synthetic Control Methods," Papers 2202.05984, arXiv.org, revised Oct 2022.
    9. Wei Tian & Seojeong Lee & Valentyn Panchenko, 2023. "Synthetic Controls with Multiple Outcomes: Estimating the Effects of Non-Pharmaceutical Interventions in the COVID-19 Pandemic," Discussion Papers 2023-05, School of Economics, The University of New South Wales.
    10. Zongwu Cai & Ying Fang & Ming Lin & Zixuan Wu, 2023. "A Quasi Synthetic Control Method for Nonlinear Models With High-Dimensional Covariates," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202305, University of Kansas, Department of Economics, revised Aug 2023.
    11. David Gilchrist & Thomas Emery & Nuno Garoupa & Rok Spruk, 2023. "Synthetic Control Method: A tool for comparative case studies in economic history," Journal of Economic Surveys, Wiley Blackwell, vol. 37(2), pages 409-445, April.
    12. Priscila Espinosa & Daniel Aparicio-Pérez & Emili Tortosa-Ausina, 2023. "On the Impact of Next Generation EU Funds: A Regional Synthetic Control Method Approach," Working Papers 2023/07, Economics Department, Universitat Jaume I, Castellón (Spain).
    13. Guido W. Imbens & Davide Viviano, 2023. "Identification and Inference for Synthetic Controls with Confounding," Papers 2312.00955, arXiv.org.
    14. Xingyu Li & Yan Shen & Qiankun Zhou, 2022. "Confidence Intervals of Treatment Effects in Panel Data Models with Interactive Fixed Effects," Papers 2202.12078, arXiv.org.
    15. Manuel Funke & Moritz Schularick & Christoph Trebesch, 2023. "Populist Leaders and the Economy," Post-Print hal-04211174, HAL.

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