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An exact and robust conformal inference method for counterfactual and synthetic controls

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  • Victor Chernozhukov

    () (Institute for Fiscal Studies and MIT)

  • Kaspar Wüthrich

    (Institute for Fiscal Studies and UCSD)

  • Yu Zhu

    (Institute for Fiscal Studies)

Abstract

This paper introduces new inference methods for counterfactual and synthetic control methods for evaluating policy effects. Our inference methods work in conjunction with many modern and classical methods for estimating the counterfactual mean outcome in the absence of a policy intervention. Specifically, our methods work together with the difference-in-difference, canonical synthetic control, constrained and penalized regression methods for synthetic control, factor/matrix completion models for panel data, interactive fixed effects panel models, time series models, as well as fused time series panel data models. The proposed method has a double justification. (i) If the residuals from estimating the counterfactuals are exchangeable as implied, for example, by i.i.d. data, our procedure achieves exact finite sample size control without any assumption on the specific approach used to estimate the counterfactuals. (ii) If the data exhibit dynamics and serial dependence, our inference procedure achieves approximate uniform size control under weak and easy-to-verify conditions on the method used to estimate the counterfactual. We verify these condition for representative methods from each group listed above. Simulation experiments demonstrate the usefulness of our approach in finite samples. We apply our method to re-evaluate the causal effect of election day registration (EDR) laws on voter turnout in the United States.

Suggested Citation

  • Victor Chernozhukov & Kaspar Wüthrich & Yu Zhu, 2017. "An exact and robust conformal inference method for counterfactual and synthetic controls," CeMMAP working papers CWP62/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:62/17
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Jianfei Cao & Connor Dowd, 2019. "Estimation and Inference for Synthetic Control Methods with Spillover Effects," Papers 1902.07343, arXiv.org.
    2. Davide Viviano & Jelena Bradic, 2019. "Synthetic learner: model-free inference on treatments over time," Papers 1904.01490, arXiv.org.
    3. Victor Chernozhukov & Kaspar Wüthrich & Yinchu Zhu, 2018. "Exact and robust conformal inference methods for predictive machine learning with dependent data," CeMMAP working papers CWP16/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Ferman, Bruno, 2017. "Matching Estimators with Few Treated and Many Control Observations," MPRA Paper 78940, University Library of Munich, Germany.
    5. Klößner, Stefan & Pfeifer, Gregor, 2015. "Synthesizing Cash for Clunkers: Stabilizing the Car Market, Hurting the Environment," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113207, Verein für Socialpolitik / German Economic Association.
    6. Victor Chernozhukov & Kaspar Wuthrich & Yinchu Zhu, 2018. "Practical and robust $t$-test based inference for synthetic control and related methods," Papers 1812.10820, arXiv.org, revised Jun 2019.
    7. Bruno Ferman, 2019. "On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls," Papers 1906.06665, arXiv.org, revised Oct 2019.
    8. Jason Poulos, 2019. "State-Building through Public Land Disposal? An Application of Matrix Completion for Counterfactual Prediction," Papers 1903.08028, arXiv.org.
    9. Eli Ben-Michael & Avi Feller & Jesse Rothstein, 2018. "The Augmented Synthetic Control Method," Papers 1811.04170, arXiv.org.

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