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Synthetic Decomposition for Counterfactual Predictions

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  • Nathan Canen
  • Kyungchul Song

Abstract

Counterfactual predictions are challenging when the policy variable goes beyond its pre-policy support. However, in many cases, information about the policy of interest is available from different ("source") regions where a similar policy has already been implemented. In this paper, we propose a novel method of using such data from source regions to predict a new policy in a target region. Instead of relying on extrapolation of a structural relationship using a parametric specification, we formulate a transferability condition and construct a synthetic outcome-policy relationship such that it is as close as possible to meeting the condition. The synthetic relationship weighs both the similarity in distributions of observables and in structural relationships. We develop a general procedure to construct asymptotic confidence intervals for counterfactual predictions and prove its asymptotic validity. We then apply our proposal to predict average teenage employment in Texas following a counterfactual increase in the minimum wage.

Suggested Citation

  • Nathan Canen & Kyungchul Song, 2023. "Synthetic Decomposition for Counterfactual Predictions," Papers 2307.05122, arXiv.org, revised Jan 2025.
    • Handle: RePEc:arx:papers:2307.05122
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    References listed on IDEAS

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    1. Diaa Al Mohamad & Erik W Van Zwet & Eric Cator & Jelle J Goeman, 2020. "Adaptive critical value for constrained likelihood ratio testing," Biometrika, Biometrika Trust, vol. 107(3), pages 677-688.
    2. Honore, Bo E. & Powell, James L., 1994. "Pairwise difference estimators of censored and truncated regression models," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 241-278.
    3. Canen, Nathan & Song, Kyungchul, 2023. "Synthetic Decomposition for Counterfactual Predictions," The Warwick Economics Research Paper Series (TWERPS) 1466, University of Warwick, Department of Economics.
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    1. Canen, Nathan & Song, Kyungchul, 2023. "Synthetic Decomposition for Counterfactual Predictions," The Warwick Economics Research Paper Series (TWERPS) 1466, University of Warwick, Department of Economics.

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    JEL classification:

    • C - Mathematical and Quantitative Methods

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