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When is a Match Sufficient? A Score-based Balance Metric for the Synthetic Control Method

Author

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  • Parast Layla

    (RAND Corporation, 1776Main Street, Santa Monica, CAU.S.A)

  • Hunt Priscillia

    (RAND Corporation, 1776Main Street, Santa Monica, CAU.S.A)

  • Griffin Beth Ann

    (RAND Corporation, 1200 S Hayes St, Arlington, VA22202U.S.A)

  • Powell David

    (RAND Corporation, 1200 S Hayes St, Arlington, VA22202U.S.A)

Abstract

In some applications, researchers using the synthetic control method (SCM) to evaluate the effect of a policy may struggle to determine whether they have identified a “good match” between the control group and treated group. In this paper, we demonstrate the utility of the mean and maximum Absolute Standardized Mean Difference (ASMD) as a test of balance between a synthetic control unit and treated unit, and provide guidance on what constitutes a poor fit when using a synthetic control. We explore and compare other potential metrics using a simulation study. We provide an application of our proposed balance metric to the 2013 Los Angeles (LA) Firearm Study [9]. Using Uniform Crime Report data, we apply the SCM to obtain a counterfactual for the LA firearm-related crime rate based on a weighted combination of control units in a donor pool of cities. We use this counterfactual to estimate the effect of the LA Firearm Study intervention and explore the impact of changing the donor pool and pre-intervention duration period on resulting matches and estimated effects. We demonstrate how decision-making about the quality of a synthetic control can be improved by using ASMD. The mean and max ASMD clearly differentiate between poor matches and good matches. Researchers need better guidance on what is a meaningful imbalance between synthetic control and treated groups. In addition to the use of gap plots, the proposed balance metric can provide an objective way of determining fit.

Suggested Citation

  • Parast Layla & Hunt Priscillia & Griffin Beth Ann & Powell David, 2020. "When is a Match Sufficient? A Score-based Balance Metric for the Synthetic Control Method," Journal of Causal Inference, De Gruyter, vol. 8(1), pages 209-228, January.
    • Handle: RePEc:bpj:causin:v:8:y:2020:i:1:p:209-228:n:10
    DOI: 10.1515/jci-2020-0013
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    References listed on IDEAS

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    1. Dmitry Arkhangelsky & Susan Athey & David A. Hirshberg & Guido W. Imbens & Stefan Wager, 2021. "Synthetic Difference-in-Differences," American Economic Review, American Economic Association, vol. 111(12), pages 4088-4118, December.
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