Cover: When Is a Match Sufficient?

When Is a Match Sufficient?

A Score-based Balance Metric for the Synthetic Control Method

Published in: Journal of Causal Inference, Volume 8, Issue 1, pages 209–228 (2020). doi: 10.1515/jci-2020-0013

Posted on Feb 2, 2021

by Layla Parast, Priscillia Hunt, Beth Ann Griffin, David Powell

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. 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.

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