Using Multiple Outcomes to Improve the Synthetic Control Method

TL;DR

This paper proposes a novel approach for synthetic control analysis with multiple outcomes by estimating common weights, which reduces bias and improves accuracy, especially as the number of outcomes increases.

Contribution

It introduces a method to estimate shared weights across multiple outcomes, enhancing bias reduction and efficiency over traditional separate-weight approaches.

Findings

Shared weights reduce bias compared to separate weights.

Averaging outcomes further improves estimation with many outcomes.

Re-analysis of Flint water crisis demonstrates practical benefits.

Abstract

When there are multiple outcome series of interest, Synthetic Control analyses typically proceed by estimating separate weights for each outcome. In this paper, we instead propose estimating a common set of weights across outcomes, by balancing either a vector of all outcomes or an index or average of them. Under a low-rank factor model, we show that these approaches lead to lower bias bounds than separate weights, and that averaging leads to further gains when the number of outcomes grows. We illustrate this via a re-analysis of the impact of the Flint water crisis on educational outcomes.