Correlated Synthetic Controls

TL;DR

The paper introduces the Correlated Synthetic Controls (CSC) estimator, which improves counterfactual predictions in settings with multiple treated units by leveraging correlations across individuals with similar observables.

Contribution

It extends synthetic control methods to microeconometric settings with multiple treated units, providing a new estimator with better theoretical properties when treatment is correlated with unobservables.

Findings

CSC estimator outperforms difference-in-differences in theory.

Applied CSC to Mariel Boatlift study for heterogeneous effects.

Leverages additional data from PSID for improved inference.

Abstract

Synthetic Control methods have recently gained considerable attention in applications with only one treated unit. Their popularity is partly based on the key insight that we can predict good synthetic counterfactuals for our treated unit. However, this insight of predicting counterfactuals is generalisable to microeconometric settings where we often observe many treated units. We propose the Correlated Synthetic Controls (CSC) estimator for such situations: intuitively, it creates synthetic controls that are correlated across individuals with similar observables. When treatment assignment is correlated with unobservables, we show that the CSC estimator has more desirable theoretical properties than the difference-in-differences estimator. We also utilise CSC in practice to obtain heterogeneous treatment effects in the well-known Mariel Boatlift study, leveraging additional information from the PSID.