Efficiently Learning Synthetic Control Models for High-dimensional Disaggregated Data

TL;DR

This paper introduces a new method combining Multivariate Square-root Lasso with synthetic control models to improve causal inference in high-dimensional, disaggregated data settings, especially with multiple treated units.

Contribution

It develops a novel integration of Multivariate Square-root Lasso into synthetic control, providing theoretical error bounds and demonstrating improved computational efficiency.

Findings

Superior computational efficiency demonstrated in simulations

Accurate estimation of causal effects in high-dimensional data

Effective application to COVID-19 policy impact analysis

Abstract

The Synthetic Control method (SC) has become a valuable tool for estimating causal effects. Originally designed for single-treated unit scenarios, it has recently found applications in high-dimensional disaggregated settings with multiple treated units. However, challenges in practical implementation and computational efficiency arise in such scenarios. To tackle these challenges, we propose a novel approach that integrates the Multivariate Square-root Lasso method into the synthetic control framework. We rigorously establish the estimation error bounds for fitting the Synthetic Control weights using Multivariate Square-root Lasso, accommodating high-dimensionality and time series dependencies. Additionally, we quantify the estimation error for the Average Treatment Effect on the Treated (ATT). Through simulation studies, we demonstrate that our method offers superior computational efficiency without compromising estimation accuracy. We apply our method to assess the causal impact of COVID-19 Stay-at-Home Orders on the monthly unemployment rate in the United States at the county level.