标题： 高效学习高维细分数据的合成控制模型 显示英文标题

标题： Efficiently Learning Synthetic Control Models for High-dimensional Disaggregated Data

摘要： 合成控制方法（SC）已成为估计因果效应的有用工具。 最初设计用于单一处理单元的情况，它最近在具有多个处理单元的高维细分设置中得到了应用。 然而，在这种情况下会出现实际实施和计算效率方面的挑战。 为了解决这些挑战，我们提出了一种新方法，将多元平方根Lasso方法整合到合成控制框架中。 我们严格建立了使用多元平方根Lasso拟合合成控制权重的估计误差界限，适应高维性和时间序列依赖性。 此外，我们量化了对处理组的平均处理效应（ATT）的估计误差。 通过模拟研究，我们证明了我们的方法在不牺牲估计准确性的情况下提供了优越的计算效率。 我们将我们的方法应用于评估美国县级每月失业率上新冠疫情居家令的因果影响。 显示英文摘要

摘要： 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.