Mixed-frequency data, where variables are observed at different temporal resolutions, commonly occur in economic and financial studies. Classical synthetic control methods (SCM) are ill-suited for such data, often necessitating aggregation or prefiltering that may discard valuable information. This paper proposes a novel Mixed-Frequency Synthetic Control Method (MF-SCM) to integrate mixed-frequency data into the synthetic control framework effectively. We develop a flexible estimation procedure to construct synthetic control weights under mixed-frequency settings and establish the theoretical properties of the MF-SCM estimator. Specifically, we first prove that the estimator achieves asymptotic optimality, in the sense that it achieves the lowest possible squared prediction error among all potential treatment effect estimators from averaging outcomes of control units. We then derive the asymptotic distribution of the average treatment effect (ATE) estimator using projection theory and construct confidence intervals for the ATE estimator. The method's effectiveness is demonstrated through numerical simulations and two empirical applications concerning the 2017 Tax Cuts and jobs Act in US and air pollution alerts.

翻译：混合频率数据（即变量以不同时间分辨率观测到的数据）普遍存在于经济和金融研究中。经典的综合控制方法（SCM）难以处理此类数据，通常需要聚合或预滤波处理，而这可能丢弃有价值的信息。本文提出一种新型的混合频率综合控制方法（MF-SCM），将混合频率数据有效整合到综合控制框架中。我们开发了一种灵活的估计程序，用于在混合频率设置下构建综合控制权重，并确立了MF-SCM估计量的理论性质。具体而言，我们首先证明该估计量达到渐近最优性，即在对控制单位结果进行平均的所有潜在处理效应估计量中，它实现了最低的平方预测误差。接着，我们利用投影理论推导出平均处理效应（ATE）估计量的渐近分布，并构建了ATE估计量的置信区间。通过数值模拟以及两项涉及2017年美国《减税与就业法案》和空气污染警报的实证应用，验证了该方法的有效性。