Synthetic Control Method with Mixed Frequency Data

TL;DR

This paper introduces a novel Mixed-Frequency Synthetic Control Method (MF-SCM) that effectively integrates mixed-frequency data into the synthetic control framework, improving estimation and inference in economic and financial studies.

Contribution

It develops a flexible estimation procedure for mixed-frequency data, establishes the theoretical properties of MF-SCM, and demonstrates its effectiveness through simulations and empirical applications.

Findings

Estimator achieves asymptotic optimality with lowest squared prediction error.

Derived the asymptotic distribution and confidence intervals for the ATE.

Method outperforms classical approaches in numerical simulations and case studies.

Abstract

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.