Naijia Liu presents "Synthetic Control Method with Pre-treatment Outcomes Missing."

Abstract: The synthetic control method (SCM) is commonly used in social science research to estimate treatment effects. It involves creating a synthesized control unit for the treated unit in observational studies. The quality of this synthesized control unit is influenced by factors like the number of pretreatment periods and missing values. Many empirical datasets, particularly those with a panel structure, often encounter issues with missing values. This project studies the impact of missing values on SCM and provides theoretical guidance to the potential bias. We formulate SCM with missing data in a vertical regression perspective. Under such setting, missing values can be deemed as omitted variables. We show that the bias of the ATT is decomposed into (1) weight of the missing unit for constructing the synthetic control and (2) the imbalance between the missing units and the weighted observed donor units. Building on these result, We propose a sensitivity analysis for SCM with pretreatment outcomes missing not at random. To illustrate the method in practice, we revisit a previous study that examines the impact of Taiwan's expulsion from the International Monetary Fund (IMF) in 1980 on its precautionary international reserves using the SCM.