Inference for Synthetic Control Methods with Multiple Treated Units

TL;DR

This paper examines the limitations of the placebo test in synthetic control methods with multiple treated units and proposes an Andrews-type inference procedure to improve validity and power, supported by simulation results.

Contribution

It introduces an Andrews-type inference method for synthetic control with multiple treated units, addressing placebo test shortcomings.

Findings

Andrews-type test shows higher validity in simulations.

Proposed method improves inference power over placebo test.

Applicable to multivariate treatment scenarios.

Abstract

Although the Synthetic Control Method (SCM) is now widely applied, its most commonly-used inference method, placebo test, is often problematic, especially when the treatment is not uniquely assigned. This paper discuss the problems with the placebo test under multivariate treatment case. And, to improve the power of inferences, I further propose an Andrews-type procedure as it potentially solve some drawbacks of placebo test. Simulations are conducted to show the Andrews' test is often valid and powerful, compared with the placebo test.