Debiasing and $t$-tests for synthetic control inference on average causal effects

Abstract

We propose a practical and robust method for making inferences on average treatment effects estimated by synthetic controls. We develop a $K$-fold cross-fitting procedure for bias correction. To avoid the difficult estimation of the long-run variance, inference is based on a self-normalized $t$-statistic, which has an asymptotically pivotal $t$-distribution. Our $t$-test is easy to implement, provably robust against misspecification, and valid with stationary and non-stationary data. It demonstrates an excellent small sample performance in application-based simulations and performs well relative to other methods. We illustrate the usefulness of the $t$-test by revisiting the effect of carbon taxes on emissions.

Cited by in corpus (3)

• The sooner the better: lives saved by the lockdown during the COVID-19 outbreak. The case of Italy
• Controlling for Unmeasured Confounding in Panel Data Using Minimal Bridge Functions: From Two-Way Fixed Effects to Factor Models
• Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy