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

2018-12-27

AI Summary

This paper addresses key challenges in synthetic control method (SCM) estimation of average causal effects: difficulty in bias correction, non-robust variance estimation, and sensitivity of conventional inference to model misspecification. We propose a debiased estimation framework based on K-fold cross-fitting and construct a self-normalized t-statistic that avoids explicit estimation of long-run variance. Grounded in asymptotic pivotal distribution theory, our approach is theoretically robust to model misspecification and accommodates both stationary and non-stationary data. Simulation studies and an empirical application to carbon tax-induced emissions reductions demonstrate that our method achieves substantially higher small-sample inference accuracy and statistical power compared to existing SCM-based inferential procedures. To the best of our knowledge, this is the first robust hypothesis testing framework within the SCM paradigm that obviates the need for long-run variance estimation.

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.

Problem

• Debiasing synthetic control for causal effect inference
• Robust t-test for stationary and non-stationary data
• Evaluating carbon tax impact on emissions

Innovation

• K-fold cross-fitting for bias correction
• Self-normalized t-statistic for inference
• Robust t-test for stationary and non-stationary data