[Paper Review] Practical and robust $t$-test based inference for synthetic control and related methods

Victor Chernozhukov, Kaspar Wüthrich+1 more|arXiv (Cornell University)|Dec 27, 2018

Statistical Methods and Inference12 references25 citations

TL;DR

This paper introduces a robust, practical $t$-test inference method for synthetic control and related estimators using a $K$-fold cross-fitting procedure for bias correction and a self-normalized $t$-statistic that asymptotically follows a pivotal $t$-distribution. The method ensures valid inference under weak regularity conditions, outperforms difference-in-differences in efficiency, and maintains strong small-sample performance even with non-stationary data.

ABSTRACT

This paper proposes a practical and robust method for making inference on average treatment effects estimated by synthetic control and related methods. 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 procedure only requires consistent (in $\ell_2$-norm) estimation of the parameters, which can be verified for synthetic control and many other popular estimators. The proposed method is easy to implement, provably robust against misspecification, more efficient than difference-in-differences, valid with non-stationary data, and demonstrates an excellent small sample performance.

Motivation & Objective

• To address the challenge of valid statistical inference in synthetic control methods when standard assumptions are violated.
• To develop a method that remains robust to model misspecification and non-stationary data.
• To improve efficiency compared to difference-in-differences while maintaining validity under minimal regularity conditions.
• To enable practical implementation with consistent parameter estimation in $\ell_2$-norm, avoiding complex long-run variance estimation.

Proposed method

• A $K$-fold cross-fitting procedure is used to correct bias in synthetic control estimators, improving robustness.
• Inference is based on a self-normalized $t$-statistic that asymptotically follows a pivotal $t$-distribution, eliminating the need to estimate long-run variance.
• The method relies only on consistent $\ell_2$-norm estimation of model parameters, which is verifiable for synthetic control and similar estimators.
• The self-normalized statistic ensures asymptotic validity under weak regularity conditions, enhancing robustness.
• The approach is designed to be computationally simple and implementable in standard statistical software.

Experimental results

Research questions

• RQ1 Can a robust inference procedure be developed for synthetic control that remains valid under model misspecification?
• RQ2 How can bias in synthetic control estimators be effectively corrected without relying on complex long-run variance estimation?
• RQ3 Does a self-normalized $t$-statistic improve small-sample performance compared to conventional $t$-tests?
• RQ4 Can the method maintain validity with non-stationary or dependent data, which are common in policy evaluation?

Key findings

• The proposed method achieves asymptotically pivotal inference via a self-normalized $t$-statistic, avoiding the need for long-run variance estimation.
• The $K$-fold cross-fitting procedure ensures bias correction with only consistent $\ell_2$-norm estimation of parameters.
• The method demonstrates superior small-sample performance compared to conventional approaches, even under non-stationary data.
• It is provably robust against model misspecification and outperforms difference-in-differences in terms of efficiency.