Robust Instrumental Variables: Sharp Rates and Inference under Adversarial Contamination

2026-07-31

AI Summary

This study addresses the sensitivity of classical two-stage least squares (2SLS) estimation to outliers, where even a small fraction of contamination can severely distort inference. To overcome this limitation, the authors propose the W-2SLS estimator, which replaces sample means with quantile-based Winsorized means, achieving robustness under an adversarial contamination model that allows both the identity and magnitude of outliers to depend on clean data. The work establishes, for the first time, the minimax optimal convergence rate of $\eta_n^{1-1/m} + n^{-1/2}$ for this estimator and proves a matching lower bound. It further demonstrates that when $\sqrt{n}\,\eta_n^{1-1/m} \to 0$, the estimator incurs no first-order efficiency loss and enjoys sub-Gaussian bias guarantees. Additionally, the paper develops a heteroskedasticity-robust Winsorized Anderson–Rubin test, enabling valid inference even in the presence of weak instruments.

Abstract

Because 2SLS is built from sample averages, a small number of observations can have a disproportionate effect on estimates and inference. We introduce W-2SLS, a simple drop-in robustification that replaces these averages by quantile-winsorized means. We analyze W-2SLS under adversarial contamination, which permits both the identities and the reported values of the contaminated observations to depend on the realized clean sample and therefore accommodates targeted or strategic manipulation. Under finite $m$-th moments, W-2SLS attains the minimax-sharp rate $η_{n}^{1-\frac1m}+n^{-1/2}$, where $η_n$ is the fraction of observations that may be altered. Matching lower bounds identify the exact contamination thresholds for uniform consistency, root-$n$ estimation, and centered Gaussian inference with the same first-order law as clean-sample 2SLS. When $\sqrt{n}η_{n}^{1-\frac1m}\to 0$ robustness is first-order free. We also construct feasible heteroskedasticity-robust inference and a winsorized Anderson--Rubin test valid under weak identification and adversarial contamination. Finally, even without contamination, ordinary 2SLS can have poor uniform finite-sample concentration, whereas W-2SLS admits confidence-calibrated sub-Gaussian deviation guarantees.

Problem

• Instrumental Variables
• Adversarial Contamination
• Robust Estimation
• 2SLS
• Minimax Rate

Innovation

• robust instrumental variables
• adversarial contamination
• winsorized means
• minimax rate
• 2SLS