Distributionally Robust Instrumental Variables Estimation

TL;DR

This paper introduces DRIVE, a distributionally robust IV estimation method that enhances causal inference reliability by accounting for distributional uncertainties using Wasserstein distance, with strong theoretical and empirical support.

Contribution

It proposes a novel Wasserstein-based distributionally robust IV estimator with new asymptotic theory ensuring consistency and robustness in finite samples and large samples.

Findings

Wasserstein DRIVE outperforms traditional IV methods in finite samples.

The estimator maintains consistency without regularization parameter vanishing.

Simulation results show improved estimation accuracy and robustness.

Abstract

Instrumental variables (IV) estimation is a fundamental method in econometrics and statistics for estimating causal effects in the presence of unobserved confounding. However, challenges such as untestable model assumptions and poor finite sample properties have undermined its reliability in practice. Viewing common issues in IV estimation as distributional uncertainties, we propose DRIVE, a distributionally robust IV estimation method. We show that DRIVE minimizes a square root variant of ridge regularized two stage least squares (TSLS) objective when the ambiguity set is based on a Wasserstein distance. In addition, we develop a novel asymptotic theory for this estimator, showing that it achieves consistency without requiring the regularization parameter to vanish. This novel property ensures that the estimator is robust to distributional uncertainties that persist in large samples. We further derive the asymptotic distribution of Wasserstein DRIVE and propose data-driven procedures to select the regularization parameter based on theoretical results. Simulation studies demonstrate the superior finite sample performance of Wasserstein DRIVE in terms of estimation error and out-of-sample prediction. Due to its regularization and robustness properties, Wasserstein DRIVE presents an appealing option when the practitioner is uncertain about model assumptions or distributional shifts in data.