Primary Submission Category: Instrumental Variables
DRIVE: A Distributionally Robust Instrumental Variable Estimation Framework
Authors: Zhaonan Qu, Yongchan Kwon,
Presenting Author: Zhaonan Qu*
We propose a distributionally robust formulation of the classical instrumental variable (IV) estimation framework, motivated by common challenges to IV estimators in practice, such as invalid and weak instruments and poor finite sample properties. When the distributional uncertainty set is a Wasserstein ball, the resulting estimator, which we call Wasserstein DRIVE, is consistent whenever the robustness parameter is bounded above by the largest singular value of the first stage coefficient and instruments are valid. We propose two data-driven procedures to select the penalty parameter, based on the first stage regression coefficient and the score quantile estimated using a nonparametric bootstrap. Thanks to its regularization and robustness properties, Wasserstein DRIVE could be preferable in practice, particularly when model assumptions are potentially violated. Simulation studies confirm the superior finite sample performance of Wasserstein DRIVE with valid and invalid instruments. Application to the Card dataset on educational returns also demonstrates its robustness at prediction under covariate shifts.