Developing Robust Inference Methods for Instrumental Variables in the Context of Machine Learning and Big Data Environments

Abstract

Instrumental variables (IV) estimation has emerged as a useful methodology for causal inference in econometrics, addressing the persistent challenge of endogeneity in observational data where unobserved confounders bias traditional regression estimates. The integration of machine learning techniques with instrumental variables estimation presents both unprecedented opportunities and significant methodological challenges, particularly in high-dimensional settings where the number of potential instruments may exceed sample sizes and where traditional asymptotic theory may not apply. This paper develops a comprehensive framework for robust instrumental variables inference in machine learning environments, introducing novel regularization techniques that simultaneously address the problems of weak instruments, many instruments, and high-dimensional confounding. We establish theoretical foundations for our proposed estimators by deriving finite-sample concentration inequalities and asymptotic normality results under heteroskedastic and potentially non-Gaussian error structures. Our methodology incorporates advanced matrix completion techniques and sparse regularization methods to handle missing data patterns commonly encountered in big data applications. Through extensive theoretical analysis involving sophisticated tools from empirical process theory and high-dimensional probability, we demonstrate that our proposed estimators achieve optimal rates of convergence while maintaining valid statistical inference properties. The practical implementation of our methods is illustrated through comprehensive simulation studies that demonstrate substantial improvements in both bias reduction and confidence interval coverage compared to existing approaches, with particular emphasis on scenarios involving weak identification and high-dimensional nuisance parameters.