Uniform inference for kernel instrumental variable regression

TL;DR

This paper develops valid and efficient confidence sets for kernel instrumental variable regression, enabling reliable causal inference with complex data and nonlinearities, using a computationally simple bootstrap method.

Contribution

It introduces the first uniform confidence sets for kernel IV regression, accommodating general nonlinearities and data types, with a practical bootstrap procedure.

Findings

Provides sharp confidence sets for causal estimates

Requires only a single bootstrap run for inference

Enhances the practical utility of kernel IV methods

Abstract

Instrumental variable regression is a foundational tool for causal analysis across the social and biomedical sciences. Recent advances use kernel methods to estimate nonparametric causal relationships, with general data types, while retaining a simple closed-form expression. Empirical researchers ultimately need reliable inference on causal estimates; however, uniform confidence sets for the method remain unavailable. To fill this gap, we develop valid and sharp confidence sets for kernel instrumental variable regression, allowing general nonlinearities and data types. Computationally, our bootstrap procedure requires only a single run of the kernel instrumental variable regression estimator. Theoretically, it relies on the same key assumptions. Overall, we provide a practical procedure for inference that substantially increases the value of kernel methods for causal analysis.