Robust Inference with High-Dimensional Instruments

TL;DR

This paper introduces a robust statistical test for high-dimensional instrumental variable regressions that remains valid under weak identification and various error dependence structures, using advanced random matrix theory techniques.

Contribution

It develops a novel self-normalized test statistic that handles high-dimensional instruments exceeding sample size and is robust to complex error dependencies.

Findings

Good size control demonstrated in simulations

Satisfactory power across different error structures

Validates the use of the test in high-dimensional settings

Abstract

We propose a weak-identification-robust test for linear instrumental variable (IV) regressions with high-dimensional instruments, whose number is allowed to exceed the sample size. In addition, our test is robust to general error dependence, such as network dependence and spatial dependence. The test statistic takes a self-normalized form and the asymptotic validity of the test is established by using random matrix theory. Simulation studies are conducted to assess the numerical performance of the test, confirming good size control and satisfactory testing power across a range of various error dependence structures.