Fast, Robust Inference for Linear Instrumental Variables Models using Self-Normalized Moments

TL;DR

This paper introduces a robust and computationally efficient method for inference in linear instrumental variables models using self-normalized moments, accommodating many weak or invalid instruments and heteroskedasticity.

Contribution

It develops a novel inference approach based on self-normalization and semidefinite programming, handling complex instrument scenarios with small sample guarantees.

Findings

Method is robust to many weak or invalid instruments.

Computational approach is fast and adaptable to existing tests.

Provides uniform coverage and small sample guarantees.

Abstract

We propose and implement an approach to inference in linear instrumental variables models which is simultaneously robust and computationally tractable. Inference is based on self-normalization of sample moment conditions, and allows for (but does not require) many (relative to the sample size), weak, potentially invalid or potentially endogenous instruments, as well as for many regressors and conditional heteroskedasticity. Our coverage results are uniform and can deliver a small sample guarantee. We develop a new computational approach based on semidefinite programming, which we show can equally be applied to rapidly invert existing tests (e.g,. AR, LM, CLR, etc.).