Testing Endogeneity with High Dimensional Covariates

TL;DR

This paper examines the performance of the Durbin-Wu-Hausman test in high-dimensional settings and introduces a new test with improved power for detecting endogeneity in instrumental variables analysis.

Contribution

It demonstrates the limitations of the DWH test in high dimensions and proposes a new, more powerful test for endogeneity detection.

Findings

DWH test maintains size but has reduced power in high dimensions

Proposed test outperforms DWH with better power

Simulation shows near-oracle performance of the new test

Abstract

Modern, high dimensional data has renewed investigation on instrumental variables (IV) analysis, primarily focusing on estimation of effects of endogenous variables and putting little attention towards specification tests. This paper studies in high dimensions the Durbin-Wu-Hausman (DWH) test, a popular specification test for endogeneity in IV regression. We show, surprisingly, that the DWH test maintains its size in high dimensions, but at an expense of power. We propose a new test that remedies this issue and has better power than the DWH test. Simulation studies reveal that our test achieves near-oracle performance to detect endogeneity.