Testing endogeneity with high dimensional covariates

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.