A Ridge-Regularised Jackknifed Anderson-Rubin Test

TL;DR

This paper introduces a ridge-regularised jackknifed Anderson-Rubin test for instrumental variable regression that controls size asymptotically, even with many weak instruments and heteroskedasticity, outperforming existing methods.

Contribution

It develops a novel ridge-regularised version of the jackknifed AR test that handles many instruments and weak identification, with improved size control and applicability.

Findings

Controls asymptotic size under heteroskedasticity and weak instruments

Performs well in finite samples with favourable size and power

Applicable to empirical analysis, demonstrated on US immigration data

Abstract

We consider hypothesis testing in instrumental variable regression models with few included exogenous covariates but many instruments -- possibly more than the number of observations. We show that a ridge-regularised version of the jackknifed Anderson Rubin (1949, henceforth AR) test controls asymptotic size in the presence of heteroskedasticity, and when the instruments may be arbitrarily weak. Asymptotic size control is established under weaker assumptions than those imposed for recently proposed jackknifed AR tests in the literature. Furthermore, ridge-regularisation extends the scope of jackknifed AR tests to situations in which there are more instruments than observations. Monte-Carlo simulations indicate that our method has favourable finite-sample size and power properties compared to recently proposed alternative approaches in the literature. An empirical application on the elasticity of substitution between immigrants and natives in the US illustrates the usefulness of the proposed method for practitioners.