A Robust Test for Weak Instruments with Multiple Endogenous Regressors

Abstract

We generalize the popular bias-based test of Stock and Yogo (2005) for instrument strength in two-stage least-squares models with multiple endogenous regressors to be robust to heteroskedasticity and autocorrelation. Equivalently, we extend the robust test of Montiel Olea and Pflueger (2013) for a single endogenous regressor to the general case with multiple endogenous regressors. We describe a simple procedure for applied researchers to conduct our generalized first-stage test of instrument strength, and provide fast Matlab code for its implementation. In simulations, our test controls size and is powerful. We demonstrate our testing procedures by considering the estimation of the state-dependent effects of fiscal policy as in Ramey and Zubairy (2018). JEL classification: C26, C36.