A Robust Test for Weak Instruments

We develop a test for weak instruments in linear instrumental variables regression that is robust to heteroscedasticity, autocorrelation, and clustering. Our test statistic is a scaled nonrobust first-stage F statistic. Instruments are considered weak when the two-stage least squares or the limited information maximum likelihood Nagar bias is large relative to a benchmark. We apply our procedures to the estimation of the elasticity of intertemporal substitution, where our test cannot reject the null of weak instruments in a larger number of countries than the test proposed by Stock and Yogo in 2005. Supplementary materials for this article are available online.