https://macropaperwarehouse.com/authors/daniel-j-lewis/Daniel J LewisHugo -- gohugo.ioen-ushttps://macropaperwarehouse.com/papers/a-robust-test-for-weak-instruments-for-2sls-with-multiple-endogenous-regressors/https://macropaperwarehouse.com/papers/a-robust-test-for-weak-instruments-for-2sls-with-multiple-endogenous-regressors/<p>This paper develops a test for instrument strength based on the bias of two-stage least squares (2SLS) that: (1) generalizes the Stock-Yogo (2005) and Sanderson-Windmeijer (2016) tests to be robust to heteroskedasticity and autocorrelation (HAC), and (2) extends the Montiel Olea-Pflueger (2013) robust test from models with a single endogenous regressor to models with multiple endogenous regressors—the important remaining gap identified by Andrews et al. (2019). The test is based on a weighted quadratic loss in the asymptotic bias of 2SLS and can use either the Stock-Yogo absolute bias criterion or the 2SLS bias relative to Montiel Olea-Pflueger&rsquo;s worst-case benchmark. Extensions are developed to test whether instruments are weak for individual 2SLS coefficients. In simulations, the test controls size and is powerful, and the authors provide efficient code packages. The test is applied to state-dependent fiscal multipliers (Ramey-Zubairy 2018).</p>