A Robust Test for Weak Instruments for 2SLS with Multiple Endogenous Regressors

Lewis, Daniel J.; Mertens, Karel

doi:10.24149/wp2208r2

Working Paper Revision

A Robust Test for Weak Instruments for 2SLS with Multiple Endogenous Regressors

Abstract: We develop a test for instrument strength based on the bias of two-stage least squares (2SLS) that (1) generalizes the tests of Stock and Yogo (2005) and Sanderson and Windmeijer (2016) to be robust to heteroskedasticity and autocorrelation, and (2) extends the Montiel Olea and Pflueger (2013) robust test for models with a single endogenous regressor to multiple endogenous regressors. Our test can be based either on Stock and Yogo’s (2005) absolute bias criterion or on the 2SLS bias relative to Montiel Olea and Pflueger’s (2013) worst-case benchmark. We also develop extensions to test whether instruments are weak for individual 2SLS coefficients. In simulations, our test controls size and is powerful, and we provide efficient code packages for its practical implementation. We demonstrate our testing procedures in the context of the estimation of state-dependent fiscal multipliers as in Ramey and Zubairy (2018).

Keywords: Instrumental Variables; Weak Instruments Test; Multiple Endogenous Regressors; Heteroskedasticity; Serial Correlation;

JEL Classification: C26; C36;

https://doi.org/10.24149/wp2208r2