The Reduced Form: A Simple Approach to Inference with Weak Instruments

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Abstract
In this paper, we consider simple methods for performing robust inference in linear instrumental variables models with weak instruments. We focus on inference based on the reduced form and show that conventional inference procedures about the relevance of the instruments excluded from the structural equation lead to tests of the structural parameters which are valid even if the instruments are weakly correlated to the endogenous variables. The use of standard heteroskedasticity and autocorrelation consistent covariance matrix estimators in constructing these tests also results in inference which is robust to heteroskedasticity, autocorrelation, and weak instruments. We provide a simulation experiment that demonstrates that the procedures have the correct size and good power in many relevant situations and conclude with an empirical example.