Weak-instrument robust inference for two-sample instrumental variables regression

Instrumental variable (IV) methods for regression are well established. More recently, methods have been developed for statistical inference when the instruments are weakly correlated with the endogenous regressor, so that estimators are biased and no longer asymptotically normally distributed. This paper extends such inference to the case where two separate samples are used to implement instrumental variables estimation. We also relax the restrictive assumptions of homoskedastic error structure and equal moments of exogenous covariates across two samples commonly employed in the two-sample IV literature for strong IV inference. Monte Carlo experiments show good size properties of the proposed tests regardless of the strength of the instruments. We apply the proposed methods to two seminal empirical studies that adopt the two-sample IV framework.