Instrument Relevance in Multivariate Linear Models: A Simple Measure

The correlation between instruments and explanatory variables is a key determinant of the performance of the instrumental variables estimator. The R² from regressing the explanatory variable on the instrument vector is a useful measure of relevance in univariate models, but can be misleading when there are multiple endogenous variables. This note proposes a computationally simple partial R² measure of instrument relevance for multivariate models.