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.
Instrument Relevance in Linear Models: a Simple MeasureJohn Shea ,
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Review of Economics and Statistics