The paper by John Shea discusses the importance of instrument relevance in multivariate linear models, particularly in the context of instrumental variables (IV) estimation. The author proposes a simple measure, called partial R-squared, to assess the relevance of instruments. This measure is designed to address the limitations of using the standard R-squared from regressing each explanatory variable on the instrument vector, which can be misleading in multivariate models. In univariate models, the R-squared from regressing an explanatory variable on the instrument vector is a useful measure of relevance. However, in multivariate models, this approach can lead to misleading results, especially when instruments are highly collinear. Shea's partial R-squared measure is computed through a series of OLS regressions and provides a more accurate assessment of instrument relevance. The paper motivates the use of partial R-squared by examining its impact on the consistency and precision of IV estimates in multivariate models. It also presents Monte Carlo evidence on the finite sample behavior of multivariate IV, showing that low instrument relevance can lead to biased and inefficient estimates. Additionally, the paper includes an empirical example from the macroeconomic literature, demonstrating how partial R-squared can be used to identify relevant instruments. Finally, the author discusses the practical applications of partial R-squared, suggesting that it can be used as a diagnostic tool and a guiding principle in instrument selection strategies. The paper concludes by emphasizing the importance of instrument relevance and providing guidelines for its effective use in applied research.The paper by John Shea discusses the importance of instrument relevance in multivariate linear models, particularly in the context of instrumental variables (IV) estimation. The author proposes a simple measure, called partial R-squared, to assess the relevance of instruments. This measure is designed to address the limitations of using the standard R-squared from regressing each explanatory variable on the instrument vector, which can be misleading in multivariate models. In univariate models, the R-squared from regressing an explanatory variable on the instrument vector is a useful measure of relevance. However, in multivariate models, this approach can lead to misleading results, especially when instruments are highly collinear. Shea's partial R-squared measure is computed through a series of OLS regressions and provides a more accurate assessment of instrument relevance. The paper motivates the use of partial R-squared by examining its impact on the consistency and precision of IV estimates in multivariate models. It also presents Monte Carlo evidence on the finite sample behavior of multivariate IV, showing that low instrument relevance can lead to biased and inefficient estimates. Additionally, the paper includes an empirical example from the macroeconomic literature, demonstrating how partial R-squared can be used to identify relevant instruments. Finally, the author discusses the practical applications of partial R-squared, suggesting that it can be used as a diagnostic tool and a guiding principle in instrument selection strategies. The paper concludes by emphasizing the importance of instrument relevance and providing guidelines for its effective use in applied research.