Two nearly identical regressors, correlation 0.99

Question

Two momentum signals in your model are almost the same series: their sample correlation is $0.99$ . They are the only two regressors.

Compute the VIF and the standard-error inflation, and comment on what it does to the individual coefficients.

Accepted Answer

Squared correlation gives the auxiliary R-squared. With just two regressors, R^2 = 0.99^2 = 0.9801. Compute the VIF. 	ext{VIF} = \frac{1}{1 - 0.9801} = \frac{1}{0.0199} \approx 50.25. Standard-error inflation. The standard error is multiplied by \sqrt{50.25} \approx 7.09, so the confidence intervals on each coefficient are about seven times wider than with independent regressors. What it means. The two signals share 98 percent of their variation, so the data can barely tell them apart. Expect the classic symptoms: individually insignificant t-statistics even though the pair is jointly signif…

Two nearly identical regressors, correlation 0.99

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