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i1 - r223)/£ 4 e x where r23 is the coefficient of correlation between X2 and X3.
It is apparent from (7.4.12) and (7.4.15) that as r23 tends toward 1, that is, as collinearity increases, the variances of the two estimators increase and in the limit when r23 = 1, they are infinite. It is equally clear from (7.4.17) that as r23 increases toward 1, the covariance of the two estimators also increases in absolute value. [Note: cov(92, ¡3) = cov(93, ¡¡2).]
Gujarati: Basic I II. Relaxing the I 10. Multicollinearity: What I I © The McGraw-Hill
Econometrics, Fourth Assumptions of the Happens if the Regressors Companies, 2004
Edition Classical Model are Correlated?
CHAPTER TEN: MULTICOLLINEARITY 351
The speed with which variances and covariances increase can be seen with the variance-inflating factor (VIF), which is defined as
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