Info

Note: In regression (11.6.2), the dependent variable is (Yi/oi) and the independent variables are (1/o-j) and (Xj/o).

Source: Data on Y and (standard deviation of compensation) are from Table 11.1. Employment size: 1 = 1-4 employees, 2 = 5-9 employees, etc. The latter data are also from Table 11.1.

Note: In regression (11.6.2), the dependent variable is (Yi/oi) and the independent variables are (1/o-j) and (Xj/o).

Source: Data on Y and (standard deviation of compensation) are from Table 11.1. Employment size: 1 = 1-4 employees, 2 = 5-9 employees, etc. The latter data are also from Table 11.1.

31As noted in footnote 3 of Chap. 6, the R2 of the regression through the origin is not directly comparable with the R2 of the intercept-present model. The reported R2 of 0.9993 takes this difference into account. (See the SAS package for further details about how the R2 is corrected to take into account the absence of the intercept term. See also App. 6A, Sec. 6A1.)

CHAPTER ELEVEN: HETEROSCEDASTICITY 417

When of Is Not Known

As noted earlier, if true a2 are known, we can use the WLS method to obtain BLUE estimators. Since the true a2 are rarely known, is there a way of obtaining consistent (in the statistical sense) estimates of the variances and covariances of OLS estimators even if there is heteroscedasticity? The answer is yes.

White's Heteroscedasticity-Consistent Variances and Standard Errors. White has shown that this estimate can be performed so that asymptotically valid (i.e., large-sample) statistical inferences can be made about the true parameter values.32 We will not present the mathematical details, for they are beyond the scope of this book. However, Appendix 11A.4 outlines White's procedure. Nowadays, several computer packages present White's heteroscedasticity-corrected variances and standard errors along with the usual OLS variances and standard errors.33 Incidentally, White's heteroscedasticity-corrected standard errors are also known as robust standard errors.

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