As we have seen, heteroscedasticity does not destroy the unbiasedness and consistency properties of the OLS estimators, but they are no longer efficient, not even asymptotically (i.e., large sample size). This lack of efficiency makes the usual hypothesis-testing procedure of dubious value. Therefore, remedial measures may be called for. There are two approaches to remediation: when a? is known and when a2 is not known.
When af Is Known: The Method of Weighted Least Squares
As we have seen in Section 11.3, if a2 is known, the most straightforward method of correcting heteroscedasticity is by means of weighted least squares, for the estimators thus obtained are BLUE.
30See M. J. Harrison and B. P. McCabe, "A Test for Heteroscedasticity Based on Ordinary Least Squares Residuals," Journal of the American Statistical Association, vol. 74, 1979, pp. 494-499; J. Szroeter, "A Class of Parametric Tests for Heteroscedasticity in Linear Econometric Models,'' Econometrica, vol. 46, 1978, pp. 1311-1327; M. A. Evans and M. L. King, "A Further Class of Tests for Heteroscedasticity,'' Journal of Econometrics, vol. 37, 1988, pp. 265-276; R. Koenker and G. Bassett, "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, vol. 50, 1982, pp. 43-61.
416 PART TWO: RELAXING THE ASSUMPTIONS OF THE CLASSICAL MODEL
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