Heteroscedasticity-consistent Standard Errors - White's Heteroscedasticity-consistent Estimator

White's Heteroscedasticity-consistent Estimator

If the regression errors are independent, but have distinct variances σi2, then which can be estimated with . This provides White's (1980) estimator, often referred to as HCE (heteroskedasticity-consistent estimator):

v_{HCE} = (X'X)^{-1} X'\operatorname{diag}(\hat u_1^2, \ldots, \hat u_n^2)X(X'X)^{-1}

The estimator can be derived in terms of the generalized method of moments (GMM).

Alternative estimators have been proposed in MacKinnon & White (1985) that correct for unequal variances of regression residuals due to different leverage. Unlike the asymptotic White's estimator, their estimators are unbiased when the data are homoscedastic.

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