White's Robust Variance Estimate


Description Method

Description

The estimator variances resulting from a Least Squares Fit are normally calculated under the assumption of the homoskedasticity of the underlying data.  However, empirical data often exhibits heteroskedastic behavior, meaning the variance is not constant across a variable or variables.  Under heteroskedastic conditions, White's Robust Variance estimates provide consistent measures of estimator variance in Least Squares regressions.

Method

White's Robust Variance is computed from the regression results using the following formula:
White's Covariance Estimate
Normally the Omega matrix is estimated by a diagonal matrix containing the squares of the variance of all terms.  However, in a heteroskedastic situation, this variance is not constant amongst all terms.  The White estimate uses the residuals of the Least Squares Fit instead of the common variance.  In other words, the Omega matrix contains the squares of the OLS residuals along the diagonal and zero elsewhere.  The resulting covariance matrix estimate is consistent when the regressed data exhibits heteroskedasticity.

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