If you use the White correction to least squares, it's a very restrictive form of GLS which assumes the noise is uncorrelated (although heteroskedastic), so the variance-covariance matrix is not the identity matrix but is still diagonal.— RealClimate
Newey-West (as referenced in Stata) isn't GLS at all; it's a correction to the standard errors for autocorrelated / heteroskedastic noise when using— RealClimate
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