[bashtage]

The GLS fit of SUR and IV3SLS (method="gls", which is the default unless every equation has the same regressors) gave the covariance estimators the unweighted residuals y - x b together with the weighted regressors sqrt(w) x. The scores of the robust, kernel and clustered covariances were then sqrt(w) x e instead of w x e, so their standard errors were wrong whenever the weights were not all equal. The coefficients, the unadjusted covariance and the OLS fit (method="ols", which already used the weighted residuals) were not affected.

With one equation, GLS is weighted least squares and the robust covariance is HC0. For a regression with 200 observations and chi-squared weights, the robust standard errors of SUR were 0.1299, 0.1823 and 0.1254, where statsmodels WLS(...).fit(cov_type="HC0") gives 0.1448, 0.1982 and 0.1324. For systems with several equations, 96 of the 140 weighted combinations of GLS or OLS, iterated GLS, full_cov, constraints, debiased and covariance type differed from a direct computation of the stacked sandwich estimator, by up to 28% of the largest covariance element, for SUR and for IV3SLS. After this change all of them agree to within 1e-7, and the unweighted fits are unchanged since the weights are all one.

The covariance estimators now get the residuals scaled by the square root of the weights.

The tests compare the weighted estimators with the unweighted estimators applied to the data scaled by the square root of the normalized weights, for every covariance type, and the robust standard errors of a weighted regression with the statsmodels WLS estimator. Seven of them fail without the change.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.59%. Comparing base (6cbd30b) to head (9ef80d9).
⚠️ Report is 67 commits behind head on main.

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  Files         128      128              
  Lines       24188    24486     +298     
  Branches     1809     1827      +18     
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+ Hits        24087    24387     +300     
+ Misses         40       39       -1     
+ Partials       61       60       -1     

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