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I already detect heteroskedasticity in the data, which means that OLS is no longer an option.

Another question, I know that robust OLS can give a good confidence interval. How about GLS and WLS's advantages in the presence of heteroskedasticity?

Tom
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Actually I would start with the fact that heteroskedasticity is not a problem if you are aiming for accurate predictions. It is only a problem when it comes to inference.

(i) If you are only interested in prediction you should stay with the simple OLS estimator because GLS and WLS typlically bias your estimates. This is because GLS is infeasible if you do not know the weight matrix (almost always the case in real world) and WLS typically relies on a two step procedure that introduces additional noise to your estimation.

(ii) If you are interested in inference, i.e. the confidence intervalls you must opt for GLS or WLS in case of heteroscedasiticity. Here your choice might depend on how much you know about the heteroscedasticity structure. In case you do not know much about it one typically recommend OLS together with heteroscdasticity robust standard errors. The reason for this is the fact that OLS is unbiased while GLS and WLS are not. If you have some clue about the functional form of the weight matrix you might opt for GLS or WLS.

So my general suggestion would be OLS with heteroscedasticity robust variance covariance matrix. See the excellent book of Wooldridge on the topic.

Michael L.
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    In this case, if we do not know the weight structure, the robust OLS is the way to get good confidence interval? What about coefficients, still unbiased using robust? – Tom Apr 17 '18 at 07:53
  • I mean this is only partly a theoretical question. A very honest approach would be the following: Estimate the model using robust OLS in order to get the unbiased coefficients. Then calculate the WLS or feasible GLS estimator and compare the coefficients and confidence intervalls. Then you can opt for those that are widest. But in general practice I would say robust OLS is a very accepted solution in order to get unbiased estimators and reasonable confidence intervalls. – Michael L. Apr 17 '18 at 08:00
  • OK, I will follow this approach in practice. Using robust first, I try WLS and feasible GLS if I can figure out the weight form. – Tom Apr 17 '18 at 08:07

  • GLS and WLS typlically bias your estimates.

    what do they both introduce bias in? and what bias is it? and by 'estimates' do you mean $\hat{\beta_{OLS}}$ and $\hat{\beta_{WLS}}$ of the independent variables?

     – Naveen Reddy Marthala Mar 28 '22 at 01:32