Bdtyktl

So I'm slowly going through the Stock and Watson book and I'm a bit confused on how to deal with the issue of homoscedacity/heteroscedacity. Specifically, it is mentioned that economic theory tells us that there's no reason for us to assume that errors will be homoscedastic, so their advice is that we assume heteroscedasticity and always use the heteroscedastic robust standard errors when performing our regression analysis. The way I'm being taught this material, in STATA for example, is that we just run the reg command, always sure to include r for robust standard error.

My question(s) is this: if our default position is to assume heteroscedacticity, then is it also correct that OLS is no longer the best unbiased linear estimator as one of the Gauss-Markov assumptions is violated? And if this is the case, is it also correct that GLS would be the BLUE estimator? Lastly, if both of these assumptions are correct, why would we not just run GLS regressions as our default and not OLS?

Thanks.

Because GLS is BLUE if you know the form of heteroskedasticity (and correlated errors). If you misspecify the form of heteroscedasticity, GLS estimates will lose their nice properties.

Under heteroscedasticity, OLS remains unbiased and consistent, but you lose efficiency.

So unless you're certain of the form of heteroscedasticity, it makes sense to stick with unbiased and consistent estimates from OLS. Then adjust inference for heteroskedasticity using robust standard errors which are valid asymptotically if you don't know the form of heteroscedasticity.

A hybrid approach is to do your best at specifying the form of heteroskedasticity but still apply robust standard errors for inference. See Resurrecting weighted least squares (PDF).

Modeling is all about tradeoffs and resources. If you are convinced there is nothing to be learned from modeling the form of heteroscedasticity, then specifying its form is a waste of time. I would argue that there is usually something to be learned in empirical applications. But tradition/convention nudges us away from studying heteroscedasticity, looking at the variances, since all they are is "error".

OLS is still unbiased when the data are correlated (provided the mean model is true). The net effect of heteroscedasticity is that it offsets the errors, so that the 95% CI for the regression is, at times, too tight and at other times too wide. Even still, you can correct the standard errors by using the sandwich or heteroscedasticity consistent standard error (HC) estimator. Technically, this is not "ordinary least squares" but it results in the same effect summary measures: a slope, interecept, and 95% CIs for their values, just no global test, or F-tests, and no validity to prediction intervals.