Confirming robust standard errors in Stata

Problem

Data: http://media.nek.lu.se/data/Final.dta

Data: http://media.nek.lu.se/data/Final.mat

The first dataset is final data in Stata format while the second is for MATLAB.

1. In Stata, run a regression of FINAL on SATV, SATM and HSGPA. “Use regress FINAL SATV SATM HSGPA, vce(robust)” to get robust standard errors.
2. Run the same regression and find the robust standard errors in MATLAB. In MATLAB, FINAL is in the vector y while X contains the explanatory variables (including a column of ones).
3. Note that Stata has a “bias correction” on the robust standard errors. It actually does not use

\[\widehat{Var}\left( b|X \right)={\left( X'X \right)}^{-1}X'{\hat{Ψ}}_WX{\left( X'X \right)}^{-1}\]

but instead

\[\widehat{Var}\left( b|X \right)= \frac{n}{n-k}{\left( X'X \right)}^{-1}X'{\hat{Ψ}}_WX{\left( X'X \right)}^{-1}\]

However, this does not make \(\widehat{Var}\left( b|X \right)\) unbiased.