Question

In White's heteroskedasticity robust standard errors, how are the robust standard errors calculated?

Answer 1

When we have a regression model under heteroskedasticity , then we can quantify unbiased std. error estimate of OLS coefficients of that regression model by using the method White's heteroskedasticity robust standard errors. It is sometime known as robust standard errors or White's heteroskedasticity robust standard errors. The most important consequence of heteroskedasticity is that, it not satisfies one of the assumption of gauss markov theorem assumption ( i.e Homoskedasticity ). Which is necessary to prove OLS estimators are best liner unbiased estimator. and most important, a regression model under heteroskedasticity lead to wrong estimate of OLS standard errors.

In such situation, if we use standard error formula which is based on the assumption of  Homoskedasticity, our std. error will be incorrect. Therefore, we use White's heteroskedasticity robust standard errors method to calculate robust standard errors.

Suppose we have following regression equation:

for   , We can calculate robust standard errors by using the following formula: