Variance of OLS estimators in the presence of heteroscedasticity

[@1982sadaf]

SSx or Sxx?

[@paulaspinola1110]

Shouldn't you divide the numerator by 1/(N-K) to account for loss of degree of freedom as you did when you replaced the true variance by the estimated variance in the previous videos (where you computed estimated variance of beta^ under homoscedastic errors)?

[@akashp01]

No, apparently White's Standard Error do not require dividing by n-k, the degrees of freedom goes out of the window because already the term is complicated by itself, we just replace the population error variance with residuals squared and call it a day, bewildering!

[@liuwayne9686]

Understood, people will need to understand what heteroscedasticity is, simple explanation here, if the model somehow doesn't include enough dependent variables then it will cause the var(ui|xi) not being a constant because there is something going on inside the ui that has some sort of relationship with y. Right? I think this is pretty straight forward. And pls note that there could be other reasons causing this, I think, like it should be a un-linear model but you are fetching a linear model.

[@paulaspinola1110]

* I think you meant independent variables (explanatory variables, regressors, variables in the right hand side of the model equation)

[@MrPortraitsofpast]

this is a very basic question, but when you say var(B_hat given Xi), do you mean "given the data, Xi for all i"? I don't think you literally mean given one data point---the ith value of X. Is this right?

[@liuwayne9686]

please note that beta hat i is "calculated" based on xi, one xi has one beta hat, therefore this means the variance of all the beta hat.

[@JeffreyYS]

Var (beta^ | Xi) is conditional on the vector of X, meaning conditional on all the Xi’s. But when it comes to the definition of heteroskedasticity, it is in fact COV (Ui, Xi) is no longer 0. By simply writing Var (Ui | Xi) = sigma ^2 (i) it does mean only conditional on only one point of Xi, as it just skips mentioning that there is no serial correlation (namely, COV (Ui, Xj) = 0 where i does not equal j).

[@skipbrainless2732]

anyone remember w=in which video he calculated the first formula he shows here? because Variance of Beta hat given Xi in the last video was different

[@kottelkannim4919]

1. Videos #77 followed by #78. 2. It was different because he went into "sort-of" estimating the variance of u_i in the numerator.

[@szpacur]

brilliant !