Suppose we estimate the model y i = + u i , where u i

Suppose we estimate the model $y_i=\mu +u_i$, where $u_i\sim {N}[0,{\sigma }_i^2]$.

(a) Show that the OLS estimator of $\mu$ simplifies to $\hat{\mu }=\overline{y}$.

(b) Hence directly obtain the variance of $\overline{y}$. Show that this equals White's heteroskedastic consistent estimate of the variance given in (4.21).

Transcribed Image Text:

VIBOLS] = (X'X) 'X'X(X'X) N N N = (xx) '* (x)'. i=1 (4.21)