Reading pp 298-299 with somewhat more care than they were written,
Tobias Wuergler from Zurich writes:
In order to demonstrate that robust standard errors are likely to
be more biased than non-robust under homoskedasticity, you use a
bivariate example, where the single regressor is assumed to be in
deviations-from-means form. Wouldn't one need, strictly speaking,
the regressand "y" to be in deviations-from-means form, too, in
order to partial out the constant? If so, the appropriate
degree-of-freedom correction should be (1-2/N) since the residual
maker in a demeaned regression is M(x)M(1), where M(1) is the
annihilator associated with the vector of ones (which one needs to
demean). The square of this residual maker is (M(1)-H(x)), hence
E(e(hat)2)=sigma2*(m(ii,1)-h(ii,x)), and the sum of
(m(ii,1)-h(ii,x)) is equal to (N-1-1) since m(ii,1)=(1-1/N).
Intuitively, a demeaned simple regression (with the original model
having a constant) still needs a degree of freedom correction of 2
as an average needs to be estimated apart from the single beta. Or
am I misunderstanding your example?
(In order to circumvent this complication one could assume a simple
regression through the origin, which would not require x (nor y) to
be demeaned.)
Good catch Toby - partialing out the constant does not change the
underlying df in the estimated residual; you can't fool mother
nature. So the df should be 2 and not 1. The argument about
relative bias of robust and conventional standard errors still
goes through, but to get the details right, change 1-1/N to 1-2/N
and make sure the leverage adds up to 2 and not 1.
How many df in that?!