Re: [Gretl-users] Wish-list: How about having robust standard error as the default on the GUI check box, etc.
On Sat, 30 Mar 2019, John C Frain wrote:
On Fri, 29 Mar 2019 at 02:54, Fred Engst <engst.uibe(a)gmail.com>
wrote:
> While we are on the topic of wish-list,
> 1. Why can’t we make the robust standard error as the default on the
> GUI check box?
> Is there any situation in which a robust standard error will be biased and
> wrong?
> By having the default being robust, those that insist on having the
> homoskedastic standard errors reported can uncheck the check box.
I would think that it is better to not have the robust standard
error as default. I would ask one to always first estimate the
equation assuming that the variance was homoskedastic. Then one
should test for homoskedasticity. If heteroskedasticity is found
one should then consider if the model was misspecified. (It is
possible that other specification tests also fail). If you are
satisfied that the model is properly specified you could then use
the robust standard error.
I agree with John on this. However, anyone who disagrees is free to
select the option "Use robust covariance by default", under the HCCME
tab in /Tools/Preferences/General.
As for whether robust standard errors are wrong in some way when the
errors are iid, one can experiment with the following script. It seems
that HC0 and HC1 (at least) often give standard errors that are too
small (and less accurate than the default classical ones).
<hansl>
set verbose off
nulldata 80 # make this bigger if you wish
series x = normal()
K = 10000 # replications
matrix B = zeros(K, 1)
matrix SE = zeros(K, 4)
loop i=1..K -q
series y = 10 + 2*x + normal()
ols y 0 x -q
B[i] = $coeff[2]
SE[i,1] = $stderr[2]
set hc_version 0
ols y 0 x -q -r
SE[i,2] = $stderr[2]
set hc_version 1
ols y 0 x -q -r
SE[i,3] = $stderr[2]
set hc_version 2
ols y 0 x -q -r
SE[i,4] = $stderr[2]
endloop
matrix X = {const, x}
matrix V = inv(X'X)
se0 = sqrt(V[2,2])
printf "\nPopulation s.d. of slope coeff: %.4f\n", se0
scalar se1 = sdc(B)
printf "Empirical s.d. of slope coeff: %.4f\n\n", se1
matrix altse = meanc(SE)
cnameset(altse, "deflt HC0 HC1 HC2")
printf "Means of estimated standard errors:\n\n%10.4f\n", altse
</hansl>
Allin