Re: st: Re: Problems with -hetgrot-

[Richard Williams <Richard.A.Williams.5@nd.edu>]

At 07:38 PM 3/14/2004 -0500, Richard Williams wrote:

> What I don't understand is why he is using the 15708.84 from the least 
> squares estimates, rather than using a ML estimate of sigma.  This would 
> seem to be inconsistent with what he says on the middle of p. 597.
Bill Greene kindly emailed me on this (he cc'd the list but I am not sure 
it got through).  Anyway, he basically pointed out that the least squares 
estimate of sigma is also the ML estimate of sigma; his reported test 
statistic of 120.915 is therefore right, the 122.89 that other programs 
produced was wrong.  I think those of us who came up with alternative 
programs were trying to fix the programming mistakes in -hetgrot- without 
realizing that there was a fundamental error in the underlying approach 
that was being used, at least with regards to cross-sectional time series.

Here is an alternative approach that finally seems to get the test 
statistic right.  It involves a chi-square contrast of the restricted 
homoskedastic model and an unrestricted heteroscedastic model.  I am again 
using Greene's data in table 15.1, 4th edition.

. quietly tsset  firm year
. * No heteroscedasticity
. quietly xtgls  i f c
. estimates store nohet

. * heteroskedasticity
. quietly xtgls  i f c, p(h) igls
. estimates store hetero

. lrtest hetero nohet, force df(4)

likelihood-ratio test                                  LR chi2(4)  =    120.91
(Assumption: nohet nested in hetero)                   Prob > chi2 =    0.0000

Presumably this could all be automated and made to work with something 
besides Greene's data, and with routines besides xtgls.  
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