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Re: st: Re: Problems with -hetgrot-
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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