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Re: st: Re: Problems with -hetgrot-

From   Richard Williams <[email protected]>
To   [email protected]
Subject   Re: st: Re: Problems with -hetgrot-
Date   Mon, 15 Mar 2004 00:16:38 -0500

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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