Re: st: Re: Problems with -hetgrot-

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

At 04:13 PM 3/14/2004 -0600, Scott Merryman wrote:
> No doubt there are more efficient ways to do this, but here is an 
> implementation
> that seems to work.
I created my own variation called -hetgrot2-.  The good news is that both 
my -hetgrot2 and Scott's -gwhet2- seem to give identical results.  The bad 
news is that neither exactly matches the results reported by Greene!  But 
they come very close, and I'm not 100% sure Greene is doing it right.

Greene, 4th edition, table 15.1, p. 598 presents an example (and the data 
are included on a CD with the book).  Estimates are presented for OLS, 
FGLS, and ML.  I found that the following Stata commands perfectly 
reproduce the parameter estimates he reports.  The LR statistic for 
groupwise heteroscedasticity he reports is 120.915, which he says is based 
on the ML statistics.  I'm editing the output to just get the most crucial 
parts.

. use "W:\Greene 4th edition\DATAFILE\STATA\TBL15_1.DTA", clear
. tsset firm year
       panel variable:  firm, 1 to 5
        time variable:  year, 1935 to 1954
. * Model 1: Least Squares
. quietly xtgls  i f c
. gwhet2

chi2 (4)  =      104.41

. * Model 2: FGLS
. quietly xtgls  i f c, p(h)
. gwhet2

chi2 (4)  =      114.31

. * Model 3: ML
. quietly xtgls  i f c, p(h) igls
. gwhet2

chi2 (4)  =      122.89

The final LR statistic of 122.89 is close but not quite to Greene's 
reported statistic of 120.915.  I believe the discrepancy is due to the 
fact that Greene uses the estimate of sigma from Model 1 (Least Squares) 
while also using the estimates of the group sigmas from Model 3 (ML).  I'm 
not sure I understand the logic of this, but his Limdep program apparently 
does it this way too.

So the moral is, if you have a mad desire to use this test and you are 
using xtgls then (1) don't use the original hetgrot, as it does it wrong, 
and (2) you seem to come closest to Greene if you include the -p(h)- and 
-igls- parameters on the -xtgls- command, and (3) if you wanted to do 
things exactly like Greene, I think you would need a program that estimated 
both models 1 and 3.  From 1 you would save the OLS estimate of sigma, and 
from 3 you would save the group sigmas, and then compute the test 
statistic.  (But again, I am not sure Greene is doing it right; at the very 
least, his formulas seems internally inconsistent.)

If your life really depends on getting these statistics right, you also may 
just want to use Limdep, as these tests and the others Greene presents are 
easily implemented with Limdep's TSCS (Time Series/Cross Section)command.



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Richard Williams, Notre Dame Dept of Sociology
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