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Re: estat hettest: Breusch-Pagan Test


From   "Sergio Correia" <sergio.correia@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: estat hettest: Breusch-Pagan Test
Date   Mon, 3 Apr 2006 11:52:45 -0500

-ivhettest, nr2- does the same as the previous program.

As stated before, if normality does not ocurr (which is the case most
of the time), this test is better than the typical B.P. Test

Sergio


On 4/3/06, Schaffer, Mark E <M.E.Schaffer@hw.ac.uk> wrote:
> -ivhettest- also handles testing following -regress-.  Does it agree with you or �hettest-?
>
> --Mark
>
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> > Michael S. Hanson
> > Sent: 03 April 2006 15:04
> > To: statalist@hsphsun2.harvard.edu
> > Subject: estat hettest: Breusch-Pagan Test
> >
> > When trying to replicate an example application of the
> > Breusch-Pagan test for heteroskedasticity in Wooldridge
> > (2006) ["Introductory Econometrics," 3rd edition, example
> > 8.4, p. 281], I noticed that the test conducted by -estat
> > hettest- returns very different values than that reported in
> > Wooldridge.  Indeed, I can reproduce the values reported by
> > Wooldridge that indicate a non-rejection of the
> > homoskedasticity null, whereas -estat hettest- indicates a
> > fairly strong rejection.  Here is the code:
> >
> >       use "http://fmwww.bc.edu/ec-p/data/wooldridge/HPRICE1";, clear
> >
> >       // Reproduce B-P test results in Wooldridge (2006, p.281)
> >       reg lprice llotsize lsqrft bdrms
> >       predict uhat, resid
> >       gen uhatsq = uhat^2
> >       reg uhatsq llotsize lsqrft bdrms
> >       scalar LM = e(r2)*e(N)
> >       scalar pvalue = chi2tail(e(df_m),LM)
> >       disp "Breusch-Pagan test: LM = " LM ", p-value = " pvalue
> >
> > The output from this code is:
> >
> >       Breusch-Pagan test : LM = 4.2232485, p-value = .23834455
> >
> > which matches the B-P test results as reported in Wooldridge (2006).
> > However, the -estat hettest- gives a very different answer:
> >
> >       // Stata implementation of B-P test
> >       reg lprice llotsize lsqrft bdrms
> >       estat hettest, rhs
> >
> > yields:
> >
> >       Breusch-Pagan / Cook-Weisberg test for heteroskedasticity
> >                Ho: Constant variance
> >                Variables: llotsize lsqrft bdrms
> >
> >                chi2(3)      =    10.69
> >                Prob > chi2  =   0.0135
> >
> > Notice that this result implies rejection of the
> > homoskedasticity null, whereas the previous hand-coded
> > version of the B-P test does not.
> >
> > Can anyone comment on this difference?  I believe the -rhs-
> > option for -estat hettest- is the appropriate one here, but I
> > could be mistaken.
> > Also, the manual states that the implementation of the B-P
> > test is based on a score test statistic, whereas Wooldridge
> > uses a Lagrange Multiplier version of the test, which he
> > attributes to Koenker (1981).
> > Nonetheless, both tests have the same null and both
> > statistics are distributed asymptotically as a chi-squared
> > with 3 degrees of freedom.
> > Thus, I am puzzled by the extreme difference in the reported
> > results.
> > Any comments that help resolve this issue would be appreciated.
> > Thanks.
> >
> >                                          -- Mike
> >
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