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RE: estat hettest: Breusch-Pagan Test


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: estat hettest: Breusch-Pagan Test
Date   Mon, 3 Apr 2006 16:41:59 +0100

-ivhettest- also handles testing following -regress-.  Does it agree with you or âhettest-?

--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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