estat hettest: Breusch-Pagan Test

["Michael S. Hanson" <mshanson@mac.com>]

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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