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estat hettest: Breusch-Pagan Test


From   "Michael S. Hanson" <mshanson@mac.com>
To   statalist@hsphsun2.harvard.edu
Subject   estat hettest: Breusch-Pagan Test
Date   Mon, 3 Apr 2006 10:04:29 -0400

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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