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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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