Definition:
A diagnostic test of a regression. It is a statistic for testing whether
dependent variable y is heteroskedastic as a function of regressors X.
If it is, that suggests use of GLS or SUR estimation in place of
OLS. The test statistic is always nonnegative. Large values of test
statistic reject the hypothesis that y is homoskedastic in X. The
meaning of 'large' varies with the number of variables in X.
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Quoting almost directly from the Stata manual: The Breusch and Pagan (1980) chi-squared statistic -- a Lagrange multiplier statistic -- is given by
l = T * [Sm=1m=M [Sn=1n=m-1 [rmn2 ]]
where rmn2 is the estimated correlation between the residuals of the M equations and T is the number of observations. It has a chi-squared distribution with M(M-1)/2 degrees of freedom.(Econterms)
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Books on The Breusch-Pagan Statistic:
- StataCorp. 1999. Stata statistical software release 6.0 manual, vol 4.
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