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Definition of Breusch-Pagan Statistic

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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.

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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• StataCorp. 1999. Stata statistical software release 6.0 manual, vol 4.
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Jodi Beggs
Economics Guide