Breusch–Pagan test

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In a linear regression model, a test of the null hypothesis of homoscedasticity against the alternative hypothesis that the variance of observation i has the form σ2/i=h(Ziα), where h is a function common for all i, zi is an (S × 1) non-stochastic vector with first element equal to one, and α is an (S × 1) vector of unknown coefficients. The test can be conveniently performed by (1) estimating the original regression by ordinary least squares (OLS) and (2) regressing squared OLS residuals on Z = (z1,…,zN). The test statistic is η = NR2, where N is the sample size and R2 is the coefficient of determination from the second regression. Under the null hypothesis H0, η is asymptotically χ2(S-1); this result does not depend on the function h.


Subjects: Economics.

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