When the Breusch-Pagan test fails to reject

Question

You fit a regression with 4 explanatory variables on $n = 500$ observations. The auxiliary regression of squared residuals on those 4 variables gives $R^2 = 0.015$ .

Compute the Breusch-Pagan statistic and state the conclusion at the 5 percent level.

Accepted Answer

Compute the statistic. 	ext{LM} = n \cdot R^2{	ext{aux}} = 500 	imes 0.015 = 7.5. Degrees of freedom and cutoff. With 4 regressors in the auxiliary regression, the null distribution is chi-square with 4 degrees of freedom, 5 percent critical value 9.488. Decision. 7.5 < 9.488, so we fail to reject the null. The test finds no significant evidence of heteroskedasticity. Note that even with a large sample of 500, the auxiliary R^2 is so small that the squared residuals are essentially unrelated to the regressors, consistent with constant variance. A caution on interpretation. Failing to rejec…

When the Breusch-Pagan test fails to reject

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