A borderline Breusch-Pagan test with two regressors

Question

You fit a regression with 2 explanatory variables on $n = 150$ observations. Regressing the squared residuals on those 2 variables gives an auxiliary $R^2 = 0.04$ .

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

Accepted Answer

Compute the statistic. 	ext{LM} = n \cdot R^2{	ext{aux}} = 150 	imes 0.04 = 6.0. Degrees of freedom and cutoff. The auxiliary regression used 2 regressors, so the null distribution is chi-square with 2 degrees of freedom, whose 5 percent critical value is 5.991. Decision. 6.0 5.991, so we reject homoskedasticity, but only barely. This is a borderline result: the p-value is just under 0.05. Treat it with appropriate caution. A borderline rejection still argues for reporting robust standard errors, since they cost nothing and protect you if the errors truly are heteroskedastic. Takeaway. 	e…

A borderline Breusch-Pagan test with two regressors

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