Re: [Gretl-users] Breusch-Pagan test for Heteroskedasticity (Gretl-users Digest, Vol 100, Issue 3)

On Mon, 2015-05-04 at 18:34 +0300, Alecos Papadopoulos wrote: > Graham, > I verified using your data set that Gretl calculates correctly the > Breusch-Pagan LM test for heteroskedasticity, as described in the > original paper, > > > A Simple Test for Heteroscedasticity and Random Coefficient Variation > Author(s): T. S. Breusch and A. R. Pagan > Source: Econometrica, Vol. 47, No. 5 (Sep., 1979), pp. 1287-1294 > Published by: The Econometric Society > Stable URL: http://www.jstor.org/stable/1911963 > > The auxiliary regression is performed using the scaled squared > residuals as Dependent variable (as indicated in the Gretl's output), > and the statistic is 0.5*R^2*(Total Sum of Squares of the Dependent > Variable), the R^2 from this auxiliary regression, where I used the > exact same regression matrix of the main regression (constant + the > three regressors) > > The scaling of the squared residual series is by the maximum > likelihood estimator for the variance from the original model, ie. sum > of squared residuals divided by nobs (not nobs-1). > > Maddala's Econometrics textbook (2001, 3d ed. pp 205-207) explains > the relation of the above statistic with the approach you implemented > (correctly) by hand, which is the "usual" way to obtain an LM > statistic. > But these are only asymptotically equivalent, and in practice the > estimated sigma^4 is involved, whose estimation is seriously biased in > any case for samples much larger than yours. > > So I do not think there is any bug or computational mistake involved, > just an (educative) case of asymptotic equivalence not materializing > at finite-sample level. > Personally I would go with the original Breusch-Pagan test statistic. OK, thanks everybody. I think I get it, and sorry for not going back to the source. What brought this up was a student using both the White and Breusch-Pagan tests and seeing (as you do) completely different P- values for each (0.485 vs 0.000360) So, how can I explain that to him? I initially thought there had to be a mistake since in my mind the Breusch-Pagan test was just the White test with some interaction terms taken out, but I see now that's not the case.