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.

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.