I'm really confused about Breusch and Pagan Lagrangian multiplier test for random effects.

The command in stata is xttest0.

Some say it is a test to choose between random and fixed effects and simple OLS

refer to slide NO 32 http://www.princeton.edu/~otorres/Panel101.pdf


And some say it is a test for heteroskedasticity in random-effects model.

look at figure 2 https://www.projectguru.in/panel-data-regression-random-effect-model-stata/


I have searched all the web to find how to do heteroskedasticity test for random effects model in Stata, but simply there is no clear answer that is agreed by all.


1 Answer 1


The second site you cite looks a bit suspicious: It mentions normality of the data set but I feel like the author wanted to say normality of residuals.

Please note there are two papers by Breusch/Pagan with a "Breusch-Pagan test":

1) Breusch, Pagan (1980). “The Lagrange Multiplier Test and Its Applications to Model Specification in Econometrics.” Review of Economic Studies, 47, 239–253.

2) Breusch & Pagan (1979), A Simple Test for Heteroscedasticity and Random Coefficient Variation. Econometrica 47, 1287–1294

The first is implemented by xttest0 in Stata (and in R in plmtest of package plm). The second in Stata by hettest (and in R in bptest of package lmtest) and - I believe - cannot readily be applied to panel models.

The 2nd webpage seems to confuse both tests/use cases.


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