Breusch and Pagan Lagrangian multiplier test for random effects for Random effect heteroskedasticity

Question

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

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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/

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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.

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.