Heteroskedasticity - Breusch–Pagan test

[Gabriele More]

Dear Stata community!


I am running the three Breusch–Pagan tests versions most common in Stata (estat hettest estat hettest, iid estat hettest, fstat). While for the estat hettest there seems to be heteroskedasticity, the other two commands (to my understanding they appear more generalised forms of BP test) show no evidence of heteroskedasticity. I cannot understand why and what to do to be honest... which of the three test should I go for (i have a stock market event study and analysing the corss-section returns).


Thank you for your explanations!
Gabriele

Breusch–Pagan/Cook–Weisberg test for heteroskedasticity
Assumption: Normal error terms
Variable: Fitted values of CAR1

H0: Constant variance

chi2(1) = 9.71
Prob > chi2 = 0.0018

. estat hettest, iid

Breusch–Pagan/Cook–Weisberg test for heteroskedasticity
Assumption: i.i.d. error terms
Variable: Fitted values of CAR1

H0: Constant variance

chi2(1) = 1.81
Prob > chi2 = 0.1781

[Maxence Morlet]

In economics in general, people with cross-sectional datasets tend to simply report by default robust standard errors, even if there is no heteroscedasticity (also even if in that case, you do simply lose efficiency in estimating the variance-covariance matrix of the residuals). Another option is to report both robust and conventional OLS standard errors side by side, and comment on their differences...

[Carlo Lazzaro]

Gabriele:
as an aside to Maxences's helpful guidance, you should also take a look at the null of those tests.
Normality in error terms is less relevant than -i.i.d.-.
In addition, if you have a large sample size, a minimal departure from normality (that you may consider negligible via a visual approach) makes the warning chime rings.
That said, from time to time heteroskedasticity is the stalking horse of more critical issues, such as a wrong functional form of the regerssand.
Last but by no means least,, take a look at the wonderful teaching notes prepared by Richard Williams (

https://www3.nd.edu/~rwilliam/stats2/l25.pdf).

ETA:

https://www.nber.org/papers/w2956

[Gabriele More]

Thank you Carlo, thank you Maxence !