Is heteroscedasticity treated in this case?

[Jonathan Quimby]

Hello all,

I have a little problem. I am using panel data. Fixed effects have been recommended by the Hausman test. It's a balanced dataset made up of 4 panels (similar countries) and 12 years of observations.

xtserial has found autocorrelation, for which I have accounted by using robust.
xttest3 has found heteroscedasticity. I am now unsure whether it is okay enough - based on Clyde's comment, the robust-ed model should work well despite it - or whether I should employ xtgls y x1 x2 x3, panels(heteroskedastic).

Can anyone help me, please? Any thought appreciated!

[George Ford]

robust won't fix autocorrelation.

cluster would be ideal, but too few clusters.

panels(correlated) would handle both, but not sure whether it suffers from the same problems as cluster.

[Jonathan Quimby]

Thank you for your answer, George.

May I ask about the "robust"? I thought this was the purpose of the command, to account for autocorrelation?

I shall research panels(correlated), hopefully i will find something.


If anyone else can offer their two cents still, I would be more than happy.

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Edit: I have found an interesting thread where, if I read it correctly, Jeff explains that using xtscc could account for both. I shall research the command more and update this comment after.
It seems to be exactly what I would need, except it generall works for large T samples - or, as Carlo notes, "small N, Large T; large N, small T; large N, large T".
I am not experienced enough in statistics to develop the needed intuition, but I feel my model is small N, small T, is it not? Does anyone know? Sadly, this would mean I can not use the command.

Edit2: I apologize for my confusion, I have mixed two similar regressions I am currently performing. All remains the same, except that THERE ARE 23 CONTRIES AND 12 YEARS OF OBSERVATIONS. I fear it is still small N, small T...

[Carlo Lazzaro]

Jonathan:
as an aside to George's helpful reply, there's a difference between -regress- and -xtreg- (that was conceived for N>T panel datasets):
1) -regress-: -robust- handles heteroskedastcity, whereas -vce(cluster clusterid)- takes autoccorrelation into account. In case you have both (and heteroskedasticity cannot be fixed by a transformation of the dependent variable), I woud go -vce(cluster clusterid);
2) -xtreg-: both the options invoke the clustered robusta standard errors, that take heteroskedasticity and/or autocorrelation into account.

[Jonathan Quimby]

Carlo:
Thank you very much for your input.

It appears that using the xtreg with fe -vce(r) does the same as xtreg with robust fe. My question is that I now feel there is some contradiction in this thread - that is, around either of these commands ensuring the regression is truthful despite heteroskedasticity and autocorrelation. I feel that while both you and Clyde support this ability, George contradicts it. May I ask you to shed some light onto this, please?


If i may inquire further - on a somewhat unrelated note - I am currently learning more about what to do with my with the first mentioned research (N=4, T=12). From what I have found on this forum (for which I am eternally grateful to you and to prof Wooldridge), it seems the best to simply use the regress command. Before that, I used the xtoverid, which returned the "saved RE estimates are degenerate (sigma_u=0) and equivalent to pooled OLS", after all. Considering the small N and small T, this would truly be the optimal way to go, is it not?

[Carlo Lazzaro]

Jonathan:
1) it's true that -xtreg, fe robust- = -xtreg, fe vce(cluster clusterid)-;
2) it may be that George had -regression. in mind when he replied. Actually, you can run the -fe- estimator from -regress- by adding the -panelvar- as a categorical predictor (despite this approach is much more computationally intensive than -xtreg,fe-);
3) as per 2), -regress. won't be my first choice in dealing with panel datasets;
4) the outcome of the community-contributed module -xtoverid- (as FAQ kindly requests you to mention non-official but approved commands) tells that you might not have a panel-wise effect. If that were the case, you should go pooled OLS, adding -vce(cluster panelid)- standard errors because the observations belonging to the same panel are not independent and Stata is not aware that you're performing a panel data regression;
5) If I had 1/1000 of Jeff Wooldridge 's knowlegde on econometrics, I would be really happy. I learnt enormously from his textbooks and posts and I'm still learning.

[Jeff Wooldridge]

Jonathan: You have very little data. You can't justify anything beyond a basic two-way fixed effects with the usual standard errors and inference -- and hope the classical linear models are roughly satisfied. You can't trust any asymptotic tests, such as xtoverid. And even robust standard errors are suspect.

[Jonathan Quimby]

Thank you both for your inputs.

Jeff, you said aloud exactly what I was afraid of since the very conception. I suppose I shall simply focus on the slightly larger dataset for now.

I wish you all a beautiful day.

[Ramiro Flores]

Hi everyone, Hi dear Prof @Jeff Wooldridge
can someone please help me with one opinion?
Continuing with heteroskedasticity in a fixed effects model, I have 2,182 groups and T = 3 separated by five years (2010, 2015 and 2020). Can I apply the Wald Heteroscedasticity Test (XTTEST3 command) or is better to plot residual versus predicted?
Greetings Ramiro Flores

[Jeff Wooldridge]

Ramiro: No need to test. Just cluster by group.

[Ramiro Flores]

Thanks dear Prof@Jeff Wooldridge

Greetings Ramiro Flores