Heteroskedasticity, autocorrelation problem-Fixed effect model

[Elizabeth Real]

Good Morning,

Currently I am working for my thesis with panel data where N> T (N=20 Latin American countries, T=15 ) after carrying out the hausman test to decide between Random- effect or Fixed-effect model, the result was that Fixed effect model would be better. After this, I applied some tests to verify problems of heteroskedasticity, autocorrelation such as:

xttest2 (Breusch-Pagan statistic for cross-sectional independence in the residuals)
xttest3 (heteroskedasticity)
xtcsd, pesaran abs (cross sectional independence)

All my models present problems of heteroskedasticity, autocorrelation. Thus, in order to solve these problems, I considered what I read here: https://www.stata.com/support/faqs/s...ersus-regress/
and I use the option xtreg .... fe, cluster (country). However, after re-estimating with this new option, I apply again the different tests for heteroscedasticity, autocorrelation and my models continue with the same problem. I intend to use the "xtgls" option, however, in some texts it is mentioned that this option would be better when T is greater than N and my case is N=20, T=15.

I will be very grateful for your opinion regarding what I am doing, it will be a great help.

Elizabeth.

[Carlo Lazzaro]

Elizabeth:
welcome to this forum.
- with a N>T panel datasets, -xtreg- is the way to go (hence, forget -xtgls- which is for T>N panel datasets and wouldn't be a better choice for your problems anyhow);
- you were right in clustering standard errors (SEs) to deal with both heteroskedasticity and autocorrelation; unfortunately, there's no white/black magic behind robust/clustered SEs, as these options takes heteroskedfasticity and/or autocorrelation into account, but cannot fix them, as they're related to your datasets;
- as an aside, with robust/clustered SEs, the choice between -fe- vs -re- specification should be supportedf by the user-written command -xtoverid- (type -search xtoverid- from within Stata to spot and install it), as -hausman- allows default SEs only. Obviously, comparing panel data regression models via -hausman-, selecting -fe- or -re- onn the according to -hausman- outcome and then add clustered/robust SEs is not correct.

[Elizabeth Real]

I really appreciate your help, always very useful as I was reading in several forums.

Regarding your answer, I was reading about your recommendation "Hausman test" and Robust Hausman test using "xtoverid", I have already installed it and again started to run the different regressions with the following code:

xtreg dependvar indpvar, fe cluster (country)
estimates store fixed
xtreg dependvarindpvar, re cluster (country)
estimates store random
xtoverid

Previously, with "Hausman test" the result was always the use of FE. Now with these new regressiones, -xtoverid- output tell that RE model is the way to go.

And again I will be grateful if you help me with my next questions,

1)Regarding "xtoverid" interpretations, is the null the same as standart Hausman fixed and random, that rejection of the null implies that the fixed effect is more appropiate ?

2) my analysis is regarding the impact of corruption on the economic growth of the Latin American countries (N = 20, T = 15, Data = strong balanced) and according to the -xtoverid- output will be better RE. I still have my doubts if RE is appropriate for my analysis, but the result is RE. Therefore, does it means that I will have to use the result of the code:
xtreg depnvar indepvar, re cluster (country) for the final presentation of results in my thesis?

3) Is it necessary to apply some type of heteroscedasticity test, autocorrelation after estimating : xtreg depnvar indepvar, re cluster (country)?

Thank you for your time and answer my questions.

[Carlo Lazzaro]

Elizabeth:
1) yes, although -xtoverid- follows a different route, the recomendation is the same: if p<0.05, go -fe-;
2) yes, your code with -re- specification is correct;
3) no (see my previous post).

[Elizabeth Real]

I really appreciate your help, thank you very much for your time Mr. Carlo Lazzaro.

Elizabeth,

[Carlo Lazzaro]

Elizabeth:
you're welcome.
Please call me Carlo, as everybody on (and many more off) the list do!. Thanks.

[Hiba Allagui]

Hello everyone,
I have a problem of heteroskedasticity similar to Elizabeth but I am dealing with a time dominant panel ( Years= 20, Countries= 4 ).

1/ I run a test to choose between fixed and random effects. Fixed effects turned out to be the better option.
2/ I then run a series of tests to check for heteroskedasticity, cross-sectional correlation, and autocorrelation within units. Turned out that my data structure has heteroskedastic errors.
3/ To correct for heteroskedasticity, I tried both the - xtreg depvar indepvar timetrend, fe vce (cluster years) - and the - xtgls depvar indepvar, panels (heteroscedastic) -

I don't know what to choose. Both methods don't remove heteroskedasticity, and I read that the vce option is not adaptable to a time dominant panel like the one I have. Can you please help me with this? Thank you in advance.

[Carlo Lazzaro]

Hiba:
welcome to ths forum.
1) With a T>N panel dataset, I would go:

 xtgls depvar indepvar, panels (heteroscedastic)

2) Repeating heteroskedasticity tests after imposing non-default standard errors means wasting your time, as those tests work on residual (that are what they are), whereas the non-default options tell standard errors to take heteroskedasticity into account.

[Zaman Asif]

Hiba:
welcome to ths forum.
1) With a T>N panel dataset, I would go:

 xtgls depvar indepvar, panels (heteroscedastic)

2) Repeating heteroskedasticity tests after imposing non-default standard errors means wasting your time, as those tests work on residual (that are what they are), whereas the non-default options tell standard errors to take heteroskedasticity into account.

Carlo, do you have any references for you comment no 1?

[Carlo Lazzaro]

Zaman:
welcome to this forum.
A possible reference for -xtgls- is: Microeconometrics using Stata. Revised Edition. Stata Press, 2010: 274-275.