RE model with AR(1), heteroskedasticity, and serial correlation

[Evgeny Uvarov]

Hello everyone!
My name is Evgeny and i want to ask you to help me.
In my panel data a RE model was choosen as the best model than a FE model and Pooled regression model.
I've conducted tests on autocorrelation, heteroskedasticity and serial correlation.
Those tests gave me a possitive effect of existing those problems.
Tell me please, what the procedure (command in STATA) that considers AR (1), heteroskedasticity and serial correlation???

[Carlo Lazzaro]

Evgeny:
welcome to this forum.
Please specify whether you have a long N, small T panel dataset or the other way round. Thanks.

[Evgeny Uvarov]

Carlo, I have a long N and small T.
N = 85 regions.
T = 5 years (2014-2018)

[Carlo Lazzaro]

Evgeny:
if your regressand (ie, dependent variable) is continuous, go as follows:

xtset regions years
xtreg <depvar> <indepvars> <controls>, re vce(cluster regions)

[Evgeny Uvarov]

Carlo, as well as i know the command
xtreg <depvar> <indepvars> <controls>, re vce(cluster regions)
only considers heteroskedasticity and serial correlation, but AR (1) does not consider.
Am i wrong?

[Carlo Lazzaro]

Evgeny:
see -xtreg, pa-.

[Evgeny Uvarov]

Carlo i want to thank you for usefull suggestions.

[Evgeny Uvarov]

I took a look at this information:
https://www.stata.com/support/faqs/s...tion-averaged/

Random-effects estimators (or other cluster-specific estimators) fit the model
Pr(Y_ij=1 | X_ij, u_i) = F(X_ij b + u_i) whereas population-average estimators fit the model:
Pr(Y_ij=1 | X_ij) = G(X_ij b*) The subtle point is that b and b* are different population parameters. Hence, the estimators are estimating different things. In practice, however, b and b* are often very close.
--------------------------------------

May you correct me if i am wrong:
* Zero correlation (u_i=0) makes them the same; big Var(u_i) makes the difference greater.

Therefore, if there is not a procedure to consider RE with AR (1), heteroskedasticity and serial correlation i have to choose xtreg pa, robust corr(ar1)?
Or what the test should i conduct to determine whether RE is better than PA?

[Carlo Lazzaro]

Evgeny:
the issue is that -xtreg,re- doesn't allow you to model serial correlation (whereas -xtreg,pa- does).
Moreover, -xtreg,pa- includes -robust- opstion that allows you to take heteroskedasticity into account.
Another option, although conceived for long panels, is -xtgls- that allows dealing with both heteroskedasticity and AR(1).

[Evgeny Uvarov]

But Carlo I don't understand.
For a short panel, there is no option to consider altogether AR(1), heteroskedasticity and serial correlation?
Right?

[Carlo Lazzaro]

Not that I know.

[Evgeny Uvarov]

Thank you for sharing your knowledge with me!

[Carlo Lazzaro]

Evgeny:
sorry I cannot be more helpful.
I guess that the core of the issue rests on the fact that AR(1) in short panel is not that frequent.

[Eric de Souza]

If T=5, forget about heteroscedasticity, serial correlation, etc., and robustify your sta,dard errors with the cluster option. Before you decide in favour of RE or FE, estimate the model with the cluster option and then use the robustified Hausman test to decide in favour of RE or FE. It is very rare that RE dominates FE. Also don't forget to introduce time dummies. By robustified I mean use the Correlated Random Effects (also known as the Mundlak approach) model. There have been lots of posts here in this connection. Please read up a bit on these methods. The textbook by Jeffrey Wooldridge entitled Introductory Econometrics contains a very good introduction to the whole issue. The book is in its seventh edition now.

[Evgeny Uvarov]

Thank you for all your suggestions!