Presence of Heteroskedasticity, Autocorrelation and Cross-sectional Dependence/Contemporaneous Correlation - Panel Data

[Mohsin Javed]

I have a quarterly balanced panel data with 8 independent variables from 2000q1:2012:q2 (n=20 and T=52).

I start off by Pooled OLS (using -regress-) and then Fixed Effects Model (using -xtreg, fe-). Next, I check for time fixed effects and conclude that they are not needed using -testparm-.

Moving on, I run a Random Effects Model (using - xtreg , re-) and to decide between FEM and REM make use of Hausman Test. The result suggests REM.

Furthermore, I check whether REM is preferred to Pooled OLS and end up with REM.

However, I find the presence of Heteroskedasticity, Autocorrelation and Cross-sectional Dependence/Contemporaneous Correlation based on the results from - xttest3- , - xtserial- and - xttest2- respectively. I have the following questions:

1. Is -xtgls- approriate in this case? Stata manual states:

" xtgls fits panel-data linear models by using feasible generalized least squares. This command allows estimation in the presence of AR(1) autocorrelation within panels and cross-sectional correlation and heteroskedasticity across panels".

2. How to test for presence of AR(1) autocorrelation within panels?

3. How to proceed ahead?

[Mohsin Javed]

Amendment:

Please ignore Q2. Alternatively, is -xtgls- independent of REM and FEM?

[Carlo Lazzaro]

Mohsin:
with a long T, small N panel dataset you can consider -xtgls- and -xtregar-.

[Mohsin Javed]

Carlo:

Thanks. Is -xtgls- for REM or FEM? In my case, Hausman Test suggests REM.

[Carlo Lazzaro]

Mohsin:
as per -gls-machinery, I would say that -xtgls- is for -re-.

[Mohsin Javed]

Carlo:

Many thanks. Is there any similar function to simultaneously correct for Autocorrelation, Heteroskedastisity and Cross Sectional Dependence using FE?

[Zahrah Rafique]

Hi Mohsin, may I ask how you tested for hetero and auto in random effects model?

[Mohsin Javed]

Zahrah:

As far as I know, tests for heteroskedasticity and autocorrelation are independent of the method of your model. You can find the commands in post #1.

[Zahrah Rafique]

Hi Mohsin,

no I think not. Whenever I run xttwst2 and xttest3, it says last estimates have to be fixed effects.

also, have you managed to find a command which removes cross sectional dependence, hetroscedadticity, and serial correlation using FE. Can it be done using xtgls?

[Mohsin Javed]

Zahrah:

As mentioned in Verbeek, it does not matter for autocorrelation and heteroskedasticity. Essentially, the heteroskedasticity command mentioned in post#1 is for FE but also holdsRE.

No, I have not been able to find that yet.

[Mohsin Javed]

Zahrah:

Check -xtscc- to tackle this problem.