Comparison between regressions with and without autocorrelation

[Julia Raciniewska]

Hello! I am using a panal data for N=11 and T=12, and I am using fixed-effect models for each of 3 of my dependent variables. I have 2 questions:
1) After runing the -xtserial- it turns out one has first-order autocorrelation. Does it still allow me to compare coefficients between the 2, after using -vce (cluster clustvar)- at the end?
2) If - xttest3 - performed after -xtreg, fe- shows I have heteroskedasticity, would that be also corrected for after using vce (cluster clustvar )?

Thank you.

[Carlo Lazzaro]

Julia:
if you have autocorrelation and/or heteroskedasticity you should impose -cluster- or -robust- option. If you don't your inference will probably be biased. Hence, I do not think it is informative to compare the coefficients between the two models.
As you N and T dimensions are similar (N=11 and T=12), you are appraoching the limit of switching to a long panel estimator, such as -xtgls- or -xtregrar-.
The issue is that, while -xtgls- accomodates for both autocorrelation within panel (AR(1) process) and heteroskedasticity, it use a random effect estimator via generalized least square (GLS); conversely, -xtregar- allows for -fe- specification and autocorrealtion, but not for heteroskedasticity.

[Julia Raciniewska]

Carlo:
Thank you for the response. I think I didn't explain my (1) question well: I wonder whether it is better to -cluster- all regressions (even though only 1 had autocorrelation, but all 3 heteroskedasticity) and then compare coefficients between them?
In terms of GLS - if Hausman test suggested FE for all my three regressions, do you think it would be better for me to use - xtgls - with N=11 and T=12?

[Carlo Lazzaro]

Julia:
- yes, it's better to cluster the standard errors for all three regression models;
- please note that -xtgls- is a random effects estimator. Discuss with your teacher/professor/supervisor if considering a N=T estimator is the way to go instead of sticking with -xtreg,fe-.