Fixed vs Random vs Pooled OLS

[Louis And]

Hello, I am currently new to Stata and this forum as I am now writing my thesis. I am currently trying to arrive at a decent model but have some trouble choosing between a fixed and random model or OLS. The data is in panel form and consists of 4289 observations.

I did a test for heteroskedasticity and it showed that I should use robust standard errors, which I have done from now.

When I use xtreg with robust random effects, my sigma_u is 0 and xttest0 also shows that random effects are not present which means that pooled OLS is preferred over a random effect model if I have understood it correctly?
Moreover, when i use xtreg, fe, the F-test is significant, and a rhausman (rhausman) is also significant, which indicates that a fixed effect model is preferred both over pooled OLS and a random effect model?

However, when i conduct a fixed effect model, all my country dummy variables disappear (which are my only dummy variables), and my R-squared is a lot lower than it is with a pooled OLS and random effects model:

R-squared adjusted with Pooled OLS:
0.7819

R-squared with random effects:
Within = 0.2839
Between = 0.9769
Overall = 0.7832

R-squared with fixed effects:
Within = 0.3069
Between = 0.0947
Overall = 0.0009

Is fixed effect the way to go in this case even though the R-squared is lowered a lot? Why do they decrease so much when I use a fixed effect model?

Sorry for writing everything in a text. I tried to use -dataex- to display each regression but I kept getting this error message every time: "input statement exceeds linesize limit. Try specifying fewer variables"

Kind Regards,
Louis

[Carlo Lazzaro]

Louis:
welcome to this forum.
1) if you need non-default standard errors, you cannot use -hausman- to choose between -fe- and -re- estimator. You should consider the community-contributed module -xtoverid- (type -search xtoverid- from within Stata and follow the instructions to install it);
2) please note that -xtoverid- test the null "-re- is the way to go". Therefore, you should go -xtreg,re vce(cluster panelid)- and then run -xtoverid-;
3) being a bit old-fashioned, -xtoverid- does not support -fvvarlist- notation. See -xi:- prefix as a possible work-around;
4) you should look at R_sq within and R_sq between when you go -fe- and -re-, respectively
5) as expected, the -fe- estimator wiped out all your time-invariant variables.

[Louis And]

Hi!

Thank you very much for all the help Carlo! Why would -rhausman-, which I've understood works as a robust hausman test, not work in this situation?

Kind Regards,
Louis

[Carlo Lazzaro]

Louis:
yes, you can use the community-contributed -rhausman-.
Oftentimes, advice are driven by personal habits or tastes .

[Louis And]

I see, thank you very much Carlo!

I have one last question. If I have time-invariant dummies that are omitted in a fixed effect model, but stay in a random effect model and want to use -xtoverid- or -rhausman- to see which model is preferred, should I conduct the test when excluding the dummies as they won't be included in the fixed effect model? For example:

xtreg gscore env dummy1 dummy2, re vce(cluster id)

estimates store re

xtreg gscore env dummy1 dummy2, fe vce(cluster id)

estimates store fe

rhausman re fe, cluster

Since the time-invariant dummies (lets say dummy1 and dummy2) will all be omitted in the fixed effect model, will that in some way affect the robust hausman test? How would I do in this situation?

[Carlo Lazzaro]

Louis:
what follows refers to the community-contributed module -xtoverid-, as I am not familiar with -rhausman-:
Go:

xi: xtreg depvar indepvars, re vce(cluster clusterid)
xtoverid

1) the -xtoverid- null is: -re- is the way to go.
2) the -xi:- prefix takes categorical variables into account, as -xtoverid- does not support -fvvarlist- notation;
3) do not delere time-invariant predictors, as the -re- estimator returns a coefficient for each one of them.

[Louis And]

Hi,

I keep getting this message: "Error - saved RE estimates are degenerate (sigma_u=0) and equivalent to pooled OLS"

Does this mean that I should instead look at the F-test for my fixed effect model to decide whether to use fixed effect over pooled OLS/random effects?

[Carlo Lazzaro]

Louis:
it means that you should go pooled OLS.