Fixed Effects Model vs. Random Effects Model vs. OLS

[Tommy Fosch]

Dear all,

I have some serious trouble when analyzing the panel data I attached to this post. I assume for some of you it's pretty basic so I'm really hoping for any help.

I want to figure out which of the three models fit best to analyze this panel data (cross-sectional time-series data). For that reason, I know that I have to run several tests:

1. OLS vs. Fixed Effects Model: F-test
2. OLS vs. Random Effects Model: Lagrange multiplier test
3. Random vs. Fixed Effects Model: Hausman test

Some facts about the data:

Dependent variables: ROE, ROA, NIIR, StockReturn
Independent variable: Hybrid
Control variables: SizeTA/SizeGWP, RiskBeta
Time period: 2009-2014
N=39

I have run the F-test (OLS vs. FEM) for the dependent variable ROE (as an example). Command: .xtreg ROE Hybrid SizeTA RiskBeta, fe
Then, there are two F-tests stated, one above the table and one under the table. Which one is the one I have to look at?

After that I have run the Lagrange multiplier test (OLS vs. REM). Command: .xtreg ROE Hybrid SizeTA RiskBeta, re; .xttest0
So, if Prob>chi2=0.05 the REM is to be preferred, correct?

Lastly, I ran the hausman test (FEM vs. REM). Command: hausman fixed random
Then, there is this kind of error message:
“the rank of the differenced variance matrix (2) does not equal the number of coefficients being tested (3); be sure this is what you expect, or there may be problems computing the test…”. There is also something mentioned with “not positive definite” on the bottom. How to deal with that? Does that mean the test is not applicable?


However, I think that the Fixed Effects Model is the one to be applied here but, of course, I have to proof it with the above-mentioned tests. When I used the Random Effects Model there is always no chi2 test result to assess the significance of the test. Thus, I guess this model is not appropriate here.

Maybe someone can run the example with the dependent variable ROE by using the stata file I attached. I would really appreciate any help as soon as possible.

Many thanks in advance!

Best,
Tommy

[Carlo Lazzaro]

Tommy:
a previous thread focused on a similar topic (please, see http://www.statalist.org/forums/foru...d-with-haumsna).
Repeating the hausman test with the -sigmamore- option (please, see -help hausman-) and checking if the outcome is still the same is worth trying.
Eventually, you may want to google with the following string: -augmented regression AND vince wiggins- for a possible solution to your problem.

[Tommy Fosch]

Carlo,

Thanks for your fast response.

However, using the -sigmamore- option does not lead to any improvement. There is still the problem with "V_b-V_B is not positive definite".

As you suggested, I also googled for -augmented regression AND vince wiggins- and found his thread:
http://hsphsun3.harvard.edu/cgi-bin/...rticle-54.html

Nevertheless, it is really outdated (from 2003) and I don't really understand how to perform this augmented regression. Could you please help me with this as I think it could lead to a solution?

Many thanks,
Tommy

[Carlo Lazzaro]

Tommy:
you may want to take a look at -help suest- and related entry in Stata 13.1 .pdf manual.
Otherwise, you may be interested in the following user-written programme on robust Hausman test, that you can access via -net describe rhausman-.

[Tommy Fosch]

Carlo,

The function -suest- does not support xtreg. I don't know anything else than xtreg.

Further, there is an error message regarding the robust Hausman test:

. net describe rhausman
file http://www.stata.com/rhausman.pkg not found
could not load rhausman.pkg from http://www.stata.com/
r(601);

Any suggestions?

Thanks and best,
Tommy

[Rich Goldstein]

try "which hausman" rather than "net describe"

[Sebastian Kripfganz]

Replace net by ssc:

ssc describe rhausman

[Tommy Fosch]

Many thanks to you all.
However, after running the rhausman test, there is a warning message (see picture attached).
Do I have to worry about that or can I just assume that the random effects model is here the one to be preferred?

Best,
Tommy

[Carlo Lazzaro]

Tommy:
the warning message may depend on the scale of your coefficients.
I do not know if variance-covariance matrix can be obtained after -rhausman- so that you can see where the cuplrit hides (probably, it is the same culprit that creeped up in standard -hausman-test).
Anyway, I would give -rhausman. another try, imposing clustered standard errors and see if the warning message pops up again.
Eventually, you may also want to inspect your database to spot any possible oddity about your data.

[Tommy Fosch]

Carlo,
Clustering did not lead to any improvement. I had a look at the descriptive statistics again and all variables show a (more or less) normal distribution, except one (see file attached). This variable represents the size of the companies and is used as a control variable. The distribution is highly skewed to the right and does not indicate any normal distribution. But isn't that natural for size? When I exclude this variable in the analyses, there are no error or warning messages any more and the results look fine. I want to include this variable though. What could I do about that?

[Carlo Lazzaro]

Tommy:
please report everything you typed and obtained in Stata format (i.e., .dta vs .xlsx). Please consider that many listers (me too) do not open .xlsx files due to the risk of downloading active contents.
That said, you have different options to choose among:
- do not include -company size- among predictors (I would go this way);
- categorize -company size- in a different way and see if the problem still remains;
- transform -company size- and see if the problem still remains.

[Tommy Fosch]

Carlo,
I classified the variable company size into three equally-sized classes and now the results look fine without any error messages.
Many thanks for your support!

Best regards,
Tommy

[Tommy Fosch]

I have just another question regarding the performance of a likelihood ratio test (lr-test).

When using the -xtreg- command there are no log likelihood estimators generated and stored which are required for running the lr-test afterwards.
I know that for the command -xtgls- those estimators are generated and stored which makes it possible to run the lr-test.

As I have to use the xtreg function, do you know if there is a way to generate and store those log likelihood estimators?

Thanks and best,
Tommy

[Marcos Almeida]

Hello Tommy,

Please take a look on this: http://www.stata.com/manuals13/xtxtr...estimation.pdf.

You may try - estimates store - followed by - lrtest.

Best,

Marcos

[Tommy Fosch]

Marcos,

After running the model, I stored the estimates with -estimates store- but the problem is that there are no log likelihood estimates to store. Thus, the lr-test cannot use them.

Best,
Tommy