Choosing the best model- Panel data regression analysis

[Didarul Islam]

Hi,
I am new in this forum, I read many useful comments related to panel data analysis. I am from finance background so I don't have much knowledge about econometrics so many of you may think it's a silly question.
Actually, I am working with panel data, mainly interested of the moderation effect (X and Z) which are continuous variables. My problem is can I choose OLS model instead of the Fixed effect model?

The OLS and Fixed effect models are attached:

I also ran the Random effect model, where I find the Fixed effect model is better through the Hausman test.
In my study I got expected result from the OLS model, however, it's assume that the OLS model consider the id as homogeneous where Fixed effect consider as heterogeneous. I read some paper where they select the OLS over Fixed effect model by placing F-test. Is that the correct way I can select the OLS model? If so could you please advise me some relevant materials where I can learn more about this process?

Any other advice and suggestions would be greatly appreciated.

[Chris Boudreaux]

Hi Didarul,

Since you are new to econometrics, I would advise you to pick up a text on the subject. Stata has many good options. I personally recommend, "Microeconometrics Using Stata" by Colin Cameron and Pravin Trivedi. (https://www.stata.com/bookstore/micr...ric%20methods.)

Getting to your question, there are two tests that come to my mind. First, is the choice between OLS and Fixed Effects and second is the choice between random effects and fixed effects. By the way, 'Fixed Effects' is an OLS estimator--it just measures differences within groups rather than between groups. So you are really choosing between 'Pooled OLS (POLS)' 'OLS with Fixed Effects (FE)" or Random Effects (RE). To decide between POLS and FE, Stata computes an F-test that all u_i=0, although this test does not show up with robust or cluster-robust standard errors. A rejection of the null hypothesis means that FE is preferred to POLS. Then, you can use the Hausman test to decide between RE and FE, as you mentioned.

[Didarul Islam]

Hi Chris,

I really appreciate your reply and recommending the text book.

Yes, actually I have to decide whether I should choice the POLS or Fixed effect model. I have the following F-Test:



I think the F-test indicating that the Fixed effect is the most appropriate model (please correct me if I am wrong). Is there any other test or option I can reconsider the POLS model?

Many thanks,

[Chris Boudreaux]

A statistically significant F-test that all u_i=0 indicates FE are preferred to POLS.

Without more information about your variables and research question, I'm afraid I cannot help you much more. One thing I did notice, but forgot to mention, was that you included industry fixed effects in the POLS model but not the FE model. Try including industry fixed effects with your FE model. This merely means you have a model with firm, industry, and year fixed effects.

[Didarul Islam]

Sorry Chris, on the last reply I couldn't attach the F-test result which is following:


F test that all u_i=0: F(478, 3243) = 4.89 Prob > F = 0.0000


I didn't include the the industry because it's appear as (omitted) and the coefficient, t-statistics and the P-value are same without controlling the industry effect on the Fixed effect model.

Thanks,

[Carlo Lazzaro]

Didarul:
the outcome of F test you shared confirms Chris' helpful advice that -fe- is better than pooled OLS.
What we do not know is whether you tested the -re- specification, too and compared -fe- vs -re- via -hausman-.
If -industry- is actually time-invariant, -fe-, as expected, wipes it out before doing any estimate.

[Carlo Lazzaro]

Didarul:
my mistake: you actually reported that, according to -hausman- outcome, -fe- is the way to go.
That said, you cannot use pooled OLS instead of -xtreg, fe- (if -fe- is the way to go) as they are different statistical workhorses.

[Didarul Islam]

Hi Carlos,

I really appreciate your comments, for now I will go with the fe model. Many thanks,