Panel data: OLS, Fixed Effects or Random Effects

[Konrad Meier]

Hello,

I have an (almost balanced) panel data-set with around 240 firm-year observations. It includes 16 firms over 15 years and I am testing certain variables regarding their impact on different financial performance indicators, e.g. ROS, ROA and turnover (dependent variables). Now I have four key questions regarding potential regression analyses:
1. I would prefer a normal OLS for the analyses. Is that ok to use or do I have to use panel regressions (like fixed or random effects models) with time-series data?
2. If panel regressions are necessary, how to decide between FE and RE? Is there only the Hausman test to use?
3. Depending on the dependent variable the test suggests RE for some models and FE for others, which makes overall interpretation of result rather difficult. Any advice on how to resolve this issue would be highly appreciated.
4. With both RE and FE regressions, would I need to include a time variable?

Many thanks in advance for any help and advice!

Regards

[Carlo Lazzaro]

Konrad:
welcome to this forum.
1) it's rare that pooled OLS outperforms -xtreg-, which remains the first choice whenever it comes to panel data regression;
2) -hausman- works if you have default standard errors (SEs); the user-written programme -xtoverid- (type -search xtoverid- from within Stata to spot it and install) works with the remaining SEs modes;
3) any regression model shoud give a fair and true view of the underlying data generating process: see what others did in the past in your research field;
4) if you mean: should I -xtset- my data including a panel variable, too?, this is not mandatory, unless you plan to use time-series commands; if you mean: should I include, say, -i.year- (take a look at -help fvvarlist- for factor notation) among my predictors?, you can add it and test whether it's significant via -testparm- after you run the panel data regression.

[Konrad Meier]

Many thanks, Carlo. That was very helpful!

[Amin Sofla]

I think that Carlo's comments are very insightful. In addition, I am a little bit suspicious about your sample size. I speculate that, given the number of observations, FE is not a right choice (even though the Huasma's test often favors it).

[Konrad Meier]

@Amin: Thanks for your additional input. What is the threshold sample size for FE or RE respectively?
Regarding point 3:
a. So far the Hausman test suggests RE for two of the three models and FE for the other one (models differ in terms of dependent variables used). Regression results are quite different though whether I use FE or RE. Would you recommend to stay with the recommended approach from the Hausman test for each model or go with RE for all models (e.g. due to sample size)?
b. The result from the Hausman test are also quite sensitive to independent variable selection. e.g. if I add additional variables, Hausman changes its recommendation. What would you suggest?

[Amin Sofla]

I do not know about the required sample size for fe or re but I have observed that sample size affects the results: Please see the attached files. In the files, the pooled, re and fe are being simulated for 16 and 1600 firms respectively. I borrowed the simulation code from here: http://www.econometricsbysimulation....-fe-vs-re.html
I think that both theory and Hausman should be your main criteria for the decision making regarding pooled, re or fe.