Panel Regression: FE vs. RE

[Claire Noh]

Dear Statalists,
I have an unbalanced panel dataset of companies and below are the fixed effect and random effect results, respectively. For the sake of space, I did not copy the results of year dummies.

Since the p-value of the F-test in FE results is 0.00, I believe FE is better than pooled OLS. And Hausman test warrants the use of FE over RE.

When you compare the results, however, the coefficients of B and G are significant in FE model whereas the coefficients of B, D, F, and G are significant in RE model.
So, I'm a bit confused about 1) what could lead to the differences in the results and want to 2) make sure my FE results are still better (and right to go with) despite the lack of statistical significance. Related, 3) is a study model with many insignificant coefficients considered as a pool and/or wrong model? By the way, the variables from D to H below are control variables, which are commonly used in the literature.

Thank you in advance for your time and advice!



. xtreg A B C D E F G H i.year, fe vce(robust)
Group variable: company Number of groups = 309
Obs per group: min = 1
max = 25
avg = 9.3
R-sq: within = 0.2046
overall = 0.0874
between = 0.0034

corr(u_i, Xb) = -0.0282
Prob > F = 0.0000
F(31,308) = 6.34


Fixed-effects (within) regression Number of obs = 2882
(Std. Err. adjusted for 309 clusters in company)
--------------------------------------------------------------------------------

A | Coef. Robust Std. Err. t P>|t| [95% Conf. Interval]
---------------+----------------------------------------------------------------
B | .1137271 .0395757 2.87 0.004 .0358543 .1916
C | .050245 .0660763 0.76 0.448 -.0797731 .1802631
D | .0030506 .0027086 1.13 0.261 -.002279 .0083803
E | .0083115 .0122413 0.68 0.498 -.0157756 .0323986
F | .0054892 .0175333 0.31 0.754 -.0290111 .0399895
G | -.0065673 .0027959 -2.35 0.019 -.0120689 -.0010658
H | .0112696 .0226106 0.50 0.619 -.0332212 .0557604


. xtreg A B C D E F G H i.year, re vce(robust)

Group variable: company Number of groups = 309
Obs per group: min = 1
avg = 9.3
max = 25
R-sq: within = 0.1875
between = 0.2364
overall = 0.2648

Wald chi2(31) = 219.10
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

Random-effects GLS regression Number of obs = 2882
(Std. Err. adjusted for 309 clusters in company)
--------------------------------------------------------------------------------
Robust
A| Coef. Robust Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
B| .1500873 .0380758 3.94 0.000 .0754601 .2247145
C| .02084 .0660701 0.32 0.752 -.1086551 .1503351
D| .0121775 .0016794 7.25 0.000 .0088859 .0154691
E| .010765 .0087428 1.23 0.218 -.0063706 .0279007
F| -.0433489 .015078 -2.87 0.004 -.0729012 -.0137966
G| -.005582 .0026169 -2.13 0.033 -.0107111 -.0004529
H| .0206136 .0157302 1.31 0.190 -.0102171 .0514443

[Carlo Lazzaro]

Claire:
how could you run -hausman- with cluster-robust standard errors when -hausman- allows default standard errrors only?.
Please note that running -hausman- with default standard errors and invoking cluster-robust standard errors afterwards is not correct.
The fix is to replace -hausman- with the user-written command -xtoverid- (type -search xtoverid- from within Stata to spot and install it) for choosing between -fe- and -re- specification.
As an aside, please note that hunting for the best model (whatever that may mean), is not the way to go: try to give a fair and true view of the data generating process instead.

[David Benson]

Claire,

Based on what you wrote, it sounds like you should go with the FE. When choosing between fixed effects and random effects , fixed effects are always appropriate. What the Hausman test tells you is whether you can appropriately substitute the more efficient random effects model. See the discussion at https://www.stata.com/statalist/arch.../msg00595.html

[Carlo Lazzaro]

David:
the -hausman- outcome that Claire reported cannot be reliable if non-default standard errors were invoked afterwards (as it seems from Claire's post)..