Pooled OLS and Random Effects

[Pepito Grillo]

Hello everyone,
Was just concerned as I have a set of panel data obvservations, and when running regressions I find that I get the same results for the normal OLS (which i suppose to be Pooled OLS regression) and the Random Effects regression. Is this possible and if so what does it mean? Or am i doing something completely wrong?
Here is my code
**OLS**
reg gincdif1 Immigrationfromforeigncountri RegionalDebtGDP1 UnemploymentRate lnRGDP,
** Fixed Effects**
xtreg gincdif1 Immigrationfromforeigncountri RegionalDebtGDP1 UnemploymentRate lnRGDP, fe
estimates store fixed
** Now we run a Random Effects**
xtreg gincdif1 Immigrationfromforeigncountri RegionalDebtGDP1 UnemploymentRate lnRGDP, re

And here the results
. ** OLS reg **
. reg gincdif1 Immigrationfromforeigncountri RegionalDebtGDP1 UnemploymentRate
> lnRGDP,

Source | SS df MS Number of obs = 68
-------------+---------------------------------- F(4, 63) = 4.33
Model | .416390252 4 .104097563 Prob > F = 0.0037
Residual | 1.51345595 63 .02402311 R-squared = 0.2158
-------------+---------------------------------- Adj R-squared = 0.1660
Total | 1.9298462 67 .028803675 Root MSE = .15499

------------------------------------------------------------------------------
gincdif1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Immigratio~i | .020578 .0072703 2.83 0.006 .0060495 .0351065
RegionalDe~1 | -.5074746 .2396663 -2.12 0.038 -.9864096 -.0285397
Unemployme~e | -1.27616 .4877509 -2.62 0.011 -2.250852 -.3014674
lnRGDP | -.3935338 .1557389 -2.53 0.014 -.7047532 -.0823145
_cons | 6.050379 1.620674 3.73 0.000 2.811721 9.289037
------------------------------------------------------------------------------

.
.
.
. ** Fixed Effects**
. xtreg gincdif1 Immigrationfromforeigncountri RegionalDebtGDP1 UnemploymentRa
> te lnRGDP, fe

Fixed-effects (within) regression Number of obs = 68
Group variable: Region1 Number of groups = 17

R-sq: Obs per group:
within = 0.2074 min = 4
between = 0.0528 avg = 4.0
overall = 0.0723 max = 4

F(4,47) = 3.07
corr(u_i, Xb) = -0.7899 Prob > F = 0.0249

------------------------------------------------------------------------------
gincdif1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Immigratio~i | .0029911 .0303781 0.10 0.922 -.0581217 .0641039
RegionalDe~1 | -1.058942 .7713853 -1.37 0.176 -2.610769 .4928855
Unemployme~e | -1.353692 1.204872 -1.12 0.267 -3.777583 1.070198
lnRGDP | .2214223 .899801 0.25 0.807 -1.588744 2.031588
_cons | .0838402 8.926705 0.01 0.993 -17.87437 18.04205
-------------+----------------------------------------------------------------
sigma_u | .14660047
sigma_e | .16457669
rho | .4424237 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(16, 47) = 0.55 Prob > F = 0.9009

. estimates store fixed

. ** Now we run a Random Effects**
. xtreg gincdif1 Immigrationfromforeigncountri RegionalDebtGDP1 UnemploymentRa
> te lnRGDP, re

Random-effects GLS regression Number of obs = 68
Group variable: Region1 Number of groups = 17

R-sq: Obs per group:
within = 0.1955 min = 4
between = 0.3172 avg = 4.0
overall = 0.2158 max = 4

Wald chi2(4) = 17.33
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0017

------------------------------------------------------------------------------
gincdif1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Immigratio~i | .020578 .0072703 2.83 0.005 .0063285 .0348275
RegionalDe~1 | -.5074746 .2396663 -2.12 0.034 -.977212 -.0377373
Unemployme~e | -1.27616 .4877509 -2.62 0.009 -2.232134 -.3201856
lnRGDP | -.3935338 .1557389 -2.53 0.012 -.6987764 -.0882912
_cons | 6.050379 1.620674 3.73 0.000 2.873917 9.226841
-------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | .16457669
rho | 0 (fraction of variance due to

Many thanks
Pepito

[Clyde Schechter]

Look carefully at your random effects output:

Random-effects GLS regression Number of obs = 68
Group variable: Region1 Number of groups = 17

R-sq: Obs per group:
within = 0.1955 min = 4
between = 0.3172 avg = 4.0
overall = 0.2158 max = 4

Wald chi2(4) = 17.33
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0017

------------------------------------------------------------------------------
gincdif1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Immigratio~i | .020578 .0072703 2.83 0.005 .0063285 .0348275
RegionalDe~1 | -.5074746 .2396663 -2.12 0.034 -.977212 -.0377373
Unemployme~e | -1.27616 .4877509 -2.62 0.009 -2.232134 -.3201856
lnRGDP | -.3935338 .1557389 -2.53 0.012 -.6987764 -.0882912
_cons | 6.050379 1.620674 3.73 0.000 2.873917 9.226841
-------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | .16457669
rho | 0 (fraction of variance due to

When sigma_u is 0, that means that all of the random effects were estimated to be 0. Otherwise said, the analysis finds no variation at the Region1 level that is not already explained by the fixed effects in the model. It follows that the random effects and OLS results will be identical.

[Pepito Grillo]

Thank you, in terms of them interpreting results, what does this actually mean? is using the results from random effects regression a plausible approach considering the Hausman test gives a 0.9375? Just not too sure how I can explain why both the results of the regression are the same? Or do I have to choose different control variables?
Many thanks
Pepito

[Clyde Schechter]

Since the RE and OLS results are the same, it makes no difference which one you use. The explanation why both results are the same is what I said in #2--there is nothing more to say about it.

Personally, I do not usually rely on Hausman or other statistical tests to select models; I prefer to select models a priori and then perhaps modify them after seeing how they fit the data. If you are going to rely on the Hausman test, the fact that the random effects came out to zero makes no difference--the Hausman test discriminates between FE and RE; the fact that RE turns out to be the same as OLS in your case is irrelevant.

If you think that it is not plausible that all region level variation is explained by your covariates, then that might be reason to change your model. But before doing that, I would go back and double-check that the data is correct. It may be that the zeroing out of the random effects is due to data errors. After you have verified the correctness of the data, if you want to use different covariates, then you should change the model in some theoretically justifiable way.

[Pepito Grillo]

Perfect, thanks a lot for your help!

[Pepito Grillo]

Sorry to be asking once again, but could you explain what you mean by "

If you think that it is not plausible that all region level variation is explained by your covariates" not too sure what are the covariates?
I hope this is not too much disturbance,
Thanks
Pepito

[Clyde Schechter]

I use the term covariates to mean what you call "control variables." I don't like the term "control variables" because in most contexts we are working with observational data and we have not "control"led those variables, nor can any analysis "control" them--we are simply attempting to adjust for them. In a true experimental situation where we actually control things, then the use of the term "control variable" strikes me as helpful.

Yes, it's a pedantic point. But I firmly believe that sloppy use of language leads to sloppy thinking, which seldom ends well.