Problem with Fixed and Random Effects Estimation?

[reto2410]

Hello Everbody

I'm currently working with panel data in EViews 6. The dataset has 26 cross-sections and 9 years and I specified it as a pool (unstacked data) and as a panal (stacked data) for comparison. After estimating a Fixed Effect Model yit = αi + βitxit + uit (EViews is using the LSDV estimator with, in my case, 26 dummy coefficients for the individual effects) which in the output can be interpretet as a diffenrence from the overall constant c.
Is it correct, that it by using the Within-estimator it would not be possible to calculate the 26 dummy coefficients for the individual effects, because these individual effects would be wiped out by differencing the Model with its average over time?

My question is about the way Eviews estimates the Random Effects Model. I thought that there are no individual effects, so why does Eviews reports 26 coefficients and how do I have to interpret these? And why does EViews always include an overall constant when estimating a Random Effects Model?

Thanks for any answer.

[EViews Glenn]

I'm afraid that I may not quite understand the question, but let me take a crack at an answer anyway.

For panel structured workfiles, we do not report the estimates of the fixed or random effects unless requested. These estimates are provided in pooled estimation. The random effects that we do report when asked are the best predictors of the realized values. As to the fixed effects, these are the estimates of the effects. As to why we are able to obtain estimates, you should note that the within estimator is simply a computational trick that allows you to get the beta coefficients without inverting the full dummy augmented moment matrix. The corresponding estimates of the fixed effects may be obtained using the within beta and a bit of linear algebra.

[reto2410]

Thanks for your answer Glenn. It helped a lot.

Still one more thing about the RE specification in a Panel or a Pool. Is it possible to estimate the Panel with a cross-section random effect without an overall constant. The idea is to use something like log(y) log(x) as equation specification. If I estimate this, EViews always reports a constant c in the estimation output. I want to use the equation for forecasting and I don't understand how to include eighter the reported constant (which I do not want to be estimated) or these so called "random effects cross" coefficients.

For a better understanding, here the two outputs. One as a Panel and one as a Pool. Both automatically reported with a constant (why this?)

Panel:

Dependent Variable: LOG(y)
Method: Panel EGLS (Cross-section random effects)
Date: 01/29/10 Time: 09:26
Sample: 1998 2006
Periods included: 9
Cross-sections included: 26
Total panel (balanced) observations: 234
Swamy and Arora estimator of component variances
White diagonal standard errors & covariance (d.f. corrected)

Coefficient Std. Error t-Statistic Prob.

C -3.140006 0.613121 -5.121344 0.0000
LOG(x) 1.099976 0.065874 16.69810 0.0000


Pool:

Dependent Variable: LOG(y)
Method: Pooled EGLS (Cross-section random effects)
Date: 01/27/10 Time: 12:03
Sample: 1998 2006
Included observations: 9
Cross-sections included: 26
Total pool (balanced) observations: 234
Swamy and Arora estimator of component variances
White diagonal standard errors & covariance (d.f. corrected)

Variable Coefficient Std. Error t-Statistic Prob.

C -3.140006 0.613121 -5.121344 0.0000
LOG(X) 1.099976 0.065874 16.69810 0.0000
Random Effects (Cross)
AI--C 0.193328
AR--C -0.284460
AG--C -0.345554
BEKL--C -0.231636
BLKL--C -0.276574
BS--C -0.006762
FR--C 0.166876
GE--C 0.507761
GL--C 0.189188
GR--C -0.349764
JU--C -0.007411
LU--C -0.142113
NE--C 0.587351
NW--C 0.122525
OW--C -0.401963
SG--C -0.414304
SH--C 0.487648
SO--C -0.278842
SZ--C 0.522771
TG--C -0.137234
TI--C 0.163391
UR--C 0.006614
VD--C -0.037254
VS--C -0.920931
ZG--C 0.944373
ZH--C -0.057022

Thanks for an answer.

[EViews Glenn]

The constant is required in estimation (and in a particular sense)...

In a deep sense, you obviously do not need an overall constant. In this case, the non-zero constant term will get absorbed in each of the individual effects estimates (much as it would be in a fixed effects estimator where the resulting effects are expressed as deviations from the overall mean). So in this sense, it really doesn't matter whether you have one or not.

The conceptual problem comes when you try to do forecasting for a "cross-section" that is not one of the existing cross-sections. In this case, with a constant in the model, a natural estimator of the realized random effect for forecasting would be zero. If you don't have a constant in the model, the effects estimates don't have a natural location, and so it is not clear what one would set the effect to for forecasting.

The way you would do forecasting in the constant included world is to set a base equal to the results with the constant and no effects, and then just add the predicted effect for each cross-section.

In your case, the composite constant term for cross-section AL would simply be

-3.140006 + 0.193328

For a mythical ZZ, it would simply be

-3.140006

Note that if you make a model out of your estimated pool object, EViews will create the appropriate specification for you...

[Khatai]

Hello

I am doing a panel data analysis for two and three countries, seperately. However, when I want to apply random effects model in order to use Hausman test, E-Views 8 give me an error messagr: "random effects estimation requires number of cross sections number of coefs for between estimator". What does this mean? And how can I handle this issue?

Thanks for your help....

[EViews Gareth]

You need more cross-sections.

[Khatai]

What should I do? Could you give me more detailed information, please?

[EViews Glenn]

Part of the random effects estimation procedure involves the equivalent of estimating a between estimator in which you run a regression using the cross-section means. If you have fewer cross-sections than the number of coefficients in your model it is impossible to do so (just as if you were trying to estimate a linear regression model with 5 coefficients and 4 observations).

As Gareth said, to estimate the random effects model, you need data for additional cross-sections. Alternately, you can simply estimate a fixed effects model.

[Khatai]

Thanks for your help....
Then you mean, I must increase the amount of participant countries in the panel?

Does simply applying fixed effects model without Housman testing make any serious shortcut for the research?

[EViews Glenn]

That's an econometric question, which we are not really in a position to evaluate. It's an alternative set of assumptions, which may be better and may be worse. But if you don't have enough cross-sections for a RE estimator, you don't have enough cross-sections.