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As Startz suggested in another post, we can use interactions to test the difference between a coefficient when regression is run across 3 (or more) sub-samples. However, the approach seems problematic when I add fixed effects to the regression.

Specifically, suppose that I have a unbalanced dated panel. The sample is then sub-divided into three sub-samples based on Size (which could have the value of 1, 2 or 3). I want to compare the coefficient on X in the regression: e.ls y c x when the sample is set to Size=1 versus when Size=3.

Using interaction, I run:
smpl @all
equation e.ls y c size=1 size=2 X (size=2)*x (size=3)*x

The last coefficient of equation e above will be numerically identical to the difference between the coefficients on X in equations e1 and e3 below:
smpl @all if size=1
e1.ls y c x
smpl @all if size=3
e3.ls y c x

Everything seems OK so far. But when I want to add the fixed effects into the regression, the problem occurs. Specifically, when I run equation (1) with time and cross-section fixed effects:
smpl @all
equation e_f.ls(cx=f,per=f) y c size=1 size=2 X (size=2)*x (size=3)*x

The last coefficient of equation e_f above is NOT numerically identical to the difference between the coefficients on X in equations e1_f and e3_f below:
smpl @all if size=1
e1_f.ls(cx=f,per=f) y c x
smpl @all if size=3
e3_f.ls(cx=f,per=f) y c x

My question is: with fixed effects, can I still use the interaction to test the difference of a coefficient across sub-samples (as explained ealier, it seems to me that I can't). If not, is there any other way to do so?

Thank you very much for any help.

I use Eviews 6.

Chau

Well, I think I now know the problem (but unfortunately I don't know how to overcome it :-(

Because adding fixed effects will essentially add year and cross-section dummies variables to the regression, it seems that I have to interact the (sub-group identifiers) dummies (i.e. Size=1, Size=2, Size=3) with each of the dummy added for fixed year and cross-section effects. So I guess I need to run the below regression:

smpl @all
equation e.ls(cx=f,per=f) y c @expand(size,@dropfirst) X @expand(size,@dropfirst)*X @expand(size,@dropfirst)*@expand(year,@dropfirst) @expand(size,@dropfirst)*@expand(companyno,@dropfirst)

(where Size can be either 1, 2 or 3; Year and Companyno are period and cross-section indentifiers, respectively)

But the problem is, when I run the above codes, Eviews returns the error message "Matrix size error: too many parameters for default coefficient vector in...". I guess it is because the number of interation terms added exceed the maximum number allowed by Eviews (how many is it???).

Any suggestion to proceed? Or is there any other way round (rather than using interaction)?

I really appreciate any help.

Chau