Interpreting fixed effects when panel identifier is a group variable

[jai gopal]

Dear Statalist members,

I have a conceptual question regarding the use of xtreg, fe when the panel identifier id reflects a group variable [gen id=group(country firm)], thus the panel variable reflects firms nested within countries. Moreover, the time variable is years, and the sample spans 50 years. If I am not mistaken, when using xtreg, fe, this implies that the fixed effect that is included in the model is an interaction between the dummy variable country and firm. My question is now: if one would want to include only country-level and/or firm-level fixed effects (so without the interaction term), does that mean xtreg cannot be used?

Thank you for your help, it is much appreciated.

Best,

Jai

[Carlo Lazzaro]

Jay:
welcome to this forum.
The first reason why you shoud not use -xtreg,fe- rests on my gut-feeling that you're dealing with a T>N panel dataset (see -xtregar,fe-).

[jai gopal]

Hi Carlo,

Thank you for the quick answer. You are right, that is a good point. It is an example I made up, as I am trying to think how to overcome the fixed effects problem I described. If I change the example now such that T= 10 years and I have many countries and firms (N>T), do you have any advice on my problem how to obtain fixed effects for countries or firms only if the panel identifier is a group? Or can xtreg, fe not be used then?

Best,

Jai

[Carlo Lazzaro]

Jai:
let's follow your assumption of a N>T panel dataset.
As far as I know, obtaining the -fe- as reported in textbook for a variabe that is not the -panelvar- (or, in your case, is a part of it) is not feasible.
Obviously, provided that perfect collinearity with the -fe- does not bite, you can plug in a categorical predictor for -countries- (for -firm- this sounds kinda overkill in term of freedom degrees), but what you can get is not -fe- in technical terms..

[jai gopal]

Hi Carlo,

I figured, thanks for your input. I agree that your proposed solution can lead to an absorptiom of too much variation by the FE. So i was thinking about not using fe. My worry is that xtreg, re may not be ideal in cases where the individual unobserved heterogeneity is correlated with the independent variables. Whereas using reg with i.country and i.firm can be an option, but using reg for panel data is not a good idea since you do not control for within panel correlation. I will continue reading about this, thanks again.

Best,

Jai

[Carlo Lazzaro]

Jay:
1) if -fe- is the way to gp, -re- proves inconsistent (that is, your coefficients are unreliable);
2) I doubt that -regress- with -i.country. and -i.firm- is a viable option (pefect collinearity probably bites and computational time takes forever);
3) while agree with your that -regress- is not the first option when it comes to panel data regression, the within panel correlation can be dealth with via clustered standarda errors in -regress-, too;
4) would -mixed- be somethng that the literature in your reearch field points you out to when dealing with this kind of researches?

[jai gopal]

Hi Carlo,

I understand your point #1. Regarding point #2, I am not sure what you mean with it not being a viable option. I understand that reg allows me to include fixed effects separately, whereas xtreg, fe by design includes country-firm fixed effects, which is not what I am after. While including both i.country and i.firm in the regression absorbs a lot of variation, but as long as there is still variation over time, such a regression can be useful right? Where does the perfect collinearity problem arise?

Regarding your third point: that is true, but from what I have read from a previous post (https://www.statalist.org/forums/for...ced-panel-data), using reg for panel data is inappropriate. Hence why I was unsure whether using reg is inappropriate when it comes to panel data. I had not heard of -mixed-, thanks for bringing it to my attention. I will look into it.

Best,

Jai

[Carlo Lazzaro]

Jay:
2) I meant that, if -fe- is the way to go, with -regress- you'll have the same problems as with -xtreg,fe-, but at prohibitive computational time;
3) I meant that, if -fe- is the way to go, autocorrealtion of the epsilon error can be dealt with the -vce(cluster panelid)- option.

[jai gopal]

Hi Carlo,

Thank you for clarifying. It is clear to me. I appreciation your time and attention.

Best,

Jai