Firm- and Industry- effect in one model using panel data

[Claire Noh]

Dear All,
I have a panel data for about 200 companies over 15 years and assume the following regression model:

dv= f(v1, v2, v1*v2)

where v2 is industry dummy (0 or 1); therefore, if I run the model with fixed effect model (xtreg dv v1 v2 v1*v2, fe) , v2 is omitted due to its time-constant nature. And I know in this case I can remove the v2 (industry dummy) in the model as the firm dummy takes care of the industry effect. But the thing is I'm interested in not only the interaction term of v1*v2, but also the coefficient on the v2, i.e., how different is my dependent variable between the industries.

If I run this analysis using a 'reg' command along with firm dummies, i.e., reg dv v1 v2 v1*v2 i.company, this produces results on the v2 (industry dummies), but I was wondering this approach is okay because there is a perfect multicollinearity between the v2 and i.company.

Does anyone have advice/suggestion in terms of the model specification or alternatives that I can take?
Thank you in advance!

[Clyde Schechter]

But the thing is I'm interested in not only the interaction term of v1*v2, but also the coefficient on the v2, i.e., how different is my dependent variable between the industries.

This is mathematically impossible in a fixed effects model with firm-level fixed effects.

So, if you really want the industry-level effects you have to give up something:

1. You can do a random-effects model.
2. You can omit the firm-level effects and just use ordinary regression with firm-level indicators.

Which of these is the most appropriate thing to do depends on your context, and your research goals. The random effects model is, in my view, the most appropriate response given what you want to accomplish. But some disciplines have strong traditions as to how this problem is resolved. Since you mention firms and industries, I'm guessing the context is either economics or finance, and in those disciplines there is a strong, though not inviolable, preference against random-effects models because they do not guarantee consistent estimation. Well, you can't have everything. So you will have to choose what you want to give up.

Let me also point out that, even if you could get your wish, the coefficients of the v2's are not the effects of the industries in this interaction model. They are the effects of the industries when v1 = 0, which may or may not be of any use, depending on the meaning of v1 and the real-world implications of v1 being 0.

If I run this analysis using a 'reg' command along with firm dummies, i.e., reg dv v1 v2 v1*v2 i.company, this produces results on the v2 (industry dummies), but I was wondering this approach is okay because there is a perfect multicollinearity between the v2 and i.company.

Then something is wrong in your data. If each firm is in only one industry, then there will be perfect colinearity between the industry and firm effects and you will not get results for all of them. It may be that what you are seeing is that some of the firm level indicators (dummies) are dropped, and some of the industry level ones, so you have the illusion of getting results for both--but it is just an illusion, not a reality. If you really have results on all of the industry and firm level indicators then something is wrong in your data.

[Claire Noh]

Clyde:
Thank you for your explanation.

One more question regarding what you answered:
Yes- one of the firm dummies is omitted when I use the 'reg' command with both firm and industry dummies. In this case, are you considering the regression results an illusion, not a reality?

Thanks again!

[Clyde Schechter]

Well, yes, they are still an illusion. Think of it this way. Pick a number, any number. You could add that number to the effect of one of the industries and then subtract that same number from each of the effects of every firm in that industry. All of the model's outcome predictions would be the same. There would be no test you could carry out that would say which of those two models was correct and which was incorrect. This is what is meant by an unidentified model. The only reason you get any results at all is that Stata forces the model into being identified by arbitrarily constraining some coefficients to zero (which it does by omitting the corresponding variable.) But if you put the variables in a different order, Stata would drop different ones, and the "effects" it calculated for the remaining firms and industries would be different. In fact, if you wanted to, you could force a certain number of the particular effects to be any values you wanted them to be, and Stata would juggle the rest to accommodate your choices. So these effect estimates are illusions: they are artifacts of the particular constraints used to identify the model.

It's linear algebra and there's no way around it. In a fixed effects model you cannot estimate effects that are constant within the panels.