Time constant group in interaction term in fixed effects model

[davidbrown]

Dear Stata Members,

I have a conceptual question. This is part of the problem I posted below, but I thought this can be discussed as a separate topic.

When calculating an interaction term, can a subsample whose variable in the interaction term is constant contribute to the coefficient in fixed effects model?
The sentence is confusing, so I'll just give you an example I have. The observation is dyad-year. Law_a is a binary variable and equals one if country a has the law and 0 if not. Same for country b and law_b.

Country A	Country B	Year	Law_A	Law_B	FDI
USA	Brazil	1990	1	0	24
USA	Brazil	1991	1	1	54
USA	Brazil	1991	1	1	45
Turkey	Japan	1990	0	0	67
Turkey	Japan	1990	1	0	69
Turkey	Japan	1990	1	1	89

Let's say I'm interested in Law_B's effect on FDI (the DV), and it's positive. Then I want to know if law_b's effect size is larger when law_a=1 (when both countries have the law).
Naturally I would think putting an interaction term of (law_a * law_b).

Here comes my question. My data set starts from 1990, so the early adopters (who adopted the law before 1990) has constant value for law_a or law_b for my time span. Thus when calculating the coefficients for law_a and law_b, only the late adopters will contribute, meaning that the coefficient should be interpreted as 'the effect of a new adoption of the law' but not as 'the effect of the existence of the law'.

Then, when I put the interaction term (law_a * law_b) along with law_a and law_b, should I interpret the coefficient as the 'interaction effect of the laws AMONG LATE ADOPTERS'? If that's the case, I should be worried because large chunk of the FDI involves early adopters either as the investor or the investee. Or does the early adopters also contribute to calculation of the interaction term, and is it legitimate to say that "this interaction term is considering all the early adopter situations too"?

Sorry for the deluge of questions in the end. But I can't take this question out of my mind at this moment.

Thank you!

Best regards,
David

[Clyde Schechter]

Well, if you have a situation, which I'm understanding you to say you do, where law_A or law_B is constant within a pair over the time span of your data, then those observations are uninformative about the interaction you are interested in (and will, in fact, be dropped from regression models automatically). Any country pairs where both countries adopt in or before 1990, or where neither adopts until the end of the data set will be dropped from analysis because the interaction term will be constant.

So that means that your analysis is based on, and only applies to, pairs of countries where at least one of them adopted between 1991 and whenever it is your data on them ends. For these country pairs, the interaction term then enables you to estimate the differential impact of adopting the law according to whether the other country already had it or not. Since I don't know the context of your research and I don't work in your field, I can't say if that's important/interesting/meaningful or not, If you're not sure, you might consult a colleague.

[davidbrown]

Thank you again, Clyde. That clears many things up in my mind.