Interaction terms with country dummies

[Nimou]

Dear all,

As far as econometrics goes I'm still very novice. I have searched the internet for a solution on the following, however to no avail. It is not as much a problem with Stata more than it is just a research problem in general. Considering the bright minds over here (based on the other suggestions I read and subsequently used on this forum), it seems only logical to turn to you people.

Here's the deal. I'm trying to capture the determination of statutory corporate income tax rates using a panel of 34 OECD over the period 1981-2014. My final (static) model looks basically like the one I added in the attachment.
Independent variables 5, 6 and 7 are dummies for economic integration. The eight variable is however the main variable of interest. It depicts the weighted average of the statutory tax rates of other countries in t-1. Running an FE regression (justified by Hausman test), I found coefficient B8 to be highly significant (and positive). Now I wanted to look how coefficient B8 differs per country in my sample. My question however is: What's the best way to do this? I could run seperate OLS regressions, but the number of observations per country is limited (34 obs). I also created interaction terms with country dummy variables (countrynumber*Tsi,t-1), but in that case my B8 coefficient became insignificant and nonsensical. Basically, my idea is to use the coefficient found in the model above as the base-line. Am I just missing the obvious here or is my approach just wrong?

I hope someone could give me some valuable input regarding this issue. In return you will receive my eternal gratitude.

Kind regards,

Niels

[Joshua D Merfeld]

I think there are several issues here, but let me address a few of them.

1) You said:
"I also created interaction terms with country dummy variables (countrynumber*Tsi,t-1), but in that case my B8 coefficient became insignificant and nonsensical."
Now, if you create interaction terms, you no longer have a single variable denoting B8, but rather you have 34 different coefficients, each of which corresponds to a single country. Your old B8 will actually be the coefficient for your omitted country, whichever it is, so it doesn't make much sense to say that the (single) B8 coefficient is insignificant. I wouldn't be surprised if B8 were not significant for a handful of countries. Also, adding the interaction terms decreases your degrees of freedom, so, all else equal, your critical values will be higher.

2) You didn't say anything about this, but you almost certainly need to cluster your standard errors at the country level. There are many reasons to think that the errors would be correlated within countries. You have 34 countries, so you have enough clusters that clustered standard errors should be OK.

3) 34 observations per country would probably be enough to run the regressions separately for each country (I've seen macroeconomists run TS regressions with fewer than that), although the coefficients you get from those individual regressions will NOT be the same as the regressions you get from including interaction terms in your FE specification (although they will likely be 'relatively' close).

Hope these help.

Josh

[Nimou]

Thank you very much Josh. With these comments I think I can brainstorm further on my research. In fact, I should have actually known the logic behind the first comment (it should be somewhere in the notes I made for myself). Using interaction terms wouldn't make much sense I think in my case. That is, in that case I should pick a country as the base-line. However, there is no non-arbitrary way to do that in my opinion.

[Joshua D Merfeld]

I'm not quite sure what you mean by "picking a country as the base-line" in this case. In your regression above, WITHOUT the interactions, B8 represents, in a sense, the "average" value of B8 for the entire sample.

[Nimou]

Hmmm, then my reasoning was wrong. That is, I thought: If I include dummy variables for all 34 countries, that there is no base-line left.

What I also initially thought of doing was a SUR, or in any case compare the betas from both regression (entire sample vs subsample). However, considering I would be comparing the entire sample to the subsamples and not subsample to subsample, this seemed rather counterintuitive to me (although I have no logic to back that up).

[Joshua D Merfeld]

If you include dummy variables for all 34 countries, then what you essentially have is a fixed-effects regression. But what do you mean by a "base-line" country? What are you trying to compare?

[Nimou]

What I'm trying to compare is how the coefficient B8 differs per country, compared to that of the full sample (so the average).