Using an interaction term in -xtreg, fe- : Interpretation issues

[Julia Simon]

Hi,

I find some difficulties understanding why I have different results regarding the significance of my coefficients when running two regressions that should conceptually be the same.

I am using cross-country monthly panel data, and I use a fixed effect regression to get rid of the time-invariant unobserved heterogeneity. My fixed-effect are defined at the country level. I am also using an interaction term involving a binary variable that is time invariant, so that the main effect is omitted from the regression, but the interaction term is not.

Let's suppose that my independent variable is called democ and is equal to one when the country is a democracy. Let's also suppose I create another variable that is the opposite of democ (name it autoc), so that when autoc is equal to 1, democ is equal to 0.

I would like to understand why this regression :

xtreg depvar interest##democ, fe vce(cluster country)

is different in terms of significance of the interaction term coefficient from

xtreg depvar interest##autoc, fe vce(cluster country)

interest is a binary that equals one if the country is in an election period.

I find in regression (1) that the interaction term cancels significantly the main effect of interest (that is negative), which means that there is a differential effect depending on whether the country is a democracy or not.

I expect regression (2) to have the same results, that is, a main effect of interest that is positive but cancelled by the interaction term between interest and autoc (which I expect to be negative). However, this time, the interaction term comes unsignificant.

Can someone explain me where does this statistical problem comes from?

Regards,

Julia

[Clyde Schechter]

You do not show the code by which you created the autoc variable from democ, nor do you show example data, nor the full output of the two regressions. The two regressions should, in principle, produce the same results except for changes in sign.

However, missing values in the democ variable could be causing problems. If, for example you did -gen autoc = !democ-, then any missing values of democ will give values of 0 for autoc. This, in turn means that they will enter the regression, whereas in the original democ regression they were excluded from the estimation sample. The most obvious tell in the results would be that the sample sizes for the two regressions are not the same. A more direct test of my hypothesis about the problem is to look at the results of -tab autoc democ, miss-. If you created autoc correctly you will see that they are always both missing, or neither one missing, and in the latter case democ + autoc == 1. Try it and see. If that's not the source of the problem, please include example data, the code you used to create -autoc-, and the output from both regressions when you post back.

[Julia Simon]

Clyde : You were indeed right, my variable was wrongly coded after verification. I thought that I didn't need to post data examples since I believed my problem was a statistics issue but now I understand why examples are often necessary. Lesson learnt!

Thank you for your help.