[Philip Gigliotti]

Isn't this because once a couple of colleges get new presidents with different sex or clerical status during the interval, then sex, clerical status become no longer time-invariant for colleges and remain in that fixed-effects model? The converse is not true, and so you will have those coefficients in the second model and not in the third. The presence of those additional explanatory variables in the second model / absence in the third naturally affect at least some of the other regression coefficients. Are you saying that there's something going on here beyond that?

I was thinking something along those lines, however since the second model also includes president dummies, those time invariant characteristics of the president should still drop out. technically both models are the same; they are ols models with all my independent variables and sets of dummy variables for year, president and university. so the results should be exactly the same.

[Joseph Coveney]

I thought that in your first post you said a couple of the college-president indicator variables were omitted for collinearity. In that case, the sex, clerical status and age might not drop out if they are no longer collinear conditional on the remaining college-president indicator variables.

[Philip Gigliotti]

I thought that in your first post you said a couple of the college-president indicator variables were omitted for collinearity. In that case, the sex, clerical status and age might not drop out if they are no longer collinear conditional on the remaining college-president indicator variables.

As I understand it, the collinearity arises when the president doesn't change over the 7 years in the panel. Therefore the dummies for president and university become collinear. Either way, what is left is a model that accounts for time invariant characteristics of all of the universities and presidents. furthermore, the dummy configurations should perform identical functions in both the second and third models.

Clearly, they are doing something very similar, because the coefficients and standard errors are exactly the same for the majority of variables including my variables of interest rank and the rank interaction. I'm trying to figure out why the 4 variables age, yearsprior, sex and clergy, are the not the same between both models.

In theory the models are exactly the same: they are ols models with my vector of variables and sets of dummies for year, institution and president. However, a different process is happening depending on which variable is selected as my panel variable. So I'm trying to figure out what that is.

[Joseph Coveney]

I'm not sure whether you can choose which collinear variable gets dropped by Stata (other than omitting it manually, of course), although I recall reading about it somewhere. Maybe you can explore which ones get dropped and try to tie that into whether sex, clergy and so on remain in the model, and then focus on peculiarities in the dataset related to them. Try comparing what gets dropped using simpler models containing only the affected coefficients, and also try manually generating the indicator variables that you assume that Stata is in areg and xtreg , fe.

xtreg lnprescomp c.age i.sex c.yearsprior i.clergy i.year i.numpres_name, i(unitid) fe
xtreg lnprescomp c.age i.sex c.yearsprior i.clergy i.year i.unitid, i(numpres_name) fe
// and compare to
regress lnprescomp c.age i.sex c.yearsprior i.clergy i.year i.unitid i.numpres_name
// and if order offers some control over what gets dropped
regress lnprescomp c.age i.sex c.yearsprior i.clergy i.year i.numpres_name i.unitid

[Philip Gigliotti]

I solved this problem. The best way to run a fixed effect model with two panel categories is to create pairs by interacting the id for each category. you then have a unique identifier for each pair that you can use as your panel variable. Now all my presumed interactions drop out.