How to deal with "outcome does not vary in any group" when dealing with xtlogit

[Phuc Nguyen]

In my case, I am finding pscore for doing PSM. To get there, I need to run the logistic regression to get the pscore. Thank you Clyde Schechter that I confirm my xtlogit with two way fixed effects.
In my setting, I have 7 countries, all firms in country A have the "treatment" variables equal to 1, otherwise 0.

My logit regression is

xtset firm year
xtlogit treatment  firm-level-variables  country-level-variables i.year, fe

while treatment equal to1 if firms in country A and 0 otherwise. firm-level-variables includes firm size, firm age... country-level variables include lngdp, unemployment ....

When running the regression

xtlogit treatment firm_age i.year, fe

I got the error immediately

outcome does not vary in any group

So, I asked myself and think this means that in at least one group, all observations have either a 0 or a 1 as the outcome variable. It makes sense because all observations of firms in country A will have treatment =1 and all observations of firms in other countries will have treatment=0, so they wont vary.

I am not sure whether my understanding is correct. If it is the case, would you please guide me how to overcome the problem. Thank you.

[Clyde Schechter]

Fixed-effects logistic regression is not an appropriate analysis for the purpose of constructing a propensity score. It would inevitably encounter the problem you have: because the "outcome" (treatment vs control) is time-invariant, and -xtlogit, fe-, like all fixed-effects models, estimates only the within-panel effects, there is nothing to estimate here. The within-panel effects of all variables are zero.

Creating a propensity model for longitudinal data is a complicated and challenging subject, about which I do not have sufficient expertise to advise you. Hopefully others who are following along do and will offer their opinions.