Incidental parameter problem - correlated random effects probit

[Marry Lee]

Hello,

I have a pooled cross-sectional data (many counties during some years (1995-1999)), it's unbalanced.
I am looking at the effect of a policy at the county level on individual outcomes.

At the begining, I used:

 probit Outcome i.Treat##i.post_Treat  (other X vars)  i.provinceXyearFE i.county, cluster(county)

Where i.provinceXyearFE is the province X year fixed effects.

I am suspecting that I have an Incidental parameter problem, in the sense that I have many counties but not a lot of observations for each county (each county is not represented in each year, and some counties have a lot of individuals and some others do not have a lot of individuals).

So I decided may be a correlated random effects probit may correct for this problem.

My questions:

• Is it possible to use this with unbalanced pooled cross-section data (and not panel data).
• Is the fact of introducing the means of time-varying variables correspond to introducing county fixed effects?

so, the model would be:

 probit Outcome i.Treat##i.post_Treat  (other X vars and the means of time varying X vars at the county level)  i.provinceXyearFE, cluster(county)

So is this model right, and will I be controling for county fixed effects with this?

So many thanks!!

[Marry Lee]

Dear all!

Is there anyone that have any comments about whether what I am saying is right or nonsense?
Please don't hesitate if you need more details about my data. Thank you!