Fixed effects with categorical variable

[Eduard Suari]

Hello everyone,


I am estimating the differences between migrants and natives in terms of access to welfare using a very simple linear probability model:

reg welfare migrant controls, vce(custer id)

where welfare is a dummy taking value one if an individual receives welfare. I have longitudinal data but cannot use fixed effects since migration status does not change over time.
However in a second stage I estimate another equation substituting the dummy "migrant" for a vector of dummies capturing the number of years since arrival into the host country:

reg i.ysa controls, vce(cluster id)

where ysa is a variable that takes value zero for natives and values from 1 to 20 for migrants. Therefore "i.ysa" generates 20 dummies and leaves natives out as a reference category.
My question is whether this second equation can be estimated using fixed effects, i.e.:

xtreg i.ysa controls, fe vce(cluster)

To my mind there should be a collinearity problem since there is no variation over time in the reference category. However, the code seems to work and I get estimates. Does anyone know the coefficients should be interpreted and why there is no collinearity problem? Any help is more than welcome

Thanks in advance.

[Carlo Lazzaro]

Eduard:
why speculating on what's going on with your data when you can share what you typed and what Stata gave you back via CODE delimiters (as per FAQ)?

[Eduard Suari]

Hello,

Apologies Carlo, I am not very familiar with posting in the forum. Find my code below.

 xtreg d_welfare i.ysa $controls, fe vce(cluster id)

I am afraid I cannot share the output since I am working with confidencial data in a remote environment that does not allow sharing (I cannot copy-paste). The code yields the output you would normally expect from fixed effects estimation, but in this case I would expect a collinearity problem because of the reasons mentioned above.

Best,
Eduard

[Carlo Lazzaro]

Eduard:
the -fe- machinery wipes out time-invariant variables.
You can test via -xttab- if -i.ysa- varies within panel or not.

[Eduard Suari]

Thanks a lot Carlo. Indeed I realized there was some longitudinal variation that was not supposed to be there. Once I corrected that I got the collinearity problem I was expecting to have.