I have a panel data set with id=52 and time variable year, 2000 to 2018 (988 observations). I would like to model log of number of marriages (y1), log of number of divorces (y2) and log of number of births (y3) at id level (where id are provinces). I ran a Hausman test and estimated a fe model accordingly. Same x covariates (gdp, pop, education, unemployment... ) in each model specification.

xtset id year
xtreg y1 x i.year, fe vce(robust)
xtreg y2 x i.year, fe vce(robust)
xtreg y3 x i.year, fe vce(robust)

Since I think it makes sense to suppose that the underlying processes for the three dependent variables might be similar, I would like to perform a seemingly unrelated regression.

First, I considered sureg - but not sure if it works with panel data. So, I had a look at xtsur (http://fmwww.bc.edu/RePEc/bocode/x/xtsur.html) - but it uses re estimators. I tried to run xtsur adding i.id to the list of regressor (does it make sense?), but Stata 15 failed in calculating...

So, I got back to sureg and tried this:

xtset id year
sureg (y1 x i.year i.id) (y2 x i.year i.id) (y3 x i.year i.id), corr

Is this a correct approach for estimating SUR with fixed effects panel data? Any alternative?

Thanks!