I am estimating the effect of some treatment on yearly district-level stillbirths and stillbirth rates and births and birthrates in a panel with district and year fixed effects.
Stillbirths are mostly 0 or close to it, so I apply Poisson. In Stata I use
xtpoisson stillbirths treat i.year, fe vce(robust) where vce(robust) relaxes the $E(Y)=Var(Y)$ assumption because for count variables, variance is larger, for the rates it is smaller. Births are never 0, their mean is above 2500 but data are still very skewed. When I estimate OLS with FE on Log(Births)
xtreg log_births treat i.year, fe robust, I do not get any significant result. But with
xtpoisson births treat i.year, fe vce(robust) I do. I use this for what I have read here http://blog.stata.com/2011/08/22/use-poisson-rather-than-regress-tell-a-friend/ and https://stats.stackexchange.com/a/38588/35284 Is this a valid approach?
I then want to estimate the effect on stillbirth per deadbirths, stillbirths per 1000 deadbirths. From my prior reading in the two links before it seems that even rates can be estimated like this. However, the scaling is arbitrary now as we do not have count data anymore. According to this thread Poisson regression with large data: is it wrong to change the unit of measurement? it is important though. Thank you for clearing up these issues on rates and large-number poisson regressions.