My outcome is counts left-censored at y<1000. I have panel data and want to run a model with fixed effects for for time and person.

I read up on this but could not find any resources about including many indicators in a censored poisson. Also, the reference for xtpoisson does not mention censoring and the reference for cpoisson does not mention fixed effects. Does anybody know more if estimating something like this below makes sense or would it run into similar problems like Tobit with many dummies?

Code:
sysuse xtline1.dta
gen outcome = runiformint(0, 100000)
replace outcome = 0 if outcome < 1000
cpoisson outcome calories i.day i.person
At least it seems to converge relatively fast...