Cpoisson LSDV

[Felix Stips]

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?

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...

[Joro Kolev]

Depends how many time periods you have. I think if you have enough time periods, you can do what you are doing and the procedure would be consistent.

Also for the Tobit there was some result that even with few time periods, you still can estimate consistently the slopes. Check out this paper:

Greene W (2004). “Fixed Effects and Bias Due to the Incidental Parameters Problem in the Tobit Model.” Econometric Reviews, 23(2), 125–147.

[Joao Santos Silva]

Dear Felix Stips,

I am afraid there is no good solution to your problem. The beauty of Poisson regression (with or without fixed effects) is its robustness, but that is totally lost when accounting for censoring. Also, I certainly would not use a Tobit to deal with censored count data.

The effect of the censoring will depend on the degree of censoring and on the range of your data. If the censoring is not too bad; it may be safer to simply use Poisson regression and ignore the censoring. To check how bad the problem is, you can replace the censored observations with random draws from a uniform distribution in the (0 1000) interval and see how much the results change from sample to sample. Of course, the estimator will not be consistent, but the inconsistency may be small.

Best wishes,

Joao

[Felix Stips]

Thank you very much to both of you for your suggestions!

Indeed, I prefer using Poisson for my count variable. I tried to simulate the censored outcome as Joao suggested and the results of the Poisson estimations were quite similar across repetitions. With cpoisson I had convergence problems. I think going with a Poisson regression and ignoring the censoring is my best option at this point.

Best,
Felix