xttobit vs tobit with dummies

[Jonghyeon Kim]

Dear all,

I have a panel dataset divided into different locations over a few years. I have theoretical reasons to include time and location fixed effects. Essentially, I am wondering the difference between the following:

xtset location year
xttobit y xvars i.year, ll(0)

AND

tobit y xvars i.year i.location, ll(0)

xttobit estimates a random effects model, but that is not inconsistent with adding year dummies (year fixed effects), correct?

As far as I understand, with the same dataset, xtreg y xvar i.year, fe and reg y xvar i.year i.location should produce same results, and I am wondering if the same goes for xttobit and tobit.

Any comment will be very much appreciated!

[Joao Santos Silva]

Dear Jonghyeon,

I am not aware of ant proof that the Tobit does not suffer from the incidental parameter problem, so Tobit with dummies is likely to be inconsistent.

On a different note, are you sure you need Tobit? In many applications where Tobit is used it would have been preferable to use Poisson regression, and there there is no incidental parameter problem. Maybe you can consider this.

Best wishes,

Joao

[Jonghyeon Kim]

Dear Joao,

Thank you very much for your response! My DV is, theoretically speaking, can be thought of as censored at zero. I doubt that Poisson can take the censoring concept into account, but I should look more into it.

I ran my data and xttobit y xvars i.year i.location, ll(0) AND tobit y xvars i.year i.location, ll(0) actually produced the same output. In this case, would it be inappropriate to use the robust option for tobit for panel data, to deal with heteroskedasticity? xttobit does not allow for the robust option. Any insight would be appreciated!

[Joao Santos Silva]

Dear Jonghyeon,

I am very concerned about the Tobit because it relies on very strong assumptions. Can you tell us more about your dependent variable?

Cheers,

Joao

[Jonghyeon Kim]

Dear Joao, thank you very much for the response. I am aware of the two important assumptions -- normality and homoscedasticity -- and checked for both. The former is met and the latter isn't, thus the use of robust SEs. My DV is the number of people involved in some particular activities, which is treated in the relevant literature as censored at zero. Thank you again for your time.

[Joao Santos Silva]

Dear Jonghyeon,

You are actually modelling a count and you should use a count data model such a Poisson (the more robust of them all). There is no censoring at all in your data because your variable simply cannot be negative. I am not surprised that some people have used Tobit in similar cases but that is just due to ignorance.

Best wishes,

Joao

[Jonghyeon Kim]

You are absolutely right that it is a count. I guess the literature uses Tobit because it considers the way in which 0s occur, but I see your point and will try other count models. Thank you very much for your advice. It's very helpful!

[Joao Santos Silva]

Glad could help. Note that with Poisson you can both sets of fixed effects without any problem.

Best wishes,

Joao