Choosing between xtnbreg fe bootstrap and xtpoisson fe cluster-robust

[Alice Campbell]

Dear Stata experts,

I have been struggling with some count panel data and I would like to estimate it with fixed effects. My data shows a little bit of overdispersion (when fitted with quasi-poisson the overdispersion parameter is 5.01 and the overdispersion test in AER in R is significant).
So to account for over dispersion, after some googling and reading the books, I gathered that there are two options: 1) to use NB regressions and 2) to use cluster-robust SE when fitting the data with Poisson, such as the xtpoisson command in Stata with FE and VCE(Robust) options.
I know there is also the quasi-poisson option but I am not ready to go there yet.
My problem is that I have not found any guidance on choosing between these two options. I am new to the list so forgive me if this has been answered before. Any help will be greatly appreciated here.

Best,
Alice

[Joao Santos Silva]

Alice,

You need to tell us about what is the problem you are dealing with and that is the purpouse of the regression. Without knowing that it is not pssible to advise.

Best wishes,

Joao

[Alice Campbell]

Hi Joao,

Thank you for your reply.

I am estimating a panel count data model with fixed effects. n=1054, t=7. I have significant results when using xtnbreg with bootstrap SEs. But my advisor said he would only believe the results if I ran xtpoisson vce(robust) and got significant results, as he considered it more robust. My confusion is that do we always have to have both models producing significant results to believe them? In my case my data have over dispersion. Apparently xtpoisson is more robust so then there is no use to ever use xtnbreg? Indeed, xtpoisson with fe vce(robust) produced larger SEs therefore nonsignificant results.

I have read online that xtnbreg is not truly fixed effects so I also tried estimating a negative binomial model with FE by creating a dummy for each userID, as suggested by Alison. That model also produced statistically significant results.

Hope this clarifies what I am doing.

Thank you!
Lian

[Joao Santos Silva]

Dear Lian,

I still do not know enough about what you are doing to be able to give you proper advice. Anyway, there are a few things I can say:

1) Starting from the end, running a NegBin model with with a dummy for each userID is not a good strategy; the model is likely to suffer from an incidental parameters problem and therefore the estimator will be inconsistent.

2) Indeed, the usual NegBin FE estimator is not a real fixed effects estimator, so it does not do what you want.

3) Indeed the Poisson estimator is very robust (Jeff Wooldridge has a very neat paper showing that) and therefore tends to be more reliable, although it is unlikely to be efficient.

4) The choice of model to use very much depends on what you want to do. If you just want to estimate the conditional expectation and see if some regressors are significant, then Poisson FE wins hand down dur to its robustness. If you want to compute the probability of a certain event (e.g., y=0), then you need to use an estimator based on the correct distribution and that may be Poisson, NegBin, or something much more sophisticated.

Best regards,

Joao

[Alice Campbell]

I see. That totally solves my problem. Thank you, Joao!

[Philip Gigliotti]

Dear Lian,

I still do not know enough about what you are doing to be able to give you proper advice. Anyway, there are a few things I can say:

1) Starting from the end, running a NegBin model with with a dummy for each userID is not a good strategy; the model is likely to suffer from an incidental parameters problem and therefore the estimator will be inconsistent.

2) Indeed, the usual NegBin FE estimator is not a real fixed effects estimator, so it does not do what you want.

3) Indeed the Poisson estimator is very robust (Jeff Wooldridge has a very neat paper showing that) and therefore tends to be more reliable, although it is unlikely to be efficient.

4) The choice of model to use very much depends on what you want to do. If you just want to estimate the conditional expectation and see if some regressors are significant, then Poisson FE wins hand down dur to its robustness. If you want to compute the probability of a certain event (e.g., y=0), then you need to use an estimator based on the correct distribution and that may be Poisson, NegBin, or something much more sophisticated.

Best regards,

Joao

Joao, can you provide a citation of the Wooldridge paper? I'm also currently debating between xtpoisson robust and some form of xtnbreg. Cameron and Trivedi also say xtpoisson with robust errors may be more robust in the presence of overdispersion, but I'm so conditioned from methods class to always choose a negative binomial model in the presence of overdispersion, that its hard to break the conditioning, and I want to have a good argument.

[Joao Santos Silva]

Dear Philip Gigliotti,

I believe that the paper is:

Wooldridge, J. M., “Distribution-Free Estimation of Some Nonlinear Panel Data Models,” Journal of Econometrics 90 (1999), 77–97.

but Jeff can correct me if I am wrong. Basically, if you do not want to estimate probabilities, it is unlikely that you need to worry about over-dispersion. If you need to estimate probabilities, NB may still be too restrictive. I guess the conclusion is that the NB is a bit overrated.

Best wishes,

Joao

[Philip Gigliotti]

I'm not sure I understand what you mean by calculating probabilities. I interpret an nbreg coefficient as the ln transformed increase in the count variable associated with a 1 unit increase in the independent variable. How do you estimate a probability from that?

[Joao Santos Silva]

Your question suggests that you are really interested in the effect of the regressors on the conditional expectation of y; I would say that for that Poisson is preferable.

Given the estimated parameters you can use the expression of the corresponding probability mass function to compute the probability of observing a given integer. For those probability estimates to be meaningful you need the probability function to be correctly specified. If you have overdispersion, you know that the Poisson function is incorrect and may prefer a more flexible distribution such as the NB.

[Philip Gigliotti]

Oh yeah, that takes me back to probability theory class. I see what you mean now. Thanks.

[Mansi Jain]

Joao Santos Silva Thank you very much! Yours posts about this topic are very helpful.