Stata commands for Negative Binomial fixed effects regression

[Emeka Dim]

Hi,

Please, can anyone help me with the commands for a negative binomial fixed effects regression? I learned that this method has some complicated history, especially according to Paul Allison, and I would like to know if there is a command that can run this method effectively.

Thank you.

[Leonardo Guizzetti]

The output of -help negative binomial regression- will lead you to the command -nbreg-.

[Joao Santos Silva]

Dear Emeka Dim

Further to Leonardo's advice, Stata also has a xtnbreg command with a FE option. However, as you noted, this is a problematic estimator and does not have the usual FE interpretation; I would stay away from it...

Best wishes,

Joao

[Emeka Dim]

Joao Santos Silva Thanks for the suggestion. I have seen in other post where you suggested that one could use the Poisson FE command in place of the xtnbreg. I used this command:
xtpoisson part_w i.partystrg discuss i.ideology i.interest info polattn ideo_values [iweight = full_wght_], fe vce(robust)
(where part_w is the dependent variable, i.partystrg to ideo_values are the predictors). I used iweights and I used the robust standard errors like you advised. However, I showed this command to Paul Allison in his blog and he said the following: `Although fixed effects Poisson should be approximately unbiased, it’s not efficient (in the technical sense). And my experience is that results often differ dramatically from those of the negative binomial.'.

I tried using Paul Allison's command, which looks like: nbreg part_w i.partystrg i.interest discuss i.ideology info i.wave i.id [iweight = full_wght_], vce(robust), because he suggested using individual dummies. According to Allison `you can do an unconditional estimation of a fixed effects negative binomial model simply by including dummy (indicator) variables for all individuals.' However, I ran this command on my system at 9 pm and as at 10:28 pm (while I am writing this comment), the command is yet to produce the full result and Allison also admitted that this kind of command may be computationally demanding for Stata. Another issue is that the model may not converge and I may have to spend hours waiting for a model that does not converge.

Please, what do you think? I intend to develop a manuscript from these analyses. If I would go along with your advice, I want to be able to cite the reason or justification for using the command from an academic material or journal. Please, do you know any academic material I could cite?

Funnily enough, the xtnbreg is still in the Stata Manual as the command to use for a negative binomial FE model for count data.

Thanks.

Eugene.

[Joao Santos Silva]

Dear Emeka Dim (Eugene),

In general, maximum likelihood estimators are biased but consistent. This applies both to the Poisson and NB estimator, so I do not really understand what "approximately unbiased" means and why Poisson and NB could differ. As for efficiency (in the technical sense), none of them will be efficient unless the distribution is correctly specified; in my view, it is extremely unlikely that either of them is exactly correctly specified and without further information I have no reason to believe that the NB is superior to Poisson.

One thing is clear, however, Poisson regression with fixed effects is more robust than the NB and it is much easier to estimate (as you have found out); moreover, adding dummies to the NB model will not be a valid approach unless you have a lot of observations in each group.

The reference you want is Wooldridge's 1999 paper

Distribution-free estimation of some nonlinear panel data models, Journal of Econometrics, 90 (1), 77-97.

Best wishes,

Joao

[Emeka Dim]

Joao Santos Silva Thanks for the material and advice.

I conversed with Prof Allison about what you said and he suggests that he has seen a number of cases where the NB may have different estimators. However, his alternative to the individual dummy method, i.e. hybrid method, does not work well for nonlinear data and I would like to settle with a final analysis and start generating my results, especially using your suggested method. I went through the article you suggested. I am not a statistics major, hence, I had a hard time understanding what the paper was saying, with regards to what I needed the paper for. I was looking for the parts of the article that suggested that the Poisson FE was similar to the Negative Binomial FE. I think there were several interesting parts in pages 80, where the author argued that (please pardon the rough copy and paste work):
Because the multinomial distribution is in the LEF, the results of GMT imply a certain amount of robustness of the QCMLE. If
E(yq?4nq, xq)"p?(xq, ? )nq (2.7)
then the multinomial QCMLE is consistent and asymptotically normal, even if the multinomial distribution is misspecified.'

In page 89, the author also added that:
`The fixed effects Poisson
model imposes ?q,1. The fixed effects negative binomial model of HHG, mentioned in Section 2, imposes ?q"1# q, which rules out underdispersion for all individuals and ties the amount of overdispersion directly to the mean effect. HHG introduced two unobserved effects in their negative binomial model, ?q and q, but it is easily seen that only the ratio 1/?q,exp(?q)/ q actually appears in their model. In addition, Eq. (5.3) is weaker than the independence assumption imposed by HHG, and no distributional assumption is made.'

The author also mentioned, in page 94, that `the fixed effects Poisson estimator is fully robust in the sense that only the structural conditional mean assumption, given in Eq. (3.1), is needed for consistency and asymptotic normality'

I also looked at Cameron & Trivedi (2013) book on `Regression Analysis of Count Data' and they state that `Negative binomial fixed effects models specify the conditional mean function to satisfy (9.13), so the Poisson fixed effects estimator still yields a consistent estimator in short panels. A negative binomial fixed effects estimator has the attraction of potentially more efficient estimation, although the inclusion of individual effects will control for much of the overdispersion.' (Page 357) The keyword for me in this statement was `short panels' as my data involves only 3 waves.

I will also appreciate it if you could point me to more parts of the paper that justifies using the Poisson FE over the Negative Binomial FE.

I would like to use the Poisson FE but I simply need an aspect of the material I could cite in the methodological section of my paper. I cannot use Allison's method because they are not feasible and I need to finally decide on the analysis for the data I am working with.

Secondly, I am using this command for my analysis:
mi est: xtpoisson part_w i.partystrg discuss ideo_values i.ideology i.interest info [iweight = full_wght_] if hippel != 1, fe vce(robust)

I added `mi est' because I ran multiple imputations. Please, do you think this command is correct for the analysis you suggested for the poisson FE? It seemed to me that you had once suggested that we added some other things in the command to get the desired results we need (I may be wrong).

Thanks and looking forward to your reply.

[Joao Santos Silva]

Dear Emeka Dim,

The bits you quote from page 94 and from the Cameron and Trivedi book are enough to justify using Poisson; they emphasize its robustness.

Also, your command looks ok to me, but I am not familiar with mi.

Best wishes,

Joao

[Jovin Lasway]

I trust all is well with you all (Statalists).

I have a question. Am investigating on the adoption and disadoption of electric stoves among households, a panel study. The dependent variable is binary (D=1: Adoption and D=0: Disadoption) and other independent variables.

How can i solve the endogenity problem through IV (2SLS)?, I would like to know the regression procedures.

Thanks