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I have a panel count dataset 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 overdispersion, 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.

However I have not found any guidance on choosing between these two options. Any help will be greatly appreciated here.

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Forget the overdispersion issue for a second, and worry first about using a consistent estimator for the parameters themselves. The fixed-effects Poisson estimator relies on very few assumptions (mainly, you need to get the form of the conditional mean right, and you need strict exogeneity), while the negative binomial (II) model assumes the panel effects are independent of the explanatory variables, which is a very strong assumption. If the assumption holds, you get a more efficient estimator, but if not, I don't think it's even a consistent estimator.

So you should stick with fixed effects Poisson with robust VCE, unless you have good reason to believe that the assumptions of the negative binomial model actually hold. I presume that a Hausman test would be useful here.

For further info (and to confirm that I didn't get all of this totally wrong), see sections 19.3.1 and 19.6 [I think; my copy is at work and the Google Docs version omits pages] of Wooldridge's Econometric Analysis of Cross Section and Panel Data.

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You should use a glm estimator. I don't know your amount of overdispersion, but this procedure is usually quite robust.

glm y x1 x2 ..., fam(negbin) link(logit) robust

You can also use a 2 step approach. estimate alpha first using nbreg and then run glm.

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    $\begingroup$ That does not really tell the OP why s/he should choose that option over another. Can you expand on it with reasons to justify? Otherwise this is really a comment not an answer. $\endgroup$ – mdewey Mar 10 '17 at 16:10
  • $\begingroup$ Although it is certainly incomplete, this does seem to me to be an answer more than a comment (& certainly not a question, etc.). I'm inclined to say Looks OK. $\endgroup$ – gung - Reinstate Monica Mar 10 '17 at 17:52
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    $\begingroup$ Note further that this doesn't address the panel aspect of the question at all. $\endgroup$ – Nick Cox Feb 23 '18 at 10:07
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I do not think you have to choose between those options. If you use xtpoisson with robust standard errors, since your data is over dispersed your coefficients would still be mis-estimated. I would use xtnb and depending on your data still try to find se that allow for autocorrelation, heteroskedasticity, etc.

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    $\begingroup$ Note: Appears to assume use of Stata. $\endgroup$ – Nick Cox Feb 23 '18 at 10:05

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