Dear forum,

My question is more theoretical, but I hope I can find an answer here.

I am running a Poisson model in a gravity framework (number of exported products as the dependent variable). My data is over-dispersed and therefore I will use the Poisson pseudo-maximum likelihood (PPML) estimator over the standard Poisson. However, in my data and methodology I would like to explain exactly how the PPML is superior - how overcomes over dispersion, where the standard Poisson cannot. After reading many resources, I still cannot pinpoint an answer.

The general message seems to ve that the PPML is consistent even if the distribution is not specified because the first-order condition SUM(yi-exp(xB))xi= 0 as long as yi = exp(xiB). (Where B = beta). Many papers refer this finding of Gourerioux et al. (1984). As I understand it, if overdispersion is present it will not matter for the PPML since there is no equidispersion assumption modelled into it.

But Cameron and Trivedi (1999) say that the standard Poisson is also consistent if the same condition holds. Therefore, what exactly does the PPML change?

I feel that there is large inconsistency and abstractness in the explanations in the non-technical papers that are out there. On the other hand, the technical papers are difficult to grasp and therefore I am trying to understand intuitively.

I appreciate this is a theoretical matter and may be difficult to answer here.

Thank you in advance,

Ray