Applying the GLM Variance Assumption to overcome the scale-dependence of the Negative Binomial QGPML estimator

Recently, various studies have used the Poisson Pseudo-Maximal Likehood (PML) to estimate gravity specifications of trade flows and non-count data models more generally. Some papers also report results based on the Negative Binomial Quasi-Generalised Pseudo-Maximum Likelihood (NB QGPML) estimator, which encompasses the Poisson assumption as a special case. This note shows that the NB QGPML estimators that have been used so far are unappealing when applied to a continuous dependent variable which unit choice is arbitrary, because estimates artificially depend on that choice. A new NB QGPML estimator is introduced to overcome this shortcoming.