GMM versus GQL inferences for panel count data

It is well known that the likelihood inferences in dynamic mixed models for count data is extremely complicated. In this paper, we, first, develop a generalized method of moments (GMM) approach for the estimation of the parameters of such models. We then consider an alternative generalized quasi-likelihood (GQL) approach. The relative efficiency of the GQL approach to the GMM approach is examined by comparing the asymptotic variances of the GQL estimates of the parameters to the corresponding asymptotic variances of the GMM estimates.