Dynamic panel of count data with initial event and correlated heterogeneity

Existing literature on the specification of a dynamic panel model for counts raises several potential challenges. These include (a) the issue of a potentially explosive model when the lagged-dependent variable appears in the conventional exponential conditional mean function and (b) appropriate handling of the problem of the initial conditions that drive a dynamic process. This study addresses both issues within the context of a panel count model with Mundlak–Chamberlain type conditionally correlated heterogeneity. This correlated random-effects model is a useful compromise between the standard fixed- and random-effects models; it is then combined with two alternative specifications of the conditional mean function; one allows exponential feedback (EFB), whereas the other allows linear feedback (LFB). Monte Carlo experiments are conducted to check the robustness of these specifications by using the traditional maximum likelihood estimator for the EFB model and a nonlinear least squares estimator for the LFB model.