Dynamic panel of count data with initial event and correlated heterogeneity

ABSTRACT

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.

KEYWORDS:

• Dynamic panel model for counts
• correlated random-effects model
• exponential feedback model
• linear feedback model
• initial conditions problem

JEL CLASSIFICATION:

• C23
• C51

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ In general, the random-effects model assumes that the individual-specific heterogeneity is not correlated to covariates. However, the richer models for random effects, such as those of Mundlak (1978) and Chamberlain (1980, 1982), allowed unobserved heterogeneity in the panel models to be determined by time averages or weighted sum of the regressors. For details, see Cameron and Trivedi (2005), p.719.

² This study focuses on the case where the quantities of information on dependent and independent variables are same for the correlated random-effects model. Note that, Blundell et al.(1995, 2002) use the pre-sample mean (PSM) estimator as a proxy for unobserved heterogeneity, which is consistent when the number of pre-samples in large; ‘the PSM estimator specially designed to exploit data sets where information on the dependent variable is available for earlier years than information on the regressors’ (Blundell, Grifffith and Windmeijer 2002, 114).

³ The initial event is correlated to individual-specific effect, which is unobserved heterogeneity, and we may expect that the effect of initial event on the future events would be large, especially in the short panel. This implies that the initial event has some predictive role, hence influence on the magnitude of state dependence; therefore, incorporating the initial event into the model can be regarded as a way to capture some parts of individual-specific microeconometric heterogeneity.

⁴ This implies that individual-specific effect ${\alpha }_i$ in Equations (1) and (2) becomes $\left\{{\alpha }_0+{\alpha }_1{y}_{i,0}+{\mathit{z}}_i^{\prime }{\alpha }_2+{\omega }_i\right\}$ in Equations (3) and (4). Thus, the individual-specific effect is determined by initial event ($y_0$) and correlated effects ($\mathbf{z}$).

⁵ For the assumption that the explanatory variable is covariance stationary, see Corollary 2 in Blundell, Grifffith and Windmeijer (2002).

⁶ Three different parameter values of $\rho$ (0.05, 0.1 and 0.15) are used to evaluate the models; however, only the case of $\rho$ = 0.1 is reported in this article. The results of other parameter values are similar to those in Table 1; however, overall the magnitudes of biases become larger as the size of state dependence increases.

⁷ As the pure random part in the individual-specific effect is considered fixed over all individuals, the EFB becomes a population-averaged model.

⁸ We applied the dynamic specification to Winkelmann’s (2004) data. The results show that the reform effect of the healthcare system in Germany is 3.6% below the dynamic system, which is less than the result of 8.7% from the nondynamic system. This may be because the initial event, state dependence and correlated heterogeneity are not considered in the nondynamic system.