Remarks on asymptotic efficient estimation for regression effects in stationary and nonstationary models for panel count data

Abstract

In a panel count data setup, repeated counts of an individual are assumed to be influenced by the individual’s random effect. Consequently, conditional on the random effect, the repeated responses of the individual are assumed to be serially correlated. Under the assumption that the random effects of the individuals follow a normal distribution, Jowaheer and Sutradhar (Statist. Probab. Letters 79 (2009) 1928–1934) have demonstrated that the generalized quasi-likelihood (GQL) estimation approach produces more efficient estimates than the so-called generalized method of moments (GMM) approach for both regression effects and the variance component of the normal random effects. For the cases where the distribution of the random effects is unknown, there exist two estimation approaches, namely the conditional maximum likelihood (CML) and instrumental variables based GMM (IVGMM) approaches, for the estimation of the regression effects. The purpose of this paper is to examine the asymptotic efficiency performances of the CML and IVGMM approaches as compared to the GQL approach for the regression estimation. When the covariates are stationary, that is, time independent, it is, however, known that the CML and IVGMM approaches are useless for the regression estimation, whereas the GQL approach does not encounter any such limitations. For the general case, that is, when the covariates are time dependent, the IVGMM approach appears to be computationally expensive and hence it is not included in efficiency comparison. Between the CML and GQL approaches, it is found through exact asymptotic variance calculations that the GQL approach is asymptotically more efficient than the CML approach in estimating the regression effects. This makes the GQL as a unified efficient approach irrespective of the cases whether the panel count data are stationary or nonstationary.