Econometric Model Analysis with Panel Count Data

摘要本研究旨在探讨面板资料模型之估计量之统计性质。计数数据不是连续的，而是离散的。它的似然函数用于估计模型中包含的未知参数是复杂的。虽然计数数据模型是静态的似然估计可以用数值方法来估计，但由于随机参数问题，动态模型的估计是困难的。本文给出了具有面板计数数据的动态模型的对数似然函数的导数。研究表明，由于似然函数是由两个非负整数值随机变量的卷积构成的，因此不能应用静态模型的条件极大似然方法。

The purpose of this research is to investigate the statistical properties of the estimators of the panel data model. The count data is not continuous but discrete. Its likelihood function is complicated to use for the estimation of unknown parameters included in the model. Although the likelihood of the count data model which is static can be evaluated numerically, the estimation of the dynamic model with panel count data is hard because of the incidental parameter problem. In this research, the derivatives of the log-likelihood function of the dynamic model with panel count data have been given. This research shows that the conditional maximum likelihood approach which is used for the static model can not be applied since the likelihood function consisted of convolutions of two non-negative integer-valued random variables.