First difference maximum likelihood and dynamic panel estimation
一阶差分极大似然与动态面板估计AI 解读 ↓
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一阶差分极大似然与动态面板估计
- 研究问题
- 一阶差分虽可消除固定效应，但将高斯差分似然扩展至非平稳区域，会如何影响动态面板估计及数值优化？
- 方法与思路
- 作者分析扩展似然的定义域、双峰和异常峰，并区分单位根下时间维度增长与面板横截面维度增长的极限行为。
- 材料陈述的贡献
- 摘要指出扩展似然可能不是真实似然，数值优化可漏掉全局最大值；单位根下不同维度渐近产生不同极限分布。
- 阅读关注点
- 应核对扩展似然的确切形式和边界、异常峰出现概率、T与n渐近的区别，以及固定T时正态结论的条件。
- 阅读边界
- 仅据所给出版社摘要，不能将这些病态推广至所有差分似然设定；摘要明确指出极限理论依赖扩展似然的形式。
原文摘要
First difference maximum likelihood (FDML) seems an attractive estimation methodology in dynamic panel data modeling because differencing eliminates fixed effects and, in the case of a unit root, differencing transforms the data to stationarity, thereby addressing both incidental parameter problems and the possible effects of nonstationarity. This paper draws attention to certain pathologies that arise in the use of FDML that have gone unnoticed in the literature and that affect both finite sample performance and asymptotics. FDML uses the Gaussian likelihood function for first differenced data and parameter estimation is based on the whole domain over which the log-likelihood is defined. However, extending the domain of the likelihood beyond the stationary region has certain consequences that have a major effect on finite sample and asymptotic performance. First, the extended likelihood is not the true likelihood even in the Gaussian case and it has a finite upper bound of definition. Second, it is often bimodal, and one of its peaks can be so peculiar that numerical maximization of the extended likelihood frequently fails to locate the global maximum. As a result of these pathologies, the FDML estimator is a restricted estimator, numerical implementation is not straightforward and asymptotics are hard to derive in cases where the peculiarity occurs with non-negligible probabilities. The peculiarities in the likelihood are found to be particularly marked in time series with a unit root. In this case, the asymptotic distribution of the FDMLE has bounded support and its density is infinite at the upper bound when the time series sample size T→∞. As the panel width n→∞ the pathology is removed and the limit theory is normal. This result applies even for T fixed and we present an expression for the asymptotic distribution which does not depend on the time dimension. We also show how this limit theory depends on the form of the extended likelihood.