一类动态空间固定效应模型研究
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摘要
本研究在综合部份学者的研究成果之上，提出了一类动态空间固定效应模型，在模型中综合考虑了可直接观测和不可直接观测或无法观测的空间效应，分别考虑了初始值为外生给定和内生确定两种情况，并基于拟极大似然方法对模型参数进行估计，同时推导并证明了拟极大似然估计量的渐近性质及其渐近分布。基于Monte-Carlo方法对参数估计量性质的检验结果表明，本研究的拟极大似然估计量随着样本容量的增加，其渐近性质得到改善而更接近于真实值，且估计量性质的改善程度对时间维度的敏感性强于对空间维度的敏感性，因此在空间单元限定的情形下有效地增加时间维度可以显著地改善估计量性质。利用本研究所建立的动态空间固定效应模型，在考虑了技术溢出、劳动力和资本等要素区域流动的基础之上，基于新古典经济增长理论与扩展的柯布-道格拉斯生产函数建立了中国省域经济增长的收敛模型，通过理论模型的动态均衡演变与实证研究结果表明：
一、中国省域经济增长符合新古典经济增长理论，存在着一定程度的经济趋同现象，即落后地区与发达地区的经济差距表现出一定程度的缩小态势。
二、研究发现，由于经济空间单元之间存在着技术溢出、劳动力和资本区域流动等推动因素，省域之间的经济存在一定程度的空间依赖和空间集聚现象，考虑空间效应后的经济收敛速度要快于不考虑这类空间效应的收敛速度。
三、通过与其它空间计量模型的对比结果发现，仅考虑可直接观测的空间效应或仅考虑不可直接观测或无法观测的空间效应都将导致对实际空间效应影响力的低估；现实经济中确实存在除技术、劳动力和资本以外，尚未纳入经济核算或被忽略的但对区域以及相邻区域经济增长起一定程度推动作用的其它影响因素，其在实证研究中须被纳入模型加以考虑。
本研究的创新之处：
一、相比于一类静态空间固定效应模型，本研究模型中引入了时间滞后因子，在空间动态(空间滞后)基础上进一步考虑了时间动态。
二、相比于部份学者所建立的动态空间固定效应模型，本研究所建立的模型对其进行了综合，模型中同时考虑了可直接观测和不可直接观测或无法观测的空间效应，可提供对现实经济系统更为完整的描述；同时也为模型选择提供了一种从一般到特殊的路径。
三、本研究基于拟极大似然方法对一类动态空间固定效应模型的参数进行估计，系统地推导和证明了参数估计量的渐近性质和渐近分布；并基于Monte-Carlo模拟实验对估计量渐近性质进行检验。
四、本研究基于新古典经济增长理论和扩展的柯布一道格拉斯生产函数，在考虑了技术溢出、劳动力和资本区域流动的基础上，构建了中国省域经济增长理论模型；并利用中国经济数据进行实证研究，得出较其它学者的研究结论更多的启示。
Based on the contributions of some researchers, this study constructs one class of dynamic spatial fixed effect models which consider both observable and unobservable spatial effects, and derives quasi maximum likelihood estimators under both exogenous and endogenous initial value. For testing the characteristics of quasi maximum likelihood estimators, the Monte-Carlo simulation is designed and the simulation results show that, the performance of quasi maximum likelihood estimators improves as the sample size grows. And what's more, the improvement of estimators seem more sensitive to time dimension than to space dimension, so it would effectively improve estimation performance by enlarging time dimension when space dimension set fixed. Based on the dynamic spatial fixed effect model in this paper, one economic growth convergence model considering technical spillover, labor and capital mobility is constructed based on the neo-classical economic growth theory and augmentative Cobb-Douglas production function. And the empirical results based on the data from mainland China provide some useful enlightenment.
First, the provincial economy in mainland China presents economic convergence, where the undeveloped provinces seem to have faster economic growth speed than the developed provinces. Such performance of provincial economy in mainland China consists with the instincts of neo-classical economic growth theory.
Second, there exist spatial dependence and spatial cluster among provinces of mainland China for there exist technical spillover, labor and capital mobility among economic regions. And the economic convergence speed after considering spatial effects shows faster than that without considering spatial effects.
Third, the comparison results show that, considering only the observable spatial effect or the unobservable spatial effect would tend to under-estimate the real spatial effect and lead to untrue conclusion. Beside of the technique, labor and capital, there exist some unaccounted factors which indeed contribute to economic growth, so they should be included into model when presenting empirical research.
The contributions of this study include:
First, comparing with the static spatial fixed effect models, the model constructed in this study includes both temporal-lagged operators and spatio-lagged operators which represent both temporal- and spatio-dynamics.
Second, comparing with the dynamic spatial fixed effect models constructed by other researchers, the model constructed in this study provides a combination by considering both observable and unobservable spatial effects and is able to provide much more complete description for real economy. And what's more, because of the "generality", our model provides an alternative path for model choose from general to special.
Third, this study completely derives and proves the asymptotic characteristics and distributions of the quasi maximum likelihood estimators and testing the theoretical performance by Monte-Carlo simulation.
Fourth, this study constructs economic growth convergence theoretical model for provincial economy in mainland China under considering the technical spillover, labor and capital mobility based on neo-classical economic growth theory and augmentative Cobb-Douglas production function. And the empirical research based on the data from mainland China presents more appealing results.
一、中国省域经济增长符合新古典经济增长理论，存在着一定程度的经济趋同现象，即落后地区与发达地区的经济差距表现出一定程度的缩小态势。
二、研究发现，由于经济空间单元之间存在着技术溢出、劳动力和资本区域流动等推动因素，省域之间的经济存在一定程度的空间依赖和空间集聚现象，考虑空间效应后的经济收敛速度要快于不考虑这类空间效应的收敛速度。
三、通过与其它空间计量模型的对比结果发现，仅考虑可直接观测的空间效应或仅考虑不可直接观测或无法观测的空间效应都将导致对实际空间效应影响力的低估；现实经济中确实存在除技术、劳动力和资本以外，尚未纳入经济核算或被忽略的但对区域以及相邻区域经济增长起一定程度推动作用的其它影响因素，其在实证研究中须被纳入模型加以考虑。
本研究的创新之处：
一、相比于一类静态空间固定效应模型，本研究模型中引入了时间滞后因子，在空间动态(空间滞后)基础上进一步考虑了时间动态。
二、相比于部份学者所建立的动态空间固定效应模型，本研究所建立的模型对其进行了综合，模型中同时考虑了可直接观测和不可直接观测或无法观测的空间效应，可提供对现实经济系统更为完整的描述；同时也为模型选择提供了一种从一般到特殊的路径。
三、本研究基于拟极大似然方法对一类动态空间固定效应模型的参数进行估计，系统地推导和证明了参数估计量的渐近性质和渐近分布；并基于Monte-Carlo模拟实验对估计量渐近性质进行检验。
四、本研究基于新古典经济增长理论和扩展的柯布一道格拉斯生产函数，在考虑了技术溢出、劳动力和资本区域流动的基础上，构建了中国省域经济增长理论模型；并利用中国经济数据进行实证研究，得出较其它学者的研究结论更多的启示。
Based on the contributions of some researchers, this study constructs one class of dynamic spatial fixed effect models which consider both observable and unobservable spatial effects, and derives quasi maximum likelihood estimators under both exogenous and endogenous initial value. For testing the characteristics of quasi maximum likelihood estimators, the Monte-Carlo simulation is designed and the simulation results show that, the performance of quasi maximum likelihood estimators improves as the sample size grows. And what's more, the improvement of estimators seem more sensitive to time dimension than to space dimension, so it would effectively improve estimation performance by enlarging time dimension when space dimension set fixed. Based on the dynamic spatial fixed effect model in this paper, one economic growth convergence model considering technical spillover, labor and capital mobility is constructed based on the neo-classical economic growth theory and augmentative Cobb-Douglas production function. And the empirical results based on the data from mainland China provide some useful enlightenment.
First, the provincial economy in mainland China presents economic convergence, where the undeveloped provinces seem to have faster economic growth speed than the developed provinces. Such performance of provincial economy in mainland China consists with the instincts of neo-classical economic growth theory.
Second, there exist spatial dependence and spatial cluster among provinces of mainland China for there exist technical spillover, labor and capital mobility among economic regions. And the economic convergence speed after considering spatial effects shows faster than that without considering spatial effects.
Third, the comparison results show that, considering only the observable spatial effect or the unobservable spatial effect would tend to under-estimate the real spatial effect and lead to untrue conclusion. Beside of the technique, labor and capital, there exist some unaccounted factors which indeed contribute to economic growth, so they should be included into model when presenting empirical research.
The contributions of this study include:
First, comparing with the static spatial fixed effect models, the model constructed in this study includes both temporal-lagged operators and spatio-lagged operators which represent both temporal- and spatio-dynamics.
Second, comparing with the dynamic spatial fixed effect models constructed by other researchers, the model constructed in this study provides a combination by considering both observable and unobservable spatial effects and is able to provide much more complete description for real economy. And what's more, because of the "generality", our model provides an alternative path for model choose from general to special.
Third, this study completely derives and proves the asymptotic characteristics and distributions of the quasi maximum likelihood estimators and testing the theoretical performance by Monte-Carlo simulation.
Fourth, this study constructs economic growth convergence theoretical model for provincial economy in mainland China under considering the technical spillover, labor and capital mobility based on neo-classical economic growth theory and augmentative Cobb-Douglas production function. And the empirical research based on the data from mainland China presents more appealing results.
引文
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