A Study On A Class Of Dynamic Spatial Fixed Effect Models

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.