Estimation Methods Of Panel Data Spatial Error Components Model

Spatial error models mainly deal with the spatial correlation in error terms,are important parts of spatial econometric analysis. However, the classic spatial error model analysis is based on the hypothesis that only spatial spillover effect in independent errors, without considering the regional specific shocks which are not spatial correlated. As a result, spatial error models may magnify spatial spillover effects, failed to be coincide with the reality of economic operation completely. In addition, error variance would be a singular matrix is also a limitation of classic spatial error models.Kelejian & Robinson （1993, 1995） proposed cross-section spatial error components （SEC） model for solving these shortages. This paper extend cross-section SEC model to panel data model, complete corresponding mathematical derivation and Monte Carlo simulation experiments: first, we study the parameters hypothesis testing, including spatial correlation tests and individual effect tests; second, study the estimation methods of panel data SEC model, propose feasible generalized least square （FGLS） estimator based on Generalized Method of Moments （GMM）, which referred to as GMM-FGLS estimator, and prove its efficiency; Third, study spatial Hausman test of panel data SEC model for selecting individual effect; at last, study the empirical analysis based on panel data SEC model, use panel data of Chinese provincial carbon dioxide emissions and economic development in 1997-2009, study the impact factors of carbon dioxide emissions.The main conclusions of this paper are as follows:1. The efficiency of spatial correlation LM tests of panel data SEC model is proved. This paper propose spatial correlation test statistics of random effect SEC model and fixed effect SEC model via mathematical derivation, including marginal test and conditional test （transformed test of fixed effect SEC model）, and then, through Monte Carlo simulation experiments, study size tortuosity and power of these test statistics. The simulation results show that, for random effect SEC model, when random effect exists, conditional tests are more effective; when random effect does not exist, marginal tests are more effective; for fixed effect SEC model, transformed tests have smaller size tortuosity and superior test power, and is not affected by the size of fixed effect, so that it is the ideal test statistic in economy empirical studies. What more, the test statistics are more effective with the increase of spatial correlation and sample size. Generally speaking, spatial weight matrixes have little effect on finite sample properties of these test statistics.2. The efficiency of GMM-FGLS estimator is proved. This paper estimate model parameters of panel data SEC model using FGLS method, based on variance parameters estimators by GMM. At the same time, we propose maximum likelihood （ML） estimator and FGLS estimator based on LS estimators （LS-FGLS in short） of panel data SEC model. Finally, through Monte Carlo simulation experiments, we compare root mean square error （RMSE） performance of these estimators. Simulation results indicate that, when error term is normally distributed, the RMSE of GMM-FGLS estimator is very close to GLS estimator and ML estimator, while far superior than LS-FGLS estimator and the ordinary least squares （OLS） estimator; when error term is not normally distributed, the RMSE of GMM-FGLS estimator is close to GLS estimator, but dominate ML estimator. The simulation results indicate that GMM-FGLS estimator is effective estimator in the empirical study of panel data SEC model.3. The efficiency of spatial Hausman test of panel data SEC model is proved. This paper proves that, when panel data SEC model is true model, classic panel data Hausman test is not effective, but the proposed spatial Hausman test is effective. And next, we optimize spatial Hausman test through auxiliary regression method. Monte Carlo simulation experiment results indicate that, classic Hausman test has larger size tortuosity when spatial correlation exist; spatial Hausman test has more superior finite sample properties, and the auxiliary regression spatial Hausman test has the best finite sample properties of all, it is an ideal test statistic. What‘s more, the increase of spatial correlation or sample size will make spatial Hausman test more effective.4. Panel data SEC model is effective in empirical analysis. This paper applies LM test, estimate methods and spatial Hausman test in empirical research, uses provincial panel data of Chinese 30 provinces （except Tibet） in 1997-2009, study the influence factors of CO₂ emission. The empirical results show that, Chinese provincial CO₂ emissions exists evident positive spatial correlation, emission of CO₂ and GDP per capita is an inverted-N type Environmental Kuznets curve （EKC）. Panel data SEC model empirical analysis result indicate that, the CO₂ emissions decreasing turning point is more higher than that without considering the spatial correlation, the spatial correlation between provinces require more GDP per capita of the CO₂ emission decreasing turning. The efficiency of panel data SEC model in empirical study is proved.