Research On The Efficiency Of Bootstrap Moran Test In Spatial Econometric Models

Research on spatial econometrics has been a very important branch of the econometric field in the past two decades.It will provide a new research perspective and analysis tool to deal with spatial interaction and structure in economy and management.Due to the complexity of spatial correlation,many problems need to be solved in spatial econometric analysis(Anselin,2007).It is very necessary to test spatial dependence among research objects in spatial econometric analysis.Under classical normality assumption of the model, several common test statistics are asymptotically normal orχ² distributed,and can be used to test spatial dependence(Anselin,1988a).However,the sample is limited,and the classical normality assumption of the model is violated in many economy and management research. Then Moran's I test is questionable.So far,under the conditions of small sample or the non-normal i.i.d errors,Moran's I test for spatial dependence is a difficult question in the international academia.In this paper,bootstrap methods are applied to construct Moran's I test statistic for spatial dependence.Then we make use of mathematical derivation and simulation analysis, and research the efficiency of Bootstrap Moran's I statistic based on OLS residuals of the linear regression model,2SLS residuals of the spatial autoregressive model.The main conclusions of this dissertation are as follows:1.The efficiency of bootstrap Moran test in the linear regression model is proved. Specifically speaking,the bootstrap Moran test gains asymptotic refinements under the classical normality assumption of the model;the asymptotic theory of Moran's I statistic is invalidated under the non-normal i.i.d,errors(e.g.,the heteroscedastic or the unknown distributed error),and then spatial dependence can be effectively checked up by the bootstrap Moran test.When the number of bootstrap is more than 399,the size distortion of the bootstrap Moran test in the linear regression model is tending towards 0,and its' power is remarkably higher than asymptotic test under the negative spatial correlation and small samples.2.The asymptotic and exact distribution of Moran's I statistic in the spatial autoregressive model are proved.In this paper,in order to test spatial dependence among 2SLS or GMM residuals of the spatial autoregressive model,we establish Moran's I statistic based the 2SLS or GMM residuals,obtain the OLL-Moran test,and prove its asymptotic distribution in theory.Then our Monte Carlo experiments indicate that OLL-Moran test has good finite sample properties,and OLL-Moran test is more effectively than KP-Moran test in Kelejian & Prucha(2001) under the normal error.Lastly,the exact distribution of Moran's I statistic is deduced in regards of theory.3.The efficiency of bootstrap Moran test in the spatial autoregressive model is proved. In this paper,we deduce the following two conclusions.Firstly,bootstrap for the asymptotic Edgeworth expansion of Moran's I statistic in the spatial autoregressive model is approximately the true distribution of one at the rate of O(N^-1) under the normal i.i.d,error, and then the bootstrap Moran test gains asymptotic refinements.Secondly,when the error is not normal i.i.d,with heteroscedasticity or unknown distribution,OLL-Moran test is invalid, and the bootstrap Moran test can be effectively find spatial dependence among the 2SLS or GMM residuals of the spatial autoregressive model.Moreover,extensive Monte Carlo simulation results validate the theoretical conclusions about the efficiency of the bootstrap Moran test.The distinguishing characteristic in this paper is that the basic theoretical research is combined with practical application.The theoretical innovation in this research separately lies in the followed four aspects:1.The thesis solves the question of Moran's I test for spatial dependence based on OLS residuals of the linear regression model.The paper makes use of mathematical theories and simulation experiments,and then researches the efficiency of bootstrap Moran test in the linear regression model under the small sample or the non-normal i.i.d,error.It provides the sound foundation of mathematical theory and simulation experiments as well as the important theoretical value.These conclusions offer a convenient and effective analysis tool of spatial dependence test among OLS residuals of the linear regression model under the small sample. Furthermore,they have the extensive practical application value.2.Moran's I test for spatial dependence in the spatial autoregressive model is improved and extended.The asymptotic distribution of OLL-Moran test is deduced by mathematical theories and simulation analysis,where the Moran's I statistic is based on 2SLS or GMM residuals of the spatial autoregressive model.The foundation is expanded from 2SLS residuals to GMM residuals,and then the large sample property of the Moran's I test for spatial dependence is improved.It provides a convenient and effective method in order to test spatial dependence of the spatial autoregressive model under the large sample.Moreover,we provide the exact distribution of OLL-Moran test in the spatial autoregressive model.Another research idea of the problem about Moran's I test for spatial dependence among 2SLS or GMM residuals in the spatial econometric model is proposed under small sample.It's very worthy of theoretical researches.3.The thesis solves the question of Moran's I test for spatial dependence based on 2SLS or GMM residuals of the spatial autoregressive model.The paper makes use of mathematical theories and simulation experiments,and then researches the efficiency of bootstrap Moran test in the spatial autoregressive model when the sample is small,or the error assumption of the asymptotic distribution of OLL-Moran test isn't satisfied.It provides the sound foundation of mathematical theory and simulation experiments as well as the important theoretical value. These conclusions offer another research idea of spatial dependence test among 2SLS or GMM residuals of the spatial autoregressive model under the small sample.Moreover,there is the broad practical application value.4.A series of programs about the bootstrap Moran test are designed and written in the Gauss software.The efficiencies of bootstrap Moran test in the linear regression model and the spatial autoregressive model are researched.It is an innovation based on the conclusion of bootstrap methods and the empirical researches of Moran's I test for spatial dependence. Furthermore,the toolbox of Gauss software is greatly enriched,and then the convenient method is provided for the spatial econometric researchers.