空间计量经济学模型的研究
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摘要
在传统的统计学中,研究变量之间相互关系时很少考虑到空间相关性,比如经典的时间学列分析,还有在时间序列和截面数据的基础上产生的面板数据(Panel Data)。然而,随着理论研究与应用实践的不断发展,越来越多学者开始注意研究变量之间的在空间上的相依关系。
空间自相关的概念来源于时间序列的自相关,它反映的是在空间域上某一位置与其邻近位置上同一变量的相关性。例如两个邻近省份的经济、教育等发展程度有无类似或者截然相反等等。在研究空间数据的相关性时,通常需要建立一些可以反映空间变量特征的模型来研究变量之间的关系。常用的模型有空间自回归模型(Spatial Autoregression model)、地理加权回归模型(Geographical weighted regression model),本文所要研究的空间面板误差分量模型和地理加权回归模型的嵌套形式,就是在这两种模型的基础上产生的。
空间误差分量模型是Kelejian和Robinson于1993年和1995年提出了一种空间回归模型,它是在空间自回归模型的基础上,对回归干扰项提出的一种新的假设,从根本上说,是对干扰项是否存在异质性的一种假设。本文在此模型的基础上将它与面板数据相结合,兼顾了截面间的截面效应和空间关系,比单纯使用空间数据和单纯使用面板数据的研究方法要更加优越,具有很高的应用价值。
地理加权回归模型是一个局部空间模型,它将空间地理位置嵌入到回归系数之中,既能反映自变量与因变量的关系,又能反映数据的空间特性。本文在此模型的基础上引入了区域嵌套的概念,将原空间单元划分为几个区域,这样在研究数据空间特性时,更多了考虑了同区域中空间单元的共性和不同区域间的异质性。
In the traditional statistics, when we study the relationship between variables, we rarely consider about the spatial dependence, like classic time serial, and the panel data based on time serial and cross data. However, with the development of theoretical study and practical application, more and more scholars have began to pay attention to study the spatial dependence between variables.the concept of spatial dependence come from the dependence of time serial, and it shows the relativity of the same variable between one area and its neighboring area. For example, if there is similarity in the developing degree of the economic or education of two adjacent provinces, or they are right obverse, and so on. When studying the relativity, usually we need to erect some models that could show the character of spatial variables in order to study the relationship between variables. The normal models are Spatial Auto-regression model and Geographical weighted regression model. The nested format of spatial panel error weighted model and the geographical weighted regressive model that this thesis is going to study is just based on these two models.
Spatial panel error weighted model is one kind of spatial regression model that was put forward by Kelejian and Robinson in 1993 and in 1995 separately. It suggested one new hypothesis to disturbing item based on the spatial model. Essentially, it is a hypothesis about if there is heterogeneity. This thesis combines it with panel data and considers the cross effect and spatial relationship between cross sections. It is more outstanding and has much more practical value comparing with the method that purely using spatial data and purely using panel data.
Geographical weighted regressive model is one local spatial model and it embeds spatial geographical location in regression coefficients. It not only shows the relationship between independent variable and dependent variable, but also shows the spatial character of data. This thesis introduces the concept of zone based on this model, and divides the initial spatial area into different zone. Thus, when studying the spatial character of data, we consider the commonness of the same zone and heterogeneity of different zone.
空间自相关的概念来源于时间序列的自相关,它反映的是在空间域上某一位置与其邻近位置上同一变量的相关性。例如两个邻近省份的经济、教育等发展程度有无类似或者截然相反等等。在研究空间数据的相关性时,通常需要建立一些可以反映空间变量特征的模型来研究变量之间的关系。常用的模型有空间自回归模型(Spatial Autoregression model)、地理加权回归模型(Geographical weighted regression model),本文所要研究的空间面板误差分量模型和地理加权回归模型的嵌套形式,就是在这两种模型的基础上产生的。
空间误差分量模型是Kelejian和Robinson于1993年和1995年提出了一种空间回归模型,它是在空间自回归模型的基础上,对回归干扰项提出的一种新的假设,从根本上说,是对干扰项是否存在异质性的一种假设。本文在此模型的基础上将它与面板数据相结合,兼顾了截面间的截面效应和空间关系,比单纯使用空间数据和单纯使用面板数据的研究方法要更加优越,具有很高的应用价值。
地理加权回归模型是一个局部空间模型,它将空间地理位置嵌入到回归系数之中,既能反映自变量与因变量的关系,又能反映数据的空间特性。本文在此模型的基础上引入了区域嵌套的概念,将原空间单元划分为几个区域,这样在研究数据空间特性时,更多了考虑了同区域中空间单元的共性和不同区域间的异质性。
In the traditional statistics, when we study the relationship between variables, we rarely consider about the spatial dependence, like classic time serial, and the panel data based on time serial and cross data. However, with the development of theoretical study and practical application, more and more scholars have began to pay attention to study the spatial dependence between variables.the concept of spatial dependence come from the dependence of time serial, and it shows the relativity of the same variable between one area and its neighboring area. For example, if there is similarity in the developing degree of the economic or education of two adjacent provinces, or they are right obverse, and so on. When studying the relativity, usually we need to erect some models that could show the character of spatial variables in order to study the relationship between variables. The normal models are Spatial Auto-regression model and Geographical weighted regression model. The nested format of spatial panel error weighted model and the geographical weighted regressive model that this thesis is going to study is just based on these two models.
Spatial panel error weighted model is one kind of spatial regression model that was put forward by Kelejian and Robinson in 1993 and in 1995 separately. It suggested one new hypothesis to disturbing item based on the spatial model. Essentially, it is a hypothesis about if there is heterogeneity. This thesis combines it with panel data and considers the cross effect and spatial relationship between cross sections. It is more outstanding and has much more practical value comparing with the method that purely using spatial data and purely using panel data.
Geographical weighted regressive model is one local spatial model and it embeds spatial geographical location in regression coefficients. It not only shows the relationship between independent variable and dependent variable, but also shows the spatial character of data. This thesis introduces the concept of zone based on this model, and divides the initial spatial area into different zone. Thus, when studying the spatial character of data, we consider the commonness of the same zone and heterogeneity of different zone.
引文
[I]Anselin, L.,1988. Spatial Econometrics:Methods and Models. Kluwer Academic Publishers, Dordrecht
[2]Anselin, L.,2001. Rao's score tests in spatial econometrics, Journal of Statistical Planning and Inference 97,113-139.\
[3]Anselin, L. Simple diagnostic tests for spatial dependence [J]. Regional Science and Urban Economics,1996,(26):77-104.
[4]Anselin, Moreno,2003, Properties of tests for spatial error components, Regional Science and Urban Economics 33,(2003):595-618.
[5]Anselin, Bera,1998, Spatial Dependence in Linear Regression Models with an Introduction to Spatial Econometrics, in Ullah, A, and Griles, D.E.A.,(Eds),
[6]Anselin, L., Le Gallo, J, Jayet, J.,2008. Spatial panel econometrics. The econometrics of panel data:fundamentals and recent developments in theory and practice. Springer, Berlin Heidelberg.
[7]Badi H. Baltagi, Seuck Heun Song, Won Koh,2003. Testing panel data regression models with spatial error correlation, Journal of Econometric 117,123-150.
[8]Baltagi, B., Song, S.H., Koh, W.,2003. Testing panel data regression models with spatial error correlation. Journal of Econometrics 117,123-150.
[9]Carriazo, F., Coulson, E., A note on testing for spatial error components, Regional Science and Urban Economics(2009), doi:10.1016/j regsciurbeco.2009.08.001.
[10]Cliff A.D., Ord, J.K.,1973. Spatial autocorrelation. Pion Ltd., London.
[11]Cliff A.D.,Ord, J.K.,1981.Spatial Processes:Models and Applications.
[12]Fotheringham,A.S., Charlton.M,, Brunsdon,C. Geographically Weighted Regression:The Analysis of Spatially Varying Relationships[M]. New York:Wiley. 2002
[13]Harry H. Kelejian, Dennis P.Robinson,1993. A suggested method of estimation for spatial interdependent models with autocorrelated errors, and an application to a county expenditure model. Papers Regional Science 72,297-312.
[14]Imhof.J.P. Computing the distribution of quadratic forms in normal variables.Biometrika,1961;48:419-426
[15]Kelejian, H.H., Robinson, D.P.,1993. A suggested method of estimation for spatial interdependent models with autocorrelated errors, and an application to a county expenditure model. Papers Regional 72,297-312
[16]Kelejian, H.H., Robinson, D.P.,1995. Spatial correlation:a suggested alternative to the autoregressive model, In:Anselin,L., Florax, R.J.(Eds.), New Directions in Spatial Econometrics, Spring-Verlag, Berlin, pp.75-95.
[17]Kelejian, H.H., Prucha, I.R.,1999. A generalized moments estimator for the autoregressive parameter in a spatial model. International Economic Review 40, 509-533.
[18]Kapoor, M., Kelejian, H.H., Prucha, I.R.,2007. Panel data models with spatially correlated error components. Journal of Econometrics 140,97-130.
[19]Martins-Filho, C., Yao, F.,(2009). Nonparametric Regression Estimation with General Parametric Error Covariance, J. Multi. Anal.to appear
[20]Ord J K, Getis A. Testing for local spatial autocorrelation in the presence of global autocorrelation. Journal of Regional Science,2001,41:411-432.
[21]Pearson. E.S. Note on an approximation to the distribution of non-central χ2[J]. Biometrika,1959;46:364
[22]Smimov, Anselin,2001, Fast maximum likelihood estimation of very large spaiial autoregressive models:a characteristic polynomial approach.
[23]Yang, Z, A robust LM test for spatial error components, Regional Science and Urban Economics (2009), doi:10.1016/j.regsciurbeco.2009.10.001.
[24]李序颖,顾岚.空间自回归模型及其估计.2004年第6期
[25]梅长林,张文修.利用局部加权拟合方法检验线性回归关系[J].系统科学与数学,2002,22(4)：467-480.
[26]梅长林.泛函系数回归模型的研究及其应用[D].西安交通大学博士论文.2000.
[27]覃文忠,王建梅,刘妙龙.地理加权回归分析空间数据的空间非平稳性[J].辽宁师范大学学报(自然科学版).2005年04期
[28]苏方林,基于地理加权回归模型的县域经济发展的空间因素分析——以辽宁省县域为例.学术论坛.2005年05期
[29]王远飞,何红林.空间数据分析方法.北京出版社.
[30]魏传华,梅长林.半参数空间变系数回归模型的两步估计方法及其数值模拟.统计与信息论坛.2005,1：16-19.
[2]Anselin, L.,2001. Rao's score tests in spatial econometrics, Journal of Statistical Planning and Inference 97,113-139.\
[3]Anselin, L. Simple diagnostic tests for spatial dependence [J]. Regional Science and Urban Economics,1996,(26):77-104.
[4]Anselin, Moreno,2003, Properties of tests for spatial error components, Regional Science and Urban Economics 33,(2003):595-618.
[5]Anselin, Bera,1998, Spatial Dependence in Linear Regression Models with an Introduction to Spatial Econometrics, in Ullah, A, and Griles, D.E.A.,(Eds),
[6]Anselin, L., Le Gallo, J, Jayet, J.,2008. Spatial panel econometrics. The econometrics of panel data:fundamentals and recent developments in theory and practice. Springer, Berlin Heidelberg.
[7]Badi H. Baltagi, Seuck Heun Song, Won Koh,2003. Testing panel data regression models with spatial error correlation, Journal of Econometric 117,123-150.
[8]Baltagi, B., Song, S.H., Koh, W.,2003. Testing panel data regression models with spatial error correlation. Journal of Econometrics 117,123-150.
[9]Carriazo, F., Coulson, E., A note on testing for spatial error components, Regional Science and Urban Economics(2009), doi:10.1016/j regsciurbeco.2009.08.001.
[10]Cliff A.D., Ord, J.K.,1973. Spatial autocorrelation. Pion Ltd., London.
[11]Cliff A.D.,Ord, J.K.,1981.Spatial Processes:Models and Applications.
[12]Fotheringham,A.S., Charlton.M,, Brunsdon,C. Geographically Weighted Regression:The Analysis of Spatially Varying Relationships[M]. New York:Wiley. 2002
[13]Harry H. Kelejian, Dennis P.Robinson,1993. A suggested method of estimation for spatial interdependent models with autocorrelated errors, and an application to a county expenditure model. Papers Regional Science 72,297-312.
[14]Imhof.J.P. Computing the distribution of quadratic forms in normal variables.Biometrika,1961;48:419-426
[15]Kelejian, H.H., Robinson, D.P.,1993. A suggested method of estimation for spatial interdependent models with autocorrelated errors, and an application to a county expenditure model. Papers Regional 72,297-312
[16]Kelejian, H.H., Robinson, D.P.,1995. Spatial correlation:a suggested alternative to the autoregressive model, In:Anselin,L., Florax, R.J.(Eds.), New Directions in Spatial Econometrics, Spring-Verlag, Berlin, pp.75-95.
[17]Kelejian, H.H., Prucha, I.R.,1999. A generalized moments estimator for the autoregressive parameter in a spatial model. International Economic Review 40, 509-533.
[18]Kapoor, M., Kelejian, H.H., Prucha, I.R.,2007. Panel data models with spatially correlated error components. Journal of Econometrics 140,97-130.
[19]Martins-Filho, C., Yao, F.,(2009). Nonparametric Regression Estimation with General Parametric Error Covariance, J. Multi. Anal.to appear
[20]Ord J K, Getis A. Testing for local spatial autocorrelation in the presence of global autocorrelation. Journal of Regional Science,2001,41:411-432.
[21]Pearson. E.S. Note on an approximation to the distribution of non-central χ2[J]. Biometrika,1959;46:364
[22]Smimov, Anselin,2001, Fast maximum likelihood estimation of very large spaiial autoregressive models:a characteristic polynomial approach.
[23]Yang, Z, A robust LM test for spatial error components, Regional Science and Urban Economics (2009), doi:10.1016/j.regsciurbeco.2009.10.001.
[24]李序颖,顾岚.空间自回归模型及其估计.2004年第6期
[25]梅长林,张文修.利用局部加权拟合方法检验线性回归关系[J].系统科学与数学,2002,22(4)：467-480.
[26]梅长林.泛函系数回归模型的研究及其应用[D].西安交通大学博士论文.2000.
[27]覃文忠,王建梅,刘妙龙.地理加权回归分析空间数据的空间非平稳性[J].辽宁师范大学学报(自然科学版).2005年04期
[28]苏方林,基于地理加权回归模型的县域经济发展的空间因素分析——以辽宁省县域为例.学术论坛.2005年05期
[29]王远飞,何红林.空间数据分析方法.北京出版社.
[30]魏传华,梅长林.半参数空间变系数回归模型的两步估计方法及其数值模拟.统计与信息论坛.2005,1：16-19.