Spatial Econometric Analysis Using GAUSS,3Kuan-Pin Lin Portland State University,Spatial Weights Matrix,Anselin (1988) anselin.1 China 30 Provinces china.1, china.2 Ertur and Kosh (2007) ek.1 Homework U.S. 48 Lower States us48_w.txt U.S. 3109 Counties us3109_w.zip us3109_wlist.txt,Spatial Contiguity Weights Matrix Anselin (1988): W1, W2, W3,Spatial Contiguity Weights Matrix China, 30 Provinces and Cities: W1, W2, W3,Distance-Based Spatial Weights Ertur and Kosh (2007),Geographical Location (x,y) Longitude (x) Latitude (y) Great Circle Distance d=gcd(x,y) (x,y) is in degree decimal units Distance-Based Spatial Weights Matrix Using Kernel Weight Function,Distance-Based Spatial Weights Ertur and Kosh (2007),Kernel Weight FunctionParzen Kernel Bartlett Kernel (Tricubic Kernel) Turkey-Hanning Kernel Guassian or Exponenetial Kernel,Kernel Weights Spatial Matrix An Example,Negative Exponential DistanceNegative Gaussian Distance,Gaussian Distance Weights Matrix Ertur and Kosh (2007),Spatial HAC Estimator,The Classical Model,Spatial HAC Estimator General Heteroscedasticity,Huber-White Estimator,Spatial HAC Estimator General Heteroscedasticity and Autocorrelation,First Law of GeographyKelejian and Prucha (2007),Time Series HAC Estimator General Heteroscedasticity and Autocorrelation,Newey-West Estimator,Crime Equation Anselin (1988) anselin.2,Basic Model (Crime Rate) = a + b (Family Income) + g (Housing Value) + e Spatial HAC Estimator,GDP Output Production China 2006 china.3,Cobb-Douglass Production Functionln(GDP) = a + b ln(L) + g ln(K) + e Spatial HAC Estimator,Spatial Exogeneity Lagged Explanatory Variables,Spatial Exogenous Model,GDP Output Production China 2006 china.4,Cobb-Douglass Production Functionln(GDP) = a + b ln(L) + g ln(K) + bw W ln(L) + gw W ln(K) + e,Spatial Endogeneity Lagged Dependent Variable,Spatial Lag Model,References,T. Conley, 1999 “GMM estimation with cross sectional dependence,” Journal of Econometrics 92, 1999, 145. H. Kelejian and I.R. Prucha, “HAC Estimation in a Spatial Framework,” Journal of Econometrics, 140: 131-154. W. Newey, and K. West, 1987, “A simple, positive semi-definite, heteroskedastic and autocorrelated consistent covariance matrix,” Econometrica, 55, 1987, 703708. H. White, “Maximum Likelihood Estimation of Misspecified Models,” Econometrica, 50, 1982, 1-26.,Spatial Econometric Analysis Using GAUSS,4Kuan-Pin Lin Portland State University,Spatial Econometric Models,Spatial Exogenous Model Spatial Lag Model Spatial Mixed Model Spatial Error Model Spatial AR(1) Spatial MA(1) Spatial ARMA(1,1) Spatial Error Components Model,Spatial Exogenous Model Lagged Explanatory Variables,The Model,Spatial Lag Model Lagged Dependent Variable,The Model,Spatial Mixed Model,The Model,Spatial Error Models,Spatial AR(1) Spatial MA(1) Spatial ARMA(1,1),Spatial Error Components Model,The Model,Spatial Econometric Models,The General Model,Spatial Model Specification Tests,Moran Test Morans I Test Statistic Asymptotic Theory Bootstrap Method LM Test and Robust LM Test Spatial Error Model Spatial Lag Model,Hypothesis Testing,The Basic Model,Moran-Based Test Statistics,Morans I IndexCan not distinguish between spatial lag or spatial error,LM-Based Test Statistics,LM Test Statistic for Spatial ErrorCan not distinguish between spatial AR or spatial MA,LM-Based Test Statistics,LM Test Statistic for Spatial Lag,LM-Based Test Statistics,Robust LM Test Statistic for Spatial Error Robust LM Test Statistic for Spatial Lag,Hypothesis Testing Example,China Output 2006 (china.6) ln(GDP) = a + b ln(L) + g ln(K) + e (numbers in parentheses are p-values of the tests),Hypothesis Testing Example,Crime Equation (anselin.3) (Crime Rate) = a + b (Family Income) + g (Housing Value) + e (numbers in parentheses are p-values of the tests),References,L. Anselin, and A. K. Bera, R. J.G.M. Florax, and M. Yoon (1996), “Simple Diagnostic Tests for Spatial Dependence,” Regional Science and Urban Economics, 26, 77-104. L. Anselin, and H. Kelejian (1997), “Testing for Spatial Autocorrelation in the Presence of Endogenous Regressors,” International Regional Science Review, 20, 153182. L. Anselin, and S. Rey (1991), “Properties of Tests for Spatial Dependence in Linear Regression Models,” Geographical Analysis, 23, 112-131. H. Kelejian, and I.R. Prucha (2001)., “On the Asymptotic Distribution of Moran I Test Statistic with Applications,” Journal Econometrics, 104, 219-257.,