1. Spatial Econometric Analysis Using GAUSS 4 Kuan-Pin Lin Portland State University

2. 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

3. Spatial Exogenous Model Lagged Explanatory Variables The Model

4. Spatial Lag Model Lagged Dependent Variable The Model

5. Spatial Mixed Model The Model

6. Spatial Error Models Spatial AR(1) Spatial MA(1) Spatial ARMA(1,1)

7. Spatial Error Components Model The Model

8. Spatial Econometric Models The General Model

9. Spatial Model Specification Tests Moran Test Moran’s I Test Statistic Asymptotic Theory Bootstrap Method LM Test and Robust LM Test Spatial Error Model Spatial Lag Model

10. Hypothesis Testing The Basic Model

11. Moran-Based Test Statistics Moran’s I Index Can not distinguish between spatial lag or spatial error

12. LM-Based Test Statistics LM Test Statistic for Spatial Error Can not distinguish between spatial AR or spatial MA

13. LM-Based Test Statistics LM Test Statistic for Spatial Lag

14. LM-Based Test Statistics Robust LM Test Statistic for Spatial Error Robust LM Test Statistic for Spatial Lag

15. Hypothesis Testing Example Crime Equation (anselin.3)anselin.3 (Crime Rate) =  +  (Family Income) +  (Housing Value) +  (numbers in parentheses are p-values of the tests) Moran-ILM-errLM-lag Robust LM-err Robust LM-lagHetero. Crime Rate 5.6753 (0.000) 26.902 (0.000) 26.902 (0.000) Family Income 4.6624 (0.000) 17.841 (0.000) 17.841 (0.000) Housing Value 2.1529 (0.031) 3.3727 (0.066) 3.3727 (0.066)  2.954 (0.003) 5.723 (0.017) 9.363 (0.002) 0.0795 (0.778) 3.72 (0.054) 1.058 (0.589)

16. Hypothesis Testing Example China Output 2006 (china.6)china.6 ln(GDP) =  +  ln(L) +  ln(K) +  (numbers in parentheses are p-values of the tests) Moran-ILM-errLM-lag Robust LM-err Robust LM-lagHetero. ln(GDP)1.949 (0.052) 2.359 (0.125) 2.359 (0.125) ln(L)1.946 (0.052) 2.351 (0.125) 2.351 (0.125) ln(K)2.387 (0.017) 3.7658 (0.052) 3.7658 (0.052)  1.534 (0.125) 0.972 (0.324) 0.005 (0.942) 1.094 (0.296) 0.127 (0.721) 1.719 (0.423)

17. 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, 153–182. 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.