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

2. Introduction to Spatial Econometric Analysis Spatial Data Cross Section Panel Data Spatial Dependence Spatial Heterogeneity Spatial Autocorrelation

3. Spatial Dependence Least Squares Estimator

4. Spatial Dependence Nonparametric Treatment Robust Inference Spatial Heteroscedasticity Autocorrelation Variance-Covariance Matrix

5. Spatial Dependence Nonparametric Treatment SHAC Estimator Kernel Function Normalized Distance

6. Spatial Dependence Parametric Representation Spatial Weights Matrix Spatial Contiguity Geographical Distance  First Law of Geography: Everything is related to everything else, but near things are more related than distant things. K-Nearest Neighbors

7. Spatial Dependence Parametric Representation Characteristics of Spatial Weights Matrix Sparseness Weights Distribution Eigenvalues Higher-Order of Spatial Weights Matrix W 2, W 3, … Redundandency Circularity

8. Spatial Weights Matrix An Example 3x3 Rook Contiguity List of 9 Observations with 1-st Order Contiguity, #NZ=24 123 456 789 12,4 21,3,5 32,6 41,5,7 52,4,6,8 63,5,9 74,8 85,7,9 96,8

9. W 1st-Order Contiguity (Symmetric) 010100000 01010000 0001000 010100 01010 0001 010 01 0

10. W All-Order Contiguity (Symmetric) 012123234 01212323 0321432 012123 01212 0321 012 01 0

11. An Example of Kernel Weights K = 1/(ii’ + W) 11/21/31/21/31/41/31/41/5 11/21/31/21/31/41/31/4 1 1/31/21/51/41/3 11/21/31/21/31/4 11/21/31/21/3 11/41/31/2 1 1/3 11/2 1

12. W 1 Non-Symmetric Row-Standardized 01/20 00000 1/30 0 0000 01/2000 000 1/3000 0 00 01/40 0 0 0 001/30 000 0001/2000 0 00001/30 0 000001/20 0

13. W 2 Non-Symmetric Row-Standardized 001/30 0 00 000 0 0 0 000 000 0 000 0 0 1/40 000 0 01/30 000 0 000 000 0 0 0 000 00 0 0 00

14. U. S. States

15. China Provinces

16. Spatial Lag Variables Spatial Independent Variables Spatial Dependent Variables Spatial Error Variables

17. Spatial Econometric Models Linear Regression Model with Spatial Variables Spatial Lag Model Spatial Mixed Model Spatial Error Model

18. Examples Anselin (1988): Crime Equation Basic Model (Crime Rate) =  +  (Family Income) +  (Housing Value) +  Spatial Lag Model (Crime Rate) =  +  (Family Income) +  (Housing Value) +  W (Crime Rate) +  Spatial Error Model ( Crime Rate) =  +  (Family Income) +  (Housing Value) +   =  W  +  Data (anselin.txt, anselin_w.txt)anselin.txtanselin_w.txt

20. Examples China Provincial GDP Output Function Basic Model ln(GDP) =  +  ln(L) +  ln(K) +  Spatial Mixed Model ln(GDP) =  +  ln(L) +  ln(K) +  w W ln(L) +  w W ln(K) + W ln(GDP) +  Data (china_gdp.txt, china_l.txt, china_k.txt, china_w.txt)china_gdp.txtchina_l.txtchina_k.txt china_w.txt

21. Examples Ertur and Kosh (2007): International Technological Interdependence and Spatial Externalities 91 countries, growth convergence in 36 years (1960-1995) Spatial Lag Solow Growth Model ln(y(t)) - ln(y(0)) =  +  ln(y(0)) +  ln(s) +  ln(n+g+  ) + W ln(y(t)) - ln(y(0))) +  Data (data-ek.txt)data-ek.txt

22. References L. Anselin, Spatial Econometrics: Methods and Models. Kluwer Academic Publishers, Boston, 1988. L. Anselin. “Spatial Econometrics,” In T.C. Mills and K. Patterson (Eds.), Palgrave Handbook of Econometrics: Volume 1, Econometric Theory. Basingstoke, Palgrave Macmillan, 2006: 901-969. L. Anselin, “Under the Hood: Issues in the Specification and Interpretation of Spatial Regression Models,” Agricultural Economics 17 (3), 2002: 247-267. T.G. Conley, “Spatial Econometrics” Entry for New Palgrave Dictionary of Economics, 2 nd Edition, S Durlauf and L Blume, eds. (May 2008). C. Ertur and W. Kosh, “Growth, Technological Interdependence, Spatial Externalities: Theory and Evidence,” Journal of Econometrics, 2007. J. LeSage and R.K. Pace, Introduction to Spatial Econometrics, Chapman & Hall, CRC Press, 2009. H. Kelejian and I.R. Prucha, “HAC Estimation in a Spatial Framework,” Journal of Econometrics, 140: 131-154.