1. Spatial Econometric Analysis1
Kuan-Pin Lin Portland State University

2. Introduction Spatial Data Spatial Dependence Cross Section Panel Data
Spatial Heterogeneity
Spatial Correlation

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
W2, W3, …
Redundandency
Circularity

8. Spatial Weights Matrix An Example
3x3 Rook Contiguity
List of 9 Observations with 1-st Order Contiguity, #NZ=24 1 2 3 4 5 6 7 8 9 1
2,4 2
1,3,5 3
2,6 4
1,5,7 5
2,4,6,8 6
3,5,9 7
4,8 8
5,7,9 9
6,8

9. W 1st-Order Contiguity (Symmetric)1

10. W All-Order Contiguity (Symmetric)1 2 3 4

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

12. W1 Non-Symmetric Row-Standardized
1/2
1/3
1/4

13. W2 Non-Symmetric Row-Standardized
1/3
1/4

14. Oregon Counties

15. U. S. States

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

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

18. Examples Anselin (1988): Crime Equation
Basic Model (Crime Rate) = a + b (Family Income) + g (Housing Value) + e
Spatial Lag Model (Crime Rate) = a + b (Family Income) + g (Housing Value) l W (Crime Rate) + e
Spatial Error Model (Crime Rate) = a + b (Family Income) + g (Housing Value) + e e = r We + u
Data (anselin.txt, anselin_w.txt)

20. Examples
Ertur and Kosh (2007): International Technological Interdependence and Spatial Externalities
91 countries, growth convergence in 36 years ( )
Spatial Lag Solow Growth Model ln(y(t)) - ln(y(0)) = a + b ln(y(0)) + g ln(s) + g ln(n+g+d) + l W ln(y(t)) - ln(y(0))) + e
Data (data-ek.txt)

21. 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:
L. Anselin, “Under the Hood: Issues in the Specification and Interpretation of Spatial Regression Models,” Agricultural Economics 17 (3), 2002:
T.G. Conley, “Spatial Econometrics” Entry for New Palgrave Dictionary of Economics, 2nd 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: