1. Spatial Econometric Analysis Using GAUSS3
Kuan-Pin Lin Portland State University

2. Spatial Weights Matrix
Anselin (1988) [anselin.1]
Ertur and Kosh (2007) [ek.1]
China 30 Provinces [china.1, china.2]
Homework
U.S. 48 Lower States [us48_w.txt]
U.S Counties [us3109_w.zip] [us3109_wlist.txt]

3. Spatial Contiguity Weights Matrix Anselin (1988): W1, W2, W3
use gpe2;
n=49;
load wd[n,n]=c:\course10\ec596\SEAUG\data\anselin\anselin_w.txt;
w1=spw(wd);
w2=spwpower(w1,2);
w3=spwpower(w1,3);
w4=spwpower(w1,4);
w5=spwpower(w1,5);
w6=spwpower(w1,6);
call spwplot(w1);
end;
#include gpe\spatial.gpe;

4. Spatial Contiguity Weights Matrix China, 30 Provinces and Cities: W1, W2, W3

5. Distance-Based Spatial Weights Ertur and Kosh (2007)
proc gcd(xc,yc);
local x,y,d;
x=pi*xc/180; @ convert to
y=pi*yc/180;
d=3963*arccos(sin(y').*sin(y)+cos(y').*cos(y).*cos(abs(x'-x)));
@ 3963 miles or 6378 km = radius of the
retp(real(d));
endp;
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

6. Distance-Based Spatial Weights Ertur and Kosh (2007)
Kernel Weight Function
Parzen Kernel
Bartlett Kernel (Tricubic Kernel)
Turkey-Hanning Kernel
Guassian or Exponenetial Kernel

7. Kernel Weights Spatial Matrix An Example
Negative Exponential Distance
Negative Gaussian Distance

8. Gaussian Distance Weights Matrix Ertur and Kosh (2007)

9. Spatial HAC Estimator
The Classical Model

10. Spatial HAC Estimator General Heteroscedasticity
Huber-White Estimator

11. Spatial HAC Estimator General Heteroscedasticity and Autocorrelation
First Law of Geography
Kelejian and Prucha (2007)

12. Time Series HAC Estimator General Heteroscedasticity and Autocorrelation
Newey-West Estimator

13. Crime Equation Anselin (1988) [anselin.2]
Basic Model (Crime Rate) = a + b (Family Income) + g (Housing Value) + e
Spatial HAC Estimator
OLS
Parameter
s.e.
Robust
s.e/hc
s.e/hac b g a
68.619
4.7355
4.1014
5.3639 R2
0.5520

14. GDP Output Production China 2006 [china.3]
Cobb-Douglass Production Function
ln(GDP) = a + b ln(L) + g ln(K) + e
Spatial HAC Estimator
OLS
Parameter
s.e.
Robust
s.e/hc
s.e/hac b g a R2

15. Spatial Exogeneity Lagged Explanatory Variables
Spatial Exogenous Model

16. GDP Output Production China 2006 [china.4]
Cobb-Douglass Production Function
ln(GDP) = a + b ln(L) + g ln(K) + bw W ln(L) + gw W ln(K) + e
OLS
Parameter
s.e.
Robust
s.e/hc
s.e/hac b g bw gw a R2

17. Spatial Endogeneity Lagged Dependent Variable
Spatial Lag Model

18. References
T. Conley, 1999 “GMM estimation with cross sectional dependence,” Journal of Econometrics 92, 1999, 1–45.
H. Kelejian and I.R. Prucha, “HAC Estimation in a Spatial Framework,” Journal of Econometrics 140, 2007,
W. Newey, and K. West, 1987, “A simple, positive semi-definite, heteroskedastic and autocorrelated consistent covariance matrix,” Econometrica, 55, 1987, 703–708.
H. White, “Maximum Likelihood Estimation of Misspecified Models,” Econometrica, 50, 1982, 1-26.