1. Spatial Econometric Analysis 3 Kuan-Pin Lin Portland State University

2. Model Estimation Spatial Lag Model SPLAG(1) OLS is biased and inconsistent.

3. Spatial Lag Model IV or 2SLS Estimation Instrumental Variables Two-Stage Least Squares

4. Spatial Lag Model IV/2SLS with SHAC

5. Spatial Lag Model GMM Estimation Strong Exogeneity of Instrumental Variables Generalized Method of Moments (GMM)

6. Spatial Lag Model GMM Estimation Efficient GMM Estimator

7. Spatial Lag Model Maximum Likelihood Estimation Normal Density Function

8. Spatial Lag Model Maximum Likelihood Estimation Jacobian Matrix

9. Spatial Lag Model Maximum Likelihood Estimation Log-Likelihood Function

10. Spatial Lag Model Maximum Likelihood Estimation Quasi Maximum Likelihood (QML) Estimator

11. Crime Equation Anselin (1988) Spatial Lag Model (Crime Rate) =  +  (Family Income) +  (Housing Value) +  W (Crime Rate) +  OLS vs. IV Estimator OLS Parameter OLS s.e. IV Parameter IV s.e 0.557330.150290.454560.17440  -0.865840.35541-1.00070.36786  -0.263850.09136-0.26550.08802  38.1819.215343.79410.496 R2R2 0.65720.6536

12. Crime Equation Anselin (1988) Spatial Lag Model (Crime Rate) =  +  (Family Income) +  (Housing Value) +  W (Crime Rate) +  IV with SHAC Estimator IV Parameter IV s.e IV s.e./hc IV s.e/hac 0.454560.174400.142590.17428  -1.00070.367860.456300.48617  -0.26550.088020.173740.17306  43.79410.4967.75798.2884 R2R2 0.6536

13. Crime Equation Anselin (1988) Spatial Lag Model (Crime Rate) =  +  (Family Income) +  (Housing Value) +  W (Crime Rate) +  GMM Estimator GMM-hc Parameter GMM-hc s.e GMM-hac Parameter GMM-hac s.e 0.420170.129620.420230.13177  -1.18910.42062-0.976830.40565  -0.216250.15437-0.274280.14808  46.2567.066844.9226.9797 R2R2 0.64740.6504

14. Crime Equation Anselin (1988) Spatial Lag Model (Crime Rate) =  +  (Family Income) +  (Housing Value) +  W (Crime Rate) +  QML vs. GMM Estimator QML Parameter QML s.e GMM-hac Parameter GMM-hac s.e 0.431010.129620.420230.13177  -1.03160.42108-0.976830.40565  -0.265930.17309-0.274280.14808  45.0806.405144.9226.9797 L-182.39-181.1

15. References Kelejian ， H. ， and I. R. Prucha ， 1999. A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model. International Economic Review 40 ， 509-533. Kelejian, H., and I. R. Prucha, 2009. Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances. Journal of Econometrics, forthcoming. Lee ， L. F. ， 2004. Asymptotic Distributions of Maximum Likelihood Estimators for Spatial Autoregressive Models. Econometrica, 72, 1899-1925.