Spatial Econometric Analysis 5 KuanPin Lin Portland State

Spatial Econometric Analysis 5 Kuan-Pin Lin Portland State Univerisity

Spatial Autoregressive Model with Autoregressive Disturbances l SARAR(1, 1) = SPLAG(1)+SPAR(1)

Spatial Autoregressive Model with Moving Average Disturbances l SARMA(1, 1) = SPLAG(1)+SPMA(1)

Spatial Autoregressive Model with ARMA Disturbances l SARARMA(1, 1, 1) = SPLAG(1)+SPAR(1)+SPMA(1)

Model Estimation Maximum Likelihood Estimation l Log-Likelihood Function SPLAG(1) + … J SPAR(1) (I-r. W) SPMA(1) (I+q. W)-1 SPARMA(1, 1) (I+q. W)-1(I-r. W)

Model Estimation Maximum Likelihood Estimation l Quasi Maximum Likelihood (QML) Estimator

Model Estimation SARAR(1, 1)

Model Estimation SARAR(1, 1): Generalized Method of Moments l Moment Functions (Kelejian and Prucha, 1998, 2009)

Model Estimation SARAR(1, 1): Generalized Method of Moments l l Sample moment functions are the same two equations of one parameter r as in the spatial error AR(1) model. The efficient GMM estimator follows exactly the same as the spatial error AR(1) model with the IV estimator of the spatial lag model.

Model Estimation SARAR(1, 1) l l l The Model Estimate l, b and r simultaneously: QML Estimate l, b and r iteratively: IV/GMM/GLS l l l IV or 2 SLS GMM GLS

Crime Equation Anselin (1988) l SARAR(1) Model (Crime Rate) = a + b (Family Income) + g (Housing Value) + + l W (Crime rate) + e , e = r We + u l GMM vs. QML Estimator GMM Parameter GMM s. e QML Parameter QML s. e l 0. 45602 0. 17491 0. 36806 0. 14947 r -0. 1221 0. 13571 0. 16669 0. 17286 b -1. 0438 0. 37611 -1. 0259 0. 44610 g -0. 2537 0. 08706 -0. 28165 0. 18534 a 43. 916 10. 738 47. 784 6. 9048 Q/L 2. 6706 -182. 23

Applications l Geographically Weighted Regression (GWR) l l l Limited Dependent Variables l l l Spatial Heterogeneity Spatial Autocorrelation Spatial Probit and Spatial Tobit Models Spatial Inference Spatial Prediction l l Best Predictors Spatial Model Comparison

References l l K. P. Bell, N. E. Bockstael, 2000, Applying the Generalized-Moments Estimation to Spatial Problems Involving Microlevel Daqta, Review of Economic s and Statistics, 82, 72 -82. H. Kelejian, and I. R. Prucha, 2010, Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances. Journal of Econometrics, 157, 53 -67. Das, D. , H. Kelejian, and I. R. Prucha, 2003. Small Sample Properties of Estimators of Spatial Autoregressive Models with Autoregressive Disturbances. Papers in Regional Science, 82, 1 -26. L. F. Lee, 2007. GMM and 2 SLS Estimation of Mixed Regressive Spatial Autoregressive Models. Journal of Econometrics, 137, 489514.