Spatial Econometric Model Estimation Spatial Lag Model.ppt

1、Spatial Econometric Analysis Using GAUSS,5 Kuan-Pin LinPortland State University,Model EstimationSpatial Lag Model,SPLAG(1) OLS is biased and inconsistent.,Spatial Lag ModelIV or 2SLS Estimation,Instrumental Variables Two-Stage Least Squares,Spatial Lag ModelIV/2SLS with SHAC,Spatial Lag ModelGMM Es

2、timation,Strong Exogeneity of Instrumental Variables Generalized Method of Moments (GMM),Spatial Lag ModelGMM Estimation,Efficient GMM Estimator,Spatial Lag ModelMaximum Likelihood Estimation,Normal Density Function,Spatial Lag ModelMaximum Likelihood Estimation,Jacobian Matrix,Spatial Lag ModelMaxi

3、mum Likelihood Estimation,Log-Likelihood Function,Spatial Lag ModelMaximum Likelihood Estimation,Quasi Maximum Likelihood (QML) Estimator,Crime EquationAnselin (1988) anselin.4,Spatial Lag Model(Crime Rate) = a + b (Family Income) + g (Housing Value) + l W (Crime Rate) + e OLS vs. IV Estimator,Crime

4、 EquationAnselin (1988) anselin.5,Spatial Lag Model(Crime Rate) = a + b (Family Income) + g (Housing Value) + l W (Crime Rate) + e IV with SHAC Estimator,Crime EquationAnselin (1988) anselin.6,Spatial Lag Model(Crime Rate) = a + b (Family Income) + g (Housing Value) + l W (Crime Rate) + e GMM Estima

5、tor,Crime EquationAnselin (1988) anselin.7,Spatial Lag Model(Crime Rate) = a + b (Family Income) + g (Housing Value) + l W (Crime Rate) + e QML vs. GMM Estimator,References,Kelejian，H.，and I. R. Prucha，1999. A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model. Interna

6、tional 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

7、 for Spatial Autoregressive Models. Econometrica, 72, 1899-1925.,Spatial Econometric Analysis Using GAUSS,6 Kuan-Pin LinPortland State Univerisity,Model EstimationSpatial Error Model,Spatial AR(1),Model EstimationSpatial Error Model,Spatial MA(1),Model EstimationSpatial Error Model,Spatial ARMA(1,1)

8、,Spatial Error AR(1) ModelMaximum Likelihood Estimation,Normal Density Function,Spatial Error AR(1) ModelMaximum Likelihood Estimation,Log-Likelihood Function,Spatial Error AR(1) ModelMaximum Likelihood Estimation,Quasi Maximum Likelihood (QML) Estimator,Spatial Error AR(1) ModelMaximum Likelihood E

9、stimation,Generalization to consider spatial MA(1) and spatial ARMA(1,1) is straightforward.,Crime EquationAnselin (1988) anselin.8,Spatial Error Model: AR, MA, ARMA(Crime Rate) = a + b (Family Income) + g (Housing Value) + ee = r We + u, or e = q Wu + u,Crime EquationAnselin (1988) anselin.8,QML Es

10、timator: SPLAG(1) vs. SPAR(1),Spatial Error AR(1) ModelGeneralized Method of Moments,Moment Functions (Kelejian and Prucha, 1998),Spatial Error AR(1) ModelGeneralized Method of Moments,Sample Moment Functions,Spatial Error AR(1) ModelGeneralized Method of Moments,Nonlinear GMM: 1 Parameter, 2 Equati

11、ons,Spatial Error AR(1) ModelGeneralized Method of Moments,Nonlinear GMM: 1 Parameter, 2 Equations,Spatial Error AR(1) ModelGeneralized Method of Moments,Minimum Distance (MD) Estimator Efficient GMM Estimator,Spatial Error AR(1) ModelGeneralized Method of Moments,Estimation of the variance-covarian

12、ce matrix of moment functions,Model EstimationSpatial Error Model,Spatial AR(1) Model Estimate b and r simultaneously: QML Estimate b and r iteratively: GMM/GLS OLS GMM GLS,Crime EquationAnselin (1988) anselin.9,Spatial Error AR(1) Model(Crime Rate) = a + b (Family Income) + g (Housing Value) + ee =

13、 r We + u GMM vs. QML Estimator,References,H. Kelejian and I. R. Prucha,1998. A Generalized Spatial Two-stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbance. Journal of Real Estate Finance and Economics, 17, 99-121. L.F.Lee，2003. Best Spatial Two-stage Least Squares Estimators for a Spatial Autoregressi