Spatial Econometric Analysis

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Presentation transcript:

Spatial Econometric Analysis 4 Kuan-Pin Lin Portland State Univerisity

Model Estimation Spatial Error Model Spatial AR(1)

Model Estimation Spatial Error Model Spatial MA(1)

Model Estimation Spatial Error Model Spatial ARMA(1,1)

Spatial Error AR(1) Model Maximum Likelihood Estimation Normal Density Function

Spatial Error AR(1) Model Maximum Likelihood Estimation Log-Likelihood Function

Spatial Error AR(1) Model Maximum Likelihood Estimation Quasi Maximum Likelihood (QML) Estimator

Spatial Error AR(1) Model Maximum Likelihood Estimation Generalization to consider spatial MA(1) and spatial ARMA(1,1) is straightforward. J SPAR(1) (I-rW) SPMA(1) (I+qW)-1 SPARMA(1,1) (I+qW)-1(I-rW)

Crime Equation Anselin (1988) Spatial Error Model: AR, MA, ARMA (Crime Rate) = a + b (Family Income) + g (Housing Value) + e e = r We + u, or e = q Wu + u SPAR(1) QML Parameter s.e SPMA(1) r 0.56178 0.14142 q 0.79909 0.24514 b -0.94131 0.43774 -0.92181 0.41823 g -0.30225 0.16214 -0.28739 0.14551 a 59.893 5.0994 59.253 5.4177 L -183.38 -183.07

Crime Equation Anselin (1988) QML Estimator: SPLAG(1) vs. SPAR(1) SPAR(1) QML Parameter s.e SPLAG(1) r 0.56178 0.14142 l 0.43101 0.12962 b -0.94131 0.43774 -1.0316 0.42108 g -0.30225 0.16214 -0.26593 0.17309 a 59.893 5.0994 45.080 6.4051 L -183.38 -182.39

Spatial Error AR(1) Model Generalized Method of Moments Moment Functions (Kelejian and Prucha, 1998)

Spatial Error AR(1) Model Generalized Method of Moments Sample Moment Functions

Spatial Error AR(1) Model Generalized Method of Moments Nonlinear GMM: 1 Parameter, 2 Equations

Spatial Error AR(1) Model Generalized Method of Moments Nonlinear GMM: 1 Parameter, 2 Equations

Spatial Error AR(1) Model Generalized Method of Moments Minimum Distance (MD) Estimator Efficient GMM Estimator

Spatial Error AR(1) Model Generalized Method of Moments Estimation of the variance-covariance matrix of moment functions

Model Estimation Spatial Error Model Spatial AR(1) Model Estimate b and r simultaneously: QML Estimate b and r iteratively: GMM/GLS OLS GMM GLS

Crime Equation Anselin (1988) Spatial Error AR(1) Model (Crime Rate) = a + b (Family Income) + g (Housing Value) + e e = r We + u GMM vs. QML Estimator GMM Parameter GMM s.e QML Parameter QML r 0.54904 0.10596 0.56179 0.14142 b -0.95537 0.33081 -0.94131 0.43774 g -0.30193 0.09017 -0.30225 0.16214 a 60.096 5.3245 59.893 5.0994 Q 0.06979

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 Autoregressive Model with Autoregressive Disturbances. Econometrics Reviews, 22, 307-335. L.F. Lee, 2007. GMM and 2SLS Estimation of Mixed Regressive Spatial Autoregressive Models. Journal of Econometrics, 137, 489-514.