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

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Presentation transcript:

Spatial Econometric Analysis 3 Kuan-Pin Lin Portland State University

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

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

Spatial Lag Model IV/2SLS with SHAC

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

Spatial Lag Model GMM Estimation Efficient GMM Estimator

Spatial Lag Model Maximum Likelihood Estimation Normal Density Function

Spatial Lag Model Maximum Likelihood Estimation Jacobian Matrix

Spatial Lag Model Maximum Likelihood Estimation Log-Likelihood Function

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

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    R2R

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    R2R

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    R2R

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    L

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