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Spatial Econometric Analysis

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).

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Spatial Econometric Analysis

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  1. Spatial Econometric Analysis 4 Kuan-Pin LinPortland State Univerisity

  2. Model EstimationSpatial Error Model • Spatial AR(1)

  3. Model EstimationSpatial Error Model • Spatial MA(1)

  4. Model EstimationSpatial Error Model • Spatial ARMA(1,1)

  5. Spatial Error AR(1) ModelMaximum Likelihood Estimation • Normal Density Function

  6. Spatial Error AR(1) ModelMaximum Likelihood Estimation • Log-Likelihood Function

  7. Spatial Error AR(1) ModelMaximum Likelihood Estimation • Quasi Maximum Likelihood (QML) Estimator

  8. Spatial Error AR(1) ModelMaximum Likelihood Estimation • Generalization to consider spatial MA(1) and spatial ARMA(1,1) is straightforward.

  9. Crime EquationAnselin (1988) • Spatial Error Model: AR, MA, ARMA(Crime Rate) = a + b (Family Income) + g (Housing Value) + ee = r We + u, or e = q Wu + u

  10. Crime EquationAnselin (1988) • QML Estimator: SPLAG(1) vs. SPAR(1)

  11. Spatial Error AR(1) ModelGeneralized Method of Moments • Moment Functions (Kelejian and Prucha, 1998)

  12. Spatial Error AR(1) ModelGeneralized Method of Moments • Sample Moment Functions

  13. Spatial Error AR(1) ModelGeneralized Method of Moments • Nonlinear GMM: 1 Parameter, 2 Equations

  14. Spatial Error AR(1) ModelGeneralized Method of Moments • Nonlinear GMM: 1 Parameter, 2 Equations

  15. Spatial Error AR(1) ModelGeneralized Method of Moments • Minimum Distance (MD) Estimator • Efficient GMM Estimator

  16. Spatial Error AR(1) ModelGeneralized Method of Moments • Estimation of the variance-covariance matrix of moment functions

  17. Model EstimationSpatial Error Model • Spatial AR(1) Model • Estimate b and r simultaneously: QML • Estimate b and r iteratively: GMM/GLS • OLS • GMM • GLS

  18. Crime EquationAnselin (1988) • Spatial Error AR(1) Model(Crime Rate) = a + b (Family Income) + g (Housing Value) + ee = r We + u • GMM vs. QML Estimator

  19. 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.

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