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Spatial Econometric Analysis

Spatial Econometric Analysis. 5 Kuan-Pin Lin Portland State Univerisity. Spatial Autoregressive Model with Autoregressive Disturbances. SARAR(1,1) = SPLAG(1)+SPAR(1). Spatial Autoregressive Model with Moving Average Disturbances. SARMA(1,1) = SPLAG(1)+SPMA(1).

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Spatial Econometric Analysis

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  1. Spatial Econometric Analysis 5 Kuan-Pin LinPortland State Univerisity

  2. Spatial Autoregressive Model with Autoregressive Disturbances • SARAR(1,1) = SPLAG(1)+SPAR(1)

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

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

  5. Model EstimationMaximum Likelihood Estimation • Log-Likelihood Function

  6. Model EstimationMaximum Likelihood Estimation • Quasi Maximum Likelihood (QML) Estimator

  7. Model EstimationSARAR(1,1)

  8. Model EstimationSARAR(1,1): Generalized Method of Moments • Moment Functions (Kelejian and Prucha, 1998, 2009)

  9. Model EstimationSARAR(1,1): Generalized Method of Moments • 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.

  10. Model EstimationSARAR(1,1) • The Model • Estimate l, b and r simultaneously: QML • Estimate l, b and r iteratively: IV/GMM/GLS • IV or 2SLS • GMM • GLS

  11. Crime EquationAnselin (1988) • SARAR(1) Model(Crime Rate) = a + b (Family Income) + g (Housing Value) + + l W (Crime rate) + e , e = r We + u • GMM vs. QML Estimator

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

  13. References • 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 2SLS Estimation of Mixed Regressive Spatial Autoregressive Models. Journal of Econometrics, 137, 489-514.

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