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Spatial Econometric Analysis

Spatial Econometric Analysis. 2 Kuan-Pin Lin Portland State University. Spatial Econometric Models. Spatial Exogenous Model Spatial Lag Model Spatial Mixed Model Spatial Error Model Spatial AR(1) Spatial MA(1) Spatial ARMA(1,1) Spatial Error Components Model.

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Spatial Econometric Analysis

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  1. Spatial Econometric Analysis 2 Kuan-Pin LinPortland State University

  2. Spatial Econometric Models • Spatial Exogenous Model • Spatial Lag Model • Spatial Mixed Model • Spatial Error Model • Spatial AR(1) • Spatial MA(1) • Spatial ARMA(1,1) • Spatial Error Components Model

  3. Spatial Exogenous ModelLagged Explanatory Variables • The Model

  4. Spatial Lag ModelLagged Dependent Variable • The Model

  5. Spatial Mixed Model • The Model

  6. Spatial Error Models • Spatial AR(1) • Spatial MA(1) • Spatial ARMA(1,1)

  7. Spatial Error Components Model • The Model

  8. Spatial Econometric Models • The General Model: SARAR(1,1) • Allowing spatial weights matrix to be different in the regression and in the error. The special case is W = M.

  9. Spatial Model Specification Tests • Moran Test • Moran’s I Test Statistic • Asymptotic Theory • Bootstrap Method • LM Test and Robust LM Test • Spatial Error Model • Spatial Lag Model

  10. Hypothesis Testing • The Basic Model

  11. Moran-Based Test Statistics • Moran’s I Index • Can not distinguish between spatial lag or spatial error

  12. LM-Based Test Statistics • LM Test Statistic for Spatial Error • Can not distinguish between spatial AR or spatial MA

  13. LM-Based Test Statistics • LM Test Statistic for Spatial Lag

  14. LM-Based Test Statistics • Robust LM Test Statistic for Spatial Error • Robust LM Test Statistic for Spatial Lag

  15. LM-Based Test Statistics • Joint LM Test for Spatial Correlation(Spatial Lag and Spatial Error)

  16. Hypothesis TestingExample • Crime Equation • (Crime Rate) = a + b (Family Income) + g (Housing Value) + e(numbers in parentheses are p-values of the tests)

  17. References • L. Anselin, and A. K. Bera, R. J.G.M. Florax, and M. Yoon (1996), “Simple Diagnostic Tests for Spatial Dependence,” Regional Science and Urban Economics, 26, 77-104. • L. Anselin, and H. Kelejian (1997), “Testing for Spatial Autocorrelation in the Presence of Endogenous Regressors,” International Regional Science Review, 20, 153–182. • L. Anselin, and S. Rey (1991), “Properties of Tests for Spatial Dependence in Linear Regression Models,” Geographical Analysis, 23, 112-131. • H. Kelejian, and I.R. Prucha (2001)., “On the Asymptotic Distribution of Moran I Test Statistic with Applications,” Journal Econometrics, 104, 219-257.

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