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Spatial Econometric Analysis Using GAUSS. 4 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 AnalysisUsing GAUSS 4 Kuan-Pin LinPortland 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
Spatial Exogenous ModelLagged Explanatory Variables • The Model
Spatial Lag ModelLagged Dependent Variable • The Model
Spatial Mixed Model • The Model
Spatial Error Models • Spatial AR(1) • Spatial MA(1) • Spatial ARMA(1,1)
Spatial Error Components Model • The Model
Spatial Econometric Models • The General Model
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
Hypothesis Testing • The Basic Model
Moran-Based Test Statistics • Moran’s I Index • Can not distinguish between spatial lag or spatial error
LM-Based Test Statistics • LM Test Statistic for Spatial Error • Can not distinguish between spatial AR or spatial MA
LM-Based Test Statistics • LM Test Statistic for Spatial Lag
LM-Based Test Statistics • Robust LM Test Statistic for Spatial Error • Robust LM Test Statistic for Spatial Lag
Hypothesis TestingExample • Crime Equation (anselin.3) • (Crime Rate) = a + b (Family Income) + g (Housing Value) + e(numbers in parentheses are p-values of the tests)
Hypothesis TestingExample • China Output 2006 (china.6) • ln(GDP) = a + b ln(L) + g ln(K) + e(numbers in parentheses are p-values of the tests)
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.