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

Spatial Exogenous Model Lagged Explanatory Variables The Model

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

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

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

Hypothesis Testing Example Crime Equation (Crime Rate) = a + b (Family Income) + g (Housing Value) + e (numbers in parentheses are p-values of the tests) Moran-I LM-err LM-lag Robust LM-err Robust Hetero. Crime Rate 5.6753 (0.000) 26.902 Family Income 4.6624 17.841 Housing Value 2.1529 (0.031) 3.3727 (0.066) e 2.954 (0.003) 5.723 (0.017) 9.363 (0.002) 0.0795 (0.778) 3.72 (0.054) 1.058 (0.589)

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.