Spatial Econometric Analysis Using GAUSS 1 Kuan-Pin Lin Portland State University

Introduction to Spatial Econometric Analysis Spatial Data Cross Section Panel Data Spatial Dependence Spatial Heterogeneity Spatial Autocorrelation

Spatial Dependence Least Squares Estimator

Spatial Dependence Nonparametric Treatment Robust Inference Spatial Heteroscedasticity Autocorrelation Variance-Covariance Matrix

Spatial Dependence Nonparametric Treatment SHAC Estimator Kernel Function Normalized Distance

Spatial Dependence Parametric Representation Spatial Weights Matrix Spatial Contiguity Geographical Distance  First Law of Geography: Everything is related to everything else, but near things are more related than distant things. K-Nearest Neighbors

Spatial Dependence Parametric Representation Characteristics of Spatial Weights Matrix Sparseness Weights Distribution Eigenvalues Higher-Order of Spatial Weights Matrix W 2, W 3, … Redundandency Circularity

Spatial Weights Matrix An Example 3x3 Rook Contiguity List of 9 Observations with 1-st Order Contiguity, #NZ= ,4 21,3,5 32,6 41,5,7 52,4,6,8 63,5,9 74,8 85,7,9 96,8

W 1st-Order Contiguity (Symmetric)

W All-Order Contiguity (Symmetric)

An Example of Kernel Weights K = 1/(ii’ + W) 11/21/31/21/31/41/31/41/5 11/21/31/21/31/41/31/4 1 1/31/21/51/41/3 11/21/31/21/31/4 11/21/31/21/3 11/41/31/2 1 1/3 11/2 1

W 1 Non-Symmetric Row-Standardized 01/ / / / / / / / /20 0

W 2 Non-Symmetric Row-Standardized 001/ / /

U. S. States

China Provinces

Spatial Lag Variables Spatial Independent Variables Spatial Dependent Variables Spatial Error Variables

Spatial Econometric Models Linear Regression Model with Spatial Variables Spatial Lag Model Spatial Mixed Model Spatial Error Model

Examples Anselin (1988): Crime Equation Basic Model (Crime Rate) =  +  (Family Income) +  (Housing Value) +  Spatial Lag Model (Crime Rate) =  +  (Family Income) +  (Housing Value) +  W (Crime Rate) +  Spatial Error Model ( Crime Rate) =  +  (Family Income) +  (Housing Value) +   =  W  +  Data (anselin.txt, anselin_w.txt)anselin.txtanselin_w.txt

Examples China Provincial GDP Output Function Basic Model ln(GDP) =  +  ln(L) +  ln(K) +  Spatial Mixed Model ln(GDP) =  +  ln(L) +  ln(K) +  w W ln(L) +  w W ln(K) + W ln(GDP) +  Data (china_gdp.txt, china_l.txt, china_k.txt, china_w.txt)china_gdp.txtchina_l.txtchina_k.txt china_w.txt

Examples Ertur and Kosh (2007): International Technological Interdependence and Spatial Externalities 91 countries, growth convergence in 36 years ( ) Spatial Lag Solow Growth Model ln(y(t)) - ln(y(0)) =  +  ln(y(0)) +  ln(s) +  ln(n+g+  ) + W ln(y(t)) - ln(y(0))) +  Data (data-ek.txt)data-ek.txt

References L. Anselin, Spatial Econometrics: Methods and Models. Kluwer Academic Publishers, Boston, L. Anselin. “Spatial Econometrics,” In T.C. Mills and K. Patterson (Eds.), Palgrave Handbook of Econometrics: Volume 1, Econometric Theory. Basingstoke, Palgrave Macmillan, 2006: L. Anselin, “Under the Hood: Issues in the Specification and Interpretation of Spatial Regression Models,” Agricultural Economics 17 (3), 2002: T.G. Conley, “Spatial Econometrics” Entry for New Palgrave Dictionary of Economics, 2 nd Edition, S Durlauf and L Blume, eds. (May 2008). C. Ertur and W. Kosh, “Growth, Technological Interdependence, Spatial Externalities: Theory and Evidence,” Journal of Econometrics, J. LeSage and R.K. Pace, Introduction to Spatial Econometrics, Chapman & Hall, CRC Press, H. Kelejian and I.R. Prucha, “HAC Estimation in a Spatial Framework,” Journal of Econometrics, 140: