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Spatial Econometric Analysis Using GAUSS

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.

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Spatial Econometric Analysis Using GAUSS

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  1. Spatial Econometric AnalysisUsing GAUSS 1 Kuan-Pin LinPortland State University

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

  3. Spatial Dependence • Least Squares Estimator

  4. Spatial DependenceNonparametric Treatment • Robust Inference • Spatial Heteroscedasticity Autocorrelation Variance-Covariance Matrix

  5. Spatial DependenceNonparametric Treatment • SHAC Estimator • Kernel Function • Normalized Distance

  6. Spatial DependenceParametric 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

  7. Spatial DependenceParametric Representation • Characteristics of Spatial Weights Matrix • Sparseness • Weights Distribution • Eigenvalues • Higher-Order of Spatial Weights Matrix • W2, W3, … • Redundandency • Circularity

  8. Spatial Weights MatrixAn Example • 3x3 Rook Contiguity • List of 9 Observations with 1-st Order Contiguity, #NZ=24

  9. W1st-Order Contiguity (Symmetric)

  10. WAll-Order Contiguity (Symmetric)

  11. An Example of Kernel WeightsK = 1/(ii’ + W)

  12. W1Non-Symmetric Row-Standardized

  13. W2 Non-Symmetric Row-Standardized

  14. U. S. States

  15. China Provinces

  16. Spatial Lag Variables • Spatial Independent Variables • Spatial Dependent Variables • Spatial Error Variables

  17. Spatial Econometric Models • Linear Regression Model with Spatial Variables • Spatial Lag Model • Spatial Mixed Model • Spatial Error Model

  18. Examples • Anselin (1988): Crime Equation • Basic Model(Crime Rate) = a + b (Family Income) + g (Housing Value) + e • Spatial Lag Model(Crime Rate) = a + b (Family Income) + g (Housing Value) + l W (Crime Rate) + e • Spatial Error Model(Crime Rate) = a + b (Family Income) + g (Housing Value) + ee = r We + u • Data (anselin.txt, anselin_w.txt)

  19. Examples • China Provincial GDP Output Function • Basic Modelln(GDP) = a + b ln(L) + g ln(K) + e • Spatial Mixed Model ln(GDP) = a + b ln(L) + g ln(K) + bw W ln(L) + gw W ln(K) + l W ln(GDP) + e • Data (china_gdp.txt, china_l.txt, china_k.txt, china_w.txt)

  20. Examples • Ertur and Kosh (2007): International Technological Interdependence and Spatial Externalities • 91 countries, growth convergence in 36 years (1960-1995) • Spatial Lag Solow Growth Modelln(y(t)) - ln(y(0)) = a + b ln(y(0)) + g ln(s) + g ln(n+g+d) + l W ln(y(t)) - ln(y(0))) + e • Data (data-ek.txt)

  21. References • L. Anselin, Spatial Econometrics: Methods and Models. Kluwer Academic Publishers, Boston, 1988. • L. Anselin. “Spatial Econometrics,” In T.C. Mills and K. Patterson (Eds.), Palgrave Handbook ofEconometrics: Volume 1, Econometric Theory. Basingstoke, Palgrave Macmillan, 2006: 901-969. • L. Anselin, “Under the Hood: Issues in the Specification and Interpretation of Spatial Regression Models,” Agricultural Economics 17 (3), 2002: 247-267. • T.G. Conley, “Spatial Econometrics” Entry for New Palgrave Dictionary of Economics, 2nd 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, 2007. • J. LeSage and R.K. Pace, Introduction to Spatial Econometrics, Chapman & Hall, CRC Press, 2009. • H. Kelejian and I.R. Prucha, “HAC Estimation in a Spatial Framework,” Journal of Econometrics, 140: 131-154.

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