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Spatial Econometric Analysis Using GAUSS

Spatial Econometric Analysis Using GAUSS. 10 Kuan-Pin Lin Portland State University. Spatial Panel Data Models. The General Model. Spatial Panel Data Models. Assumptions Fixed Effects Random Effects Spatial Error Model: A= I or l =0 Spatial Lag Model: B= I or r =0

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Spatial Econometric Analysis Using GAUSS

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  1. Spatial Econometric AnalysisUsing GAUSS 10 Kuan-Pin LinPortland State University

  2. Spatial Panel Data Models • The General Model

  3. Spatial Panel Data Models Assumptions Fixed Effects Random Effects Spatial Error Model: A=I or l=0 Spatial Lag Model: B=I or r=0 Panel Data Model: A=B=I

  4. Spatial Panel Data ModelsExample: U. S. Productivity (48 States, 17 Years) Panel Data Model ln(GSP) = b0 + b1ln(Public) + b2ln(Private) + b3ln(Labor) + b4(Unemp) + e e = iu + v Spatial Lag Model ln(GSP) = b0 + b1ln(Public) + b2ln(Private) + b3ln(Labor)+ b4(Unemp) + λWln(GSP) + e e = iu + v Spatial Error Model ln(GSP) = b0 + b1ln(Public) + b2ln(Private) + b3ln(Labor) + b4(Unemp) + e e = r We+ e , e = iu + v Spatial Mixed Model ln(GSP) = b0 + b1ln(Public) + b2ln(Private) + b3ln(Labor) + b4(Unemp) + λWln(GSP) + e e = r We+ e , e = iu + v

  5. Model Estimation Based on panel data models (pooled, fixed effects, random effects), we consider: Spatial Error Model Spatial Lag Model Spatial Mixed Model Model Estimation Generalized Least Squares (IV/GLS) Generalized Method of Moments (GMM/GLS) Maximum Likelihood Estimation

  6. Spatial Lag Model Estimation • The Model: SPLAG(1) • OLS is biased and inconsistent.

  7. Spatial Lag Model Estimation Fixed Effects

  8. Spatial Lag Model Estimation Fixed Effects: IV or 2SLS Instrumental Variables Two-Stage Least Squares

  9. Spatial Lag Model Estimation Random Effects

  10. Spatial Lag Model Estimation Random Effects: IV/GLS Instrumental Variables Two-Stage Generalized Least Squares

  11. Spatial Lag Model Estimation Random Effects: IV/GLS • Feasible Generalized Least Squares • Estimate sv2 and su2 from the fixed effects model: • FGLS for random effects model:

  12. Spatial Error Model Estimation • The Model: SPAR(1) • Fixed Effects • Random Effects

  13. Spatial Error Model EstimationFixed Effects Moment Functions

  14. Spatial Error Model Estimation Fixed Effects • The Model: SPAR(1) • Estimate b and r iteratively: GMM/GLS • OLS • GMM • GLS

  15. Spatial Error Model Estimation Random Effects Moment Functions (Kapoor, Kelejian and Prucha, 2006)

  16. Spatial Error Model Estimation Random Effects • The Model: SPAR(1) • Estimate b and r iteratively: GMM/GLS • OLS • GMM • GLS

  17. Spatial Mixed Model Estimation • The Model: SARAR(1,1)

  18. Spatial Mixed Model Estimation • Two-Stage Estimation • Sample moment functions are the same as in the spatial error AR(1) model. The efficient GMM estimator follows exactly the same as the spatial error AR(1) model. • The transformed model which removes spatial error AR(1) correlation is estimated the same way as the spatial lag model using IV and GLS.

  19. Spatial Mixed Model Estimation Fixed Effects The Model: SPARAR(1,1)

  20. Spatial Mixed Model Estimation Fixed Effects • Estimate b and r iteratively: GMM/GLS • IV/2SLS • GMM • GLS

  21. Spatial Mixed Model Estimation Random Effects The Model: SPARAR(1,1)

  22. Spatial Mixed Model Estimation Random Effects • Estimate b,l and r iteratively: GMM/GLS • IV/2SLS • GMM • GLS

  23. Example: U. S. ProductivityBaltagi (2008) [munnell.5] Spatial Panel Data Model: GMM/GLS (Spatial Error)ln(GSP) = b0 + b1ln(Public) + b2ln(Private) + b3ln(Labor) + b4(Unemp) + e, e =ρW e + e, e = iu + v

  24. Example: U. S. ProductivityBaltagi (2008) [munnell.5] Spatial Panel Data Model: GMM/GLS (Spatial Mixed) ln(GSP) = b0 + b1ln(Public) + b2ln(Private) + b3ln(Labor) + b4(Unemp) + λWln(GSP) + e , e =ρW e + e , e = iu + v

  25. Another ExampleChina Provincial Productivity [china.9] Spatial Panel Data Model: GMM/GLS (Spatial Error) ln(Q) = a + bln(L) + g ln(K) + e e =ρW e + e , e = iu + v

  26. Another ExampleChina Provincial Productivity [china.9] Spatial Panel Data Model: GMM/GLS (Spatial Mixed)ln(Q) = a + bln(L) + g ln(K) + l Wln(Q) + e e =ρW e + e , e = iu + v

  27. Maximum Likelihood Estimation Error Components Assumptions Fixed Effects: Random Effects:

  28. Maximum Likelihood EstimationFixed Effects • Log-Likelihood Function

  29. Maximum Likelihood EstimationFixed Effects • Log-Likelihood Function (Lee and Yu, 2010) • Where z* is the transformation of z using the orthogonal eigenvector matrix of Q.

  30. Maximum Likelihood EstimationRandom Effects • Log-Likelihood Function

  31. Example: U. S. ProductivityBaltagi (2008) [munnell.4] Spatial Panel Data Model: QML (Spatial Lag)ln(GSP) = b0 + b1ln(Public) + b2ln(Private) + b3ln(Labor) + b4(Unemp) + λWln(GSP) + e , e = iu + v

  32. Example: U. S. ProductivityBaltagi (2008) [munnell.4] Spatial Panel Data Model: QML (Spatial Error) ln(GSP) = b0 + b1ln(Public) + b2ln(Private) + b3ln(Labor) + b4(Unemp) + e, e =ρW e + e , e = iu + v

  33. Example: U. S. ProductivityBaltagi (2008) [munnell.4] Spatial Panel Data Model: QML (Spatial Mixed)ln(GSP) = b0 + b1ln(Public) + b2ln(Private) + b3ln(Labor) + b4(Unemp) + λWln(GSP) + e , e =ρW e + e , e = iu + v

  34. Another ExampleChina Provincial Productivity [china.8] Spatial Panel Data Model: QML (Spatial Lag)ln(Q) = a + bln(L) + g ln(K) + l Wln(Q) + e e = iu + v

  35. Another ExampleChina Provincial Productivity [china.8] Spatial Panel Data Model: QML (Spatial Error) ln(Q) = a + bln(L) + g ln(K) + e e =ρW e + e , e = iu + v

  36. Another ExampleChina Provincial Productivity [china.8] Spatial Panel Data Model: QML (Spatial Mixed)ln(Q) = a + bln(L) + g ln(K) + l Wln(Q) + e e =ρW e + e , e = iu + v

  37. References • Elhorst, J. P. (2003). Specification and estimation of spatial panel data models, International Regional Science Review 26, 244-268. • Kapoor M., Kelejian, H. and I. R. Prucha, “Panel Data Models with Spatially Correlated Error Components,” Journal of Econometrics, 140, 2006: 97-130. • Lee, L. F., and J. Yu, “Estimation of Spatial Autoregressive Panel Data Models with Fixed Effects,” Journal of Econometrics 154, 2010: 165-185.

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