Spatial Econometric Analysis Using GAUSS

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Spatial Econometric Analysis Using GAUSS

• 10
• Kuan-Pin LinPortland State University

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Spatial Panel Data Models

• The General Model

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Spatial Panel Data Models

• Assumptions
• Fixed Effects
• Random Effects
• Spatial Error Model AI or l0
• Spatial Lag Model BI or r0
• Panel Data Model ABI

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Spatial Panel Data Models Example U. S.
Productivity (48 States, 17 Years)

• Panel Data Model
• ln(GSP) b0 b1 ln(Public) b2ln(Private)
  b3ln(Labor) b4(Unemp) e
• e i?u v
• Spatial Lag Model
• ln(GSP) b0 b1 ln(Public) b2ln(Private)
  b3ln(Labor) b4(Unemp) ?W ln(GSP) e
• e i?u v
• Spatial Error Model
• ln(GSP) b0 b1 ln(Public) b2ln(Private)
  b3ln(Labor) b4(Unemp) e
• e r We e , e i?u v
• Spatial Mixed Model
• ln(GSP) b0 b1 ln(Public) b2ln(Private)
  b3ln(Labor) b4(Unemp) ?W ln(GSP) e
• e r We e , e i?u v

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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

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Spatial Lag Model Estimation

• The Model SPLAG(1)
• OLS is biased and inconsistent.

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Spatial Lag Model Estimation

• Fixed Effects

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Spatial Lag Model Estimation Fixed Effects IV
or 2SLS

• Instrumental Variables
• Two-Stage Least Squares

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Spatial Lag Model Estimation

• Random Effects

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Spatial Lag Model Estimation Random Effects
IV/GLS

• Instrumental Variables
• Two-Stage Generalized Least Squares

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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

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Spatial Error Model Estimation

• The Model SPAR(1)
• Fixed Effects
• Random Effects

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Spatial Error Model EstimationFixed Effects

• Moment Functions

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Spatial Error Model Estimation Fixed Effects

• The Model SPAR(1)
• Estimate b and r iteratively GMM/GLS
• OLS
• GMM
• GLS

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Spatial Error Model Estimation Random Effects

• Moment Functions (Kapoor, Kelejian and Prucha,
  2006)

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Spatial Error Model Estimation Random Effects

• The Model SPAR(1)
• Estimate b and r iteratively GMM/GLS
• OLS
• GMM
• GLS

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Spatial Mixed Model Estimation

• The Model SARAR(1,1)

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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.

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Spatial Mixed Model Estimation Fixed Effects

• The Model SPARAR(1,1)

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Spatial Mixed Model Estimation Fixed Effects

• Estimate b and r iteratively GMM/GLS
• IV/2SLS
• GMM
• GLS

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Spatial Mixed Model Estimation Random Effects

• The Model SPARAR(1,1)

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Spatial Mixed Model Estimation Random Effects

• Estimate b,l and r iteratively GMM/GLS
• IV/2SLS
• GMM
• GLS

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Example U. S. ProductivityBaltagi (2008)
munnell.5

• Spatial Panel Data Model GMM/GLS (Spatial Error)
  ln(GSP) b0 b1 ln(Public) b2ln(Private)
  b3ln(Labor) b4(Unemp)
  e, e ?W e e, e i?u v

Fixed Effects s.e Random Effects s.e
b1 0.005 0.026 0.031 0.023
b2 0.202 0.024 0.273 0.021
b3 0.782 0.029 0.736 0.025
b4 -0.002 0.001 -0.005 0.001
b0 - - 2.222 0.136
? 0.578 0.046 0.321 0.060
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Example U. S. ProductivityBaltagi (2008)
munnell.5

• Spatial Panel Data Model GMM/GLS (Spatial Mixed)
  ln(GSP) b0 b1 ln(Public) b2ln(Private)
  b3ln(Labor) b4(Unemp) ?W ln(GSP) e ,
  e ?W e e , e i?u v

Fixed Effects s.e Random Effects s.e
b1 -0.010 0.026 0.040 0.024
b2 0.185 0.025 0.259 0.022
b3 0.756 0.029 0.728 0.026
b4 -0.003 0.001 -0.005 0.001
b0 - - 2.031 0.174
? 0.093 0.024 0.030 0.015
? 0.488 0.051 0.312 0.059
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Another ExampleChina Provincial Productivity
china.9

• Spatial Panel Data Model GMM/GLS (Spatial Error)
  ln(Q) a b ln(L) g ln(K) e
  e ?W e e , e i?u v

Fixed Effects s.e Random Effects s.e
b 0.2928 0.073 0.4898 0.062
g 0.0282 0.017 0.0090 0.017
a - - 2.6298 0.587
? 0.5013 0.059 0.6424 0.071
26
Another ExampleChina Provincial Productivity
china.9

• Spatial Panel Data Model GMM/GLS (Spatial Mixed)
  ln(Q) a b ln(L) g ln(K) l W ln(Q)
  e e ?W e e , e i?u v

Fixed Effects s.e Random Effects s.e
b 0.256 0.080 0.481 0.076
g 0.022 0.019 0.013 0.015
a - - 6.513 2.394
? 0.287 0.189 1.203 0.059
? 0.267 0.074 -0.475 0.239
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Maximum Likelihood Estimation

• Error Components
• Assumptions
• Fixed Effects
• Random Effects

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Maximum Likelihood EstimationFixed Effects

• Log-Likelihood Function

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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.

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Maximum Likelihood EstimationRandom Effects

• Log-Likelihood Function

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Example U. S. ProductivityBaltagi (2008)
munnell.4

• Spatial Panel Data Model QML (Spatial Lag)
  ln(GSP) b0 b1 ln(Public) b2ln(Private)
  b3ln(Labor) b4(Unemp) ?W
  ln(GSP) e , e i?u v

Fixed Effects s.e Random Effects s.e
b1 -0.047 0.026 0.013 0.028
b2 0.187 0.025 0.226 0.025
b3 0.625 0.029 0.671 0.029
b4 -0.005 0.0009 -0.006 0.0009
b0 - - 1.658 0.166
? 0.275 0.022 0.162 0.029
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Example U. S. ProductivityBaltagi (2008)
munnell.4

• Spatial Panel Data Model QML (Spatial Error)
  ln(GSP) b0 b1 ln(Public) b2ln(Private)
  b3ln(Labor) b4(Unemp) e, e
  ?W e e , e i?u v

Fixed Effects s.e Random Effects s.e
b1 0.005 0.026 0.045 0.027
b2 0.205 0.025 0.246 0.023
b3 0.782 0.029 0.743 0.027
b4 -0.002 0.001 -0.004 0.001
b0 - - 2.325 0.155
? 0.557 0.034 0.527 0.033
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Example U. S. ProductivityBaltagi (2008)
munnell.4

• Spatial Panel Data Model QML (Spatial Mixed)
  ln(GSP) b0 b1 ln(Public) b2ln(Private)
  b3ln(Labor) b4(Unemp) ?W ln(GSP) e , e
  ?W e e , e i?u v

Fixed Effects s.e Random Effects s.e
b1 -0.010 0.027 0.044 0.023
b2 0.191 0.025 0.249 0.023
b3 0.755 0.031 0.742 0.027
b4 -0.003 0.001 -0.004 0.001
b0 - - 2.289 0.212
? 0.089 0.031 0.004 0.017
? 0.455 0.052 0.522 0.038
34
Another ExampleChina Provincial Productivity
china.8

• Spatial Panel Data Model QML (Spatial Lag)
  ln(Q) a b ln(L) g ln(K) l W ln(Q) e
  e i?u
  v

Fixed Effects s.e Random Effects s.e
b 0.2203 0.0707 0.3794 0.074
g 0.0177 0.0163 -0.0046 0.016
a - - 0.9081 0.626
? 0.4361 0.0557 0.3941 0.055
35
Another ExampleChina Provincial Productivity
china.8

• Spatial Panel Data Model QML (Spatial Error)
  ln(Q) a b ln(L) g ln(K) e
  e ?W e e , e i?u v

Fixed Effects s.e Random Effects s.e
b 0.2969 0.073 0.4928 0.077
g 0.0297 0.017 0.0091 0.017
a - - 2.6548 0.657
? 0.4521 0.058 0.4364 0.055
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Another ExampleChina Provincial Productivity
china.8

• Spatial Panel Data Model QML (Spatial Mixed)
  ln(Q) a b ln(L) g ln(K) l W ln(Q) e
  e ?W e e , e i?u v

Fixed Effects s.e Random Effects s.e
b 0.143 0.058 0.247 0.062
g 0.004 0.013 -0.014 0.013
a - - -0.119 0.496
? 0.731 0.058 0.712 0.064
? -0.571 0.136 -0.563 0.145
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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.