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Spatial Econometric Analysis Using GAUSS

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Title: Spatial Econometric Analysis Using GAUSS


1
Spatial Econometric Analysis Using GAUSS
  • 10
  • Kuan-Pin Lin Portland State University

2
Spatial Panel Data Models
  • The General Model

3
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

4
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

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 Estimation Fixed 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. Productivity Baltagi (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
24
Example U. S. Productivity Baltagi (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
25
Another Example China 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 Example China 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
27
Maximum Likelihood Estimation
  • Error Components
  • Assumptions
  • Fixed Effects
  • Random Effects

28
Maximum Likelihood Estimation Fixed Effects
  • Log-Likelihood Function

29
Maximum Likelihood Estimation Fixed 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 Estimation Random Effects
  • Log-Likelihood Function

31
Example U. S. Productivity Baltagi (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
32
Example U. S. Productivity Baltagi (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
33
Example U. S. Productivity Baltagi (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 Example China 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 Example China 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
36
Another Example China 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
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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