# RECORD 00fe81644f944eeadcdbef9deb3f1be4026fb701
# TITLE: Maximum Likelihood Estimation and Lagrange Multiplier Tests for Panel Seemingly Unrelated Regressions with Spatial Lag and Spatial Errors: An Application to Hedonic Housing Prices in Paris
# YEAR: 2010.0  VENUE: Social Science Research Network  DOI: 10.1016/j.jue.2010.08.007
# AUTHORS: B. Baltagi; G. Bresson
# PAGES: 48  CANDIDATE TABLE PAGES (1-based): [47, 48]
# ABSTRACT: This paper proposes maximum likelihood estimators for panel seemingly unrelated regressions with both spatial lag and spatial error components. We study the general case where spatial effects are incorporated via spatial errors terms and via a spatial lag dependent variable and where the heterogeneity in the panel is incorporated via an error component specification. We generalize the approach of Wang and Kockelman (2007) and propose joint and conditional Lagrange Multiplier tests for spatial autocorrelation and random effects for this spatial SUR panel model. The small sample performance of the proposed estimators and tests are examined using Monte Carlo experiments. An empirical application to hedonic housing prices in Paris illustrates these methods. The proposed specification uses a system of three SUR equations corresponding to three types of flats within 80 districts of Paris over the period 1990-2003. We test for spatial effects and heterogeneity and find reasonable estimates of the shadow prices for housing characteristics.


===== PAGE 1 (score 0, numeric-paren 0, table-words 0, var-words 0) =====

D I S C U S S I O N  P A P E R  S E R I E S
Forschungsinstitut 
zur Zukunft der Arbeit
Institute for the Study 
of Labor 
Maximum Likelihood Estimation and Lagrange 
Multiplier Tests for Panel Seemingly Unrelated 
Regressions with Spatial Lag and Spatial Errors: 
An Application to Hedonic Housing Prices in Paris
IZA DP No. 5227
September 2010
Badi H. Baltagi
Georges Bresson


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Table 11 - Hedonic housing price SUR Equations for Paris (N=80 quartiers , 1990-2003)  (distances weight matrices W1j and W2j)(*)
ln(price per sq.meter)
Coeff.
T-stat
Coeff.
T-stat
Coeff.
T-stat
ln(price per sq.meter)
Coeff.
T-stat
Coeff.
T-stat
Coeff.
T-stat
Intercept
6.367
7.191
5.055
4.804
4.704
4.762
no bathroom
ref.
ref.
ref.
ref.
ref.
ref.
λj (j=1,2,3)
0.735
16.102
0.756
20.237
0.730
16.784
one bathroom
1.178
10.401
1.636
12.434
1.876
14.255
γj (j=1,2,3)
-0.004
-0.051
0.007
0.083
0.008
0.103
two bathrooms
1.169
1.037
1.527
3.291
2.004
10.160
three bathrooms and more
1.319
0.257
3.639
3.127
2.332
4.655
no maid's room
ref.
ref.
ref.
ref.
ref.
ref.
one maid's room
1.463
4.803
1.276
4.707
1.204
6.803
Coeff.
T-stat
Coeff.
T-stat
two maid's rooms and more
-0.690
-0.598
1.369
1.386
1.062
2.520
σ2
µ1
0.271
6.033
0.182
22.724
no garage plot
ref.
ref.
ref.
ref.
ref.
ref.
σ2
µ2
0.394
5.829
0.466
22.739
one garage plot
0.265
1.098
-0.163
-0.633
0.375
1.794
σ2
µ3
0.480
5.920
0.457
22.735
two garage plots
-2.005
-1.034
-1.359
-1.186
1.242
3.071
σµ12
0.331
6.099
0.089
9.381
three garage plots and more
0.490
0.039
-1.842
-0.162
-1.187
-0.358
σµ13
0.355
6.076
0.019
2.130
Balcony
Balcony (yes or no)
-0.590
-1.241
0.274
0.539
0.352
0.927
σµ23
0.435
5.990
0.202
12.920
Floor level (0 to 3)
ref.
ref.
ref.
ref.
ref.
ref.
Floor level (4 to 7)
0.807
7.573
1.236
10.341
0.700
5.733
log-likelihood
146.710
AIC
-35.428
Floor level (8 to 11)
1.532
2.666
0.534
0.815
-0.120
-0.284
Floor level (12 and more)
0.913
0.622
-0.149
-0.119
-1.112
-1.379
ddl
p-value
Square footage (20 to 40 m2)
ref.
ref.
1.899
6.373
2.355
0.989
H0
a : [γj , λj , σµlm]' =0
12
0
Square footage (41 to 60 m2)
0.500
5.825
ref.
ref.
0.026
0.082
H0
b : [γj , λj ]' =0
6
0
Square footage (61 to 80 m2)
0.912
4.811
0.794
7.478
1.032
7.046
H0
c : [γj ,σµlm]' =0
9
0
Square footage (81 to 100 m2)
-0.348
-0.653
0.961
5.351
1.029
7.818
H0
d : [λj , σµlm]' =0
9
0
Square footage (> 100 m2)
-1.338
-0.585
0.389
0.695
ref.
ref.
H0
e : [γj] =0
3
1
<1850
0.736
6.822
1.107
8.386
1.848
13.907
H0
f : [λj] =0
3
0
1850-1913
ref.
ref.
ref.
ref.
ref.
ref.
H0
g : [σµlm] =0
6
0
1914-1947
0.183
1.036
0.998
4.537
0.740
2.966
1948-1969
0.128
0.678
0.068
0.311
0.355
1.671
(*): Regression includes time dummies
1970-1980
-0.658
-2.362
0.304
0.972
0.350
1.433
1981-2003
0.805
3.035
0.876
1.713
0.023
0.049
Avenue
0.425
2.319
0.255
1.196
0.439
2.212
Boulevard
0.836
3.687
1.412
6.300
0.930
5.283
Place
0.630
1.425
1.928
3.262
0.978
1.899
Street
ref.
ref.
ref.
ref.
ref.
ref.
Dist.center.arrond.(m)
-0.0003
-5.365
-0.0006
-6.473
-0.0007
-6.953
Dist.center.quartier (m)
-0.0013
-8.325
-0.0022
-9.126
-0.0025
-10.009
Upper
0.340
3.492
0.554
3.566
0.340
2.241
Rich
0.299
3.242
-0.026
-0.177
0.364
2.460
Golden
0.282
3.750
0.526
4.341
0.654
5.397
Others
ref.
ref.
ref.
ref.
ref.
ref.
SUR with spatial lags and spatial errors (SAR)
two rooms
three rooms
more than three rooms
Time of building
Kind of street
location
Bathroom
Maid's roo
Garage plot
Floor level
Arrondisseme
Spatial dep.
σ2
v1
LM test
43486.0
3208.6
48806.0
43402.0
0.0
Square footage
SUR with spatial lags and spatial errors (SAR)
two rooms
three rooms
more than three rooms
4017.1
48782.0
σv23
Error comp. Var-cov. Matrices
σ2
v2
σ2
v3
σv12
σv13


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Table 12 - Hedonic housing price SUR Equations for Paris (N=80 quartiers , 1990-2003)  (contiguity weight matrices W1j and W2j)(*)
ln(price per sq.meter)
Coeff.
T-stat
Coeff.
T-stat
Coeff.
T-stat
ln(price per sq.meter)
Coeff.
T-stat
Coeff.
T-stat
Coeff.
T-stat
Intercept
7.104
14.711
6.061
9.815
5.466
10.162
no bathroom
ref.
ref.
ref.
ref.
ref.
ref.
λj (j=1,2,3)
0.575
11.930
0.634
16.213
0.571
12.448
one bathroom
1.149
10.111
1.601
12.106
2.007
15.240
γj (j=1,2,3)
-0.045
-0.769
-0.065
-1.018
-0.043
-0.817
two bathrooms
1.166
1.027
1.639
3.546
2.075
10.411
three bathrooms and more
2.487
0.485
4.015
3.459
2.503
4.959
no maid's room
ref.
ref.
ref.
ref.
ref.
ref.
one maid's room
1.507
4.947
1.322
4.855
1.170
6.582
Coeff.
T-stat
Coeff.
T-stat
two maid's rooms and more
-0.738
-0.640
1.292
1.316
1.100
2.595
σ2
µ1
0.276
6.031
0.186
22.680
no garage plot
ref.
ref.
ref.
ref.
ref.
ref.
σ2
µ2
0.404
5.832
0.474
22.676
one garage plot
0.392
1.610
-0.055
-0.213
0.381
1.804
σ2
µ3
0.506
5.931
0.468
22.695
two garage plots
-2.175
-1.111
-1.127
-0.985
1.258
3.086
σµ12
0.337
6.083
0.096
9.870
three garage plots and more
0.018
0.001
-1.714
-0.149
-1.359
-0.405
σµ13
0.367
6.065
0.026
2.845
Balcony
Balcony (yes or no)
-0.695
-1.460
0.340
0.670
0.371
0.963
σµ23
0.452
6.001
0.204
12.799
Floor level (0 to 3)
ref.
ref.
ref.
ref.
ref.
ref.
Floor level (4 to 7)
0.790
7.375
1.248
10.397
0.645
5.234
log-likelihood
103.730
AIC
50.534
Floor level (8 to 11)
1.484
2.572
0.453
0.693
-0.161
-0.377
Floor level (12 and more)
0.927
0.617
-0.230
-0.180
-0.942
-1.147
ddl
p-value
Square footage (20 to 40 m2)
ref.
ref.
1.837
6.150
3.305
1.376
H0
a : [γj , λj , σµlm]' =0
12
0
Square footage (41 to 60 m2)
0.480
5.594
ref.
ref.
0.121
0.380
H0
b : [γj , λj ]' =0
6
0
Square footage (61 to 80 m2)
0.988
5.173
0.827
7.587
1.072
7.257
H0
c : [γj ,σµlm]' =0
9
0
Square footage (81 to 100 m2)
-0.787
-1.468
1.046
5.790
1.111
8.265
H0
d : [λj , σµlm]' =0
9
0
Square footage (> 100 m2)
-1.304
-0.566
0.428
0.761
ref.
ref.
H0
e : [γj] =0
3
0.994
<1850
0.717
6.688
1.129
8.483
1.774
13.095
H0
f : [λj] =0
3
0
1850-1913
ref.
ref.
ref.
ref.
ref.
ref.
H0
g : [σµlm] =0
6
0
1914-1947
0.225
1.282
0.976
4.376
0.842
3.353
1948-1969
0.197
1.054
0.136
0.624
0.378
1.765
(*): Regression includes time dummies
1970-1980
-0.547
-1.954
0.383
1.211
0.362
1.457
1981-2003
0.756
2.802
0.829
1.609
0.115
0.242
Avenue
0.507
2.700
0.274
1.267
0.492
2.441
Boulevard
0.920
4.005
1.439
6.261
0.934
5.204
Place
0.678
1.537
1.951
3.244
0.947
1.823
Street
ref.
ref.
ref.
ref.
ref.
ref.
Dist.center.arrond.(m)
-0.0003
-4.881
-0.0006
-5.705
-0.0007
-6.632
Dist.center.quartier (m)
-0.0013
-8.291
-0.0021
-8.582
-0.0024
-9.485
Upper
0.356
4.104
0.562
3.823
0.395
2.897
Rich
0.354
4.185
-0.035
-0.245
0.428
3.117
Golden
0.335
4.693
0.547
4.556
0.731
6.232
Others
ref.
ref.
ref.
ref.
ref.
ref.
SUR with spatial lags and spatial errors (SAR)
SUR with spatial lags and spatial errors (SAR)
two rooms
three rooms
more than three rooms
two rooms
three rooms
more than three rooms
Bathroom
Maid's roo
Garage plot
Floor level
Spatial dep.
Square footage
Error comp. Var-cov. Matrices
σ2
v1
Time of building
σ2
v2
σ2
v3
σv12
σv13
σv23
Kind of street
LM test
2297300.0
location
1268.0
57351.0
Arrondisseme
51132.0
0.338
3255.6
47592.0