# RECORD e6c58cb070edd6cfaff8b1bababd256016f5ed90
# TITLE: Hedonic real estate price estimation with the spatiotemporal geostatistical model
# YEAR: 2023.0  VENUE: Journal of Spatial Econometrics  DOI: 10.1007/s43071-023-00039-w
# AUTHORS: Sachio Muto; Shonosuke Sugasawa; Masatomo Suzuki
# PAGES: 37  CANDIDATE TABLE PAGES (1-based): [14, 15, 16, 17, 18, 24, 25, 31, 32]
# ABSTRACT: This study argues that the spatiotemporal geostatistical model for real estate prices, which accounts for and incorporates spatial autocorrelation, can be estimated successfully using the Bayesian Markov Chain Monte Carlo (MCMC) estimation. While this procedure often encounters difficulty in calculating probabilistic densities in the Metropolis–Hastings (MH) algorithm, this study introduces a feasible and practical estimation method, providing useful estimated parameters for the model. Using single-family house transaction data, we show that ordinary estimations of real estate prices, with respect to certain explanatory variables, may lead to the underestimation of standard errors of coefficients for explanatory variables with spatial effects unless spatial autocorrelation is controlled for. Our model also makes it possible to obtain accurate in-sample predictions and moderately improved out-of-sample predictions for real estate prices. This study further estimates a “decay rate:” a diminishing correlation between real estate prices and increasing distance, showing that geographical proximities are likely to have an important impact on real estate prices, especially at a range under 600 m.


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Vol.:(0123456789)
Journal of Spatial Econometrics (2023) 4:10
https://doi.org/10.1007/s43071-023-00039-w
1 3
ORIGINAL PAPER
Hedonic real estate price estimation 
with the spatiotemporal geostatistical model
Sachio Muto1   · Shonosuke Sugasawa2 · Masatomo Suzuki3
Received: 31 August 2021 / Accepted: 15 October 2023 / Published online: 14 November 2023 
© The Author(s) 2023
Abstract
This study argues that the spatiotemporal geostatistical model for real estate prices, 
which accounts for and incorporates spatial autocorrelation, can be estimated suc-
cessfully using the Bayesian Markov Chain Monte Carlo (MCMC) estimation. 
While this procedure often encounters difficulty in calculating probabilistic densi-
ties in the Metropolis–Hastings (MH) algorithm, this study introduces a feasible and 
practical estimation method, providing useful estimated parameters for the model. 
Using single-family house transaction data, we show that ordinary estimations of 
real estate prices, with respect to certain explanatory variables, may lead to the 
underestimation of standard errors of coefficients for explanatory variables with 
spatial effects unless spatial autocorrelation is controlled for. Our model also makes 
it possible to obtain accurate in-sample predictions and moderately improved out-
of-sample predictions for real estate prices. This study further estimates a “decay 
rate:” a diminishing correlation between real estate prices and increasing distance, 
showing that geographical proximities are likely to have an important impact on real 
estate prices, especially at a range under 600 m.
Keywords  Real estate pricing · Bayesian econometrics · MCMC · Geostatistical 
model · Metropolis–Hastings algorithm
JEL Classification  R39
 *	 Sachio Muto 
	
s-muto@e.u-tokyo.ac.jp
1	
Center for Real Estate Innovation (CREI), The University of Tokyo, 7‑3‑1, Hongo, Bunkyo‑ku, 
Tokyo 113‑0033, Japan
2	
Faculty of Economics, Keio University, Tokyo, Japan
3	
School of Data Science, Yokohama, Yokohama City University, Yokohama, Japan


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Table 2   Comparison of estimation and in-sample prediction of the OLS and the geostatistical model. (Data Year: 2016–2019)
Dependent variable: transaction price [ten thousand JPY]
(1)
(2)
(3)
No time dummy, No regional dummy
No time dummy & No regional dummy
No time dummy & With regional 
dummy
With less property-level spatial variable
With full property-level spatial variable
With full property-level spatial variable
OLS
Geostatstical model OLS
Geostatstical model OLS
Geostatstical 
model
Explanatory variables
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Property characteristics
Newly built dummy
 − 0.112
(0.106)
0.079
(0.085)
 − 0.067
(0.099)
0.068
(0.086)
0.039
(0.080)
0.078
(0.092)
Property age [years]/10
 − 0.744
(0.087)
 − 0.661
(0.069)
 − 0.736
(0.082)
 − 0.664
(0.069)
 − 0.675
(0.067)
 − 0.655
(0.076)
(Property age [years]/10)2
0.076
(0.017)
0.062
(0.013)
0.077
(0.016)
0.063
(0.013)
0.065
(0.013)
0.062
(0.015)
Floor space ­[m2] /100
0.289
(0.024)
0.205
(0.021)
0.234
(0.023)
0.198
(0.020)
0.160
(0.019)
0.178
(0.023)
(Floor space ­[m2] /100)2
 − 0.003
(0.001)
 − 0.003
(0.001)
 − 0.002
(0.001)
 − 0.002
(0.001)
 − 0.001
(0.001)
 − 0.002
(0.001)
Land area ­[m2]/100
0.141
(0.027)
0.164
(0.022)
0.144
(0.025)
0.162
(0.022)
0.204
(0.036)
0.181
(0.041)
(Land area ­[m2] /100)2
 − 0.004
(0.001)
 − 0.004
(0.001)
 − 0.004
(0.001)
 − 0.004
(0.001)
 − 0.009
(0.002)
 − 0.007
(0.002)
Date of transaction registered
(yearly conversion)
 − 0.004
(0.023)
 − 0.010
(0.018)
 − 0.008
(0.017)
 − 0.006
(0.023)
0.007
(0.014)
0.007
(0.019)
Property-level spatial variables
Access environment
  Walking time to nearest station [min]
 − 0.025
(0.004)
 − 0.020
(0.006)
 − 0.031
(0.004)
 − 0.026
(0.006)
 − 0.033
(0.006)
 − 0.031
(0.008)
  Bus to closest station dummy
 − 0.393
(0.071)
 − 0.421
(0.128)
 − 0.636
(0.077)
 − 0.563
(0.125)
 − 0.685
(0.132)
 − 0.666
(0.166)
  Number of daily passengers of the 
closest station [ten thousand per-
sons / day]
–
–
–
–
0.010
(0.022)
0.004
(0.042)
0.002
(0.043)
0.009
(0.059)


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Table 2   (continued)
Dependent variable: transaction price [ten thousand JPY]
(1)
(2)
(3)
No time dummy, No regional dummy
No time dummy & No regional dummy
No time dummy & With regional 
dummy
With less property-level spatial variable
With full property-level spatial variable
With full property-level spatial variable
OLS
Geostatstical model OLS
Geostatstical model OLS
Geostatstical 
model
Explanatory variables
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Development Age
  Included in DID in 1960s or before
–
–
–
–
 − 0.596
(0.105)
 − 0.269
(0.175)
 − 0.177
(0.205)
 − 0.213
(0.276)
  Included in DID in 1970s
–
–
–
–
 − 0.662
(0.106)
 − 0.288
(0.173)
 − 0.191
(0.198)
 − 0.223
(0.268)
  Included in DID in 1980s
–
–
–
–
 − 0.600
(0.095)
 − 0.213
(0.164)
 − 0.140
(0.190)
 − 0.163
(0.259)
  Included in DID in 1990s
–
–
–
–
 − 0.649
(0.148)
 − 0.311
(0.199)
 − 0.201
(0.188)
 − 0.239
(0.263)
  Included in DID in 2000s
–
–
–
–
 − 0.523
(0.169)
 − 0.117
(0.225)
 − 0.164
(0.216)
 − 0.096
(0.286)
  Included in DID in 2010s
–
–
–
–
 − 0.466
(0.167)
 − 0.137
(0.262)
 − 0.035
(0.245)
 − 0.107
(0.329)
Disaster risk
  Tsunami risk dummy (over 3 m)
–
–
–
–
0.350
(0.098)
0.072
(0.124)
 − 0.096
(0.108)
 − 0.002
(0.135)
  Sediment disaster risk dummy
–
–
–
–
 − 0.233
(0.047)
 − 0.140
(0.046)
 − 0.101
(0.041)
 − 0.110
(0.049)
District level variables
Ratio of residents over 20 years
–
–
–
–
 − 0.089
(0.045)
 − 0.026
(0.060)
 − 0.344
(0.388)
 − 0.172
(0.512)
Hillside area dummy
–
–
–
–
 − 0.158
(0.069)
 − 0.173
(0.086)
–
–
–
–
Promotion area dummy
–
–
–
–
0.287
(0.047)
0.262
(0.074)
–
–
–
–
Constant
0.822
(0.190)
1.377
(0.191)
1.877
(0.220)
1.733
(0.257)
1.905
(0.297)
1.847
(0.427)
Time dummy (monthly)
No
No
No
No
No
No


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Table 2   (continued)
Dependent variable: transaction price [ten thousand JPY]
(1)
(2)
(3)
No time dummy, No regional dummy
No time dummy & No regional dummy
No time dummy & With regional 
dummy
With less property-level spatial variable
With full property-level spatial variable
With full property-level spatial variable
OLS
Geostatstical model OLS
Geostatstical model OLS
Geostatstical 
model
Explanatory variables
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
District dummy
No
No
No
No
Yes
Yes
Parameters for error stracture (Geostatistics)
τ
–
–
0.224
(0.024)
–
–
0.212
(0.026)
–
–
0.159
(0.029)
σ
–
–
0.710
(0.030)
–
–
0.670
(0.028)
–
–
0.542
(0.027)
ϕ
–
–
3.521
(0.518)
–
–
2.987
(0.482)
–
–
1.395
(0.323)
δ
–
–
9.957
(3.716)
–
–
7.620
(2.641)
–
–
4.848
(1.832)
Performance of predicted values
R2 (in-sample)
0.617
0.990
0.667
0.992
0.850
0.998
MSE (in-sample)
0.460
0.012
0.400
0.009
0.180
0.003


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Table 2   (continued)
Dependent variable: Transaction price [Ten thousand JPY]
(4)
(5)
With time dummy & No regional dummy
With time dummy & With regional dummy
With full property-level spatial variable
With full property-level spatial variable
OLS
Geostatstical Model
OLS
Geostatstical Model
Explanatory variables
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Property characteristics
Newly built dummy
 − 0.071
(0.099)
0.066
(0.088)
0.037
(0.080)
0.063
(0.097)
Property age [years]/10
 − 0.757
(0.082)
 − 0.685
(0.071)
 − 0.694
(0.067)
 − 0.684
(0.081)
(Property age [years]/10)2
0.081
(0.016)
0.067
(0.013)
0.068
(0.013)
0.067
(0.016)
Floor space ­[m2] /100
0.240
(0.023)
0.206
(0.021)
0.169
(0.019)
0.189
(0.024)
(Floor space ­[m2] /100)2
 − 0.002
(0.001)
 − 0.003
(0.001)
 − 0.001
(0.001)
 − 0.002
(0.001)
Land area ­[m2]/100
0.145
(0.025)
0.158
(0.023)
0.189
(0.036)
0.167
(0.043)
(Land area ­[m2] /100)2
 − 0.004
(0.001)
 − 0.004
(0.001)
 − 0.008
(0.002)
 − 0.006
(0.002)
Date of transaction registered (yearly conversion)
–
–
–
–
–
–
–
–
Property-level spatial variables
Access environment
  Walking time to nearest station [min]
 − 0.031
(0.004)
 − 0.027
(0.006)
 − 0.035
(0.006)
 − 0.031
(0.008)
  Bus to closest station dummy
 − 0.646
(0.077)
 − 0.575
(0.129)
 − 0.724
(0.133)
 − 0.677
(0.170)
  Number of daily passengers of the closest station 
[ten thousand persons / day]
0.002
(0.022)
 − 0.005
(0.042)
0.011
(0.043)
0.007
(0.062)
Development age
  Included in DID in 1960s or before
 − 0.610
(0.105)
 − 0.279
(0.177)
 − 0.227
(0.204)
 − 0.243
(0.282)
  Included in DID in 1970s
 − 0.669
(0.106)
 − 0.301
(0.175)
 − 0.234
(0.198)
 − 0.254
(0.275)


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Table 2   (continued)
Dependent variable: Transaction price [Ten thousand JPY]
(4)
(5)
With time dummy & No regional dummy
With time dummy & With regional dummy
With full property-level spatial variable
With full property-level spatial variable
OLS
Geostatstical Model
OLS
Geostatstical Model
Explanatory variables
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
  Included in DID in 1980s
 − 0.613
(0.095)
 − 0.220
(0.166)
 − 0.147
(0.190)
 − 0.160
(0.264)
  Included in DID in 1990s
 − 0.651
(0.148)
 − 0.313
(0.201)
 − 0.226
(0.186)
 − 0.227
(0.269)
  Included in DID in 2000s
 − 0.495
(0.168)
 − 0.123
(0.228)
 − 0.163
(0.215)
 − 0.102
(0.292)
  Included in DID in 2010s
 − 0.489
(0.167)
 − 0.183
(0.265)
 − 0.085
(0.244)
 − 0.098
(0.341)
Disaster Risk
  Tsunami risk dummy (over 3 m)
0.390
(0.098)
0.098
(0.125)
 − 0.011
(0.108)
0.034
(0.139)
  Sediment disaster risk dummy
 − 0.216
(0.047)
 − 0.123
(0.047)
 − 0.088
(0.041)
-0.095
(0.052)
District level variables
Ratio of residents over 20 years
 − 0.074
(0.045)
 − 0.021
(0.061)
 − 0.341
(0.390)
 − 0.226
(0.528)
Hillside area dummy
 − 0.160
(0.069)
 − 0.173
(0.088)
–
–
–
–
Promotion area dummy
0.276
(0.047)
0.254
(0.075)
–
–
–
–
Constant
1.869
(0.245)
1.703
(0.272)
1.880
(0.307)
1.852
(0.442)
Time dummy (monthly)
Yes
Yes
Yes
Yes
District dummy
No
No
Yes
Yes
Parameters for error structure (Geostatistics)
τ
–
–
0.212
(0.027)
–
–
0.174
(0.031)
σ
–
–
0.673
(0.027)
–
–
0.533
(0.022)
ϕ
–
–
2.958
(0.474)
–
–
1.188
(0.227)


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Table 2   (continued)
Dependent variable: Transaction price [Ten thousand JPY]
(4)
(5)
With time dummy & No regional dummy
With time dummy & With regional dummy
With full property-level spatial variable
With full property-level spatial variable
OLS
Geostatstical Model
OLS
Geostatstical Model
Explanatory variables
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
δ
–
–
8.260
(2.872)
–
–
3.498
(2.771)
Performance of predicted values
R2 (in-sample)
0.667
0.993
0.857
0.997
MSE (in-sample)
0.400
0.009
0.171
0.004


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Table 3   Comparison of out-of-sample prediction of the OLS and the geostatistical model. (In-Sample Data Year: 2016–2018, Out-Of-Sample Data Year: 2019)
Dependent variable: Transaction price [Ten thousand JPY]
(1)
(2)
(3)
No time dummy, No regional dummy
No time dummy & No regional dummy
No time dummy & With regional dummy
With less property-level spatial variable
With full property-level spatial variable
With full property-level spatial variable
OLS
Geostatstical Model
OLS
Geostatstical Model
OLS
Geostatstical Model
Explanatory variables
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Property characteristics
Newly built dummy
− 0.036
(0.124)
0.052
(0.099)
0.003
(0.116)
0.044
(0.100)
0.086
(0.093)
0.089
(0.115)
Property age [years]/10
− 0.720
(0.103)
− 0.646
(0.081)
− 0.704
(0.097)
− 0.652
(0.081)
− 0.563
(0.077)
− 0.593
(0.094)
(Property age [years]/10)2
0.078
(0.020)
0.061
(0.015)
0.078
(0.019)
0.062
(0.016)
0.043
(0.015)
0.048
(0.018)
Floor space ­[m2] /100
0.289
(0.027)
0.225
(0.023)
0.239
(0.026)
0.215
(0.023)
0.173
(0.022)
0.178
(0.027)
(Floor space ­[m2] /100)2
− 0.003
(0.001)
− 0.003
(0.001)
− 0.002
(0.001)
− 0.003
(0.001)
− 0.001
(0.001)
− 0.002
(0.001)
Land area ­[m2]/100
0.133
(0.029)
0.143
(0.025)
0.145
(0.028)
0.146
(0.025)
0.242
(0.045)
0.247
(0.054)
(Land area ­[m2] /100)2
− 0.004
(0.001)
− 0.004
(0.001)
− 0.004
(0.001)
− 0.004
(0.001)
− 0.012
(0.003)
− 0.012
(0.003)
Date of transaction registered (yearly conversion)
− 0.014
(0.029)
0.026
(0.032)
− 0.010
(0.028)
0.024
(0.032)
0.022
(0.022)
0.029
(0.031)
Property-level spatial variables
  Access environment
   Walking time to nearest station [min]
− 0.020
(0.005)
− 0.015
(0.007)
− 0.026
(0.005)
− 0.021
(0.007)
− 0.025
(0.007)
− 0.025
(0.009)
   Bus to closest station dummy
− 0.370
(0.085)
− 0.330
(0.150)
− 0.596
(0.092)
− 0.476
(0.150)
− 0.464
(0.150)
− 0.495
(0.193)
   Number of daily passengers of the closest station 
[ten thousand persons / day]
–
–
–
–
0.008
(0.027)
0.026
(0.048)
0.080
(0.052)
0.108
(0.074)
Development age
  Included in DID in 1960s or before
–
–
–
–
− 0.614
(0.126)
− 0.317
(0.204)
− 0.073
(0.231)
− 0.087
(0.336)
  Included in DID in 1970s
–
–
–
–
− 0.694
(0.126)
− 0.348
(0.203)
− 0.164
(0.224)
− 0.142
(0.326)
  Included in DID in 1980s
–
–
–
–
− 0.614
(0.114)
− 0.269
(0.191)
− 0.056
(0.217)
− 0.046
(0.317)


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Table 3   (continued)
Dependent variable: Transaction price [Ten thousand JPY]
(1)
(2)
(3)
No time dummy, No regional dummy
No time dummy & No regional dummy
No time dummy & With regional dummy
With less property-level spatial variable
With full property-level spatial variable
With full property-level spatial variable
OLS
Geostatstical Model
OLS
Geostatstical Model
OLS
Geostatstical Model
Explanatory variables
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
  Included in DID in 1990s
–
–
–
–
− 0.628
(0.179)
− 0.366
(0.233)
− 0.116
(0.219)
− 0.115
(0.333)
  Included in DID in 2000s
–
–
–
–
− 0.544
(0.206)
− 0.163
(0.278)
− 0.177
(0.267)
− 0.053
(0.386)
  Included in DID in 2010s
–
–
–
–
− 0.498
(0.185)
− 0.198
(0.297)
− 0.044
(0.271)
− 0.029
(0.394)
Disaster risk
  Tsunami risk dummy (over 3 m)
–
–
–
–
0.206
(0.116)
− 0.114
(0.159)
− 0.291
(0.138)
− 0.264
(0.186)
  Sediment disaster risk dummy
–
–
–
–
− 0.232
(0.056)
− 0.140
(0.054)
− 0.098
(0.049)
− 0.130
(0.063)
District level variables
Ratio of residents over 20 years
–
–
–
–
− 0.129
(0.054)
− 0.050
(0.069)
− 0.454
(0.408)
− 0.309
(0.585)
Hillside area dummy
–
–
–
–
− 0.204
(0.083)
− 0.209
(0.100)
–
–
–
–
Promotion area dummy
–
–
–
–
0.243
(0.055)
0.221
(0.084)
–
–
–
–
Constant
0.668
(0.220)
1.124
(0.220)
1.740
(0.258)
1.544
(0.300)
1.161
(0.348)
1.142
(0.510)
Time dummy (monthly)
No
No
Yes
Yes
Yes
Yes
District dummy
No
No
No
No
Yes
Yes
Parameters for error stracture (Geostatistics)
τ
–
–
0.242
(0.027)
–
–
0.233
(0.027)
–
–
0.176
(0.034)
σ
–
–
0.744
(0.041)
–
–
0.704
(0.036)
–
–
0.535
(0.027)
ϕ
–
–
4.100
(0.702)
–
–
3.535
(0.605)
–
–
1.253
(0.305)


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Table 3   (continued)
Dependent variable: Transaction price [Ten thousand JPY]
(1)
(2)
(3)
No time dummy, No regional dummy
No time dummy & No regional dummy
No time dummy & With regional dummy
With less property-level spatial variable
With full property-level spatial variable
With full property-level spatial variable
OLS
Geostatstical Model
OLS
Geostatstical Model
OLS
Geostatstical Model
Explanatory variables
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
Estimate
S. E
δ
–
–
16.558
(9.143)
–
–
12.227
(5.408)
–
–
2.392
(0.736)
Performance of predicted values
R2 (in-sample)
0.603
0.987
0.653
0.989
0.861
0.997
MSE (in-sample)
0.474
0.015
0.414
0.013
0.165
0.004
R2 (out-of-sample)
0.647
0.728
0.694
0.734
0.682
0.695
MSE (out-of-sample)
0.432
0.333
0.375
0.326
0.389
0.373


===== PAGE 31 (score 106, numeric-paren 95, table-words 3, var-words 5) =====

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Table 4   Comparison of estimation results with the SLX and the SDEM. (Specification (4) of Table 2)
Dependent variable: Transaction price [ten thousand JPY]
OLS
Geostatistical 
model
SLX
SDEM
β
β
β
θ
β
θ
Estimate
S.E
Estimate
S.E
Estimate
S.E
Estimate
S.E
Estimate
S.E
Estimate
S.E
Property characteristics
Newly built dummy
 − 0.071
(0.099)
0.066
(0.088)
 − 0.021
(0.095)
 − 0.980
(0.816)
 − 0.014
(0.091)
 − 1.135
(0.932)
Property age [years]/10
 − 0.757
(0.082)
 − 0.685
(0.071)
 − 0.733
(0.076)
 − 0.598
(0.725)
 − 0.728
(0.074)
 − 0.764
(0.816)
(Property age [years]/10)2
0.081
(0.016)
0.067
(0.013)
0.074
(0.015)
0.116
(0.146)
0.073
(0.014)
0.142
(0.164)
Floor space ­[m2] /100
0.240
(0.023)
0.206
(0.021)
0.261
(0.022)
0.018
(0.201)
0.254
(0.021)
0.168
(0.228)
(Floor space ­[m2] /100)2
 − 0.002
(0.001)
 − 0.003
(0.001)
 − 0.004
(0.001)
0.012
(0.005)
 − 0.004
(0.001)
0.008
(0.006)
Land area ­[m2]/100
0.145
(0.025)
0.158
(0.023)
0.169
(0.023)
0.844
(0.448)
0.168
(0.023)
0.562
(0.506)
(Land area ­[m2] /100)2
 − 0.004
(0.001)
 − 0.004
 − 0.004
(0.001)
 − 0.060
(0.024)
 − 0.004
(0.001)
-0.043
(0.026)
Date of transaction registered (yearly conversion)
–
–
–
–
–
–
–
–
–
–
–
–
Property-level spatial variables-access environment
Walking time to nearest station [min]
 − 0.031
(0.004)
 − 0.027
(0.006)
 − 0.024
(0.006)
 − 0.022
(0.027)
 − 0.023
(0.006)
 − 0.018
(0.033)
Bus to closest station dummy
 − 0.646
(0.077)
 − 0.575
(0.129)
 − 0.548
(0.112)
 − 0.940
(0.586)
 − 0.539
(0.113)
 − 0.642
(0.675)
Number of daily passengers of the closest station 
[ten thousand persons / day]
0.002
(0.022)
 − 0.005
(0.042)
0.020
(0.034)
 − 0.133
(0.189)
0.011
(0.036)
 − 0.018
(0.223)
Development Age
   Included in DID in 1960s or before
 − 0.610
(0.105)
 − 0.279
(0.177)
 − 0.004
(0.149)
 − 0.759
(0.639)
 − 0.036
(0.152)
 − 0.604
(0.778)
   Included in DID in 1970s
 − 0.669
(0.106)
 − 0.301
(0.175)
 − 0.029
(0.149)
 − 0.920
(0.708)
 − 0.048
(0.151)
 − 0.904
(0.835)
   Included in DID in 1980s
 − 0.613
(0.095)
 − 0.220
(0.166)
0.056
(0.140)
 − 0.836
(0.583)
0.058
(0.143)
 − 1.002
(0.723)
   Included in DID in 1990s
 − 0.651
(0.148)
 − 0.313
(0.201)
 − 0.141
(0.180)
1.477
(1.265)
 − 0.161
(0.180)
1.542
(1.469)
   Included in DID in 2000s
 − 0.495
(0.168)
 − 0.123
(0.228)
 − 0.028
(0.211)
 − 0.176
(1.484)
 − 0.023
(0.208)
 − 0.382
(1.634)
   Included in DID in 2010s
 − 0.489
(0.167)
 − 0.183
(0.265)
0.071
(0.257)
 − 0.066
(0.927)
0.032
(0.254)
 − 0.016
(1.128)


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Table 4   (continued)
Dependent variable: Transaction price [ten thousand JPY]
OLS
Geostatistical 
model
SLX
SDEM
β
β
β
θ
β
θ
Estimate
S.E
Estimate
S.E
Estimate
S.E
Estimate
S.E
Estimate
S.E
Estimate
S.E
Disaster risk
   Tsunami risk dummy (over 3 m)
0.390
(0.098)
0.098
(0.125)
0.238
(0.114)
0.726
(0.634)
0.190
(0.120)
1.534
(1.368)
   Sediment disaster risk dummy
 − 0.216
(0.047)
 − 0.123
(0.047)
 − 0.115
(0.048)
 − 0.716
(0.370)
 − 0.112
(0.046)
 − 0.578
(0.436)
District level variables
Ratio of residents over 20 years
 − 0.074
(0.045)
 − 0.021
(0.061)
 − 0.057
(0.061)
0.247
(0.359)
 − 0.066
(0.061)
0.133
(0.407)
Hillside area dummy
 − 0.160
(0.069)
 − 0.173
(0.088)
 − 0.072
(0.089)
 − 1.200
(0.688)
 − 0.099
(0.087)
 − 0.754
(0.762)
Promotion area dummy
0.276
(0.047)
0.254
(0.075)
0.284
(0.072)
 − 0.478
(0.344)
0.292
(0.074)
 − 0.383
(0.408)
Constant
1.869
(0.245)
1.703
(0.272)
1.420
(0.303)
–
–
1.495
(0.306)
–
–
Time dummy (monthly)
Yes
Yes
Yes
Yes
District dummy
No
No
No
No
Parameters for Error Stracture (Geostatistics)
τ
–
–
0.212
(0.027)
–
–
–
–
–
–
–
–
σ
–
–
0.673
(0.027)
–
–
–
–
–
–
–
–
ϕ
–
–
2.958
(0.474)
–
–
–
–
–
–
–
–
δ
–
–
8.260
(2.872)
–
–
–
–
–
–
–
–
Variance parameter (SLX and SDEM)
–
–
0.297
(0.012)
0.279
(0.012)
R2 (Pseudo ­R2 for SLX and SDEM)
0.681
0.993
0.753
0.734


===== PAGE 33 (score 3, numeric-paren 0, table-words 1, var-words 1) =====

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Table 5   Convergence check of the algorithm
(a) The numerical standard errors (NSEs) and the relative numerical efficiency (RNE) for the MCMC 
samples
Convergence check
Geweke diagnostics for each parameter chain
Variable
NSE iid
RNE iid
β1
0.0017
1.0000
τ
0.0002
1.0000
σ
0.0002
1.0000
ϕ
0.0029
1.0000
δ
0.0175
1.0000
(b) The Geweke’s chi-square probability test
Variable
τ
NSE estimate
Mean
N.S.E
Chi-sq Prob
i.i.d
0.2125
0.0002
0.0000
4% taper
0.2123
0.0013
0.3478
8% taper
0.2121
0.0014
0.3539
15% taper
0.2120
0.0015
0.3803
Variable
ϕ
NSE estimate
Mean
N.S.E
Chi-sq Prob
i.i.d
2.9656
0.0037
0.0667
4% taper
2.9663
0.0239
0.7580
8% taper
2.9657
0.0236
0.7735
15% taper
2.9652
0.0220
0.7795
Variable
σ
NSE estimate
Mean
N.S.E
Chi-sq Prob
i.i.d
0.6723
0.0002
0.0000
4% taper
0.6722
0.0011
0.4784
8% taper
0.6720
0.0008
0.5093
15% taper
0.6720
0.0007
0.5534
Variable
δ
NSE estimate
Mean
N.S.E
Chi-sq Prob
i.i.d
8.2275
0.0226
0.0004
4% taper
8.2515
0.1807
0.5865
8% taper
8.2455
0.1771
0.5933
15% taper
8.2409
0.1730
0.5973