1# RECORD e6c58cb070edd6cfaff8b1bababd256016f5ed902# TITLE: Hedonic real estate price estimation with the spatiotemporal geostatistical model3# YEAR: 2023.0 VENUE: Journal of Spatial Econometrics DOI: 10.1007/s43071-023-00039-w4# AUTHORS: Sachio Muto; Shonosuke Sugasawa; Masatomo Suzuki5# PAGES: 37 CANDIDATE TABLE PAGES (1-based): [14, 15, 16, 17, 18, 24, 25, 31, 32]6# 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.789===== PAGE 1 (score 4, numeric-paren 0, table-words 0, var-words 4) =====1011Vol.:(0123456789)12Journal of Spatial Econometrics (2023) 4:1013https://doi.org/10.1007/s43071-023-00039-w141 315ORIGINAL PAPER16Hedonic real estate price estimation 17with the spatiotemporal geostatistical model18Sachio Muto1 · Shonosuke Sugasawa2 · Masatomo Suzuki319Received: 31 August 2021 / Accepted: 15 October 2023 / Published online: 14 November 2023 20© The Author(s) 202321Abstract22This study argues that the spatiotemporal geostatistical model for real estate prices, 23which accounts for and incorporates spatial autocorrelation, can be estimated suc-24cessfully using the Bayesian Markov Chain Monte Carlo (MCMC) estimation. 25While this procedure often encounters difficulty in calculating probabilistic densi-26ties in the Metropolis–Hastings (MH) algorithm, this study introduces a feasible and 27practical estimation method, providing useful estimated parameters for the model. 28Using single-family house transaction data, we show that ordinary estimations of 29real estate prices, with respect to certain explanatory variables, may lead to the 30underestimation of standard errors of coefficients for explanatory variables with 31spatial effects unless spatial autocorrelation is controlled for. Our model also makes 32it possible to obtain accurate in-sample predictions and moderately improved out-33of-sample predictions for real estate prices. This study further estimates a “decay 34rate:” a diminishing correlation between real estate prices and increasing distance, 35showing that geographical proximities are likely to have an important impact on real 36estate prices, especially at a range under 600 m.37Keywords Real estate pricing · Bayesian econometrics · MCMC · Geostatistical 38model · Metropolis–Hastings algorithm39JEL Classification R3940 * Sachio Muto 41 42s-muto@e.u-tokyo.ac.jp431 44Center for Real Estate Innovation (CREI), The University of Tokyo, 7‑3‑1, Hongo, Bunkyo‑ku, 45Tokyo 113‑0033, Japan462 47Faculty of Economics, Keio University, Tokyo, Japan483 49School of Data Science, Yokohama, Yokohama City University, Yokohama, Japan505152===== PAGE 14 (score 73, numeric-paren 64, table-words 2, var-words 5) =====5354 55S. Muto et al.561 35710 58Page 14 of 3759Table 2 Comparison of estimation and in-sample prediction of the OLS and the geostatistical model. (Data Year: 2016–2019)60Dependent variable: transaction price [ten thousand JPY]61(1)62(2)63(3)64No time dummy, No regional dummy65No time dummy & No regional dummy66No time dummy & With regional 67dummy68With less property-level spatial variable69With full property-level spatial variable70With full property-level spatial variable71OLS72Geostatstical model OLS73Geostatstical model OLS74Geostatstical 75model76Explanatory variables77Estimate78S. E79Estimate80S. E81Estimate82S. E83Estimate84S. E85Estimate86S. E87Estimate88S. E89Property characteristics90Newly built dummy91 − 0.11292(0.106)930.07994(0.085)95 − 0.06796(0.099)970.06898(0.086)990.039100(0.080)1010.078102(0.092)103Property age [years]/10104 − 0.744105(0.087)106 − 0.661107(0.069)108 − 0.736109(0.082)110 − 0.664111(0.069)112 − 0.675113(0.067)114 − 0.655115(0.076)116(Property age [years]/10)21170.076118(0.017)1190.062120(0.013)1210.077122(0.016)1230.063124(0.013)1250.065126(0.013)1270.062128(0.015)129Floor space [m2] /1001300.289131(0.024)1320.205133(0.021)1340.234135(0.023)1360.198137(0.020)1380.160139(0.019)1400.178141(0.023)142(Floor space [m2] /100)2143 − 0.003144(0.001)145 − 0.003146(0.001)147 − 0.002148(0.001)149 − 0.002150(0.001)151 − 0.001152(0.001)153 − 0.002154(0.001)155Land area [m2]/1001560.141157(0.027)1580.164159(0.022)1600.144161(0.025)1620.162163(0.022)1640.204165(0.036)1660.181167(0.041)168(Land area [m2] /100)2169 − 0.004170(0.001)171 − 0.004172(0.001)173 − 0.004174(0.001)175 − 0.004176(0.001)177 − 0.009178(0.002)179 − 0.007180(0.002)181Date of transaction registered182(yearly conversion)183 − 0.004184(0.023)185 − 0.010186(0.018)187 − 0.008188(0.017)189 − 0.006190(0.023)1910.007192(0.014)1930.007194(0.019)195Property-level spatial variables196Access environment197 Walking time to nearest station [min]198 − 0.025199(0.004)200 − 0.020201(0.006)202 − 0.031203(0.004)204 − 0.026205(0.006)206 − 0.033207(0.006)208 − 0.031209(0.008)210 Bus to closest station dummy211 − 0.393212(0.071)213 − 0.421214(0.128)215 − 0.636216(0.077)217 − 0.563218(0.125)219 − 0.685220(0.132)221 − 0.666222(0.166)223 Number of daily passengers of the 224closest station [ten thousand per-225sons / day]226–227–228–229–2300.010231(0.022)2320.004233(0.042)2340.002235(0.043)2360.009237(0.059)238239240===== PAGE 15 (score 53, numeric-paren 46, table-words 2, var-words 3) =====2412421 3243Hedonic real estate price estimation with the spatiotemporal…244Page 15 of 37 24510246Table 2 (continued)247Dependent variable: transaction price [ten thousand JPY]248(1)249(2)250(3)251No time dummy, No regional dummy252No time dummy & No regional dummy253No time dummy & With regional 254dummy255With less property-level spatial variable256With full property-level spatial variable257With full property-level spatial variable258OLS259Geostatstical model OLS260Geostatstical model OLS261Geostatstical 262model263Explanatory variables264Estimate265S. E266Estimate267S. E268Estimate269S. E270Estimate271S. E272Estimate273S. E274Estimate275S. E276Development Age277 Included in DID in 1960s or before278–279–280–281–282 − 0.596283(0.105)284 − 0.269285(0.175)286 − 0.177287(0.205)288 − 0.213289(0.276)290 Included in DID in 1970s291–292–293–294–295 − 0.662296(0.106)297 − 0.288298(0.173)299 − 0.191300(0.198)301 − 0.223302(0.268)303 Included in DID in 1980s304–305–306–307–308 − 0.600309(0.095)310 − 0.213311(0.164)312 − 0.140313(0.190)314 − 0.163315(0.259)316 Included in DID in 1990s317–318–319–320–321 − 0.649322(0.148)323 − 0.311324(0.199)325 − 0.201326(0.188)327 − 0.239328(0.263)329 Included in DID in 2000s330–331–332–333–334 − 0.523335(0.169)336 − 0.117337(0.225)338 − 0.164339(0.216)340 − 0.096341(0.286)342 Included in DID in 2010s343–344–345–346–347 − 0.466348(0.167)349 − 0.137350(0.262)351 − 0.035352(0.245)353 − 0.107354(0.329)355Disaster risk356 Tsunami risk dummy (over 3 m)357–358–359–360–3610.350362(0.098)3630.072364(0.124)365 − 0.096366(0.108)367 − 0.002368(0.135)369 Sediment disaster risk dummy370–371–372–373–374 − 0.233375(0.047)376 − 0.140377(0.046)378 − 0.101379(0.041)380 − 0.110381(0.049)382District level variables383Ratio of residents over 20 years384–385–386–387–388 − 0.089389(0.045)390 − 0.026391(0.060)392 − 0.344393(0.388)394 − 0.172395(0.512)396Hillside area dummy397–398–399–400–401 − 0.158402(0.069)403 − 0.173404(0.086)405–406–407–408–409Promotion area dummy410–411–412–413–4140.287415(0.047)4160.262417(0.074)418–419–420–421–422Constant4230.822424(0.190)4251.377426(0.191)4271.877428(0.220)4291.733430(0.257)4311.905432(0.297)4331.847434(0.427)435Time dummy (monthly)436No437No438No439No440No441No442443444===== PAGE 16 (score 19, numeric-paren 12, table-words 3, var-words 1) =====445446 447S. Muto et al.4481 344910 450Page 16 of 37451Table 2 (continued)452Dependent variable: transaction price [ten thousand JPY]453(1)454(2)455(3)456No time dummy, No regional dummy457No time dummy & No regional dummy458No time dummy & With regional 459dummy460With less property-level spatial variable461With full property-level spatial variable462With full property-level spatial variable463OLS464Geostatstical model OLS465Geostatstical model OLS466Geostatstical 467model468Explanatory variables469Estimate470S. E471Estimate472S. E473Estimate474S. E475Estimate476S. E477Estimate478S. E479Estimate480S. E481District dummy482No483No484No485No486Yes487Yes488Parameters for error stracture (Geostatistics)489τ490–491–4920.224493(0.024)494–495–4960.212497(0.026)498–499–5000.159501(0.029)502σ503–504–5050.710506(0.030)507–508–5090.670510(0.028)511–512–5130.542514(0.027)515ϕ516–517–5183.521519(0.518)520–521–5222.987523(0.482)524–525–5261.395527(0.323)528δ529–530–5319.957532(3.716)533–534–5357.620536(2.641)537–538–5394.848540(1.832)541Performance of predicted values542R2 (in-sample)5430.6175440.9905450.6675460.9925470.8505480.998549MSE (in-sample)5500.4605510.0125520.4005530.0095540.1805550.003556557558===== PAGE 17 (score 58, numeric-paren 48, table-words 2, var-words 6) =====5595601 3561Hedonic real estate price estimation with the spatiotemporal…562Page 17 of 37 56310564Table 2 (continued)565Dependent variable: Transaction price [Ten thousand JPY]566(4)567(5)568With time dummy & No regional dummy569With time dummy & With regional dummy570With full property-level spatial variable571With full property-level spatial variable572OLS573Geostatstical Model574OLS575Geostatstical Model576Explanatory variables577Estimate578S. E579Estimate580S. E581Estimate582S. E583Estimate584S. E585Property characteristics586Newly built dummy587 − 0.071588(0.099)5890.066590(0.088)5910.037592(0.080)5930.063594(0.097)595Property age [years]/10596 − 0.757597(0.082)598 − 0.685599(0.071)600 − 0.694601(0.067)602 − 0.684603(0.081)604(Property age [years]/10)26050.081606(0.016)6070.067608(0.013)6090.068610(0.013)6110.067612(0.016)613Floor space [m2] /1006140.240615(0.023)6160.206617(0.021)6180.169619(0.019)6200.189621(0.024)622(Floor space [m2] /100)2623 − 0.002624(0.001)625 − 0.003626(0.001)627 − 0.001628(0.001)629 − 0.002630(0.001)631Land area [m2]/1006320.145633(0.025)6340.158635(0.023)6360.189637(0.036)6380.167639(0.043)640(Land area [m2] /100)2641 − 0.004642(0.001)643 − 0.004644(0.001)645 − 0.008646(0.002)647 − 0.006648(0.002)649Date of transaction registered (yearly conversion)650–651–652–653–654–655–656–657–658Property-level spatial variables659Access environment660 Walking time to nearest station [min]661 − 0.031662(0.004)663 − 0.027664(0.006)665 − 0.035666(0.006)667 − 0.031668(0.008)669 Bus to closest station dummy670 − 0.646671(0.077)672 − 0.575673(0.129)674 − 0.724675(0.133)676 − 0.677677(0.170)678 Number of daily passengers of the closest station 679[ten thousand persons / day]6800.002681(0.022)682 − 0.005683(0.042)6840.011685(0.043)6860.007687(0.062)688Development age689 Included in DID in 1960s or before690 − 0.610691(0.105)692 − 0.279693(0.177)694 − 0.227695(0.204)696 − 0.243697(0.282)698 Included in DID in 1970s699 − 0.669700(0.106)701 − 0.301702(0.175)703 − 0.234704(0.198)705 − 0.254706(0.275)707708709===== PAGE 18 (score 48, numeric-paren 42, table-words 2, var-words 2) =====710711 712S. Muto et al.7131 371410 715Page 18 of 37716Table 2 (continued)717Dependent variable: Transaction price [Ten thousand JPY]718(4)719(5)720With time dummy & No regional dummy721With time dummy & With regional dummy722With full property-level spatial variable723With full property-level spatial variable724OLS725Geostatstical Model726OLS727Geostatstical Model728Explanatory variables729Estimate730S. E731Estimate732S. E733Estimate734S. E735Estimate736S. E737 Included in DID in 1980s738 − 0.613739(0.095)740 − 0.220741(0.166)742 − 0.147743(0.190)744 − 0.160745(0.264)746 Included in DID in 1990s747 − 0.651748(0.148)749 − 0.313750(0.201)751 − 0.226752(0.186)753 − 0.227754(0.269)755 Included in DID in 2000s756 − 0.495757(0.168)758 − 0.123759(0.228)760 − 0.163761(0.215)762 − 0.102763(0.292)764 Included in DID in 2010s765 − 0.489766(0.167)767 − 0.183768(0.265)769 − 0.085770(0.244)771 − 0.098772(0.341)773Disaster Risk774 Tsunami risk dummy (over 3 m)7750.390776(0.098)7770.098778(0.125)779 − 0.011780(0.108)7810.034782(0.139)783 Sediment disaster risk dummy784 − 0.216785(0.047)786 − 0.123787(0.047)788 − 0.088789(0.041)790-0.095791(0.052)792District level variables793Ratio of residents over 20 years794 − 0.074795(0.045)796 − 0.021797(0.061)798 − 0.341799(0.390)800 − 0.226801(0.528)802Hillside area dummy803 − 0.160804(0.069)805 − 0.173806(0.088)807–808–809–810–811Promotion area dummy8120.276813(0.047)8140.254815(0.075)816–817–818–819–820Constant8211.869822(0.245)8231.703824(0.272)8251.880826(0.307)8271.852828(0.442)829Time dummy (monthly)830Yes831Yes832Yes833Yes834District dummy835No836No837Yes838Yes839Parameters for error structure (Geostatistics)840τ841–842–8430.212844(0.027)845–846–8470.174848(0.031)849σ850–851–8520.673853(0.027)854–855–8560.533857(0.022)858ϕ859–860–8612.958862(0.474)863–864–8651.188866(0.227)867868869===== PAGE 19 (score 10, numeric-paren 2, table-words 3, var-words 2) =====8708711 3872Hedonic real estate price estimation with the spatiotemporal…873Page 19 of 37 87410875Table 2 (continued)876Dependent variable: Transaction price [Ten thousand JPY]877(4)878(5)879With time dummy & No regional dummy880With time dummy & With regional dummy881With full property-level spatial variable882With full property-level spatial variable883OLS884Geostatstical Model885OLS886Geostatstical Model887Explanatory variables888Estimate889S. E890Estimate891S. E892Estimate893S. E894Estimate895S. E896δ897–898–8998.260900(2.872)901–902–9033.498904(2.771)905Performance of predicted values906R2 (in-sample)9070.6679080.9939090.8579100.997911MSE (in-sample)9120.4009130.0099140.1719150.004916917918===== PAGE 24 (score 85, numeric-paren 76, table-words 2, var-words 5) =====919920 921S. Muto et al.9221 392310 924Page 24 of 37925Table 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)926Dependent variable: Transaction price [Ten thousand JPY]927(1)928(2)929(3)930No time dummy, No regional dummy931No time dummy & No regional dummy932No time dummy & With regional dummy933With less property-level spatial variable934With full property-level spatial variable935With full property-level spatial variable936OLS937Geostatstical Model938OLS939Geostatstical Model940OLS941Geostatstical Model942Explanatory variables943Estimate944S. E945Estimate946S. E947Estimate948S. E949Estimate950S. E951Estimate952S. E953Estimate954S. E955Property characteristics956Newly built dummy957− 0.036958(0.124)9590.052960(0.099)9610.003962(0.116)9630.044964(0.100)9650.086966(0.093)9670.089968(0.115)969Property age [years]/10970− 0.720971(0.103)972− 0.646973(0.081)974− 0.704975(0.097)976− 0.652977(0.081)978− 0.563979(0.077)980− 0.593981(0.094)982(Property age [years]/10)29830.078984(0.020)9850.061986(0.015)9870.078988(0.019)9890.062990(0.016)9910.043992(0.015)9930.048994(0.018)995Floor space [m2] /1009960.289997(0.027)9980.225999(0.023)10000.2391001(0.026)10020.2151003(0.023)10040.1731005(0.022)10060.1781007(0.027)1008(Floor space [m2] /100)21009− 0.0031010(0.001)1011− 0.0031012(0.001)1013− 0.0021014(0.001)1015− 0.0031016(0.001)1017− 0.0011018(0.001)1019− 0.0021020(0.001)1021Land area [m2]/10010220.1331023(0.029)10240.1431025(0.025)10260.1451027(0.028)10280.1461029(0.025)10300.2421031(0.045)10320.2471033(0.054)1034(Land area [m2] /100)21035− 0.0041036(0.001)1037− 0.0041038(0.001)1039− 0.0041040(0.001)1041− 0.0041042(0.001)1043− 0.0121044(0.003)1045− 0.0121046(0.003)1047Date of transaction registered (yearly conversion)1048− 0.0141049(0.029)10500.0261051(0.032)1052− 0.0101053(0.028)10540.0241055(0.032)10560.0221057(0.022)10580.0291059(0.031)1060Property-level spatial variables1061 Access environment1062 Walking time to nearest station [min]1063− 0.0201064(0.005)1065− 0.0151066(0.007)1067− 0.0261068(0.005)1069− 0.0211070(0.007)1071− 0.0251072(0.007)1073− 0.0251074(0.009)1075 Bus to closest station dummy1076− 0.3701077(0.085)1078− 0.3301079(0.150)1080− 0.5961081(0.092)1082− 0.4761083(0.150)1084− 0.4641085(0.150)1086− 0.4951087(0.193)1088 Number of daily passengers of the closest station 1089[ten thousand persons / day]1090–1091–1092–1093–10940.0081095(0.027)10960.0261097(0.048)10980.0801099(0.052)11000.1081101(0.074)1102Development age1103 Included in DID in 1960s or before1104–1105–1106–1107–1108− 0.6141109(0.126)1110− 0.3171111(0.204)1112− 0.0731113(0.231)1114− 0.0871115(0.336)1116 Included in DID in 1970s1117–1118–1119–1120–1121− 0.6941122(0.126)1123− 0.3481124(0.203)1125− 0.1641126(0.224)1127− 0.1421128(0.326)1129 Included in DID in 1980s1130–1131–1132–1133–1134− 0.6141135(0.114)1136− 0.2691137(0.191)1138− 0.0561139(0.217)1140− 0.0461141(0.317)114211431144===== PAGE 25 (score 50, numeric-paren 43, table-words 2, var-words 3) =====114511461 31147Hedonic real estate price estimation with the spatiotemporal…1148Page 25 of 37 1149101150Table 3 (continued)1151Dependent variable: Transaction price [Ten thousand JPY]1152(1)1153(2)1154(3)1155No time dummy, No regional dummy1156No time dummy & No regional dummy1157No time dummy & With regional dummy1158With less property-level spatial variable1159With full property-level spatial variable1160With full property-level spatial variable1161OLS1162Geostatstical Model1163OLS1164Geostatstical Model1165OLS1166Geostatstical Model1167Explanatory variables1168Estimate1169S. E1170Estimate1171S. E1172Estimate1173S. E1174Estimate1175S. E1176Estimate1177S. E1178Estimate1179S. E1180 Included in DID in 1990s1181–1182–1183–1184–1185− 0.6281186(0.179)1187− 0.3661188(0.233)1189− 0.1161190(0.219)1191− 0.1151192(0.333)1193 Included in DID in 2000s1194–1195–1196–1197–1198− 0.5441199(0.206)1200− 0.1631201(0.278)1202− 0.1771203(0.267)1204− 0.0531205(0.386)1206 Included in DID in 2010s1207–1208–1209–1210–1211− 0.4981212(0.185)1213− 0.1981214(0.297)1215− 0.0441216(0.271)1217− 0.0291218(0.394)1219Disaster risk1220 Tsunami risk dummy (over 3 m)1221–1222–1223–1224–12250.2061226(0.116)1227− 0.1141228(0.159)1229− 0.2911230(0.138)1231− 0.2641232(0.186)1233 Sediment disaster risk dummy1234–1235–1236–1237–1238− 0.2321239(0.056)1240− 0.1401241(0.054)1242− 0.0981243(0.049)1244− 0.1301245(0.063)1246District level variables1247Ratio of residents over 20 years1248–1249–1250–1251–1252− 0.1291253(0.054)1254− 0.0501255(0.069)1256− 0.4541257(0.408)1258− 0.3091259(0.585)1260Hillside area dummy1261–1262–1263–1264–1265− 0.2041266(0.083)1267− 0.2091268(0.100)1269–1270–1271–1272–1273Promotion area dummy1274–1275–1276–1277–12780.2431279(0.055)12800.2211281(0.084)1282–1283–1284–1285–1286Constant12870.6681288(0.220)12891.1241290(0.220)12911.7401292(0.258)12931.5441294(0.300)12951.1611296(0.348)12971.1421298(0.510)1299Time dummy (monthly)1300No1301No1302Yes1303Yes1304Yes1305Yes1306District dummy1307No1308No1309No1310No1311Yes1312Yes1313Parameters for error stracture (Geostatistics)1314τ1315–1316–13170.2421318(0.027)1319–1320–13210.2331322(0.027)1323–1324–13250.1761326(0.034)1327σ1328–1329–13300.7441331(0.041)1332–1333–13340.7041335(0.036)1336–1337–13380.5351339(0.027)1340ϕ1341–1342–13434.1001344(0.702)1345–1346–13473.5351348(0.605)1349–1350–13511.2531352(0.305)135313541355===== PAGE 26 (score 12, numeric-paren 3, table-words 4, var-words 1) =====13561357 1358S. Muto et al.13591 3136010 1361Page 26 of 371362Table 3 (continued)1363Dependent variable: Transaction price [Ten thousand JPY]1364(1)1365(2)1366(3)1367No time dummy, No regional dummy1368No time dummy & No regional dummy1369No time dummy & With regional dummy1370With less property-level spatial variable1371With full property-level spatial variable1372With full property-level spatial variable1373OLS1374Geostatstical Model1375OLS1376Geostatstical Model1377OLS1378Geostatstical Model1379Explanatory variables1380Estimate1381S. E1382Estimate1383S. E1384Estimate1385S. E1386Estimate1387S. E1388Estimate1389S. E1390Estimate1391S. E1392δ1393–1394–139516.5581396(9.143)1397–1398–139912.2271400(5.408)1401–1402–14032.3921404(0.736)1405Performance of predicted values1406R2 (in-sample)14070.60314080.98714090.65314100.98914110.86114120.9971413MSE (in-sample)14140.47414150.01514160.41414170.01314180.16514190.0041420R2 (out-of-sample)14210.64714220.72814230.69414240.73414250.68214260.6951427MSE (out-of-sample)14280.43214290.33314300.37514310.32614320.38914330.373143414351436===== PAGE 31 (score 106, numeric-paren 95, table-words 3, var-words 5) =====143714381 31439Hedonic real estate price estimation with the spatiotemporal…1440Page 31 of 37 1441101442Table 4 Comparison of estimation results with the SLX and the SDEM. (Specification (4) of Table 2)1443Dependent variable: Transaction price [ten thousand JPY]1444OLS1445Geostatistical 1446model1447SLX1448SDEM1449β1450β1451β1452θ1453β1454θ1455Estimate1456S.E1457Estimate1458S.E1459Estimate1460S.E1461Estimate1462S.E1463Estimate1464S.E1465Estimate1466S.E1467Property characteristics1468Newly built dummy1469 − 0.0711470(0.099)14710.0661472(0.088)1473 − 0.0211474(0.095)1475 − 0.9801476(0.816)1477 − 0.0141478(0.091)1479 − 1.1351480(0.932)1481Property age [years]/101482 − 0.7571483(0.082)1484 − 0.6851485(0.071)1486 − 0.7331487(0.076)1488 − 0.5981489(0.725)1490 − 0.7281491(0.074)1492 − 0.7641493(0.816)1494(Property age [years]/10)214950.0811496(0.016)14970.0671498(0.013)14990.0741500(0.015)15010.1161502(0.146)15030.0731504(0.014)15050.1421506(0.164)1507Floor space [m2] /10015080.2401509(0.023)15100.2061511(0.021)15120.2611513(0.022)15140.0181515(0.201)15160.2541517(0.021)15180.1681519(0.228)1520(Floor space [m2] /100)21521 − 0.0021522(0.001)1523 − 0.0031524(0.001)1525 − 0.0041526(0.001)15270.0121528(0.005)1529 − 0.0041530(0.001)15310.0081532(0.006)1533Land area [m2]/10015340.1451535(0.025)15360.1581537(0.023)15380.1691539(0.023)15400.8441541(0.448)15420.1681543(0.023)15440.5621545(0.506)1546(Land area [m2] /100)21547 − 0.0041548(0.001)1549 − 0.0041550 − 0.0041551(0.001)1552 − 0.0601553(0.024)1554 − 0.0041555(0.001)1556-0.0431557(0.026)1558Date of transaction registered (yearly conversion)1559–1560–1561–1562–1563–1564–1565–1566–1567–1568–1569–1570–1571Property-level spatial variables-access environment1572Walking time to nearest station [min]1573 − 0.0311574(0.004)1575 − 0.0271576(0.006)1577 − 0.0241578(0.006)1579 − 0.0221580(0.027)1581 − 0.0231582(0.006)1583 − 0.0181584(0.033)1585Bus to closest station dummy1586 − 0.6461587(0.077)1588 − 0.5751589(0.129)1590 − 0.5481591(0.112)1592 − 0.9401593(0.586)1594 − 0.5391595(0.113)1596 − 0.6421597(0.675)1598Number of daily passengers of the closest station 1599[ten thousand persons / day]16000.0021601(0.022)1602 − 0.0051603(0.042)16040.0201605(0.034)1606 − 0.1331607(0.189)16080.0111609(0.036)1610 − 0.0181611(0.223)1612Development Age1613 Included in DID in 1960s or before1614 − 0.6101615(0.105)1616 − 0.2791617(0.177)1618 − 0.0041619(0.149)1620 − 0.7591621(0.639)1622 − 0.0361623(0.152)1624 − 0.6041625(0.778)1626 Included in DID in 1970s1627 − 0.6691628(0.106)1629 − 0.3011630(0.175)1631 − 0.0291632(0.149)1633 − 0.9201634(0.708)1635 − 0.0481636(0.151)1637 − 0.9041638(0.835)1639 Included in DID in 1980s1640 − 0.6131641(0.095)1642 − 0.2201643(0.166)16440.0561645(0.140)1646 − 0.8361647(0.583)16480.0581649(0.143)1650 − 1.0021651(0.723)1652 Included in DID in 1990s1653 − 0.6511654(0.148)1655 − 0.3131656(0.201)1657 − 0.1411658(0.180)16591.4771660(1.265)1661 − 0.1611662(0.180)16631.5421664(1.469)1665 Included in DID in 2000s1666 − 0.4951667(0.168)1668 − 0.1231669(0.228)1670 − 0.0281671(0.211)1672 − 0.1761673(1.484)1674 − 0.0231675(0.208)1676 − 0.3821677(1.634)1678 Included in DID in 2010s1679 − 0.4891680(0.167)1681 − 0.1831682(0.265)16830.0711684(0.257)1685 − 0.0661686(0.927)16870.0321688(0.254)1689 − 0.0161690(1.128)169116921693===== PAGE 32 (score 50, numeric-paren 40, table-words 4, var-words 2) =====16941695 1696S. Muto et al.16971 3169810 1699Page 32 of 371700Table 4 (continued)1701Dependent variable: Transaction price [ten thousand JPY]1702OLS1703Geostatistical 1704model1705SLX1706SDEM1707β1708β1709β1710θ1711β1712θ1713Estimate1714S.E1715Estimate1716S.E1717Estimate1718S.E1719Estimate1720S.E1721Estimate1722S.E1723Estimate1724S.E1725Disaster risk1726 Tsunami risk dummy (over 3 m)17270.3901728(0.098)17290.0981730(0.125)17310.2381732(0.114)17330.7261734(0.634)17350.1901736(0.120)17371.5341738(1.368)1739 Sediment disaster risk dummy1740 − 0.2161741(0.047)1742 − 0.1231743(0.047)1744 − 0.1151745(0.048)1746 − 0.7161747(0.370)1748 − 0.1121749(0.046)1750 − 0.5781751(0.436)1752District level variables1753Ratio of residents over 20 years1754 − 0.0741755(0.045)1756 − 0.0211757(0.061)1758 − 0.0571759(0.061)17600.2471761(0.359)1762 − 0.0661763(0.061)17640.1331765(0.407)1766Hillside area dummy1767 − 0.1601768(0.069)1769 − 0.1731770(0.088)1771 − 0.0721772(0.089)1773 − 1.2001774(0.688)1775 − 0.0991776(0.087)1777 − 0.7541778(0.762)1779Promotion area dummy17800.2761781(0.047)17820.2541783(0.075)17840.2841785(0.072)1786 − 0.4781787(0.344)17880.2921789(0.074)1790 − 0.3831791(0.408)1792Constant17931.8691794(0.245)17951.7031796(0.272)17971.4201798(0.303)1799–1800–18011.4951802(0.306)1803–1804–1805Time dummy (monthly)1806Yes1807Yes1808Yes1809Yes1810District dummy1811No1812No1813No1814No1815Parameters for Error Stracture (Geostatistics)1816τ1817–1818–18190.2121820(0.027)1821–1822–1823–1824–1825–1826–1827–1828–1829σ1830–1831–18320.6731833(0.027)1834–1835–1836–1837–1838–1839–1840–1841–1842ϕ1843–1844–18452.9581846(0.474)1847–1848–1849–1850–1851–1852–1853–1854–1855δ1856–1857–18588.2601859(2.872)1860–1861–1862–1863–1864–1865–1866–1867–1868Variance parameter (SLX and SDEM)1869–1870–18710.2971872(0.012)18730.2791874(0.012)1875R2 (Pseudo R2 for SLX and SDEM)18760.68118770.99318780.75318790.734188018811882===== PAGE 33 (score 3, numeric-paren 0, table-words 1, var-words 1) =====188318841 31885Hedonic real estate price estimation with the spatiotemporal…1886Page 33 of 37 1887101888Table 5 Convergence check of the algorithm1889(a) The numerical standard errors (NSEs) and the relative numerical efficiency (RNE) for the MCMC 1890samples1891Convergence check1892Geweke diagnostics for each parameter chain1893Variable1894NSE iid1895RNE iid1896β118970.001718981.00001899τ19000.000219011.00001902σ19030.000219041.00001905ϕ19060.002919071.00001908δ19090.017519101.00001911(b) The Geweke’s chi-square probability test1912Variable1913τ1914NSE estimate1915Mean1916N.S.E1917Chi-sq Prob1918i.i.d19190.212519200.000219210.000019224% taper19230.212319240.001319250.347819268% taper19270.212119280.001419290.3539193015% taper19310.212019320.001519330.38031934Variable1935ϕ1936NSE estimate1937Mean1938N.S.E1939Chi-sq Prob1940i.i.d19412.965619420.003719430.066719444% taper19452.966319460.023919470.758019488% taper19492.965719500.023619510.7735195215% taper19532.965219540.022019550.77951956Variable1957σ1958NSE estimate1959Mean1960N.S.E1961Chi-sq Prob1962i.i.d19630.672319640.000219650.000019664% taper19670.672219680.001119690.478419708% taper19710.672019720.000819730.5093197415% taper19750.672019760.000719770.55341978Variable1979δ1980NSE estimate1981Mean1982N.S.E1983Chi-sq Prob1984i.i.d19858.227519860.022619870.000419884% taper19898.251519900.180719910.586519928% taper19938.245519940.177119950.5933199615% taper19978.240919980.173019990.59732000