1# RECORD 03c7319d6d03a3326e49bd775951ee9918110cee2# TITLE: Does my house have a premium or discount in relation to my neighbors? A regression-kriging approach3# YEAR: 2020.0 VENUE: nan DOI: 10.1016/j.seps.2020.1009144# AUTHORS: Jorge Chica-Olmo; Rafael Cano-Guervos5# PAGES: 24 CANDIDATE TABLE PAGES (1-based): [14, 18]6# ABSTRACT: Abstract In the real estate literature, numerous studies have applied hedonic models to estimate the implicit value of the characteristics that influence housing prices. However, few studies have quantified the weight of location in the price of residential properties, and still fewer have quantified the premium or discount used to weigh the price of a home. In this paper, the regression-kriging method is applied to address the two previous objectives in the city of Granada, Spain. This method is also adapted, interpreted and made accessible to real estate appraisers with a view to providing these professionals with an objective, sophisticated and powerful tool in accordance with their know-how. This method can also be useful for investors, urban planners, public administrators and revenue departments, among others, as it can determine the value distribution of the location.789===== PAGE 1 (score 4, numeric-paren 0, table-words 0, var-words 4) =====1011112Does my house have a premium or discount in13relation to my neighbors? A regression-kriging14approach15Jorge Chica-Olmo16jchica@ugr.es17Department of Quantitative Methods for Economics and Business18Campus de la Cartuja s/n 18071, Granada, Spain19Rafael Cano-Guervos20rcano@ugr.es21Department of Quantitative Methods for Economics and Business22Campus de la Cartuja s/n 18071, Granada, Spain23Abstract24In the real estate literature, numerous studies have applied hedonic models to estimate25the implicit value of the characteristics that influence housing prices. However, few studies have26quantified the weight of location in the price of residential properties, and still fewer have27quantified the premium or discount used to weigh the price of a home. In this paper, the28regression-kriging method is applied to address the two previous objectives in the city of29Granada, Spain. This method is also adapted, interpreted and made accessible to real estate30appraisers with a view to providing these professionals with an objective, sophisticated and31powerful tool in accordance with their know-how. This method can also be useful for investors,32urban planners, public administrators and revenue departments, among others, as it can33determine the value distribution of the location.343536===== PAGE 14 (score 28, numeric-paren 18, table-words 4, var-words 2) =====37381439Dependent variable:40log(PRICE)41OLS42RK43Const4410.84745(0.000)4610.96547(0.000)48AREA490.00650(0.000)510.00652(0.000)53AGE54-0.06355(0.020)56-0.08457(0.000)58BATH590.14860(0.005)610.12862(0.002)63PENT640.16965(0.016)660.12467(0.020)68HEAT690.11270(0.029)710.08472(0.030)73AIRCON740.14175(0.001)760.10977(0.000)78ELEV790.36980(0.000)810.29582(0.000)83FURNISH840.12485(0.003)860.11387(0.000)88Variogram: Spherical89nugget90--910.05892partial-sill93--940.04595range (meters)96--97167698Cross-validation99R-squared1000.5961010.733102ME1030.000104-0.008105RMSE1060.3451070.281108n109296110296111Note: p-value in parenthesis112Figure 5. Cross-validation. Dashed line represents regression line and solid line represents 1:1113line.11410115111161211713118141191012011121121221312314124OLS125Observed126Predicted127Predicted 4.88 0.6Observed128R1292 0.596130RMSE 0.34513110132111331213413135141361013711138121391314014141RK142Observed143Predicted144Predicted 2.81 0.77Observed145R1462 0.733147RMSE 0.281148149150===== PAGE 15 (score 0, numeric-paren 0, table-words 0, var-words 0) =====15115215153In this work the fitted model is semi-logarithmic, so the expression used to estimate the154logarithm of the price of a home at any point on the plane,1550s (the kriging predictor) is:15601570158015901600161ˆ162ˆ163ln(164)165( )166s167ns168k169y170z s171z172z173z174175176177178179180181(8)182The following expression is then used to estimate the price:1830184018501860187ˆ (188)1890ˆ190s191ns192kz193s194z195z196z197y198e199e200201202203204205206207(9)208The previous equation is equivalent to either of the two following expressions:2091.2100211021202130ˆ214·215s216ns217z218z219z220e221y222e223e224225226227228(10)2292.2300231023202330ˆ234·235s236ns237z238z239z240e241y242e243e244245246247248(11)249where:2500ze251is the weighted average of the prices of houses near the subject property located at2520s .2530254sze255is the estimated prices of the house taking into account only the structural256characteristics of the subject property located at2570s .2580259ns260ze261is the weighted average of the estimated prices of houses near the subject property262taking into account only the structural characteristics of the houses.263Hence, expression (10) indicates that the estimated price of a house located at2640s (2650ˆy )266is equal to the weighted average of the prices of houses located in the vicinity of the subject267property (2680ze269) weighted by a weight2700271w272(273027402750276s277ns278z279z280e281w282e283284285286). This weight indicates if a premium or a287discount has been applied. If2880289w is greater than one, the structural characteristics of the subject290property are better than those of the neighboring houses. In this case it is necessary to make an291upward adjustment on the weighted average of the observed prices of the properties close to the292293294===== PAGE 18 (score 20, numeric-paren 12, table-words 1, var-words 6) =====29529618297property is almost double the average of its neighbors, that of the Normal property represents29870% of the average of its neighbors and that of the Discount property is almost half the average299of its neighbors. As for the AGE variable, the Discount property is higher than the average of its300neighbors, while the other two properties are similar to their averages. Something similar occurs301with the variable BATH. Of the three dwellings, the only one with heating (HEAT) is the302Premium+ dwelling, and the only one that does not have air conditioning (AIRCON) is the303dwelling with the Discount. However, if we compare the prices of the three dwellings, the most304expensive one, as would be expected, is the Premium+ property (€360,000). However, if we305compare the prices per square meter, the Premium+ house is the least expensive, which is306paradoxical since it has structural characteristics other than surface (AREA) that are superior to307the other two houses.308Table 4. Structural characteristics of the three properties309Structural310characteristic311Premium+312Normal313Discount314AREA315200 (107.5)31693 (131.2)31779 (140.1)318AGE31928 (30.5)32028 (32)32138 (32)322BATH3232 (1.75)3242 (1.8)3251 (2)326PENT3270 (0)3280 (0)3290 (0)330HEAT3311 (0.5)3320 (0.5)3330 (0.5)334AIRCON3351 (0.5)3361 (0.6)3370 (0.8)338ELEV3391 (1)3401 (1)3411 (1)342FURNISH3431 (1)3441 (1)3451 (1)346Price m23471800€3482311.2€3492278.5€350Note: Average of each characteristic of the 5 nearest neighboring houses in parentheses.351The main advantage of the proposed clustering method is that RK is multivariate and352considers the structural characteristics that explain the price of the dwelling, while classical353methods using local autocorrelation indicators, such as LISA or Getis-Ord-Gi, are univariate354and do not consider these factors.355On the other hand, expression 11 indicates that the estimated price of the subject356property (3570ˆy ) is equal to the estimated price of the structural characteristics (3580359sze360) weighted by361362363===== PAGE 19 (score 6, numeric-paren 0, table-words 0, var-words 6) =====36436519366location3670l (368036903700371ns372z373z374e375l376e377378379380) . This weight is given by the quotient between the weighted average of381the price of the properties adjacent to the subject property and the estimated price of their382structural characteristics. Weights greater than one in a given location indicate that the price of383the property is higher than estimated price of its structural characteristics, and location therefore384has a positive effect, that is, the property is located in a good area. Weights less than one385indicate that the property is in a bad location. When the estimated price of the subject property386coincides approximately with the estimated price of its structural characteristics, the weight of387the location is close to one, so the location of the subject property has little effect on its price.388The virtue of this procedure is that weights can be obtained to quantify the effect of location on389the price of the property, without the need to specify the location variables in the model. This390has several advantages such as avoiding subjectivity when choosing and measuring the location391variables, reducing appraisal costs, simplifying the appraiser’s task and avoiding the problem of392quantifying the radius of influence of these location factors, among others.393An additional advantage of this methodology is that weights can be obtained at any394point of the plane and represented by means of isovalue maps. Figure 7 shows the spatial395distribution of the location weights in the city of Granada. As can be seen, the areas marked in396warm colors (red, orange, yellow) are in the central part of the city, especially in the downtown397area where the central business district is located. This area is close to the Alhambra and has a398large number of services, commerce and leisure establishments, as well as some of the city’s399other main monuments. When moving away from the central zone towards the periphery, the400location value decreases. The lowest location values are found mainly in the north district,401where there is an economically and socially deprived enclave. Figure 5 shows that the location402weights in Granada vary from 0.461 to 1.623, thus indicating that, depending on the location,403the actual price of a property with certain structural characteristics could be almost four times its404estimated price.405These findings are of social and economic interest. For example, from the viewpoint of406real estate appraisals (whether for mortgage, taxation or investment purposes, etc.), homes that407