# RECORD 03c7319d6d03a3326e49bd775951ee9918110cee
# TITLE: Does my house have a premium or discount in relation to my neighbors? A regression-kriging approach
# YEAR: 2020.0  VENUE: nan  DOI: 10.1016/j.seps.2020.100914
# AUTHORS: Jorge Chica-Olmo; Rafael Cano-Guervos
# PAGES: 24  CANDIDATE TABLE PAGES (1-based): [14, 18]
# 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.


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Does my house have a premium or discount in
relation to my neighbors? A regression-kriging
approach
Jorge Chica-Olmo
jchica@ugr.es
Department of Quantitative Methods for Economics and Business
Campus de la Cartuja s/n 18071, Granada, Spain
Rafael Cano-Guervos
rcano@ugr.es
Department of Quantitative Methods for Economics and Business
Campus de la Cartuja s/n 18071, Granada, Spain
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.


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Dependent variable:
log(PRICE)
OLS
RK
Const
10.847
(0.000)
10.965
(0.000)
AREA
0.006
(0.000)
0.006
(0.000)
AGE
-0.063
(0.020)
-0.084
(0.000)
BATH
0.148
(0.005)
0.128
(0.002)
PENT
0.169
(0.016)
0.124
(0.020)
HEAT
0.112
(0.029)
0.084
(0.030)
AIRCON
0.141
(0.001)
0.109
(0.000)
ELEV
0.369
(0.000)
0.295
(0.000)
FURNISH
0.124
(0.003)
0.113
(0.000)
Variogram: Spherical
nugget
--
0.058
partial-sill
--
0.045
range (meters)
--
1676
Cross-validation
R-squared
0.596
0.733
ME
0.000
-0.008
RMSE
0.345
0.281
n
296
296
Note: p-value in parenthesis
Figure 5. Cross-validation. Dashed line represents regression line and solid line represents 1:1
line.
10
11
12
13
14
10
11
12
13
14
OLS
Observed
Predicted
Predicted 4.88 0.6Observed
R
2 0.596
RMSE 0.345
10
11
12
13
14
10
11
12
13
14
RK
Observed
Predicted
Predicted 2.81 0.77Observed
R
2 0.733
RMSE 0.281


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In this work the fitted model is semi-logarithmic, so the expression used to estimate the
logarithm of the price of a home at any point on the plane,
0s (the kriging predictor) is:
0
0
0
0
0
ˆ
ˆ
ln(
)
( )
s
ns
k
y
z s
z
z
z







(8)
The following expression is then used to estimate the price:
0
0
0
0
ˆ (
)
0ˆ
s
ns
kz
s
z
z
z
y
e
e







(9)
The previous equation is equivalent to either of the two following expressions:
1.
0
0
0
0ˆ
·
s
ns
z
z
z
e
y
e
e




(10)
2.
0
0
0
0ˆ
·
s
ns
z
z
z
e
y
e
e




(11)
where:
0ze
is the weighted average of the prices of houses near the subject property located at
0s .
0
sze
is the estimated prices of the house taking into account only the structural
characteristics of the subject property located at
0s .
0
ns
ze
is the weighted average of the estimated prices of houses near the subject property
taking into account only the structural characteristics of the houses.
Hence, expression (10) indicates that the estimated price of a house located at
0s (
0ˆy )
is equal to the weighted average of the prices of houses located in the vicinity of the subject
property (
0ze
) weighted by a weight
0
w
(
0
0
0
s
ns
z
z
e
w
e



). This weight indicates if a premium or a
discount has been applied. If
0
w is greater than one, the structural characteristics of the subject
property are better than those of the neighboring houses. In this case it is necessary to make an
upward adjustment on the weighted average of the observed prices of the properties close to the


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property is almost double the average of its neighbors, that of the Normal property represents
70% of the average of its neighbors and that of the Discount property is almost half the average
of its neighbors. As for the AGE variable, the Discount property is higher than the average of its
neighbors, while the other two properties are similar to their averages. Something similar occurs
with the variable BATH. Of the three dwellings, the only one with heating (HEAT) is the
Premium+ dwelling, and the only one that does not have air conditioning (AIRCON) is the
dwelling with the Discount. However, if we compare the prices of the three dwellings, the most
expensive one, as would be expected, is the Premium+ property (€360,000). However, if we
compare the prices per square meter, the Premium+ house is the least expensive, which is
paradoxical since it has structural characteristics other than surface (AREA) that are superior to
the other two houses.
Table 4. Structural characteristics of the three properties
Structural
characteristic
Premium+
Normal
Discount
AREA
200 (107.5)
93 (131.2)
79 (140.1)
AGE
28 (30.5)
28 (32)
38 (32)
BATH
2 (1.75)
2 (1.8)
1 (2)
PENT
0 (0)
0 (0)
0 (0)
HEAT
1 (0.5)
0 (0.5)
0 (0.5)
AIRCON
1 (0.5)
1 (0.6)
0 (0.8)
ELEV
1 (1)
1 (1)
1 (1)
FURNISH
1 (1)
1 (1)
1 (1)
Price m2
1800€
2311.2€
2278.5€
Note: Average of each characteristic of the 5 nearest neighboring houses in parentheses.
The main advantage of the proposed clustering method is that RK is multivariate and
considers the structural characteristics that explain the price of the dwelling, while classical
methods using local autocorrelation indicators, such as LISA or Getis-Ord-Gi, are univariate
and do not consider these factors.
On the other hand, expression 11 indicates that the estimated price of the subject
property (
0ˆy ) is equal to the estimated price of the structural characteristics (
0
sze
) weighted by


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location
0l (
0
0
0
ns
z
z
e
l
e



) . This weight is given by the quotient between the weighted average of
the price of the properties adjacent to the subject property and the estimated price of their
structural characteristics. Weights greater than one in a given location indicate that the price of
the property is higher than estimated price of its structural characteristics, and location therefore
has a positive effect, that is, the property is located in a good area. Weights less than one
indicate that the property is in a bad location. When the estimated price of the subject property
coincides approximately with the estimated price of its structural characteristics, the weight of
the location is close to one, so the location of the subject property has little effect on its price.
The virtue of this procedure is that weights can be obtained to quantify the effect of location on
the price of the property, without the need to specify the location variables in the model. This
has several advantages such as avoiding subjectivity when choosing and measuring the location
variables, reducing appraisal costs, simplifying the appraiser’s task and avoiding the problem of
quantifying the radius of influence of these location factors, among others.
An additional advantage of this methodology is that weights can be obtained at any
point of the plane and represented by means of isovalue maps. Figure 7 shows the spatial
distribution of the location weights in the city of Granada. As can be seen, the areas marked in
warm colors (red, orange, yellow) are in the central part of the city, especially in the downtown
area where the central business district is located.  This area is close to the Alhambra and has a
large number of services, commerce and leisure establishments, as well as some of the city’s
other main monuments. When moving away from the central zone towards the periphery, the
location value decreases. The lowest location values are found mainly in the north district,
where there is an economically and socially deprived enclave. Figure 5 shows that the location
weights in Granada vary from 0.461 to 1.623, thus indicating that, depending on the location,
the actual price of a property with certain structural characteristics could be almost four times its
estimated price.
These findings are of social and economic interest. For example, from the viewpoint of
real estate appraisals (whether for mortgage, taxation or investment purposes, etc.), homes that