# RECORD c7b242d28013321bceaeef0f994fd2d0dab032c0
# TITLE: Implicit Prices in Urban Real Estate Valuation
# YEAR: 2013.0  VENUE: nan  DOI: 10.4067/s0718-915x2013000200009
# AUTHORS: J. Nuñez Tabales; F. R. Rey Carmona; J. M. C. Y. Ocerin
# PAGES: 11  CANDIDATE TABLE PAGES (1-based): [7]
# ABSTRACT: Econometric hedonic models encounter several theoretical and practical difficulties when applied to the real estate market, such as downward biases in the estimation of hedonic prices, subjective decisions in the measurement process of categorical attributes, frontier problems related to an imperfect information framework and uniequational specification. Many of these are linked to the parametric approach. Artificial Neural Networks (ANN) provide an attractive alternative: better dwelling prices estimates, avoidance of bias at different market segments, direct use of categorical data and full use of the information available. The price to be paid is the difficulties in the economic interpretation of network parameters. Nowadays, if the final objective to produce better estimates of the transaction prices, this methodology show lower errors, provided of a broad representative database of sales are recorded. A case study is presented for a medium size city in the South of Spain. Keywords: Urban Economics; Hedonic Models; Neural Networks.


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116 ]
Revista de la Construcción
Volumen 12 No 2 - 2013     
Precios implícitos en 
valoración inmobiliaria 
urbana
Implicit Prices in Urban 
Real Estate Valuation
Autores
NÚÑEZ TABALES, J.
University of Córdoba, Faculty of Economics
Puerta Nueva s/n, 14071, Córdoba, Spain
es2nutaj@uco.es
REY CARMONA, F.
University of Córdoba, Faculty of Economics
Puerta Nueva s/n, 14071, Córdoba, Spain
CARIDAD Y OCERIN, J. Mª.
University of Córdoba, Faculty of Economics
Puerta Nueva s/n, 14071, Córdoba, Spain
Fecha de recepción
19/6/2013
Fecha de aceptación
1/8/2013
Código interno RDLC
0146
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122 ] Revista de la Construcción
Volumen 12 No 2 - 2013     
páginas: 116 - 126
[     Núñez Tabales, J. et al     ]
directly in a model. But the statistical problems like 
multicollinearity make impossible to proceed in this 
way. To tackle these difficulties, several indices have 
been built, as a way to obtain quantitative information 
from the original attributes. In the process, it has to 
be kept in mind that the interpretation of these new 
variables has to be straightforward, and that it has to 
be avoided to use complicated weights that introduce 
subjective beliefs in the indices. The indices have to 
be compatible with the consumer’s perceptions of the 
characteristics of each property.
The indices defined have been scaled to fit in the 
interval [0; 1]. Values near the upper end refer to 
optimum values in relation to higher prices, and low 
values of an index reflect lack of importance of this 
variable in the final price. These can be treated as 
numerical data in the modelling processes, as in Saura 
(1995) and Jaén and Molina (1995).
Table 2. Indexes associated to each property
Index
Variables included
Quality Index
• Age, accesses, balconies 
and terrace
External Building index
• Pavement, carpentry, 
kitchen furniture and 
reforms
Internal building index
• Pool, tennis court and 
garden
Orientation index
• Orientation of building 
and balconies
Annex index
• Garage and store room
Location index
• Location in the city and 
residents income
The conservation index reflects the general state of the 
property, at first sight. It is constructed from several 
categorical data, like the maintenance condition of the 
kitchen, baths, floor, plumbing, and electric wiring, 
if these have been updated. The complementary size 
index includes the information about some additional 
facilities, like a washing room, embedded wardrobes, 
and food storage place. The situation index reflects 
the position of the apartment or flat in the building, 
the availability of a lift, and the external views. The 
building index includes information about the quality 
of the building, its age, the entrance, and additional 
facilities like swimming pool or satellite and cable 
television. The location index includes data about the 
situation of the property in the city, the surroundings 
and the income level of the zone.
Price of transaction is the endogenous variable in 
both hedonic and NN models. The decision about the 
functional form is treated in the literature. Here is 
used a quadratic model, preferring it over the semi-
logarithmic usual transformation. The explanatory 
variables included show a high level of collinearity, 
introducing practical difficulties in the estimation 
process. Using simplicity criteria, parsimonious models 
are preferred over more complicated specifications. 
Some interactions between exogenous variables 
are considered, using quadratic forms as shown in 
formulae 1.
although the final model used is linear but for an 
interaction term. The variables finally selected to 
be included in the model are the following: size of 
the flat (in square metres, including common areas), 
age of the building, index of location (based on its 
position, characteristics of the area and income of 
the zone), index of additional facilities (as garages 
or store room), common expenses (in euros), and the 
interaction between qualities variables regarding the 
pavement condition and the external carpentry, as 
show in formulae 2.
Table 3. Hedonic model
Endogenous variable: Sales price
Variable
Coeficients
Standard 
error
t-Student
Prob.
Intercept
193.6790
10237.53
0.018919
0.9849
Surface
1109.951
83.62050
13.27368
0.0000
Age
-1067.449
173.5725
-6.149872
0.0000
Location
64297.29
5494.403
11.70232
0.0000
Annexes
18458.66
4572.246
4.037111
0.0001
Expenses
1296.708
105.9213
12.24218
0.0000
Pav xCarp
5117.270
504.0529
10.15225
0.0000
[1]
[2]
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[ 123 
Revista de la Construcción
Volumen 12 No 2 - 2013     
[     Núñez Tabales, J. et al     ]
The usual diagnostics tests have been successfully 
applied. The stability of the model is supported by 
the Chow test, and the condition index is k = 16.6, 
supporting that the multicollinearity is not worrisome. 
The goodness of fit is similar to other hedonic 
modelling, R2 = 0.7738 and the U Theil index is 0.09 
(Table 3).
NN provide a non linear alternative to estimate 
price models. The usual MLP is applied, as in several 
previous works, ad in Haykin (1999), Freeman and 
Skapura (1993) and Garcia Rubio (2004). To facilitate 
comparisons with the proposed hedonic model, the 
exogenous variables selected have been used as inputs 
to the different NN employed. Different topologies 
have been tried, with different number of hidden 
layers and neurons, as several activation functions and 
learning algorithms. Finally a 6:6-6-1:1 structured is 
selected (Figure 1), and the Trajan Software for NN 
is employed, with a lineal activation function, in the 
input, while in the other layers a sigmoid function 
is applied. The training set is composed of 80% of 
the sample, and the remaining data is used as test to 
evaluate the forecasting power. The back propagation 
method employed was limited to 5000 iterations, with 
a learning ratio of 0.1.
Figure 1. ANN 6:6-6-1:1Topology
The NN increase the determination coefficient value 
to R2 = 0.8605, higher than in the hedonic model, 
although one has to take into account the larger 
number of parameters in the network. The root mean 
square error is lower in the network (39540.36) than 
in the hedonic model (41645.43), and similar results 
are observed with other measures, at can be seen in 
the Table 4.
Table 4. Comparison of hedonic a ANN modelling
MH
NN
Determination coefficient (R2)
77,38%
86,05%
Root mean square error 
(RMSE)
41.645,43
39.540,36
Residual standard error
41.911,91
39.102,13
Mean absolute error
30.579,18
28.551,34
Mean relative error
14,45%
13,69%
The implicit prices are constant in the hedonic model, 
while in the NN, these marginal effects are non linear 
functions of the explanatory variables. To obtain the 
marginal or implicit prices, it is necessary to evaluate 
the derivatives 
 for each explanatory variable, 
it is a cumbersome process that, nevertheless, allows 
to study the evolution of the hedonic prices attributed 
to each exogenous variable. For example, to estimate 
the influence of the area upon the marginal price of 
an additional square metre.
The hedonic model shows a linear influence of area 
upon de value attribute (Figure 2), while the NN shows 
a concavity in this value. The remaining explanatory 
variables are held constant (in this case, with average 
values over the sample). An additional square metre 
in the dwelling size increases its value by over a 
thousand euros, increasing with size in the network. 
The conclusions are in line of the finding of García 
Rubio (2004) in a smaller city. The adaptability of the 
networks to the situations at both extremes of the size 
range is not possible with classical hedonic models.
Figure 2. Implicit prices (Euros) associated to the 
dwelling surface (meters)
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