An Econometric Model for the Analysis of the Influence of the
Refurbishment Costs on Housing Prices
P. MORANO1, F. TAJANI2, F. DI LIDDO1*, M. LOCURCIO1, D. ANELLI2
1Department of Civil, Environmental, Land, Building Engineering and Chemistry,
Polytechnic University of Bari, Via Edoardo Orabona, 4, 70126, Bari, ITALY
2Department of Architecture and Design, Sapienza University of Rome
Via Flaminia, 359, 00196, Rome, ITALY
Abstract:- With reference to the Italian context, the present research intends to analyze the functional
relationships between the unit cost of restructuring and the selling prices in the residential segment. The
analysis has been contextualized to the three clusters (Northern Italy, Central Italy, Southern Italy and Islands)
in which the Italian territory is commonly divided. The case study concerns 965 residential units sold in the
first half of 2019 and located in the 103 provincial capitals. The implemented econometric technique is a data-
driven method that employs a genetic algorithm and allows the identification of the most influencing factors
among the explanatory variables considered. For each cluster, a model has been selected in order to study the
influence of unit cost of restructuring on housing prices.
Key-Words: - refurbishment, restructuring, costs, econometric analysis, housing prices, market value
Received: August 7, 2021. Revised: December 30, 2021. Accepted: January 17, 2022. Published: January 18, 2022.
1 Introduction
In the international and European context, in the last
years a relevant variation in the policies aimed at the
renovation of the existing property assets and at its
functional reuse through different interventions
according to the buildings maintenance conditions
has occurred [1, 2, 3]. In this sense, on the basis of
the deterioration level, refurbishment projects with
partial or total demolition, restoration and/or
conservative rehabilitation initiatives, ordinary or
extraordinary maintenance operations are planned
and implemented. In the cases of large complexes,
the redevelopment acquires an urban connotation,
by determining a transformation of an entire city
portion.
With reference to the Italian territory, the
building and infrastructural stock is characterized by
a growing obsolescence condition: nearly 60% of
12.2 million of residential properties included in the
15th ISTAT population and housing census [4] were
built before 1980 and 42.5% are over 50 years old.
Furthermore, currently, a quarter of the entire
residential stock consists of properties built before
1946 and 15.0% was realized before 1919, and 4.1%
of them are in very poor conservation conditions.
In the framework outlined, according to the Goal
number 11 defined by 2030 Agenda for Sustainable
Development [5] in recent years one of the main
challenges in the building sector has been
represented by the innovation of construction
processes and systems for the refurbishment of the
existing real estate assets and the reconversion of
properties characterized by energy efficiency,
seismic safety, and living comfort inadequate levels
according to the current community needs [6, 7]. In
the current financial situation, the building stock
renovation constitutes an effective driving force for
the national economic recovery: the contraction in
the real estate market, in fact, has generated a
significant number of unsold properties, unable to
be absorbed by reference market without adequate
and specific enhancement policies.
The two main questions directly associated to the
building assets oldness concern i) the energy
efficiency and ii) the static safety linked to the
regional territory seismicity level. It should be
highlighted that the relationship between the scarce
energy efficiency and the housing stock age could
be justified by taking into account that the first law
on energy saving related to construction sector dates
back to 1977 [8] and, consequently, the houses built
before this date (nearly 58.4% of the total residential
property assets [4]) have been realized by neglecting
the energy efficiency and static security aspects.
Within the current Italian legislative framework,
different fiscal incentives have been drawn up in
order to promote the residential stock renovation
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P. Morano, F. Tajani, F. Di Liddo,
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and to financially support the houses owners to start
construction work aimed at improving the energy
performance indices and at the static safety of the
properties. The tax benefit on building
refurbishment interventions is regulated by art. 16-
bis of Presidential Decree No. 917/1986 [9] and
subsequent updates and modifications (Law No.
449/1997 [8], Law Decree No. 83/2012 [10], Law
Decree No. 63/2013 [11], Law Decree No. 34/2020
[12]). The main fiscal measure provides for a
deduction from the income tax - divided into ten
annual instalments of the same monetary amount -
at 50% for building renovation with a spending limit
of 96,000 € per residential unit and at 65% for
energy retrofit initiatives aimed at saving primary
energy need for a maximum deduction equal to
100.000 € or to 60.000 € for installation of
photovoltaic panels or to 30.000 € for the
replacement of air conditioning systems (Arts. 14 e
16-ter, Law Decree No. 63/2013 [11] updated in
Law No. 90/2013 [13] and art. 1, par. 58 Law No.
178/2020 [14]).
Furthermore, the art. 121 of 2020 Budget Law
No. 34 [12] has included i) the “discount on the
invoice” among the benefits provided, i.e. a
contribution up to a maximum total intervention
amount estimated, advanced by the construction
companies and recovered by them in the tax credit
form, equal to the deduction due, with the
possibility to subsequently assign the credit to other
subjects, including credit institutions and other
financial intermediaries and ii) the transfer of a tax
credit equal to the intervention amount, with the
option of subsequent credit assignment to banks or
financial institutions.
Finally, with regards to the energy efficiency
interventions (named “Eco-Bonus”) and to seismic
risk reduction (named “Sisma-Bonus”), the Super-
Bonus 110% (art. 119 of Law Decree No. 34/2020
[12], updated by the Law No. 77/2020 [15]) plays a
relevant role in the existing properties assets
refurbishment, by raising the deduction rate for
costs incurred from 1 July 2020 to 30 June 2022 to
110%, for specific energy efficiency and anti-
seismic interventions, installation of photovoltaic
systems or infrastructures for charging electric
vehicles. The incentive allows, on the one hand, to
trigger new construction sites and, on the other
hand, to strongly reduce the energy expenditure for
the housing owners, to make their residential
properties healthier, static safer and more
comfortable and to obtain significant monetary
savings.
This research concerns of the topic illustrated.
With reference to the existing property assets, the
issue of the costs constitutes a relevant question, in
particular related to the modalities for the building
transformation interventions costs estimation. In this
sense, several studies have been developed with the
goal to assess the amounts necessary for the project
implementation in monetary terms, both by
considering realization ex-novo interventions [16,
17, 18] that of reconstruction or redevelopment
ones. Furthermore, others studies have been focused
on the analysis of the existence of likely changes in
the residential selling prices determined by the
construction costs for the building realization. These
researches, in fact, have aimed at investigating the
functional correlations between the construction
costs and the housing prices of the properties. A
detailed analysis of the existing reference literature
has been included in Morano et al. [19] intended to
explore the relationships between the construction
and refurbishment costs and the properties prices
and in which the convenience of refurbishment
investments related to housings in the Italian context
has been examined.
2 Aim
With reference to a study sample of 965 recently
refurbished residential properties and collected in
103 Italian provincial capitals, the paper aims at
investigating the functional correlation between the
refurbishment costs in the residential property
segment and the relative selling prices.
Firstly, it should be outlined that in the present
research for each city the "ordinary" refurbishment
costs have been examined, by taking into account a
standard renovation project that concerns the
complete reconstructing of the floors, plasters,
fixtures and windows and systems (water, heating
and electric ones) [19].
In the analysis, the implementation of an
econometric technique on the study sample, divided
into three territorial clusters – Northern Italy,
Central Italy, Southern Italy and Islands [4] – aims
to study the different functional relationships
between the refurbishment costs and the housing
prices. According to the differences in the costs and
the income that characterize the three Italian
clusters, the analysis intends to compare the outputs
obtained for each area in terms of average influence
of refurbishment costs in the formation mechanisms
of the residential selling prices.
The results obtained could constitute a useful
reference for i) the Public Administrations in order
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P. Morano, F. Tajani, F. Di Liddo,
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to develop fiscal incentives aimed at existing
residential properties asset refurbishment and to
promote specific strategies in according to the
municipality and its socio-economic dynamics and
ii) the private market operators to provide a model
able to indicate the investment convenience in terms
of correlations between the refurbishment costs to
bear and the housing prices. In this sense, the model
proposed could be represent a tool for monitoring
the market mechanisms related to the impacts of
renovated properties on housing market processes.
The paper is structured as follows. In the third
section, the case study relating to the three property
samples located in the three macro-areas mentioned
is introduced and the explanatory variables
considered are presented. In the fourth section, the
econometric methodology adopted for the analysis
is explained. In the fifth section, the application of
the method to the study sample is carried out and the
main functional relationships obtained are
interpreted. Finally, the results of the work are
discussed in the sixth section.
3 Case Study
The analysis is carried out on three study samples
consisting of 965 residential properties sold in the
first half of 2019 and located in the 103 provincial
capitals included in the three clusters (443 properties
for the 46 provincial capitals of Northern Italy, 210
properties for the 21 provincial capitals of Central
Italy and 312 for the 36 provincial capitals of
Southern Italy and the Islands). Within each cluster,
the properties considered in the work are residential
units located in multi-floor buildings and equally
distributed in the three urban areas (central, semi-
central and peripheral). Moreover, each housing unit
is characterized by an excellent maintenance state
and a medium-high energy efficiency rating (A+, A,
B labels).
For each property, the most influencing factors have
been analyzed, by considering the indications
provided by the housing market operators on the
ordinary appreciations detected in the residential
sector of the different Italian provincial capitals.
In particular, the variables considered are:
• the property total selling price (Y), expressed in €,
that represents the dependent variable of the
model;
• the total surface of the property (S), expressed in
square meters of gross floor area;
• the floor on which the property is located (Lp);
• the presence of the lift [A], considered as a dummy
variable (0 = absence of the lift; 1 = presence of
the lift);
• the presence of the private parking space [Pa],
assessed as a dummy variable (0 = absence of the
private parking space; 1 = presence of the
private parking space);
• the "ordinary" unit cost of restructuring [Cr] at the
municipal level expressed in €/m2, defined by
taking into account the CRESME database [20].
It should be recalled that in the ordinary
restructuring intervention category the operations
required to the complete reconstructing of the
floors, plasters, fixtures and windows and
systems (water, heating and electrical) with
medium-high finishing level are included;
• the per capita income [R], calculated on the
number of inhabitants in each municipality and
expressed in € per year [21];
• the municipal trade area in which the property is
located, borrowing the geographical distribution
defined by the Italian Revenue Agency [22]:
"central" [Zc], "semi-central" [Zs], "peripheral"
[Zp]. For each property, the score 1 indicates the
belonging to the specific trade area, whereas the
score 0 is assigned for all the remaining ones.
4 Method
The method implemented in the present research is
named Evolutionary Polynomial Regression (EPR).
This represents an Automated Valuation Method
that derives from the need to exploit the available
data through algorithms able to analyze, adapt and
effectively replicate the observed phenomena. In
this sense, from the detected data, this kind of
econometric techniques allows to identify the
relationships between the property prices and the
most influencing factors in terms of mathematical
equations, according to the empirical knowledge of
the phenomenon [23, 24, 25]. The methodology
applied in the study is a data-driven technique that
uses a simple genetic algorithm engine for the
combination of symbolic and numerical regression
methods by implementing polynomial expressions
[26, 27].
On the base of experimental data, EPR represents
an econometric technique able to generate a set of
mathematical models, whose generic structure is
given by Eq. (1):
n
i
)j,i(
j
)j,i()j,i(
j
),i(
i)])X(...)X((f)X(...)X(a[aY
1
21
1
1
10
(1)
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The terms included in the Eq.(1) are described
below: a0 is the bias, i.e. the constant term, n is the
number of additive terms of the polynomial
expression (bias excluded), ai are the numerical
coefficients to be valued, Xj are candidate
explanatory variables selected by the algorithm
during the elaboration, (i, l) - with l = (1, ..., 2j) - is
the exponent of the l-th input within the i-th term in
Eq. (1), f is a function selected in the preliminary
phase of EPR elaboration.
In this sense, in fact, the user chooses i) the
structure of the function f among some predefined
options, including no function selection and ii) the
exponents (i, l) among a set of candidate values (real
numbers) by including the value "0". The
coefficients of the function are assessed through a
Least Squares method. The number and the
complexity of the mathematical models that EPR
generates during the elaboration phase depend on
the possible exponents and the maximum number of
additive terms. The EPR technique is able to define
several structured mathematical expressions of
input–output characterized by different statistical
accuracy and, consequently, by various complexity
levels in the functional correlations. EPR, in fact, is
a procedure consisting of two main steps: the first is
aimed at searching the structure of the models by
generating a set of algebraic expressions; in the
second one, the classical numerical regression
method is implemented for the polynomial
parameters assessment.
In this sense, the EPR method allows to define a
wide set of functional expressions based on their
ability to be adapted to the starting data included in
the analysis. Furthermore, the automatic process
underlying EPR is able to generate different models
that simultaneously pursue different objective
functions, that are i) to maximize the model
accuracy, ii) to maximize the model’s parsimony,
i.e. to minimize the equation terms number (ai), iii)
to reduce the complexity of the model, i.e. to
minimize the explanatory variables number (Xi).
Furthermore, in order to verify the statistical
accuracy of each equation, the Coefficient of
Determination (CoD) [28], the Root Mean Square
Error (RMSE), the Mean Absolute Percentage Error
(MAPE), the Maximum Absolute Percentage Error
(MaxAPE), the Akaike Information Criterion (AIC)
are determined.
5 Application of the Method
In the present research, EPR has been applied to the
case study considering the structure of the generic
model identified in Eq. (1) without the function f
selected. The maximum number of terms of each
expression and the possible positive exponents,
selected in the preliminary phase, are equal to ten
terms and four exponents (0, 0.5, 1, 2). For each
cluster (Northern Italy, Central Italy, Southern Italy
and Islands) the model chosen between those
provided by the EPR technique are shown below in
the Eqs. (2), (3) and (4). The CoD determined for
each mathematical expression is: 69.02% for the
Northern Italy cluster, 73.24% for the Central Italy
one, 61.30% for the Southern Italy and Islands one.
NORTHERN ITALY
Y = + 37833038.9899 Cr0.5 – 22989347.9782 Cr
– 2609967.4989 R + 2630601.1501 R2 Cr2 +
- 125133.8173 Zc0.5 + 668845.943 S0.5 + +
206205.5813 S Lp0.5 Zs0.5 R2 - 14711383.1007
CENTRAL ITALY
Y = - 2629062.0644 Cr2 – 12038459.6183 R +
7525570.156 R2 Cr + 512112.6293 Zp R2 -
+ 2433496.387 S R2 - 3039297.1181 S Zp0.5
R0.5 Cr – 1216503.0159 S2 +
+ 2686261.0046 S2 Zp2 Cr2 + 7253037.7497
SOUTHERN ITALY
Y = + 2984481.9059 Cr – 1803618.372 Cr2 +
2510863.3907 S0.5 R2 +
+ 99070.0171 S A0.5 Zc0.5 - 1384468.8745 S2
Lp2 Pa0.5 A2 R2 – 1275326.7339
It should be noted that the models of Eq. (2), (3)
and (4) have been identified among the several
models generated by the technique implementation
as the best ones for their algebraic form composed
by additive terms of simple empirical interpretation,
for the good statistical accuracy level and for the
inclusion of the explanatory variable “unit cost of
restructuring” (Cr) that is the core of the research
according to the mentioned aim.
The verification of the empirical consistency of
the explanatory variable coefficients’ signs has been
carried out taking into account the variation of the i-
th variable analyzed in the variation interval of the
(2)
(3)
(4)
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observed cluster and keeping constant and equal to
the respective average value the terms of the other
variables.
For all the factors considered in the analysis, the
functional correlations between the variables and the
total selling price are empirically verified, as they
are consistent with the expected phenomena related
to the dynamics of the selling price formation. In
fact, the total surface of the property (S) is directly
linked to the dependent variable of the total selling
price, the presence of the lift (A) in the building in
which the residential unit is located determines an
increase in housing prices. Furthermore, a growth in
the per capita income (R) is associated to an
increase in prices, and the presence of the private
parking space (Pa) is positively appreciation by
potential buyers in all clusters considered. Finally,
higher selling prices have been observed for
properties located in central trade area (C) compared
to more peripheral ones (P). Anyway, in the present
research the attention is focused on the variable
related to the unit cost of restructuring, by taking
into account the high interest relating to the topic
analysed.
With reference to the three clusters considered,
Table 1 shows the functional relationships between
the dependent variable selling price and the
independent variable “unit cost of restructuring” in
terms of i) the trend obtained, ii) the average
percentage variations of the selling prices (average
%), iii) the minimum and the maximum percentage
variations observed (min % and max %), iv) the
percentage variation detected in correspondence of
the passage from the minimum unit cost of
restructuring found in each cluster and the
maximum one (min/max %).
Table 1. Functional relationships between the total selling price and the unit cost of restructuring in the three
clusters considered and the total selling price percentage variations detected
The graphs in Table 1 express the selling prices
trend detected in correspondence of an increase of
the unit restructuring cost. For the clusters of
Northern Italy and Southern Italy and Islands the
growth of the unit restructuring cost determines an
increase in the selling prices, until a maximum value
beyond which, the increase of the unit restructuring
cost leads a decrease in the selling price. In
particular, in the Northern Italy macro-area the
parabolic trend is more emphasized compared to the
curve observed for the Southern Italy and Islands.
According to the study sample collected, the graph
obtained for the Central Italy cluster shows an initial
increase in the total selling price in correspondence
of the unit restructuring costs growth and, then, an
attenuation of the positive variation corresponding
to the highest unit restructuring costs. In this sense,
the study highlights that other extrinsic and intrinsic
TREND
AVERAGE
%
MIN % AND
MAX %
MIN/MAX
%
+ 0.372%
MIN = -
8.61%
10.75%
MAX =
9.60%
+ 7.03%
MIN = 0.90%
144.13%
MAX =
21.85%
-0.48%
MIN = -
5.46%
-6.69%
MAX =
4.55%
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factors could cause the trend observed: these
variables play a more significant role in the housing
price formation mechanisms. For example, the
positional factors may strongly influence the
residential prices as the characteristics of the urban
context in which the property is located, e.g. the
accessibility level, the presence of green areas –
public gardens, parks or urban squares -, the level of
security, the presence of local collective services,
etc., can determine a reduction in the unit
restructuring cost contribution.
6 Conclusions
The present research has aimed at analyzing the
functional correlations between the total selling
prices and the unit cost of restructuring in the three
clusters of Northern Italy, Central Italy, Southern
Italy and Islands.
With reference to 965 residential properties sold
in the first half of 2019 and located in the 103 Italian
provincial capitals, the study has focused on the
implementation of an econometric technique able to
i) identify the most influencing factors among those
considered and ii) explicate the functional links
typology and the influence of each variable selected
on selling prices in percentage terms. In this sense,
in the work three models – one for each cluster -
have been selected and examined among the several
polynomial expressions generated by the
methodology in order to determine the contribution
of unit cost of restructuring on housing prices.
Therefore, for each study sample a unique model
has been identified. This has allowed to verify the
existence of a parabolic functional trend of the total
housing prices, by taking into account the increase
of the unit cost of restructuring for Northern Italy
and Southern Italy and Islands, whereas a positive
and growing trend for Central Italy. In particular, for
the Central Italy cluster a progressive attenuation of
the incidence of the restructuring costs variable on
the prices has been observed in correspondence of
the highest costs detected in the study sample
analyzed.
The topic of the present research is part of a
current and relevant issue associated to the
significant need to refurbishment the existing
residential property assets in order to adapt it i) to
the regulatory standards, ii) to the national laws and
iii) to the requirements of the community. The
methodological approach illustrated could be a valid
tool for Public Administrations and private investors
for monitoring the restructuring costs component
influence in the residential selling price formation
mechanisms. It should be outlined, in fact, that the
approach adopted in the analysis is flexible and
easily applicable to any geographical context and to
the same urban territory for the update of results and
the determination of relevant variations, also by
taking into account the several fiscal incentives
developed to promote the renovation of the
residential buildings. By keeping the same aim,
further insights of the present research may concern
the development of other methodologies for the
analysis of the functional relationships between the
unitary restructuring costs and the final selling
prices, in order to compare the outputs and to verify
the reliability of results obtained in this study.
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