# RECORD 8bd308f78fb4466f73af2035a6682d0f84ccee3e
# TITLE: Residential Property Behavior Forecasting in the Metropolitan City of Milan: Socio-Economic Characteristics as Drivers of Residential Market Value Trends
# YEAR: 2021.0  VENUE: Sustainability  DOI: 10.3390/su13073612
# AUTHORS: Marzia Morena; G. Cia; L. Baiardi; Juan Sebastián Rodríguez Rojas
# PAGES: 25  CANDIDATE TABLE PAGES (1-based): [15, 16, 17]
# ABSTRACT: The phenomenon of urbanization of cities has been the subject of numerous studies and evaluation protocols proposing to analyze the degree of economic and social sustainability of development projects. Through careful research and synthesis of the theoretical framework regarding residential properties’ performance measurement and forecasting, this paper goes deeper into the proposition of property development as an asset class that represents the biggest share of the Italian property market and yet is avoided by the big portfolios. The analysis model was applied to the city of Milan and its Metropolitan Area. The method is based on the development of correlation indices to evaluate different behaviors, through time and a Geographic Information System (GIS) based on the Hedonic Price Method (HPM). Results from a hedonic model estimated for several recent years suggest that, depending on the particular view, the relation between the rent/price performance and the different external and intrinsic variables can represent a useful parameter for evaluating the feasibility of different real estate investments.


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sustainability
Article
Residential Property Behavior Forecasting in the Metropolitan
City of Milan: Socio-Economic Characteristics as Drivers of
Residential Market Value Trends
Marzia Morena *
, Genny Cia
, Liala Baiardi
and Juan Sebastián Rodríguez Rojas





Citation: Morena, M.; Cia, G.;
Baiardi, L.; Rodríguez Rojas, J.S.
Residential Property Behavior
Forecasting in the Metropolitan City
of Milan: Socio-Economic
Characteristics as Drivers of
Residential Market Value Trends.
Sustainability 2021, 13, 3612.
https://doi.org/10.3390/su13073612
Academic Editor: Jorge Chica-Olmo
Received: 1 February 2021
Accepted: 17 March 2021
Published: 24 March 2021
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
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iations.
Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed
under
the
terms
and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Department of Architecture, Built Environment and Construction Engineering, Politecnico di Milano,
Via Bonardi 9, 20133 Milan, Italy; genny.cia@polimi.it (G.C.); liala.baiardi@polimi.it (L.B.);
juansebastian.rodriguez@mail.polimi.it (J.S.R.R.)
* Correspondence: marzia.morena@polimi.it; Tel.: +39-02-2399-5189
Abstract: The phenomenon of urbanization of cities has been the subject of numerous studies
and evaluation protocols proposing to analyze the degree of economic and social sustainability of
development projects. Through careful research and synthesis of the theoretical framework regarding
residential properties’ performance measurement and forecasting, this paper goes deeper into the
proposition of property development as an asset class that represents the biggest share of the Italian
property market and yet is avoided by the big portfolios. The analysis model was applied to the city
of Milan and its Metropolitan Area. The method is based on the development of correlation indices
to evaluate different behaviors, through time and a Geographic Information System (GIS) based on
the Hedonic Price Method (HPM). Results from a hedonic model estimated for several recent years
suggest that, depending on the particular view, the relation between the rent/price performance
and the different external and intrinsic variables can represent a useful parameter for evaluating the
feasibility of different real estate investments.
Keywords: real estate market; residential property; hedonic price method (HPM); urban sustainabil-
ity; urban transformation
1. Introduction
The nature of the property market causes the construction of predictions to be de-
pendent on many factors that are often ignored or undervalued, as well as on the already
existing factors that determine less perceptible changes. According to various international
research works carried out at an urban level, the true nature of the change in real estate
values lies in trends that may be due to the simple perception of the population [1,2], a
complex urban process [3,4], or, on occasion, situations where the price system may not
immediately reflect the changes suffered by the area in recent times [5,6].
The possibility that residential Real Estate might not be efficiently upraised was
given a strong foundation by Case and Shiller (1989) [7]. The authors state that there is a
correlation and predictability in the average cost of housing prices but establishes the idea
of a possible correlation between future prices with immediate rents as a natural behavior
of residential real estate. When considering residential properties, predictability states and
reinforces the idea of a sequential correlation [8].
The susceptibility of house prices, and the model with which such prices are calculated,
are presented by Poterba (1984) [9] stating that a perfectly informed model of house prices
may have positive shocks followed by declining prices and vice versa; this is related to the
lags in the supply of new assets. Even if these scenarios are known and incorporated into
the model, the nature of the market creates a serial correlation and then, even if these lags
are well known and fully incorporated into expectations, “they still create serial correlation
and (somewhat) predictable house price movements in reaction to shocks” [10].
Sustainability 2021, 13, 3612. https://doi.org/10.3390/su13073612
https://www.mdpi.com/journal/sustainability


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Sustainability 2021, 13, 3612
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Figure 5. Transactions used for the construction of the model.
The model was built by a natural log transformation of the housing price (Y) and a
total of 25 variables (X). The first run with all variables can be seen below. Since a non-linear
nature of the variables is expected, a logarithmic (log-log) regression was tested (Table 3);
log-log transformation implies that coefficients are a percentage change of the variable Y to
a percentage change of the variable X.
Table 3. First run regression with all the variables.
Variable
Coeff
Coeff. EE
T Value
P Value
FIV
Constante
10.836
0.965
11.23
0.000
Bathrooms
0.120
0.114
1.05
0.299
3.59
Rooms
−0.2385
0.0956
−2.50
0.016
2.84
Old Coefficient
0.2321
0.0837
2.77
0.008
2.24
State
0.2811
0.0948
2.96
0.005
1.39
Status of the neighbourhood
0.1295
0.0664
1.95
0.057
2.07
Distance to the center
−0.369
0.108
−3.41
0.001
7.19
Degradation Proximity Coefficient
−0.0734
0.0204
−3.59
0.001
2.36
Big Park Proximity Index
0.1089
0.0462
2.35
0.023
2.05
UrbanVegetation Proximity Index
−0.0175
0.0121
−1.44
0.157
1.36
Special green areas Index
0.0587
0.0301
1.95
0.057
2.64
Equiped Green Areas Proximity Index
−0.0355
0.0272
−1.30
0.199
1.96
Contaminated areas Index
−0.0056
0.0193
−0.29
0.772
1.96
Potentially Contaminated Areas Index
0.0141
0.0218
0.65
0.520
2.58
Metro Proximity Index
0.0587
0.0223
2.63
0.011
2.97
Bus and Tram Proximity
−0.0203
0.0296
−0.69
0.496
1.74
Train Proximity Index
0.0398
0.0204
1.96
0.056
1.77
Iconic places Proximity Index
0.0579
0.0347
1.67
0.102
10.93
Kindergarden Proximity Index
−0.0403
0.0685
−0.59
0.559
5.63


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Sustainability 2021, 13, 3612
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Table 3. Cont.
Variable
Coeff
Coeff. EE
T Value
P Value
FIV
Primary schools Proximity Index
−0.1786
0.0862
−2.07
0.044
7.61
Secondary schools Proximity Index
0.0446
0.0422
1.06
0.296
5.11
Universities Proximity Index
0.0196
0.0248
0.79
0.434
4.48
C6H6
−0.0110
0.0228
−0.48
0.632
1.21
CO_8H
0.0003
0.0149
0.02
0.985
1.45
NO2
−0.0148
0.0320
−0.46
0.647
2.44
PM10
−0.0001
0.0137
−0.01
0.993
1.38
where: Coeff: Percentage change of the variable Y to a percentage change of the specific variable. Coeff. EE
standard error of the coefficient. T Value: t-statistics value (ratio of the departure of the estimated value of a
parameter from its hypothesized value to its standard error). P Statistical significance value. FIV: VIF, Variance
Inflation Factor.
The first run of the regression presented an R2 adjusted value of 0.723 indicating a
‘good fit’, yet according to statistical significance rules, the variables with p value ≤0.05
prove strong presumption against the null hypothesis. Therefore, using a stepwise forward
selection, the following variables were found to be statistically significant (Table 4):
Table 4. Second run regression.
Variable
Coeff
Coeff. EE
T Value
P Value
FIV
Constante
10.860
0.758
14.33
0.000
Rooms
−0.1346
0.0645
−2.09
0.041
1.35
Old Coefficient
0.2006
0.0675
2.97
0.004
1.52
State
0.3811
0.0825
4.62
0.000
1.10
Status of the neighbourhood
0.1446
0.0606
2.39
0.020
1.80
Distance to the center
−0.4057
0.0787
−5.15
0.000
3.97
Degradation Proximity Coefficient
−0.0639
0.0158
−4.05
0.000
1.47
Big Park Proximity Index
0.0973
0.0373
2.61
0.011
1.39
Metro Proximity Index
0.0439
0.0194
2.26
0.028
2.35
Train Proximity Index
0.0352
0.0178
1.98
0.052
1.41
Iconic places Proximity Index
0.0683
0.0254
2.69
0.009
6.08
Primary schools Proximity Index
−0.1080
0.0443
−2.44
0.018
2.09
where: Coeff: Percentage change of the variable Y to a percentage change of the specific variable. Coeff. EE
standard error of the coefficient. T Value: t-statistics value (ratio of the departure of the estimated value of a
parameter from its hypothesized value to its standard error). P Statistical significance value. FIV: VIF, Variance
Inflation Factor.
The adjusted coefficient of determination, denoted by R2 adjusted, is 0.8274, which
suggests that 82.74% of the total variation in the Y (house price/sqm) is explained by
the relationships between Y and the selected variables. This implies that the model is
significantly ‘good fit’ (Table 5).
Table 5. Goodness of fit of the model.
S
R-Squared
R-Squared (Adjusted)
R-Squared (Pred)
0.196382
85.34%
82.74%
78.75%
The regressions results in the following:
Ln(Price €/m2) = 10,860 −0.1346 × Ln(Rooms) + 0.2006 × Ln(OldCo) + 0.3811 ×
Ln(State) + 0.1446 × Ln(NeighSt) −0.4057 × Ln(DistCBD) −0.0639×Ln(DegpCo) + 0.0973
× Ln(ParkP) + 0.0439×Ln(MetroPI) + 0.0352×Ln(TrainPI) + 0.0683×Ln(IconPI) −0.108 ×
Ln(PrsPI) + e


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Sustainability 2021, 13, 3612
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As stated by the result above, the regression analysis shows a statistically significant
premium price for the location of the asset (in particular, location in the Central Business
District) and for the parameter of dimensions, quality of the building, proximity of green
areas, metro, and primary schools.
A statistical description of the independent variables intrinsic to each transaction is
presented in the table below (Table 6).
Table 6. Statistical description of the residential intrinsic independent variables.
PRICE
[€/M2]
Rooms
Old
Coefficient
State
Status of the
Neighbour-
hood
Distance to
the Center
[m]
Calculation
Method
Given
Given
1/10 × Years
from
construction
year up to
1941
1 = bad
2 = normal
3 = good
4 = New
From 1=bad
perception
up to
6= Very
Prestigious
Given
Interpretation
-
-
Lower =
Recently built
-
Mean
3.637
2.91
9.81
2.64
3.08
4.689
Standard
Error
111
0.07
0.18
0.04
0.07
116
Median
2.980
3.00
9.90
3.00
3.00
4.373
Mode
2.200
2.00
9.90
3.00
2.00
1.872
Standard
Deviation
2.083
1.34
3.35
0.66
1.38
2.171
Coefficient
of Variation
0.70
0.45
0.34
0.22
0.46
0.50
Kurtosis
1.47
9.53
−0.45
0.01
−0.69
−0.7
Skewness
0.67
2.34
−0.03
−0.27
0.35
0.2
Minimum
1.263
1.00
1.90
1.00
1.00
546
Maximum
12.432
10.00
15.70
4.00
6.00
9.687
As can be seen from the coefficients of variation (<1.0) of each intrinsic variable, the
sample used manages to represent a general picture of all the property types that are
generally transacted in the city during Q3 2019 without biases of location and/or physical
characteristics; as can be seen furthermore, the skewness values allow to understand that
the variables considered adequately represent the whole spectrum of property quality, year
of construction, and location, represented by the distance to the city center. In the case of
number of rooms, it is clear that the number of rooms in Milan’s residential properties is
considerably asymmetrical, with an average of three rooms.
In order to understand the distribution of the spatial variables that are statistically
significant and therefore considered in the regression, a synthesis of the calculation method
is presented in Table 7.
Table 7. Calculation method of each spatial variable.
Index
Calculation Method
Degradation Proximity Coefficient
Σ of Area of degraded areas over distance to each specific
transaction in km (at least 200 sqm within 2 km).
Big Park Proximity
Σ of Area of urban parks over distance to each specific
transaction in km (at least 100 sqm within 3 km).
Metro Proximity
10 × Σ of number of metro stations to the specified transactions
over distance to each specific transaction in km (within 1.5 km).
Train Proximity
10 × Σ of number of train stations close to the transaction over
distance to each specific transaction in km (within 1 km).
Iconic Places Proximity
10 × Σ of number of monuments and historical landmarks over
distance to each specific transaction in km (within 1.5 km).
Primary Schools Proximity
Σ of number of primary schools over distance to each specific
transaction in km (within 1 km).


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Sustainability 2021, 13, 3612
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A statistical description of the independent spatial variable is presented in the table
below (Table 8):
Table 8. Statistical description of the spatial independent variables.
Degradation
Proximity
Coefficient
Big Park
Proximity
Index
Metro
Proximity
Index
Train
Proximity
Index
Iconic Places
Proximity Index
Primary Schools
Proximity Index
Mean
863.3
0.7
44.0
10.2
193.8
9.8
Standard Error
67.1
0.0
2.8
0.8
19.5
0.3
Median
259.3
0.6
33.9
9.0
35.4
9.9
Mode
0.0
0.6
0.0
7.2
0.0
0.0
Standard Deviation
125.0
0.5
25.3
15.0
365.8
6.3
Coefficient of Variation
0.48
0.83
0.75
1.67
10.32
0.64
Kurtosis
0.7
2.1
0.9
3.9
6,4
8.1
Skewness
1.1
1.7
1.3
1.8
2.6
1.9
Minimum
0.0
0.0
0.0
0.0
0,0
0.0
Maximum
5657.2
2.4
90.5
74.6
1681.3
42.3
As can be seen from the coefficients of variation, a strong aggregation of iconic places
is evident, yet it has statistical significance, due to the fact that is not directly correlated with
the spatial distance to the city center, and due to this aggregation, several transactions are
not affected by iconic places. The remarkable city center public transportation connectivity
is well represented, and yet the sample with transactions covering different neighborhoods
is not affected by a particular aggregation of Metro stations in one single area.
The following map shows the general price situation of the used transactions. It is
important to note that the map represents the data used to build up the model, and not the
average price in the city’s areas (Figure 6). It represents a snapshot of the prices per sqm
for the 352 properties used to build the model; as can be seen, the transactions located in
the city center and its business district (Above Brera area) presented at the time span of
data collection (Q3 2019) the highest prices in the city. Some areas outside the historical
center present a prime price, such as the Tortona area and Tre Torri.
 
Figure 6. Prices of the transactions used for the model.
In order to geographically check the precision of the model, the resulting regression
was used for recalculation the prices of the transactions used to build the model, and this