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Rethinking the economic region…
PART III Applications of Spatial Analysis with Samll Areas Observations
15 03 2012
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Chapter 14
Traffic noise and air pollution effects on housing prices:
A multilevel modelling analysis
Julie Le Gallo
Université de Franche-Comté, France
Coro Chasco
Universidad Autonoma de Madrid, España
1. Introduction.
Urban areas are affected by high levels of air pollution and noise,
usually generated by road traffic, industry and construction
operations. The environmental and health consequences are
important. For instance, according to the World Health
Organization, almost 2.5 million people die each year from causes
directly attributable to air pollution (WHO, 2006). Moreover, it has
been suggested that more than 20% of the population of the
European Union (EU) are exposed to important noise levels
(European Commission, 1996). Consequently, both air and
acoustic pollution constitute major concerns of city dwellers while
“Air pollution” and “Urban problems, noise and odours” are two
of the European Commission’s action fields (EEA, 2000).
In this chapter, we focus on the city of Madrid where, as in other
urban areas in the world, road noise is the dominant source of
nuisance in residential areas. Several Action Plan projects have
been implemented in the period 2008-2011, aimed at restoring and
revitalizing several areas of downtown Madrid. As these projects
are costly, it is therefore of interest for the local government to
monetize the social value of changes in pollution and noise levels.
In this study, we apply hedonic regression to examine the effect of
air and noise pollution on property prices in downtown Madrid.
Indeed, the fact that housing markets value road air pollution and
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road noise has been shown using hedonic regression models by,
among others, Day et al (2007), Kim et al (2007) or Andersson et al
(2009).
Our aim is therefore to estimate the households’ marginal
willingness to pay for better air quality and reduced noise in the
areas of downtown Madrid that are the most affected by these
problems. To that purpose, we use a dataset of 3.302 houses. Three
innovations are proposed in this chapter.
Firstly, we use measures of both air and noise pollution.
Analyzing both the effect of air and noise pollution on housing
prices is not so frequent in hedonic specifications that typically
only include air pollutants. Since the seminal studies of Nourse
(1967) and Ridker and Henning (1967), many authors have tried to
estimate the marginal willingness of people to pay for a reduction
in the local concentration of diverse air pollutants (see Smith and
Huang, 1993, 1995 for a review and meta-analysis). On the other
hand, studies focusing on noise are less frequent although they can
be traced back to the seventies (Mieszkowski and Saper, 1978;
Nelson, 1979) in order to measure the economic costs of airports,
railroads and motorways. Papers analyzing the effects of both air
and noise pollution are scarce (see for instance Li and Brown, 1980;
Wardman and Bristow, 2004; Baranzini and Ramírez, 2005; Banfi et
al, 2007 and Hui et al, 2008).
Secondly, in this work we use subjective measures of noise and air
pollution. All the studies mentioned above use “objective” air
quality and noise variables, such as concentrations of various
pollutants and decibel levels. Conversely, “subjective” measures of
air pollution and noise have been exceptionally considered in
hedonic specifications. These measures are based on people’s
perceptions and are more difficult to obtain (Murti et al, 2003;
Hartley et al, 2005; Berezansky et al, 2010). However, there are
some advantages in using subjective measures rather than
objective measures. On the one hand, Boyle and Kiel (2001) state
that the objective measures of air quality may not be measures that
are relevant to homeowners. Berezanski et al (2010) show that
housing prices in urbanized areas can be better explained by
subjective evaluation factors rather than objective measurements.
On the other hand, using subjective measures in our case may
limit measurement error problems. Indeed, objective measures are
typically recorded at some monitoring stations and then kriged to
obtain individual values for each house in the sample. Whenever
the number of stations is low, measurement errors in the kriged air
pollution or noise surface may be important, hence requiring
instruments to alleviate the attenuation bias caused by
measurement errors (Anselin and Lozano-Garcia, 2008). In our
case, subjective measures are provided for a fine spatial level (the
census tract) so that the measurement error implied by the kriging
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PART III Applications of Spatial Analysis with Samll Areas Observations
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7
procedure will be lower than if we had used objective measures
stemming from monitoring stations.
Thirdly, from a methodological point of view, we apply spatial
multilevel modelling to our hedonic housing price specifications
as our dataset has a hierarchical structure. During the last two
decades, hedonic models have incorporated several
methodological innovations in order to introduce pollution into
the utility function of potential house buyers, such as alternative
specification functions (Graves et al, 1988), neural networks (Shaaf
and Erfani, 1996), spatial econometrics (e.g. Kim et al, 2003;
Anselin and Le Gallo, 2006; Anselin and Lozano-Gracia, 2008) and
spatio-temporal geostatistics (Beamonte et al, 2008), among others.
Though multilevel models have also been applied to hedonic
housing price models (Jones and Bullen, 1994; Gelfand et al, 2007;
Djurdjevic et al, 2008; Bonin, 2009; Leishman, 2009), only Beron et
al (1999) and Orford (2000)’s papers use them to measure the role
of air pollution on property prices. As we show in the next section,
multilevel models are very useful when considering the effects of
neighbourhood amenities (operating at upper-scaled spatial level),
such as environmental quality, on households’ preferences.
The chapter is structured as follows. First, we describe the
database underlying this study. Second, we present the empirical
model providing a short description of multilevel modelling
applied to hedonic models. Third, we present the econometric
results of the study, which allow us to provide some evaluation of
the projects plans implemented by the city of Madrid. Finally, the
last section concludes.
2. Data.
The city of Madrid is a municipality with a population of roughly
3.3 million inhabitants (as of January 2010). It comprises the city
centre or ‘Central Almond’ and a constellation of fourteen
surrounding districts. Central Almond is the area formed by seven
districts that are encircled by the first metropolitan ring-road (the
M30). With more than 30% of the population and 50% of GDP of
the city, Central Almond is clearly recognized as a unity with its
own idiosyncrasy. Indeed, since 2004 to 2011, the Urbanism and
Housing Area of the municipality government has launched two
main “action plans” in order to restore and revitalize several areas
of Central Almond (Ayuntamiento de Madrid 2009a, 2010, INE
2010). Many of these projects are devoted to construct new green
belts with trails and cultural spaces on either decadent residential
or industrial enclaves or highly congested tracks, in order to make
Central Almond a more friendly and sustainable city.
Our study focuses on 49 main urban tracks present in this specific
area (Fig. 1). They are the group of avenues and streets with more
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PART III Applications of Spatial Analysis with Samll Areas Observations
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than 5,000 vehicles per day as reported in the ‘Average Daily
Intensity of Urban Traffic’ report (Ayuntamiento de Madrid
2009b). These different intensities by tracks can be visualized in
Fig. 2a. Each track is characterized by a similar traffic intensity,
spatial continuity and socioeconomic homogeneity of the resident
population. We have selected those dwellings located at 150
meters (in average, depending on the track range) along either the
three tracks of the M30 ring-road adjoined to Central Almond
(non-tunnelled Eastern side, semi-tunnelled Southern side and
tunnelled South-Western side), as well as nineteen main North-
South tracks and twenty-seven East-West tracks. As depicted in
Fig. 1 and 2, the consideration of not only the tracks but their
corresponding influence area allows us to include in the sample
almost the total area of Central Almond. Therefore, our aim is to
shed light on an important issue, i.e. the people’s marginal
willingness to pay for air quality and reduced noise in the most
congested avenues of downtown Madrid. Such an evaluation
allows a first economic evaluation of certain environmental
policies that are being implemented in Central Almond.
Figure 1 - The Central Almond urban tracks.
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Urban tracks
1: M30 SW side
2: M30 SE side
3: Mediterr.-R. Cristina
4: Atocha Station
5: Sta. Mª Cabeza
6: Rondas-Bailén
7: Delicias
8: M30 Eastern side
9: Chamartín Station
10: Castellana Av.
11: Prado-Recoletos
12: Dr. Esquerdo
13: Bravo Murillo
14: P.Iglesias-O.Nieto
15: P.Vergara-M.Pelayo
16: A.Alcocer-C.Rica
17: M.Viana-S.A.Cruz
18: G.Yagüe-Francos R.
19: C.Espina-R.Cajal
20: R.F.Villav.-R.Victoria
21: J.Costa-F.Silvela
22: R.Rosas-I.Filipinas
23: Cea B.-J.Abascal
24: Mª Molina-América
25: A.Aguilera-Génova
26: Cibel.-G.Vía-Princesa
27: Alcalá-O'Donell
28: Alcalá-Ventas
29: P.Segovia-Cerrada
30: López de Hoyos
31: Ciudad de Barcelona
32: Planetario-Antracita
33: Atocha Street
34: Cortes-Mayor
35: Hortaleza-Fuencarral
36: San Bernardo
37: Guzmán el Bueno
38: Vallehermoso
39: Isaac Peral-H.Eslava
40: Jerónima Llorente
41: Orense-Inf.Mercedes
42: Capit. Blanco Argibay
43: Asturias-Sag. Corazón
44: Pradillo Street
45: Clara del Rey
46: Azcona-M.Izquierdo
47: Cartagena-Toreros
48: C.Peñalver-Narváez
49: Velázquez Street
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PART III Applications of Spatial Analysis with Samll Areas Observations
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Due to confidentiality constraints, it is not easy to obtain housing
prices microdata from Spanish official institutions. For this reason,
our records were drawn from a well-known on-line real estate
database, ‘idealista.com’. Since this catalogue immediately
publishes the asking price of properties, we extracted the
information during January 2008. The asking price has been used
as a proxy for the selling price, as it is usual in many other cases
(e.g. Cheshire and Sheppard, 1998 or Orford, 2000). In total,
around 3,302 housing prices were finally recorded for the
aforementioned 49 main urban tracks after the corresponding
consolidation and geocoding processes, which have been
performed with the ‘Callejero del Censo Electoral’ (INE, 008). The
geographical distribution of houses is displayed in Figure 2b.
Figure 2 - (a) Average Daily Intensity of Urban Traffic
(vehicles/day). (b) Sample of houses.
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ADIUT
in thousands
5-10
10-20
20-40
40-60
60-80
80-100
> 100
(a) (b)
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PART III Applications of Spatial Analysis with Samll Areas Observations
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The database ‘idealista.com’ also provides some property attribute
data related to dwelling type, living space, number of bedrooms,
floor level and modernization and repair. In Table 1, we present
the definitions of the variables used in this study.
Table 1 - Variable definitions.
Variable Description Source Units Period
LEVEL 1: HOUSES
Lprice
Housing price Idealista Euros
(in logs)
Jan. 2008
A) Structural variables
fl_1
First floor and upper Idealista 0-1 Jan. 2008
Attic
Attic Idealista 0-1 Jan. 2008
House
House (‘chalet’) Idealista 0-1 Jan. 2008
Duplex
Duplex Idealista 0-1 Jan. 2008
Bedsit
Bedsit Idealista 0-1 Jan. 2008
State
To be reformed: 0, new houses: 2,
others: 1
Idealista 0-1-2 Jan. 2008
Bedr
Bedrooms Idealista # Jan. 2008
lm2
Living space Idealista Square meter
(in logs)
Jan. 2008
B) Accessibility variables
Discen
Distance to the financial district Self-elab Km. -
Axis
Distance to the main commercial
avenues
Self-elab Km. -
Disair
Distance to the airport terminals Self-elab Km. -
dismetro
Distance to the nearest metro or railway
station
Self-elab Km. -
dism30
Distance to the M30 ring-road Self-elab Km. -
dispark
Distance to the nearest park
Self-elab. Km. -
C) Air and noise variables
Pollu
Objective air-pollution indicator Munimadrid
100=average 2007
dBA
Objective noise indicator Munimadrid
dB(A) 2008
Cont
Subjective air-pollution indicator Census % Nov. 2001
Noise
Subjective noise indicator
Census % Nov. 2001
LEVEL 2: CENSUS TRACTS
p65
Percent of population over 65 years Padrón, INE
% Jan. 2008
Forei
Percent of foreign population Census, INE
% 2001
Educ
Education level (secondary/university) Census, INE
% 2001
Unem
Unemployment rate Census, INE
% 2001
ha90
House built after 1990 Census, INE
% 2001
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PART III Applications of Spatial Analysis with Samll Areas Observations
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Proximity of dwellings to enclaves like CBD (Central Business
District), accessibility infrastructures (airports, motorways, and
metro and rail stations), shopping facilities, parks, etc. is
advertised by real estate agents and often capitalized in housing
prices. For this reason, in order to capture these elements, we
constructed the following accessibility measures: 1) distance to the
airport terminals, 2) distance to the nearest metro or railway
station, 3) distance to the M30 ring-road, 4) distance to the
financial district, 5) distance to the main road-axis and commercial
avenues and 6) distance to parks.
From these, only the two first ones were statistically significant in
the estimated models, with distance to the financial district the
most determinant indicator (see below). In effect, the new CBD,
which is located at the geographical centre of the Central Almond,
is a huge block of modern office buildings with metro, railway and
airport connections beside the government complex of Nuevos
Ministerios. Another important variable is nearness to the main
road-axis and commercial avenues. We have selected those
dwellings located at 250 meters (in average) along the main North-
South axis (Castellana-Recoletos-Prado) and four East-West axes,
i.e. Raimundo Fernández Villaverde-Concha Espina, José Abascal-
María de Molina-América, Alberto Aguilera-Bilbao-Colón-Goya
and Princesa-Gran Vía-Alcalá. This variable will capture the effects
linked to the proximity of accessibility infrastructures.
From an administrative point of view, the Central Almond is
divided into 7 districts and 780 census tracts, from which 660 are
crossed by the 49 main urban tracks.1 The 2001 Census provides a
series of variables on socioeconomic and demographic
characteristics related to home-ownership at the level of census
tracts. In Table 1, we present the most significant ones: percent of
population over 65 years, percent of foreign population, percent of
population with secondary and university degrees,
unemployment rate and percent of houses built after 1990. Though
these variables are all referred to 2001, they are population
averages, which are very stable in time. This validates their
inclusion in our model.
In order to measure air-quality and noise effects on housing prices,
we use two ‘subjective’ indicators, which are based on the
population’s perception of pollution and noise around their
residences. They are measured by the 2001 Census for each census
tract as the percentage of households that estimate that their
homes’ surroundings are polluted or noisy. These variables have
been interpolated by ordinary kriging at the level of houses.
Subjective data of air quality or noise pollution are not always
1
Although road tracks are the sum of census tracts, there are some census tracts,
mainly in the track intersections, which are part of more than one track.
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PART III Applications of Spatial Analysis with Samll Areas Observations
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correlated with objective measures of pollutants, which are usually
recorded at some fixed monitoring stations. Even though some
authors have pointed the limitations of subjective measures based
on individuals’ perceptions (e.g. Cummins, 2000), subjective
approaches seem to provide a better perspective for evaluating
certain latent variables connected with quality of life (Delfim and
Martins, 2007). For example, prospective homebuyers most
probably evaluate air quality based on whether or not the air
‘appears’ to be polluted or based on what other people and the
media say about local air pollution (Delucchi et al, 2002). The same
applies for noise (Miedema and Oudshoorn, 2001; Nelson, 2004;
Palmquist, 2005).
Air and noise pollution are similar though not an identifiable
phenomenon, even when they are caused by the same font (vehicle
flows, industrial activity, etc.). Noise operates at a more local scale
depending on the traffic intensity or the time of the day, while
airborne pollutants are not so location specific since they are
relevant on a global scale (Bickel et al., 1999). For this reason, air-
pollution and noise marginal costs in a same place neither coincide
nor are equally perceived by population.
In order to analyse these differences for our sample, we represent
on a map the values of the four quadrants of a scatterplot of air-
pollution versus noise in Central Almond, so that it is possible to
identify some peculiar non-coincidences between these variables
(Fig. 3a). In general, air and noise pollution are reported to be high
in the South and South-Western tracks, which are affected by the
commercial activity of the historical centre, as well as the accesses
to Atocha Station, the M30 and some national radial highways
located in this area. However, there are also some interesting
disparities in people’s perceptions affecting some tracks where
noise is considered as excessive, though air-pollution is reported
as low level. This is the case of tracks with some relevant value
added (such as accessibility to the financial district or to main
road-axis), in which their residents -though aware of the
drawbacks of noise in their neighbourhoods- do not have the
perception of living in a so air polluted area (while, from an
objective point of view, they probably are). The M30 Eastern side
accesses, as well as certain parts of Castellana, Orense, Príncipe de
Vergara, Velázquez, Alcalá or O’Donell tracks, among others (in
orange, in Fig. 3a), have such location advantages that could be
exerting some kind of “halo effect” on the air-pollution people’s
perception (Brody et al., 2004). In effect, air-pollution is frequently
associated with industries, bad odours and somehow depressed
neighbourhoods that have nothing in common with the
aforementioned residential avenues.
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PART III Applications of Spatial Analysis with Samll Areas Observations
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Figure 3 - (a) Scatterplot map of air-pollution (C) and noise (N).
(b) Projects for the construction of parks, new green belts with
trails and cultural spaces
*
.
Note: 1: Metro depots tunnelling (Cuatro Caminos, Castilla, Ventas and Cavanilles). 2: Delicias-
Méndez Álvaro especial plan. 3: Gran Vía director plan, 4: Old boulevards restoration. 5: S.
Francisco el Grande revitalization. 6: Vicente Calderón-Mahou restoration. 7: Legazpi
subterranean suburban bus station. 8: Azca remodelling. 9: Recoletos-Prado project. 10:
Construction of the Pº Dirección green-trail.
It is interesting to highlight that most projects of the last Urban
Action Plan for Central Almond in 2008-2011 (Ayuntamiento de
Madrid 2009a) are directly or indirectly oriented to the
improvement of air and noise environmental conditions. As
depicted in Fig. 3b, these projects are located in highly congested
enclaves and tracks where population reports the highest air
and/or noise contamination levels. We evaluate the impact that a
reduction in the contamination levels has in each place with the
help of a multilevel hedonic housing model.
3. Empirical multilevel hedonic housing model.
In this section, we briefly present multilevel models. These models
are adapted whenever the data have a hierarchical structure,
where a hierarchy refers to units clustered at different levels. In
Pollution
High C - High
N
Low C - High N
Low C - Low N
High C - Low N
¹
º
»
»
½
¼
¾
À
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¸
»
¿
¸
·
¸
¸
»
»
(a) (b)
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PART III Applications of Spatial Analysis with Samll Areas Observations
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our case, the houses are nested within census tracts. As detailed
above, there is also a higher level, the urban tracks, which are the
sum of census tracts. While many applications of multilevel
modelling can be found in education science, biology or
geography, economic applications are scarcer, although they have
been increasing in the last few years. Among others, multilevel
models have been applied to the study of female labour force
participation (Ward and Dale, 2006), unemployment in Israel
(Khattab, 2007), wage disparities in Brazil (Fontes et al, 2009), -
convergence in Europe (Chasco and López, 2009), internal
migration in Estonia (Kulu and Billari, 2010) or geography of
innovation (Srholec, 2010). Some applications of multilevel models
to hedonic models can be found in Beron et al (1999), Orford
(2000), Djurdjevic et al (2008) or Leishman (2009). We follow this
latter strand of literature and use multilevel models to evaluate the
differential impacts of subjective measures of noise and air quality
on housing prices in downtown Madrid.
Indeed, employing multilevel modelling for hierarchical data
presents advantages. Firstly, from an economic perspective, taking
into account a hierarchical structure makes it possible to analyse
more accurately the extent to which differences in housing prices
come from differences in housing characteristics and/or from
differences in the environment of the transactions, i.e. the
characteristics of the census tracts or the urban tracks. In our case,
this is an appealing feature, as we integrate in the econometric
specification various explanatory factors that operate at the first
two spatial levels. It is also possible to capture cross-level effects.
Secondly, from an econometric perspective, inference is more
reliable than in single-level models that assume independent
observations. Actually, if the units belonging to the same group
(for instance houses in the same census tract) are associated with
correlated residuals, these models are not relevant. More efficient
estimates are obtained when this independence assumption is
relaxed and when this intra-group correlation is modelled
explicitly.
Formally, consider a transaction i, located in census tract j, which
is itself located in urban track k. In the most general case, we can
specify a 3-level model with transactions at level 1 located in
census tracts at level 2 and urban tracks at level 3.
At level 1, we specify a linear relationship as follows:
(1)
where refers to the transaction, refers to the
census tract and refers to the urban track. is the
y
ijk
0, jk
s, jk
x
s,ijk
s1
S
ijk
1,...,iN
1,...,jM
1,...,kK
y
ijk
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housing price (or its logarithm) of transaction i in census tract j
and urban track k ; (with ) are the level 1
predictors; is a random term with . This is a
multilevel model since the intercept and the slopes are
allowed to vary randomly at the census tract level such as (level 2):
(2)
for ; where is the total number of variables operating
at the census tract level affecting each transaction-specific
parameter ; (with ) are the level 2 predictors
for the parameters ; is a random
term distributed as a multivariate normal with 0 mean and
as a
full variance-covariance matrix of dimension . Finally, the
intercept and the slopes of equation (2) are themselves
allowed to vary randomly at the urban track level such as (level 3):
(3)
for and ; where is the total number of
variables operating at the urban track level affecting each census
tract-specific parameter ; (with ) are the
level 3 predictors for the parameters ;
is a random term
distributed as a multivariate normal with 0 mean and
as a full
variance-covariance matrix of dimension . Note that
the coefficients in equation (3) are not random but fixed. Finally,
the errors terms ( , and ) are assumed to be
independent of each other.
Substituting equations (2) and (3) in the level 1 model (equation 1)
yields a mixed specification where the dependent variable is
x
s,ijk s
1,...,S
ijk
ijk
: Nid(0,
2
)
0, jk
s, jk
s, jk
s0,k
sl,k
x
sl, jk
l1
N
s
w
s, jk
0,...,sS
0,...,sS
N
s
s, jk
x
sl, jk
l 1,...,N
s
s, jk
w
jk
(w
0, jk
...w
s, jk
...w
S, jk
)'
S 1
s1,k
sl,k
sl,k
sl0
slm
x
slm,k
m1
N
sl
u
sl,k
0,...,sS
0,...,
s
lN
N
sl
sl,k
x
slm,k
m 1,...,N
sl
sl,k
u
k
(u
00,k
...u
0l
...u
0N
s
...u
S0,k
...u
Sl
...u
SN
s
)'
N
s
1
s0
S
ijk
w
s, jk
u
sn,k
y
ijk
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the sum of a fixed part and a random part. The former includes
explanatory variables operating at the 3 different spatial levels (
, , ), together with interactions between these levels,
while the latter is a complex combination of the random terms ,
and . This model is usually estimated using restricted
maximum likelihood, noted thereafter REML (see for instance
Raudenbush and Bryk, 2002 or Goldstein, 2003 for more details on
the estimation method).
The full multilevel model (1)-(3) is very general with potentially a
high number of unknown parameters to estimate. In practice,
simpler models are estimated. In particular, not all parameters at
level 1 vary randomly at the census tract level and/or not all
parameters at level 2 vary randomly at the urban track level. We
specify in the empirical analysis our assumptions concerning the
variability of each parameter.
4. Results and discussion.
4.1. Grand mean model.
In order to determine how variations in housing prices are
allocated across each spatial level, we first specify the grand mean
model. This model is fully unconditional in the sense that no
predictor variables are specified at any level. Formally, it is
represented as the following log-linear model:
0,
0, 00, 0, 000 00, 0,
00, 000 00,
ijk jk ijk
jk k jk ijk k jk ijk
kk
lprice
w lprice u w
u
(4)
where
lprice
ijk
is the log of price of transaction i in census tract j
and urban track k. The coefficients are interpreted as follows:
0, jk
is the mean log of price of census tract j in urban track k;
00,k
is
the mean log of price in urban track k;
000
is the grand mean.
Finally, the error terms have the following properties:
2
0,
ijk
Nid
is the random term measuring the deviation of
transaction ijk’s log of price from the mean log of price in census
tract j;
2
0,
0,
j
kw
wNid
is the random term measuring the
deviation of census tract jk’s mean log of price from the mean log
x
s,ijk
x
sl, jk
x
slm,k
ijk
w
s, jk
u
sl,k
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9
7
of price in urban track k;
2
00,
0,
ku
uNid
is the random term
measuring the deviation of urban track k’s mean log of price from
the grand mean.
Table 2 - The Grand Mean model and Models 1 and 2
Variables
Grand Mean
model
Benchmark
model
Model 2
Noise Air-pollution
Fixed
Const.
12.96223
***
8.696402
***
8.837826
***
8.957598
***
Structural
Floor
- 0.102336
***
0.103926
***
0.105367
***
Attic
- 0.036974
***
0.032498
***
0.037773
***
House
- 0.406189
***
0.364783
***
0.407730
***
Bedsit
- 0.067244
***
0.075373
***
0.063030
***
lm2
- 2.100856
***
2.123871
***
2.098390
***
State
- 0.111625
***
0.115538
***
0.114543
***
Accessibility variables
Discen
-
-
-0.000092
***
-0.000070
***
Axis
-
-
0.057878
***
0.043855
***
Air and noise variables
Noise
-
-
0.000452 -
Cont
-
-
- -0.003560
***
Random: Variance (std. error)
Tracks
0.067248
(0.01547)
0.018476
(0.00405)
-
0.008912
(0.00215)
Census
0. 051929
(0. 00600)
0.008431
(0.00090)
0.013419
(0.00120)
0.007277
(0.00082)
Houses
0. 186692
(0. 00534)
0.026395
(0.00076)
0.026362
(0.00075)
0.026255
(0.00075)
Intra-class (tracks)
22% 35% 0% 21%
Intra-class (census)
17% 16% 33% 17%
LIK
-2255.50
***
915.51
***
869.34
***
948.35
***
Deviance (H
0
: previous -if
nested- model)
- 6,342.01
***
-
65.69
***
LR vs linear model
775.09
***
1,141.67
***
492.05
***
624.71
***
* significant at 0.10, ** significant at 0.05, *** significant at 0.01
The REML estimation results are displayed in Table 2 (third
column). The average house price for the main urban tracks of
‘Central Almond’ in Madrid amounts to 426,015 € (Table 2).2 The
variation around this grand mean can be decomposed into
variations at the level of the individual transaction, census tract
and urban tracks using the variances of the error terms at the
different levels.3 The greatest variation occurs between individual
2
Since we use a log-linear model, this figure is the result of computing
exp(12.96223).
3
They are computed respectively as follows:
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transactions (61%) although almost one-fourth of the variation
takes place between tracks (22%). Therefore, housing prices vary
significantly between tracks. Finally, a multilevel model is indeed
relevant since the LR test of absence of random effects strongly
rejects the null.
Table 3 - Urban tracks level premiums for the Grand Mean, Benchmark and Model 2.
Grand Mean model Benchmark model Model 2
Rank order Price
(€)
Rank order Price
(€)
Rank order Price
(€)
Valázquez Street 334,948 Prado-Recoletos 2,586 Prado-Recoletos 2,195
Prado-Recoletos 313,219 Velázquez Street 2,576 Velázquez Street 1,913
Castellana Av. 305,381 Castellana Av. 1,845 Castellana Av. 1,529
Concha Espina-R.
Cajal 254,884
Cibeles-Alcalá-
O'Donell 1,153 Isaac Peral-H. Eslava 94
7
Cibeles-Alcalá-
O'Donell 229,961 P. Vergara-M. Pelayo 966 A. Alcocer-C. Rica 822
P. Vergara-M. Pelayo 117,759
Concha Espina-R.
Cajal 821 P. Vergara-M. Pelayo 786
Isaac Peral-H. Eslava 110,666 Cartagena-Toreros 78
7
Cortes-Mayor 709
A. Alcocer-C. Rica 82,759 Isaac Peral-H. Eslava 762
Concha Espina-R.
Cajal 601
M30 Eastern side 76,409
C. Bermúdez.-J.
Abascal 728
Cibeles-Alcalá-
O'Donell 575
C. Bermúdez.-J.
Abascal 73,149 A. Aguilera-Génova 686 Planetario-Antracita 55
7
R. Rosas-I. Filipinas 61,507 R. Rosas-I. Filipinas 679 Alcalá-Ventas 429
Asturias-Sag. Corazón 61,097 Alcalá-Ventas 663
Asturias-Sag.
Corazón 356
Alcalá-Ventas 55,484 A. Alcocer-C. Rica 546 R. Rosas-I. Filipinas 339
Cartagena-Toreros 46,436 Cortes-Mayor 468 Cartagena-Toreros 330
Orense-Infanta
Mercedes 45,096 Guzmán el Bueno 409 Guzmán el Bueno 301
Planetario-Antracita 32,510
Joaquín Costa-F.
Silvela 321 M30 SE side 299
Guzmán el Bueno 29,744 Vallehermoso 251
C. Bermúdez.-J.
Abascal 260
Chamartín Station 25,973
Orense-Infanta
Mercedes 130 Ciudad de Barcelona 188
A. Aguilera-Génova 23,439 Hortaleza-Fuencarral 80 Rondas-Bailén 174
Joaquín Costa-F.
Silvela 16,505
Cibeles-G. Vía-
Princesa 40
Orense-Infanta
Mercedes 163
Mediterráneo-R.
Cristina 14,509 Mª de Molina-América 24 A. Aguilera-Génova 163
; and .
The last two equations correspond respectively to the intra-class correlation for
tracks and census tracts that are reported in Table 2.
2
/
2
w
2
u
2
w
2
/
2
w
2
u
2
u
2
/
2
w
2
u
2
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Grand Mean model Benchmark model Model 2
Rank order Price
(€)
Rank order Price
(€)
Rank order Price
(€)
Vallehermoso 13,857 R.F. Villav.-R. Victoria -64 Chamartín Station 55
R.F. Villav.-R. Victoria 6,434
Azcona-Mnez.
Izquierdo -125 Dr. Esquerdo -2
Mª de Molina-América 388 M30 Eastern side -129 M30 Eastern side -8
Dr. Esquerdo -2,112 Dr. Esquerdo -139 Vallehermoso -22
Cibeles-G. Vía-
Princesa -6,863 San Bernardo -152
P. Segovia-Cerr.-
Toledo -6
7
Conde Peñalver-
Narváez -9,911 Ciudad de Barcelona -180 Atocha Street -162
Cortes-Mayor -11,025 Bravo Murillo -195
Mediterráneo-R.
Cristina -178
Hortaleza-Fuencarral -11,958 Asturias-Sag. Corazón -243 M30 SW side -192
M30 SE side -14,743 Rondas-Bailén -27
7
Joaquín Costa-F.
Silvela -194
Azcona-Mnez.
Izquierdo -23,636 Atocha Street -289 Hortaleza-Fuencarral -26
7
Pradillo Street -29,888
Conde Peñalver-
Narváez -332 Atocha Station -303
Ciudad de Barcelona -40,572
P. Segovia-Cerr.-
Toledo -373 Sta. Mª Cabeza -315
Atocha Station -50,607 Pradillo Street -385
Cibeles-G. Vía-
Princesa -316
López de Hoyos -56,702
Mediterráneo-R.
Cristina -388 San Bernardo -392
P. Segovia-Cerr.-
Toledo -61,895 Planetario-Antracita -406 R.F. Vill.-R. Victoria -416
Clara del Rey -65,817 López de Hoyos -432 Bravo Murillo -419
San Bernardo -79,978 Clara del Rey -466 Pº Delicias -503
Rondas-Bailén -83,247 Chamartín Station -470
Azcona-Mnez.
Izquierdo -536
G. Yagüe-Francos Rgz. -88,731 M30 SE side -596 M. Viana-S.A. Cruz -55
7
Bravo Murillo -89,368 Atocha Station -611
Capit. Blanco
Argibay -59
7
Atocha Street -89,947 G. Yagüe-Francos Rgz. -720 Pradillo Street -626
Sta. Mª Cabeza -92,251 M. Viana-S.A. Cruz -852
Conde Peñalver-
Narváez -633
M30 SW side -101,645 Sta. Mª Cabeza -904
Mª de Molina-
América -696
M. Viana-S.A. Cruz -110,390 M30 SW side -905
G. Yagüe-Francos
Rgz. -715
Pº Delicias -131,708 Pº Delicias -961 López de Hoyos -758
Capit. Blanco Argibay -132,078 P. Iglesias-O. Nieto -981 Clara del Rey -805
P. Iglesias-O. Nieto -136,130 Capit. Blanco Argibay -1,040 P. Iglesias-O. Nieto -999
Jerónima Llorente -163,490 Jerónima Llorente -1,334 Jerónima Llorente -1,533
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The first column of Table 3 describes the price variations around
the grand mean (426,015 €) at the urban track level. For instance,
transactions in Velázquez, Prado-Recoletos and Castellana Av. are
more than 300,000 € more expensive than the average price in
Central Almond main tracks, while transactions in Pº Delicias,
Capitán Blanco Argibay, Pablo Iglesias-Ofelia Nieto and Jerónima
Llorente tracks are more than 130,000 € cheaper.
These results are illustrated graphically in the upper left part of
Fig. 4. The cheapest tracks are concentrated in the southwestern
and northwestern parts of the area whereas the tracks with the
highest premiums are located along Castellana and Recoletos-
Prado tracks as well as some Eastern main streets. The deviations
of prices in census tracts compared to the grand mean (right part
of Fig. 4) follow a similar pattern but displaying some variations in
more heterogeneous tracks like those located in the south and
western part of Central Almond.
Figure 4 - Urban track (left) and census tract-level (right)
premiums (mile €).
4.2. The benchmark model.
Next, we estimate our benchmark model, labelled as Model 1. It
consists in the grand mean model to which only structural
attributes of each transaction are included in the level 1 equation:
Grand mean
61 to 335
0 to 61
-62 to 0
-164 to -62
Benchmark
0.2 to 1.4
0 to 0.2
-0.2 to 0
-1.4 to -0.2
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(Model 1)
(5)
where S is the number of structural attributes. We assume that the
associated coefficients are fixed: they do no vary randomly across
census tracts and/or tracks.Note that this assumption will be
relaxed in the following section for some variables. The REML
results are reported in Table 2. Among all structural variables
considered, we only report the coefficients that are significant at
5%. All the structural attributes coefficients estimates show the
expected sign. They are strongly statistically significant at 1% with
the exception of ‘duplex’ and ‘number of bedrooms’. Specifically,
the number of bedrooms variable, which is usually relevant in
hedonic price models, is not significant even at the 5% level
because it shows a strong correlation with ‘floor area’.
The deviance or likelihood test, i.e. the difference in the likelihood
ratio statistic of this model and the grand mean model, is equal to
6,342.01. Under the null hypothesis, it follows a chi-squared
distribution with degrees of freedom equal to 6, i.e. the number of
new parameters (Woodhouse et al, 1996). The p-value is less than
0.001: the structural attributes therefore significantly explain house
price variation in the model.
lprice
ijk
0, jk
s
x
s,ijk
s1
S
ijk
0, jk
00,k
w
0, jk
00,k
000
u
00,k
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Figure 5 - Road track (left) and census tract-level (right)
premiums (mile €) in the benchmark model.
Looking at the intra-class correlations, we see that the inclusion of
structural attributes implies a strong decline of the transaction-
level variance. Consequently, a large part of price differences
between individual transactions is a result of differences in these
attributes. In contrast, 35% of the total variation now occurs
between tracks, compared to 22% in the grand mean model. This
result is reflected by the analysis of the track-level differences
(Table 3) as both the rank of tracks and the size of their contextual
effects are modified. For instance, two of the previous most
expensive urban tracks, Asturias-Sagrado Corazón and Chamartín
Station are now closer to Central Almond average, while a
previously below-average track, Cortes-Mayor, is now
significantly above average. Much more evident are the
modifications in the rank of the census tracts (right part of Fig. 5).
There still exists some concentration of higher premiums in part of
the census tracts of the central axis (Castellana and Prado-
Recoletos), with the rest of the values more or less scattered all
over the Central Almond. Also, the size of the neighbourhood and
census tract premiums has declined substantially, meaning that
they were previously mainly capturing the effects of structural
attributes. Furthermore, buyers are getting much less for their
money in tracks like Prado-Recoletos and Velázquez than in areas
like Jerónima Llorente and Capitán Blanco Argibay.
4.3. Model with structural and accessibility variables
Benchmark
0.7 to 2.6
0 to 0.7
-0.4 to 0
-1.4 to -0.4
Benchmark
0.2 to 1.4
0 to 0.2
-0.2 to 0
-1.4 to -0.2
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Model 2 includes additional fixed accessibility indicators and
pollution variables (noise or air pollution) at the individual level.
Among all the accessibility variables that we tried, only two
accessibility indicators are significant at 5%: distance to the CBD
(discen) and distance to the main city axis (axis). Concerning the
analysis of the impact of noise and air pollution on housing prices,
we have specified two different models depending on the selected
pollution variable: (i) model 2N includes the subjective measure of
noise (noise) and (ii) model 2C includes the subjective measure of
air pollution (cont). Due to the high correlation between air and
noise pollution levels (Li and Brown, 1980), it is necessary to sort
out these separate effects in order to measure their marginal effect
on housing prices.
The REML estimation results are displayed in Table 2. The
inclusion of these accessibility and pollution variables does not
alter either the values or the sign of the structural attributes, which
are all significant at 5%. Distance to the CBD (discen) and distance
to main axis (axis), they are significant at 1%. We note that the
former plays a negative effect on housing prices while the latter
has a positive effect. Households therefore have a higher
willingness to pay whenever they are located closer to the CBD
and farther away from the main axis.
The coefficient for air pollution is significant at 5% while the noise
parameter is positive and it does not seem to have any impact on
housing prices. The deviance statistic (with Model 1 as the null
hypothesis) indicates that the addition of accessibility and air-
pollution attributes has a significant effect on housing prices.
Interestingly, we find that in the model for noise, the track-level
random effect is no longer significant
4
resulting in the census tract
level now explaining 33% of house price variations. This result
means that noise seems to be a more “local” phenomenon than air
quality so that random variations at the census tract level are
enough to capture price variability. Indeed, according to Falzone
(1999) and Bickel et al (2003), noise is often transitory and seldom
catastrophic. It is therefore considered as an environmental
intrusion with a very local effect, which depends, among other
things, on the time of the day or the distribution and distance of
exposed persons from the source.
Finally, we analyse how the track premiums have changed
following the inclusion of accessibility and air-pollution variables
(last column of Table 3). First, the effects of area are not
significantly different from the benchmark model, meaning that
this one was not capturing the effects of accessibility and/or air-
pollution variables. However, there are interesting changes in
rank, as the promotion of the M30 East side, Planetario-Antracita
4
This is why the deviance statistic has not been computed in as Model 1 is not
nested in this model.
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104
and Rondas-Bailén, between others. These tracks command a higher
premium, given the accessibility and air-pollution attributes of the
areas, which may be caused by other features, such as social class.
Other tracks have experienced an important decrease in the
premium rank with respect to the previous models. This is the case
of María de Molina-América, Conde de Peñalver-Narváez and Azcona-
Martínez Izquierdo, in which buyers are getting much more for their
money.
4.4. Model with structural, accessibility and census tract
variables.
We now estimate a model with the same random and transaction
level fixed terms as in the previous model, but which further
incorporates attributes available at the census tract level (Model 3):
(Model 3)
(6)
We assume that these N
0
census tract level variables only affect the
intercept of the level 1 model (β
0,jk
) and that they remain fixed
across census tracts, i.e. they do not vary randomly at the track
level. Among all the attribute variables that we tried, only two of
the census tracts variables shown in Table 1 are significant in the
following models: p65 and educ.
The REML estimation results are displayed in Table 4. Compared
to model 2, since the census tract variables do not vary at the level
of houses, the fixed and random estimates for the transaction-level
attributes remain more or less unchanged, mainly for the
structural attributes. However, the census tract-level and urban
track-level random effects have decreased, so that the transaction
level now explains more than two thirds of house price variations
(67% for noise and 72% for air-pollution). Again, the track random
effect is not significant for the model with noise.
lprice
ijk
0, jk
s
x
s,ijk
s1
S
ijk
0, jk
00,k
0l
x
0l, jk
l1
N
0
w
0, jk
00,k
000
u
00,k
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Table 4 - Models 3 and 4 with structural attributes, accessibility variables and census
tract level variables, as well as varying slopes.
Model 3 Model 4
Noise
Air-
pollution
Noise
Air-
pollution
Constant
8.253940
***
8.531377
***
8.333635
***
8.602855
***
Structural
Floor
0.103200
***
0.105547
***
0.113124
***
0.109873
***
Attic
0.037431
***
0.040765
***
0.043705
***
0.044288
***
House
0.365515
***
0.401797
***
0.361952
***
0.364110
***
Bedsit
0.071369
***
0.060026
***
0.066536
***
0.057481
***
lm2
2.098307
***
2.082467
***
2.076103
***
2.061383
***
State
0.117685
***
0.114747
***
0.120419
***
0.117618
***
Accesibility
Discen
-0.000066
***
-0.000059
***
-0.000056
***
-0.000060
***
Axis
0.047643
***
0.036963
***
0.038183
***
0.038063
***
Census tracts
Educ
0.008429
***
0.006765
***
0.007602
***
0.006181
***
p65
- -0.003885
***
- -0.002730
***
Pollution
variables
Noise
0.000158 - -0.000294 -
Cont
- -0.002535
**
- -0.003073
***
Variance and
covariance
(standard
error)
Neighb. constant
-
0.0069519
(0.00171)
-
0.005040
(0.00134)
Census constant
0.010638
(0.00102)
0.006020
(0.00075)
0.235241
(0.05514)
1.65e-19
(-)
noise/air-
pollution
- -
0.000018
(8.04e-06)
0.000041
(0.00001)
lm2
-
-
0.071494
(0.01121)
0.016990
(0.00310)
noise/airp
oll.-lm2
- -
-0.000033
(0.00024)
-0.000820
(0.00018)
noise var-
constant
- -
-0.00082
(0.00057)
-
lm2-consta
n
- -
-0.116629
(0.02258)
-
Houses
0.026837
(0.00074)
0.026241
(0.00075)
0.023663
(0.00070)
0.024613
(0.00071)
Intra-class (tracks) 0% 18% - -
Intra-class (census) 28% 15% - -
LIK 917.28
***
976.25
***
1,010.53
***
1,025.00
***
Deviance (H
0
: Model 2) 95.89
***
55.81
***
- -
LR vs linear model 374.28
***
473.12
***
560.78
***
570.62
***
As the census tract variables act as a proxy for social class, they
have a significant effect upon house price differentials with the
expected sign. This result is confirmed by the computation of the
deviance statistic with Model 2 as the null hypothesis. The
differential impacts of noise and air pollution on house prices
remain unchanged: noise coefficient is positive and statistically
non-significant while air-pollution still exerts an inverse
significant effect on house prices.
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106
4.5. Model with varying slopes for lm2 and, in case, noise/cont.
All the previous models assumed that the structural attributes and
the pollution variables are constant across downtown Madrid.
However, in Model 3, approximately one third of house price
variation occurs between census tracts and/or urban tracks (28%
for the noise equation and 33% for the air-pollution one). These
unexplained variations might in fact be caused by variation in the
implicit prices of structural attributes and/or pollution variables at
both spatial levels. Therefore, we finally estimate models in which
some level 1 coefficients are allowed to vary randomly at higher
spatial levels.
Since floor area (lm2) is the main structural attribute, it is allowed
to vary randomly at the census tract level. The measures of noise
and air-pollution are also allowed to vary randomly at the census
tract and urban track levels. After several tries, we found that the
measure of noise does not allow random variations at the urban
track level, either in its own coefficient or in the constant term. In
the case of air-pollution equation, only the constant term
significantly varies at the level of urban tracks. These results
would be confirming the local nature of noise with respect to air-
pollution.
Formally, for the noise measure, our final specification is as
follows:
0
0, 1, 2, ,
3
0, 00 0 0 , 0,
1
1, 10 1,
2, 20 2,
2
S
ijk j j ijk j ijk s s ijk ijk
s
N
jlljkjk
l
jjk
jjk
lprice lm noise x
xw
w
w
(7)
For air pollution, our final specification is as follows:
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PART III Applications of Spatial Analysis with Samll Areas Observations
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10
7
0
0, 1, 2, ,
3
0, 00, 0 0 , 0,
1
1, 10 1,
2, 20 2,
00, 000 00,
2
S
ijk j j ijk j ijk s s ijk ijk
s
N
j k l l jk jk
l
jjk
jjk
kk
lprice lm cont x
xw
w
w
u
(8)
where cont is the variable for air-pollution.
The REML estimation results are displayed in Table 4. All the
structural, locational and pollution variables are strongly
significant, with the exception of noise. Interestingly, this model is
the only one -for noise- in which the coefficient associated to this
variable is negative, as expected, although it still remains non-
significant, once higher-level interactions at the level of census
tracts are explicitly considered. In spite of not being statistically
significant, we find that this coefficient significantly varies at the
level of census tracts, showing positive and negative values
depending on the spatial location. Therefore, noise and air
pollution have a negative influence on housing prices which is
only globally significant for the second one.
5
Fig. 6a displays the change implied by the inclusion of the random
floor area and air pollution terms on the implicit prices by census
tracts in Model 4. Compared to the grand mean model (Fig. 4), the
ranks greatly change. Fig. 6a shows the existence of a split between
the census tracts located along the vertical Castellana-Recoletos-
Prado axis joint with the northeast edge of Central Almond, and
the peripheral areas (northwestern and eastern edges), becoming
the first less expensive once the differential prices of floor area and
perceived air-pollution have been taken into account, and vice
versa. Overall, the map gives an idea of which areas require an
additional premium, what could be viewed as a measurement of
‘desirability’. This is the case of the urban tracks located in the
district of Tetuán (northwest) and the districts of Salamanca and
Retiro (east). These two big clusters are characterized for being
closed to either the CBD -in the first case- and the most exclusive
shopping centres -in the second case-, as well as having an
excellent accessibility to both inner and outer city.
5
As stated in Bickel et al. (2003), noise costs are extremely variable since they
depend on several factors and exhibit large non-linearities. This is why it is more
difficult to find a generalization for marginal noise costs than for air pollution.
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108
Figure 6 - Model 4: (a) Census tract-level premiums, (b) census
tract-level floor area differential prices of floor area.
Model 4 also allows the implicit price of floor area to vary at the
census tract level. The variance reported in Table 4 measures the
variation in the price of floor area between census tracts and the
covariance term measures the relationship between other variables
(average census tract-level house price, noise and air-pollution)
and the implicit price of floor area. With the exception of the
covariance term between air-pollution and floor area price, these
terms are all significant. On average across Central Almond, an
extra square metre of floor area raises house price by 7.86 € (a
general slope of 2.06 in the equation for air-pollution), but this
figure varies from place to place in a range from 12.40 € (in
Recoletos-Prado urban track) to 5.91 € (in Jerónima Llorente urban
track). These differences reflect the differences in supply and
demand that operate in these tracks. In Fig. 6b, we have
represented the differential implicit prices of floor area by census
tracts. This variable shows a more or less opposite spatial
distribution than the census tract-level premiums; i.e. the
‘discount’ of floor area variations from house prices spatial
distribution reveals a different pattern for the urban tracks
premiums or the desirability that people show for certain sub-
markets. This result highlights the importance of considering floor
area spatial variations in order to explain house prices distribution
in Central Almond.
Finally, in Model 4 the marginal prices of noise and air pollution
(parameters) are allowed to vary at the census tract level. We see
that the effects of noise and air-pollution per se vary quite
Premiums (€)
(Model 4, air-pollution)
670 to 6,330
0 to 670
-520 to 0
-2,810 to -520
Floor area prices (€)
(Model 4, air-pollution)
0.28 to 3.15
0.00 to 0.28
-0.33 to 0.00
-1.95 to -0.33
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109
significantly between census tracts, though with a different sign
(Fig. 7). We observe a spatial coincidence between clusters of
lower negative coefficients of both noise and air-pollution. They
are mainly located along some of the busiest tracks of Central
Almond (see Fig. 2a), like the Atocha and Chamartín Station areas,
the M30 Southwestern side, Rondas-Bailén, Recoletos-Prado,
Castellana, Raimundo Fernández Villaverde-Reina Victoria, Cibeles-
Alcalá-O’Donell and Alberto Alcocer-Costa Rica. There are also other
coincident clusters of positive coefficients, which are more or less
concentrated in the Northwestern, Eastern and Southern parts of
Central Almond. In these places, residents are willing to pay more
money for houses with more perceived noise and air-pollution.
This counter-intuitive sign could be the result of the influence of
other variables acting in people’s mind, such as location in wider
streets and proximity to principal or historical places, like the
Royal Palace. In fact, these areas are characterized by high
population density living in old buildings, which are in narrow
streets with traffic access and no good visibility. Probably, this is
one of the reasons why people are willing to pay more money for
houses located in open spaces like avenues or squares, though
they are perceived as being noisier.
At this point, it is possible to make a first evaluation of the Action
Plan projects for Central Almond in the period 2008-2011 (see Fig.
3b). It must be said that not all the projects have been finished
(even started in some cases) because of the severe constraints
imposed by the economic crisis. For this reason, the computation
of the air-pollution costs from the significant coefficient variations
across census tracts can help us to establish a first rank of
priorities. Building a buffer of 500 metres around each project, it is
possible to analyze the impact of air-pollution on housing prices in
each area. We can detect four projects almost totally located in
those census tracts registering the highest cost in air-pollution (the
ones in dark blue, in Fig. 7): Recoletos-Prado project (9), Delicias-
Méndez Álvaro especial plan (2), Castellana and Velázquez boulevard
restoration (4). These are the areas in which a reduction of air-
pollution will have the maximum impact.
Secondly, there are another four projects partially located in
census tracts with the highest air-pollution cost: tunnelling of
metro depot in Plaza de Castilla (1), Vicente Calderón-Mahou
restoration (6), San Francisco el Grande revitalization (5) and Alberto
Alcocer-Génova boulevard restoration (4). From the environmental
point of view, these eight projects should have the highest priority
for the local authorities. In contrast, there are two projects mostly
located in census tracts for which air-pollution is an amenity (with
a positive slope in the model): the metro depot tunnelling in Cuatro
Caminos and Ventas. In terms of air-pollution costs exclusively,
these projects should have the least priority in the future action
plan.
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Figure 7 - Changes in census-tract-level prices due to noise and
air-pollution.
5. Conclusions.
The aim of this chapter was to evaluate the households’ marginal
willingness to pay for reduced noise and better air quality in the
most congested areas of downtown Madrid. For that purpose, we
have applied hedonic regression to a sample of 3,302 houses.
Contrary to most hedonic studies in the literature, we use
subjective rather than objective measures of noise and air
pollution. Moreover, as the dataset has a hierarchical structure, i.e.
the houses are nested within census tracts and urban tracks, we
use multilevel modelling. These models allow using variables
operating at different scales and allow the marginal prices of air
and noise pollution to vary randomly at higher levels. Moreover,
by taking into account the clustered nature of the residuals, more
reliable inference can be achieved.
We found that noise does not seem to influence housing prices
globally but that it significantly varies randomly at the level of
census tracts, showing positive and negative values depending on
the spatial location. The impact of air pollution is negative and
significant and also randomly varies at the level of tracks. Spatial
coincidence of lower negative coefficients of both noise and air
pollution are found located along some of the busiest tracks of
Central Almond. These results allow making a first evaluation of
the Action Plan projects for Central Almond that have been
Nose slope
(Model 4)
-0.012 to -0.001
-0.001 to 0.000
0.000 to 0.006
Air-pollution slope
(Model 4)
-0.019 to -0.005
-0.005 to 0.000
0.000 to 0.010
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undertaken in the period 2008-2011. Using the estimation results,
we detect the projects located in the areas in which a reduction of
air pollution will have the maximum impact and that should
therefore have the highest priority in the future action plan.
Future research should concentrate in checking the robustness of
our results by means of including new observations to the sample.
For instance, adding a time dimension to the spatial multilevel
model would allow checking the possible evolution of marginal
prices for air and noise pollution in Central Almond. We could
also consider the peripheral districts information in order to detect
possible spatial discontinuities between our model results in
Central Almond and the vast area outside the M30 belt, which is
known to operate as a strong barrier in the city of Madrid.
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