The Use of Environmental
Quality Indexes for the
E ti
Estimation
ti
off Housing
H
i
Prices
P i
Cuenca, 22 y 23 de octubre de 2008
Turismo y Medio Ambiente
José-María Montero1, Gema Fernández-Avilés1, Jorge
g Mateu2, Emilio Porcu2
1 University of Castilla-La Mancha, Toledo, Spain; 2 University Jaume I, Castellón, Spain.
Background
„
Hedonic house price models that incorporate environmental
variables are becoming more and more popular.
popular Anselin and
Lozano-Gracia (2008); Freeman (1993).
„
This is not surprising because a substantial body of research
empirically confirms the hedonic theory and suggests that
consumers are willing to pay for environmental goods.
goods Braden J.B.
JB
and Kolstad C.K. (1991)
„
Good examples of the focus on hedonic property-value models for
estimating the marginal willingness of people to pay for a reduction
p
air p
pollutants are: Smith and
in the local concentration of specified
Huang (1993), (1995); Kim, Phipps, and Anselin (2003), Anselin
and Le Gallo (2006) and Anselin and Lozano-Gracia (2008).
The
h problem:
bl
there is a mismatch between the spatial
‘support’ for the environmental measured variables and
the property prices.
prices
The
solution:
to interpolate the environmental
variable(s)
i bl ( ) to
t
obtain
bt i
th i interpolated
their
i t
l t d values
l
i
in
th
the
locations where house prices are available. It can be
considered three possibilities (Myers, 1983):
(i) Interpolate such
variables and include all
variables in the model.
It is p
preferred when
dealing with only one
environmental variable.
(ii) Elaborate an
environmental index,
index
and then interpolating it.
(iii) Interpolate the
environmental variables
considered and elaborate
an environmental index.
It is the one chosen
in the specialized
literature.
Our proposal is option (iii)
b
because
the
th variance
i
of the estimation errors
is lesser than using (ii).
Whi h is
Which
i the
th objective?
bj ti ?
Options (ii) and (iii) are
empirically compared using six environmental variables to
elaborate an Environmental Quality Index in Madrid City (Spain).
(Spain)
The data used in this paper:
„
They come from the Atmosphere Pollution Monitoring System of Madrid municipality.
„
They have been hourly measured at the 25 fixed operative monitoring stations
during January, 2008.
„
Six pollutants: Sulphur dioxide (SO2), nitrogen oxides (NOx), nitrogen dioxide
(NO2), carbon monoxide (CO), particulate matter (PM10), ground-level ozone (O3).
EQI ( s j ) = ∑ λi EQI ( s i )
m
Option (ii)
Option (iii)
*
j =1
nj
k
k
(s ) = A ' X = a X (s ) =
EQI
a
λ
X
s
(
∑ k
∑∑ k i k i )
j
j
K
*
j
k =1
K
*
k
k =1 i =1
( s ) − EQI ( s ) ⎤
Var ⎡⎣ EQI * ( s ) − EQI ( s ) ⎤⎦ > Var ⎡ EQI
⎣
⎦
Traditional and Alternative Approaches for Estimating EQIs.
ECM estimating an EQI for Madrid City (Spain).
Hour
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
MSE ((i))
Kriging
Enviromental
Variables
MSE ((ii))
0,99
0,82
0,87
0,82
1,02
0,86
0,75
0,77
0,83
0,83
0,96
0,96
1,08
1,07
1,09
1,07
1,05
1,00
0,96
0,91
0,87
0,85
0,72
0,72
0,57
0,57
0,53
0,54
0,56
0,58
0,54
0,55
0 66
0,66
0 67
0,67
0,75
0,72
1,06
0,89
1,09
0,98
1,08
1,07
1,08
1,05
1,05
0,93
1,00
0,87
0,17
0,05
0,16
-0,02
0,00
0,00
0,01
0,02
0,05
0,05
0,02
0,00
0 00
0,00
-0,01
-0,02
-0,02
-0 01
-0,01
0,03
0,17
0,11
0,01
0,03
0,12
0,13
Total
0,89
0,84
0,05
Kiriging the
EQI
MSE (i)-MSE (ii)
Results and concluding remarks
„
In this research we have empirically compared both the traditional and the
pp
byy elaborating
g an EQI
Q for Madrid Cityy (Spain).
( p )
alternative approaches
„
The database includes 24 daily averaged (January 2008) datasets, one per hour.
„
Results indicate that in the hours when traffic is denser and/or heating is working
th alternative
the
lt
ti procedure
d
h a notable
has
t bl advantage,
d
t
while
hil in
i the
th restt off the
th hours
h
both procedures generate similar results. But, the most important insight is that
the stronger the spatial dependencies are the bigger the advantage of the
alternative procedure is.
„
This case study empirically confirms an important aspect of the geostatistical
theory when dealing with several variables and the objective is to transform a
multivariate problem in a univariate one: In general,
general prediction MSE is lesser
when interpolating the variables involved in a linear combination and then
elaborating such a linear combination. But the literature continues to obviate this
important result and the usual procedure is to first elaborating the linear
combination
b
and
d then
h interpolating
l
it.