Neighborhood green and services diversity effects on land prices: Evidence from a multilevel hedonic analysis in Luxembourg

Abstract

The article aims at revealing the role of green space diversity and the mix of neighborhood services on the price of residential land in Luxembourg. We use a multilevel approach to estimate a hedonic model in order to benefit from the hierarchical structure of the data and to reveal spatial heterogeneity in the valuation of these neighborhood qualities. In addition to standard accessibility and socio-economic variables, we include geographical variables in the form of neighborhood mix indices and a Shannon diversity index of land-uses. Via a spatial cross-regressive specification we also test whether our nested levels are able to capture most of the spatial dependence. Our results show that the presence of a mix of services and green space does not directly impact prices, but that the diversity of land-uses (Shannon index) matters, and has negative effects when considered within immediate proximity and positive effects within a walking distance. Land use effects however vary spatially and emphasize the contrast between regions that are particularly attractive and picturesque, and the former industrial conurbation. In our case we also show the ability of the multilevel approach to capture spatial auto-correlation effects.

Full text

Landscape
and
Urban
Planning
143
(2015)
100–111
Contents
lists
available
at
ScienceDirect
Landscape
and
Urban
Planning
j
o
ur
na
l
ho
me
pag
e:
www.elsevier.com/locate/landurbplan
Neighborhood
green
and
services
diversity
effects
on
land
prices:
Evidence
from
a
multilevel
hedonic
analysis
in
Luxembourg
Marie-Line
Glaesenera,b,1,
Geoffrey
Carusoa,∗
aInstitute
of
Geography
and
Spatial
Planning,
Belval,
Luxembourg
bLuxembourg
Institute
of
Socio-Economic
Research,
Belval,
Luxembourg
h
i
g
h
l
i
g
h
t
s
•First
multilevel
hedonic
model
with
landscape
amenities
and
neighbourhood
services.
•Opposite
effects
of
landscape
diversity
at
different
distances.
•Spatial
heterogeneity
effects
in
the
valuation
of
local
land-use
diversity.
•No
impact
of
services
diversity
at
sub-municipal
scale.
•Multilevel
model
captures
context
effects
and
spatial
autocorrelation.
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
13
December
2014
Received
in
revised
form
30
May
2015
Accepted
5
June
2015
Keywords:
Hedonic
pricing
Multilevel
approach
Cross-regressive
model
Land-use
diversity
Neighborhood
amenities
a
b
s
t
r
a
c
t
The
article
aims
at
revealing
the
role
of
green
space
diversity
and
the
mix
of
neighborhood
services
on
the
price
of
residential
land
in
Luxembourg.
We
use
a
multilevel
approach
to
estimate
a
hedonic
model
in
order
to
benefit
from
the
hierarchical
structure
of
the
data
and
to
reveal
spatial
heterogeneity
in
the
valu-
ation
of
these
neighborhood
qualities.
In
addition
to
standard
accessibility
and
socio-economic
variables,
we
include
geographical
variables
in
the
form
of
neighborhood
mix
indices
and
a
Shannon
diversity
index
of
land-uses.
Via
a
spatial
cross-regressive
specification
we
also
test
whether
our
nested
levels
are
able
to
capture
most
of
the
spatial
dependence.
Our
results
show
that
the
presence
of
a
mix
of
services
and
green
space
does
not
directly
impact
prices,
but
that
the
diversity
of
land-uses
(Shannon
index)
matters,
and
has
negative
effects
when
considered
within
immediate
proximity
and
positive
effects
within
a
walking
distance.
Land
use
effects
however
vary
spatially
and
emphasize
the
contrast
between
regions
that
are
particularly
attractive
and
picturesque,
and
the
former
industrial
conurbation.
In
our
case
we
also
show
the
ability
of
the
multilevel
approach
to
capture
spatial
auto-correlation
effects.
©
2015
Elsevier
B.V.
All
rights
reserved.
1.
Introduction
The
spatial
distribution
of
residential
land
values
around
cities
mainly
arises
from
trading-off
accessibility
to
jobs
against
housing
consumption
(Alonso,
1964;
Fujita,
1989).
However
neighborhood
qualities
and
landscape
features
add
up
to
this
trade-off
and
add
further
complexity
to
the
spatial
structure
of
land
values.
Cheshire
and
Sheppard
(1995)
emphasized
the
need
to
consider
a
broad
∗Corresponding
author.
Tel.:
+352
46
66
44
6625.
E-mail
addresses:
marie-line.glaesener@liser.lu
(M.-L.
Glaesener),
geoffrey.caruso@uni.lu
(G.
Caruso).
1The
work
presented
in
this
paper
is
part
of
the
outcome
of
the
Ph.D
thesis
under-
taken
at
the
University
of
Luxembourg
in
the
Institute
of
Geography
and
Spatial
Planning
between
2009
and
2014.
range
of
location-specific
attributes,
and
over
the
last
20
years
numerous
studies
have
attempted
to
include
local
amenities
in
the
analysis
of
land
prices
to
better
understand
how
much
these
local
features
are
decisive
in
residential
choice.
Since
urban
growth
pat-
terns
challenge
sustainability
and
social
goals,
and
many
urban
and
land-use
planning
actions
seek
to
address
them
at
the
local
scale
(municipality
or
smaller),
it
is
particularly
important
for
the
suc-
cess
of
urban
policies
that
the
benefits
of
local
amenities
are
well
understood
to
design
effective
and
acceptable
neighborhood
plans.
Of
particular
attention
here
is
the
presence,
spatial
distribution
and
diversity
of
both
land-uses
and
green
space,
and
neighborhood
retail
and
services
around
residential
places.
Recent
theoretical
advances
have
shown
that
the
local
arrange-
ment
of
green
space
impact
on
urban
form
and
its
scattered
or
leapfrogging
nature
(Caruso,
Peeters,
Cavailhès,
&
Rounsevell,
2007;
Caruso
et
al.,
2011).
Brueckner,
Thisse,
and
Zenou
(1999)
http://dx.doi.org/10.1016/j.landurbplan.2015.06.008
0169-2046/©
2015
Elsevier
B.V.
All
rights
reserved.

M.-L.
Glaesener,
G.
Caruso
/
Landscape
and
Urban
Planning
143
(2015)
100–111
101
also
showed
the
impact
of
urban
versus
exurban
amenities
on
the
income
sorting
of
households
and
it
is
well-known
since
Tiebout
(1956)
that
the
provision
of
local
public
goods
is
an
important
aspect
of
residential
competition.
On
the
empirical
side,
results
are
less
clearly
conducive
(see
below)
but
there
is
a
trend
to
use
more
micro-scale
data
and
GIS
to
better
measure
these
elements.
Many
hedonic
studies
now
embed
local
amenities
and
proximity
to
ser-
vices
or
shops.
However
very
few
consider
the
diversity
of
both
services
and
land-uses
and
very
few
look
at
the
spatial
heterogene-
ity
of
their
valuation.
We
can
hypothesize
that
those
local
effects
vary
considerably
with
the
wider
landscape
or
socio-economic
con-
text,
even
after
controlling
for
the
most
important
socio-economic
drivers
that
would
proxy
a
Tiebout
effect
and
the
center-periphery
contrast.
We
contribute
such
an
analysis
here
using
developable
land
transactions
in
the
Grand
Duchy
of
Luxembourg
as
a
case
study.
We
use
a
multilevel
approach,
which
is
still
uncommon
in
spatial
hedonic
analysis.
Our
expectation
is
to
capture
addi-
tional
contextual
effects
after
controlling
for
neighborhood
scale
attributes
and
standard
center-periphery
trade-off.
Moreover
the
structure
of
the
data
available
in
Luxembourg
lends
itself
to
the
multi-scale
approach.
The
remainder
of
the
paper
is
organized
as
follows:
in
Section
2
we
conduct
a
short
review
of
the
empirical
literature
that
is
most
directly
linked
to
our
thematic
scope
and
methods.
Then
we
present
the
study
area
and
the
different
data-sets
(Section
3).
The
imple-
mentation
of
the
approach
is
then
described
as
applied
to
our
case
study
(Section
4).
Results
are
discussed
in
Section
5
before
conclud-
ing.
2.
Literature
review
2.1.
The
value
of
neighborhood
services
and
green
We
review
here
some
empirical
literature
on
the
value
of
prox-
imity
and
diversity
of
both
neighborhood
services
and
land-uses.
This
review
is
not
meant
to
be
exhaustive
but
to
pick
up
the
ratio-
nale
for
our
empirical
experiment
and
the
closest
related
work.
The
impact
of
local
public
goods
and
externalities
within
the
city
has
been
largely
discussed
since
Tiebout
(1956).
Residential
land
consumers
benefit
from
the
presence
of
different
local
urban
amenities
(e.g.:
public
services,
education
and
sports
facilities,
health
care,
retail).
Fujita
and
Thisse
(2013)
claim
that,
as
for
com-
muting
to
work,
consumers
rather
prefer
short
trips
to
retail
and
services.
Moreover,
the
spatial
pattern
of
exogenous
amenities
in
a
city
(e.g.:
natural
and
historical
amenities)
impacts
on
the
location
of
different
income
groups
within
the
urban
area
(Brueckner
et
al.,
1999).
Several
hedonic
pricing
studies
have
investigated
the
impact
on
property
values
of
distance
to
different
local
urban
amenities
(Des
Rosiers
&
Thériault,
2006;
Öner,
2013;
Thériault,
Des
Rosiers,
&
Vandersmissen,
1999;
Youssoufi,
2011).
Urban
amenities
generally
accounted
for
are,
among
others,
measures
of
school
quality
(Clapp,
Nanda,
&
Ross,
2008;
Kiel
&
Zabel,
2008;
Thériault
et
al.,
1999;
Uyar
&
Brown,
2007),
distance
to
public
open-space
(Espey
&
Owusu-Edusei,
2001;
Mahmoudi,
Hatton
MacDonald,
Crossman,
Summers,
&
van
der
Hoek,
2013;
Wu
&
Dong,
2014)
or
the
proximity
of
retail
and
services
(Thériault,
Des
Rosiers,
&
Joerin,
2005;
Youssoufi,
2011;
Öner,
2013).
Besides
prox-
imity
to
different
local
urban
amenities,
a
rich
diversity
of
the
offer
has
been
shown
to
have
a
positive
marginal
effect
on
individuals’
utility
(Brueckner
et
al.,
1999;
Youssoufi,
2011).
Considering
explic-
itly
the
diversity
of
urban
amenities
is
however
not
so
frequent
in
the
hedonic
pricing
context
and
we
do
not
know
of
studies
that
would
have
analyzed
its
spatial
variation
in
a
multi-scalar
context.
The
role
of
local
green
and
diversity
has
been
addressed
in
many
hedonic
pricing
studies.
Over
52
studies
addressing
the
valuation
of
open-space,
mainly
at
micro-scale,
have
been
identified
and
analyzed
in
Brander
and
Koetse’s
(2011)
meta-analysis.
These
stud-
ies
include
either
distance
measures
to
different
green
amenities
(Cho,
Poudyal,
&
Roberts,
2008;
Des
Rosiers,
Thériault,
Kestens,
&
Villeneuve,
2002;
Kestens,
Thériault,
&
Des
Rosiers,
2004;
Shultz
&
King,
2001)
and/or
consider
landscape
amenities
in
varying
buffer
zones
(Cavailhès
et
al.,
2007;
Kadish
&
Netusil,
2012;
Melchiar
&
Kaprovà,
2013;
Sander,
Polasky,
&
Haight,
2010;
Youssoufi,
2011).
Using
the
same
data-set
as
herein,
Glaesener
(2014)
has
tested
for
these
spatial
proximity
effects
at
aggregated
scale
but
showed
that
the
lack
of
spatial
precision
for
this
particular
data-set
does
not
allow
to
capture
close
proximity
effects
with
sufficient
robust-
ness.
Besides
proximity
to
different
green
amenities,
the
purchase
decision
of
land
consumers
is
also
influenced
by
the
configuration
of
the
neighboring
land-uses.
Geoghegan,
Wainger,
and
Bockstael
(1997)
show
that
increasing
land-use
diversity
affects
property
val-
ues
in
two
ways:
negatively
as
they
introduce
higher
chances
of
negative
visual
and
noise
externalities,
but
in
the
meantime
posi-
tively
as
diversity
may
implicitly
signify
the
proximity
of
important
local
urban
amenities.
Based
on
their
findings,
increased
land-use
diversity
is
expected
to
be
valued
negatively
in
immediate
prox-
imity,
while
within
walking
distance
a
positive
impact
is
expected.
Furthermore,
spatial
variation
in
the
marginal
effects
of
land-use
diversity
can
be
expected.
Geoghegan
et
al.
(1997)
show
that
diver-
sity
is
valued
differently
by
consumers
with
distance
to
CBD
and
that
it
is
generally
not
a
desirable
feature
in
the
suburban
area.
In
this
study,
we
follow
this
literature
steam
on
pricing
the
presence
and
proximity
of
land-uses.
We
also
consider
the
spatial
hetero-
geneity
(as
Geoghegan
et
al.,
1997
or
Cho
et
al.,
2008),
but
we
do
so
via
a
multi-scale
setting
that
fits
our
data
and,
we
expect,
can
identify
non-stationary
marginal
effects
across
space.
2.2.
Spatial
effects
and
the
multilevel
approach
The
hedonic
pricing
method
(Rosen,
1974)
is
applied
to
estimate
the
implicit
value
of
the
non-market
attributes
composing
land
prices,
from
which
consumers
obtain
utility,
under
the
assump-
tion
of
a
unitary
market
in
equilibrium.
This
assumption
however
prescribes
that
the
implicit
prices
of
the
attributes
are
invariant.
However,
market
segmentation
might
arise
when
consumers’
demand
for
a
particular
structural
or
location-specific
characteris-
tic
is
highly
inelastic
and
that
the
preference
for
this
characteristic
is
shared
by
many
other
consumers
(Goodman
&
Thibodeau,
1998).
Such
market
segmentation
usually
causes
the
emergence
of
sub-
markets,
in
which
“persistent
and
significant
disparities
in
attribute
prices
are
present
across
housing
bundles
and
urban
space”
(Orford,
2000,
p.1645).
Spatial
heterogeneity
is
likely
to
arise
if
the
price-
attribute
relationship
varies
spatially
by
such
sub-markets,
so
if
the
marginal
price
of
a
plots
characteristics’
varies
substantially
with
its
location
in
space
(Le
Gallo,
2004).
Consequently
OLS
estimates,
imposing
spatial
homogeneity,
will
be
miss-specified
and
affect
the
validity
of
diagnostic
tests
(Anselin
&
Lozano-Gracia,
2009).
Differ-
ent
methods
to
account
for
this
spatial
heterogeneity
have
been
considered
in
the
hedonic
context
(i.e.:
geographically
weighted
regression;
Cho
et
al.,
2008,
spatial
expansion
method;
Geoghegan
et
al.,
1997).
Besides
spatial
heterogeneity,
spatial
dependence
might
also
bias
estimation
results,
and
different
auto-regressive
estimation
methods
have
been
developed
to
account
for
this
(among
oth-
ers
Anselin,
1988;
Elhorst,
2010;
Ward
&
Gleditsch,
2008).
These
models
should
allow
to
identify
and
correct
for
the
potential
bias
induced
by
spatial
dependence
and
have
been
largely
applied
in
hedonic
literature,
that
will
not
be
further
reviewed
here.
According
to
Orford
(2000)
the
auto-regressive
functions
devel-
oped
in
spatial
econometrics
literature
can
be
seen
as
“technical
fixes”
to
the
problems
of
modeling
spatial
data,
especially
as
they

102
M.-L.
Glaesener,
G.
Caruso
/
Landscape
and
Urban
Planning
143
(2015)
100–111
do
not
account
for
the
issues
related
to
spatial
heterogeneity.
As
an
alternative,
Orford
(2000)
proposes
the
multilevel
approach.
This
approach
has
been
widely
applied
among
others
in
the
field
of
education
studies
(Hill
&
Rowe,
1996)
and
health
research
(Chaix,
Merlo,
&
Chauvin,
2005;
Duncan,
Jones,
&
Moon,
1998;
Lebel,
Kestens,
Clary,
Bisset,
&
Subramanian,
2014;
Park
&
Kim,
2014)
and
with
increasing
interest
as
well
from
other
economic
fields
(Fontes,
Simões,
De
Oliveira,
&
Hermeto,
2009;
Meijer
&
Rouwendal,
2006),
for
instance
to
evaluate
business
performance
and
strategies
at
different
levels
(Favero
&
Lopes,
2011)
or
the
rela-
tion
between
infrastructure
and
income
convergence
(Almeida
&
Guimarães,
2014).
To
date
there
have
been
few
implementations
of
this
approach
in
the
hedonic
pricing
context.
Moreover,
to
the
best
of
our
knowledge,
existing
applications
have
not
considered
residential
land
but
focused
on
housing
markets.
The
multilevel
modeling
approach
accounts
for
the
hierarchical
data
structure
by
modeling
price
variability
at
each
of
the
spatial
levels.
In
addition,
it
allows
individual
observations
belonging
to
a
particular
spatial
unit
to
be
more
similar
than
a
random
sam-
ple
(Jones,
1991).
The
multilevel
approach
models
the
structure
of
the
variation
not
accounted
for
by
the
explanatory
variables
and
it
does
not
assume
a
constant
variance
captured
by
a
single
error
term
(Orford,
2000).
The
assumption
of
a
unitary
housing
market
is
relaxed
and
estimation
biases
related
to
spatial
effects
should
be
captured
by
this
approach.
With
the
independence
assumption
relaxed
and
the
intra-group
correlation
explicitly
modeled,
more
efficient
estimates
are
obtained
and
thus
inference
becomes
more
reliable
(Chasco
&
Le
Gallo,
2013).
Goodman
and
Thibodeau
(1998)
introduced
the
concept
of
multilevel
modeling
in
the
hedonic
pricing
context
as
a
method
to
delineate
housing
sub-markets.
Orford
(2000)
relies
on
this
approach
to
investigate
means
to
contextualize
the
hedonic
spec-
ification
to
capture
additional
spatial
dynamics
of
local
housing
markets
and
to
model
explicitly
the
processes
leading
to
spa-
tial
auto-correlation
in
house
prices.
Chasco
and
Le
Gallo
(2013)
implement
a
three-level
multilevel
hedonic
model
to
measure
the
marginal
impact
on
house
prices
of
objective
and
subjective
meas-
ures
of
air
and
noise
pollution
in
down-town
Madrid.
Besides
dwelling
size,
they
consider
the
noise
and
pollution
variables
as
random
effects
at
different
scales.
They
find
that
air
pollution
is
only
varying
randomly
at
the
highest
neighborhood
level,
while
noise
pollution
is
perceived
mainly
at
the
census
tract.
Chasco
and
Le
Gallo’s
(2013)
results
confirm
the
local
nature
of
noise
in
com-
pared
to
air
pollution.
Djurdjevic,
Eugster,
and
Haase
(2008)
aim
mainly
at
accounting
for
aggregated
data
at
two
levels
and
they
allow
the
marginal
effect
of
dwelling
size
to
vary
across
munic-
ipalities.
Brunauer
(2013)
apply
a
four
level
structured
additive
regression
model,
incorporating
spatial
effects
and
complex
inter-
actions
at
the
different
levels,
to
decompose
the
distribution
of
the
spatial
heterogeneity
effect
over
Austria.
They
highlight
the
impor-
tance
of
the
inclusion
of
neighborhood
attributes
to
explain
spatial
heterogeneity.
Doubts
have
been
raised
on
the
multilevel
model’s
ability
to
cap-
ture
all
spatial
effects.
With
regard
to
spatial
error
dependence
in
multilevel
models,
Elhorst
and
Zeilstra
(2007)
made
first
advances
to
combine
the
multilevel
framework
to
the
more
standard
spa-
tial
econometric
error
model.
Multilevel
models
with
spatial
fixed
and
spatial
random
effects
have
been
discussed
by
Corrado
and
Fingleton
(2011),
however
raising
several
issues
related
to
the
estimation
of
such
spatial
multilevel
models.
More
recently,
Park
and
Kim
(2014)
applied
a
spatially
filtered
multilevel
model
using
eigenvectors
function
as
additional
explanatory
variables.
Almeida
and
Guimarães
(2014)
tested
several
spatial
multilevel
models
and
found
that
the
spatial
effects,
operating
in
the
relationship
between
infrastructure
and
income
convergence,
were
captured
only
by
the
multilevel
spatial
autoregressive
(SAR)
model.
In
the
context
of
neural
tube
defects,
Ren,
Wang,
Liao,
and
Zheng
(2013)
relied
on
a
multilevel
model
with
spatial
autocorrelated
errors
structure
and
show
how
these
account
for
remaining
spatial
error
dependence.
In
the
hedonic
pricing
context,
Chasco
and
Le
Gallo
(2012)
illus-
trate
that
the
multilevel
approach
only
accounts
for
some
part
of
spatial
dependence
by
adding
spatial
multipliers.
Following
Chasco
and
Le
Gallo
(2012),
the
robustness
of
our
results,
with
regard
to
spatial
dependence,
will
be
tested
via
a
cross-regressive
multilevel
model.
Overall
the
originality
of
our
paper
is
to
test
the
ability
of
the
multilevel
model
to
identify
spatial
heterogeneity
in
estimating
the
marginal
effects
of
local
amenities
on
land
prices;
in
particular
neighborhood
services
and
land-use
diversity.
3.
Study
area
and
data
3.1.
Context
In
a
context
of
sustained
economic
and
demographic
growth
the
part
of
built-up
surface
has
almost
doubled
in
the
last
20
years
(Chilla
&
Schulz,
2011).
The
distribution
of
population
and
its
growth
is
not
homogeneous
in
space,
population
densities
and
land
prices
are
declining
from
the
capital-city,
namely
Luxem-
bourg
(Fig.
A1
Map
A).
Besides
the
agglomeration
of
Luxembourg,
strongest
population
growth
is
mainly
observed
in
the
more
rural
and
remote
regions
of
the
country.
The
evolution
of
these
fun-
damental
parameters
and
their
spatial
distribution
illustrate
the
ongoing
outward
urban
growth
in
Luxembourg,
leading
to
a
mixed
periurban
belt
under
strong
under
urban
influence
(high
com-
muting
rates)
with
a
rural
character
(low
population
densities
and
residential
areas
scattered
within
agricultural
land)
(Caruso,
2005;
Cavailhès,
Frankhauser,
Peeters,
&
Thomas,
2004a;
Cavailhès,
Peeters,
Sekeris,
&
Thisse,
2004b;
Irwin
&
Bockstael,
2007).
Local
authorities
in
Luxembourg
are
aware
of
these
periurban-
isation
trends
and
a
more
careful
management
of
open-space
has
been
an
important
issue
in
recent
planning
policies.
The
“Pro-
gramme
Directeur
de
l’Aménagement
du
Territoire”
(PDAT)
(MIAT,
2003)
suggests
to
strengthen
secondary
urban
centers
and
encour-
ages
households
to
settle
in
more
compact
and
denser
urban
areas
in
predefined
regional
centers
(“decentralized
concentration”;
MIAT,
2004).
More
specifically
the
PDAT
aims
at
directly
influenc-
ing
residential
preferences
to
reach
these
goals.
A
recent
evaluation
of
the
planning
measures
(CEPS/INSTEAD,
2008)
revealed
however
that
these
measures
were
of
limited
success,
mainly
because
the
fundamentals
of
urban
growth
were
underestimated
in
first
place.
Moreover,
we
can
argue
about
the
acceptability
of
measures
that
specifically
target
preference
choices
with
regard
to
the
quality-
of-life
and
neighborhoods.
In
this
perspective
there
is
a
need
in
Luxembourg
for
more
detailed
insights
on
the
land
consumers’
preferences
for
the
characteristics
of
the
local
geographical
con-
text.
3.2.
Data
Quantitative
research,
on
real
estate
market
in
Luxembourg,
is
to
date
mainly
exploratory
and
aggregated
at
municipal
scale
(e.g.:
Decoville,
Feltgen,
&
Durand,
2013).
Due
to
data
privacy
concerns,
the
location
of
the
residential
land
transactions
was
only
available
at
sub-municipal
(section)
level.
Further,
socio-economic
variables
based
on
census
data
are
only
available
at
municipal
scale
the
second
important
administrative
and
planning
level
in
Luxembourg
(Chilla
&
Schulz,
2011).
With
regard
to
the
parcels’
structural
information
at
transaction
scale,
we
were
thus
confronted
to
three
hierarchically
nested
levels:
transactions,
sections
and
municipalities.

M.-L.
Glaesener,
G.
Caruso
/
Landscape
and
Urban
Planning
143
(2015)
100–111
103
We
describe
variables
at
each
level
below
and
descriptive
statis-
tics
are
given
in
Appendix
Table
A1.
Four
groups
of
variables
were
considered
in
order
to
account
for
the
structural
characteristics,
accessibility
to
Luxembourg-city,
the
neighborhood
variables
and
eventually
the
socio-economic
controls.
We
show
here
our
final
model
specification
for
these
effects.
Further
details
can
be
found
in
Glaesener
(2014)
and
the
summary
statistics
for
the
explanatory
variables
are
illustrated
in
Appendix
Table
A1.
3.2.1.
Level
One:
Transactions
The
developable
land
transactions,
registered
at
the
notaries
between
January
2007
and
December
2011,
were
provided
by
the
Administration
of
Deeds
(AED).
After
different
steps
of
data
clean-
up,
the
data-set
contains
6367
observations,
on
average
19.83
are
registered
per
section
and
57.16
per
municipality.
Their
spatial
dis-
tribution
is
illustrated
in
Appendix,
Fig.
A1
Map
A.
The
transaction
price
was
deflated
to
the
value
of
January
2007-euros
based
on
the
consumer
price
index
generated
on
a
monthly
basis
by
the
National
Statistics
Institute
(STATEC).
Limited
information
on
the
structural
characteristics
of
the
parcels
was
available.
Property
size
is
con-
sidered
to
estimate
the
marginal
effect
of
an
additional
are
to
a
mean-sized
parcel.
In
multilevel
hedonic
literature,
a
random
slope
is
generally
allowed
for
the
price-size
relationship
at
the
higher
level(s).
Allowing
the
marginal
effect
of
size
to
vary
at
higher
spatial
level(s),
hence
a
coefficient
per
spatial
unit,
is
expected
to
account
for
size
related
heteroskedasticity
(Djurdjevic
et
al.,
2008;
Jones
&
Bullen,
1994;
Orford,
2000;
Treg,
2010).
The
random
intercept
and
slope
models
are
further
discussed
in
Sections
4.2
and
4.3.
Further,
a
binary
variable
is
included
to
identify
plots
sold
with
a
building
plan
(dVFA),
since
they
were
found
to
register
higher
unit
prices
and
to
be
of
smaller
size.
dVFA
transactions
are
assumed
to
be
generally
sold
by
professional
real
estate
developers
to
individual
end-users,
mostly
in
the
framework
of
larger
development
projects.
This
variable
is
thus
expected
to
capture
for
the
marginal
impact
of
the
implication
of
professional
developers
in
a
land
transaction.
3.2.2.
Level
Two:
Sections
3.2.2.1.
Accessibility
to
CBD.
Following
urban
economic
literature,
access
to
the
main
employment
center
is
considered
as
the
major
determinant
of
property
prices
(Alonso,
1964;
Fujita,
1989).
There-
fore,
time-distance
to
Luxembourg-city
was
included
in
two
ways.
First,
travel-time
by
road
network
(tLUXci)
was
computed
based
on
an
application
generalizing
the
itinerary
function
of
Google
Maps®
(Medard
de
Chardon
&
Caruso,
2010).
Second,
travel-time
by
public
transport
(tLUXpi)
was
generated
via
Mobiliteit.lu®,
an
official
online
schedule
engine
for
public
transport
in
Luxembourg.
These
travel-time
measures
are
expected
to
identify
the
negative
marginal
effects
of
distance
to
Luxembourg-city
and
furthermore
provide
insights
into
differences
in
the
valuation
of
individual
and
public
transport.
3.2.2.2.
Local
urban
amenities.
The
urban
amenity
data-set
was
generated
based
on
different
official
and
on-line
sources
and
represents
the
main
retail
and
public
service
opportunities.
To
identify
the
marginal
impact
of
service
diversity
and
to
avoid
mul-
ticollinearity
issues,
a
diversity
index
(DI)
was
generated
following
Youssoufi
(2011).
The
diversity
index
is
formalized
in
Eq.
(1),
where
ncdesignates
the
quantity
of
observations
for
the
cth category
and
n
the
total
amount
of
retail
and
service
opportunities
per
section.
DI
=
c
nc
n2
(1)
The
different
local
urban
amenities
have
been
weighted
accord-
ing
to
the
frequency
of
their
use.
Further
information
on
the
variables
considered
and
the
weighting
can
be
found
in
Glaesener
(2014).
Since
consumers
are
assumed
to
value
proximity
to
a
diverse
offer
of
local
urban
amenities
a
higher
DI
is
expected
to
be
val-
ued
positively
by
land
consumers
and
should
capture
an
urban
concentration
effect.
3.2.2.3.
Green
and
land-use
diversity
measures.
The
different
land-
use
diversity
measures
are
based
on
the
land-use
data
provided
by
the
Land
Registry
(Administration
du
Cadastre
et
de
la
Topographie,
2008a,
2008b).
As
discussed
earlier,
green
land-use
diversity
is
expected
to
be
considered
by
land
consumers
in
their
purchase
decision.
In
this
perspective,
based
on
the
index
displayed
in
Eq.
(1),
a
diversity
index
for
green
land-use
(DIGreen)
was
generated
with
based
on
the
area
(n)
occupied
by
different
green
land-uses
(forest,
brushwood,
watershed,
rivers,
vineyards,
gardens,
pastures
and
crop-land
(c))
was
generated.
The
index
varies
between
0
and
1;
with
1
being
maximum
diversity
and
0
standing
for
the
pres-
ence
of
a
single
land-use
(Appendix
Fig.
A1
Map
B).
DIGreen
should
identify
the
marginal
effect
of
green
land-use
diversity
on
land
price.
Further,
to
account
for
differences
in
the
valuation
of
diver-
sity
with
regard
to
proximity
to
the
available
land,
the
Shannon
land-use
diversity
index
was
generated.
This
diversity
index
con-
siders
on
the
one
hand
the
richness
of
land-uses
and
on
the
other
hand
their
proportional
area
distribution,
the
evenness
(Jenness,
Brost,
&
Beier,
2013).
The
Shannon
diversity
indices
were
com-
puted
using
the
open-source
add-in
provided
by
Jenness
et
al.
(2013).
Two
extents
were
considered
(100
m
and
1000
m)
around
all
plots
registered
as
available
(AP),
similar
to
what
was
done
at
micro-scale
in
previous
studies
(Baranzini,
Ramirez,
Schaerer,
&
Philippe,
2008;
Geoghegan
et
al.,
1997;
Luke,
2004;
MIAT,
2003;
Mieszkowski
&
Mills,
1993;
Peeters
et
al.
2015;
Treg,
2010;
Turner,
2005;
Wu
&
Dong,
2014;
Youssoufi
&
Foltête,
2013).
Follow-
ing
Geoghegan
et
al.
(1997),
the
100
m
radius
should
capture
the
effect
of
diversity
in
the
immediate
neighborhood
and
the
1000
m
radius
the
effect
of
increased
diversity
in
walking
dis-
tance
to
AP
(Appendix
Fig.
A1
Maps
C
and
D).
In
general,
a
positive
marginal
effect
of
increased
land-use
diversity
price
is
expected
within
walking
distance
(mAPsh1000),
while
in
the
close
prox-
imity
(mAPsh100)
the
effect
is
expected
to
be
negative.
These
marginal
effects
are
expected
to
be
non-stationary
through
space
and
will
hence
be
considered
in
the
fully
random
model,
see
later.
Finally,
the
ratio
of
available
plots
(rAP)
relative
to
the
exist-
ing
built-up
area
was
considered.
This
ratio
is
based
on
the
area
of
all
available
plots
that
is
divided
by
the
sum
of
all
developable
land
available
and
the
parcels
occupied
by
residential
land-use.
This
variable
should
on
the
one
hand
allow
to
account
for
the
supply
of
land
and
on
the
other
hand
provide
insights
into
its
marginal
impact
on
price
that
could
be
either
positive
(Nilsson,
2014;
Ooi
&
Le,
2013)
or
negative
(Kiel
&
Zabel,
2008;
Liu
&
Hite,
2013).
3.2.3.
Level
three:
Municipalities
Individuals
value
the
social
and
economic
composition
of
their
neighborhood
and
have
preferences
for
more
homogeneous
neighborhoods
(Mieszkowski
and
Mills,
1993);
this
neighborhood
context
should
be
controlled
for
to
approximate
spatial
hetero-
geneity
and
allow
to
capture
some
additional
contextual
effects
at
the
municipal
scale.
Socio-economic
neighborhood
character-
istics
in
hedonic
pricing
models
considered
in
this
study
were
provided
by
the
National
Statistic
Agency
(STATEC)
at
municipal
scale
(Table
A1).
In
this
context,
unemployment
rate
or
median
income
are
frequently
considered
as
a
proxy
for
disposable
income
(Chasco
&
Le
Gallo,
2013;
Treg,
2010)
while
age
or
education
level
(Beron,
Murdoch,
&
Thayer,
1999;
Brunauer,
2013;
Chasco
&
Le

104
M.-L.
Glaesener,
G.
Caruso
/
Landscape
and
Urban
Planning
143
(2015)
100–111
Gallo,
2013;
Treg,
2010)
are
usually
considered
as
a
proxy
for
social
composition
or
structural
weakness
of
a
neighborhood.
The
part
of
population
above
65
years
and
unemployment
rate
are
expected
to
characterize
residents’
socio-economic
weaknesses
and
to
have
a
negative
marginal
impact
on
land
prices.
Furthermore
population
density
and
its
variation
rate
may
be
seen
as
a
measure
for
demand
and
relative
scarcity
of
residential
land
(Treg,
2010;
Brander
&
Koetse,
2011).
Therefore,
population
variation
between
2001
and
2007
and
density
should
approximate,
respectively,
the
marginal
effect
of
a
high
demand
for
real
estate
and
the
scarcity
of
undevel-
oped
space.
Information
on
income
or
the
level
of
education
were
not
available
to
this
research.
4.
Methods
The
standard
procedure
in
the
multilevel
modeling
literature
is
to
start
with
an
Unconditional
Model
(UM)
to
determine
whether
there
is
price
variability
at
the
three
levels
identified
in
our
data,
namely
the
transactions
(i),
the
sections
(j)
and
the
municipali-
ties
(k).
In
case
the
variances
equal
zero,
no
sub-market
effects
are
present
and
a
single-level
model
would
be
sufficient
to
the
data.
With
the
UM
confirming
price
variability
at
the
three
levels,
the
Random
Intercept
Model
(RIM)
is
estimated,
accounting
for
the
explanatory
variables
and
eventually
we
present
the
Fully
Random
Model
(FRM)
where
random
slopes
are
added
for
selected
explana-
tory
variables
for
which
we
want
to
identify
spatial
segments.
4.1.
Unconditional
model
(UM)
and
intraclass
correlation
coefficients
(ICC)
Under
UM
we
denote
a
multilevel
model
including
no
fixed
explanatory
variables
except
for
the
overall
intercept
(Jones
&
Bullen,
1993).
Different
intraclass
correlation
coefficients
(ICC)
can
be
computed
to
identify
at
degree
of
price
variability
of
the
differ-
ent
levels.
First,
the
‘level-two
ICC’
expresses
the
similarity
of
mean
section
prices
for
sections
within
a
same
municipality.
The
inter-
pretation
would
be
that
if
one
selects
randomly
two
sections
within
one
municipality
and
calculates
the
mean
transaction
price
in
one
of
the
two
sections,
the
average
transaction
price
in
the
other
sec-
tion
could
be
predicted
reasonably
accurately
(Snijders
&
Bosker,
1999).
Second,
the
‘ICC
for
level-two
(and
three)
relative
to
level-
one
expresses
the
likeness
of
transaction
prices
in
a
same
section
within
a
same
municipality,
measuring
cluster
homogeneity
Jones
and
Bullen
(1994).
4.2.
Random
intercept
model
(RIM)
In
the
RIM,
the
intercept
catches
random
effects,
considering
all
explanatory
variables
as
fixed
through
the
different
spatial
levels.
The
functional
form
of
hedonic
pricing
models
has
been
largely
dis-
cussed
in
literature
(Ahlfeldt,
2011;
Dube,
Des
Rosiers,
&
Thériault,
2011).
In
the
following
models
the
semi-log
functional
form
will
be
applied
following
the
approach
suggested
by
Verbeek
(2008),
often
applied
in
multilevel
modeling
context
(Chasco
&
Le
Gallo,
2013;
Giuliano,
Gorden,
Pan,
&
Park,
2010;
Shin,
Saginor,
&
Van
Zandt,
2011;
Treg,
2010).
We
will
estimate
a
three
level
RIM
that
can
be
denoted
as
follows:
Yijk =
000 +
ˇjkxijk +V00k+
U0jk +
Rijk(2)
The
dependent
variable
Yijk refers
to
the
natural
log
of
the
price
of
a
transaction
i
in
section
j
within
municipality
k,
with
a
single
explanatory
variable
ˇjkxijk and
000,
the
overall
intercept.
The
error
part
of
the
model
contains
three
random
terms
(V00k,
U0jk,
Rijk),
one
for
each
level
describing
the
differential
to
the
higher
level
inter-
cept.
With
Rijk,
the
error
term
at
level
one,
describing
the
differential
to
the
average
section
price;
U0jk and
V00kbeing,
respectively,
the
random
term
estimated
at
section
or
municipal
scale,
describing
the
differential
to
the
mean
municipal,
respectively,
to
the
overall
intercept.
The
level-one
error
term
(Rijk)
is
assumed
to
follow
a
nor-
mal
distribution,
with
mean
zero
and
constant
variance;
the
higher
level
residuals
(V00kand
U0jk)
are
assumed
to
be
independent
from
the
lower
level
residuals.
The
variance
between
transactions
within
sections
within
municipalities,
var(Rijk),
is
denoted
by
2.
2
0is
the
variance
of
the
mean
section
price
between
sections
within
munic-
ipalities
var(U0jk)
compared
to
mean
municipal
price
and
ϕ2
0is
the
variance
of
the
mean
price
between
municipalities,
var(V00k),
com-
pared
to
the
overall
mean
transaction
price.
The
RIM
implies
that
the
price-attribute
relationship
does
not
vary
according
to
the
different
levels;
however
this
relationship
can
differ
between
the
spatial
levels
in
more
ways
(Snijders
&
Bosker,
1999).
The
RIM
is
however
a
restrictive
specification
if
the
marginal
effect
of
the
explanatory
variables
varies
in
space.
4.3.
Fully
random
model
(FRM)
In
the
FRM,
the
explanatory
variables
can
vary
according
to
a
higher-level
distribution,
by
specifying,
in
the
three
level
con-
text,
one
or
two
additional
macro-models,
which
should
control
for
residual
heteroskedasticity
at
the
individual
level.
By
including
additional
macro-models
for
the
slope
for
the
two
higher
levels
to
Eq.
(1),
the
FRM
takes
the
following
form:
Yijk =
000 +
100xijk +
ˇjkxijk
+
(V10kxijk +
V00k+
U1jkxijk +
U0jk +
Rijk)
(3)
The
random
part
of
the
model
is
completed
by
two
additional
error
terms
(V10kxijk and
U1jkxijk ),
allowing
conclusions
on
the
marginal
effect
of
the
explanatory
variable
with
regard
to
the
inter-
cepts
of
the
higher
units;
100xijk describing
the
overall
slope.
Their
variances
are
denoted
var U1
jk=
2
1for
the
random
section
slope
and
var (V10
k)=
ϕ2
1for
the
municipal
slope.
The
covariance
terms
(cov(U0jk;
U1jk)
=
01
and
cov(V00k;
V10k)
=
ϕ01)
allow
the
random
intercepts
and
slopes
“to
co-vary
according
to
a
higher-level,
joint
distribution”
(Jones
&
Bullen,
1994,
p.257).
A
more
exhaustive
presentation
of
the
multilevel
approach
and
technique
can
be
found
in
Luke
(2004)
or
Snijders
and
Bosker
(1999)
and
with
focus
on
the
hedonic
model
specification
by
Jones
(1991),
Jones
and
Bullen
(1993,
1994),
Orford
(2000).
4.4.
Cross-regressive
multilevel
model
(CRMM)
To
test
the
multilevel
model’s
ability
to
account
for
spatial
auto-
correlation,
Chasco
and
Le
Gallo
(2012)
estimated
a
CRMM.
They
added
a
set
of
spatially
lagged
explanatory
variables
as
control
vari-
ables
and
concluded
that
they
were
not
able
to
fully
capture
the
spatial
auto-correlation
in
their
model.
This
approach
relies
on
the
‘spatial
multiplier’
model
as
presented
in
Anselin
(2003),
adding
to
the
right-hand-side
of
the
equation
a
set
of
spatially
lagged
explanatory
variables.
This
model
assumes
spatial
effects
within
the
observed
x
variables
only
(Morenoff,
2003).
As
the
spatial
lags
(Wxijk)
are
at
the
right-hand-side
of
the
equation,
there
will
not
be
an
endogeneity
problem
and
thus
the
model
can
be
estimated
via
multilevel
approach.
Yijk =
000 +
100xijk +
Wxijk +
(V10kxijk
+
V00k+
U1jkxijk +
U0jk +
Rijk)
(4)
If
the
multilevel
model
accounts
properly
for
spatial
auto-
correlation,
the
spatially
lagged
variables
should
not
be
significant
(Chasco
&
Le
Gallo,
2012).

M.-L.
Glaesener,
G.
Caruso
/
Landscape
and
Urban
Planning
143
(2015)
100–111
105
Table
1
OLS
and
fixed
effects.
Dependent
variable:
lnprice
OLS
(1)
RIM
(3)
FRM
(4)
CRMM
(5)
Level
1
Transaction
Intercept
12.420*** (0.007)
12.420*** (0.014)
12.420*** (0.016)
12.430*** (0.027)
lnSize
0.612*** (0.010) 0.613*** (0.011) 0.608*** (0.019) 0.608*** (0.019)
dVFA
0.188*** (0.017)
0.214*** (0.018)
0.230*** (0.017)
0.227*** (0.017)
Level
2
Section
tLUXci −0.012*** (0.001)
−0.013*** (0.002)
−0.014*** (0.002)
−0.013*** (0.002)
tLUXpi −0.003*** (0.001)
−0.002*(0.001)
−0.003*(0.001)
−0.003*(0.001)
DI
−0.030
(0.026)
−0.014
(0.042)
−0.029
(0.041)
−0.038
(0.041)
rAP
0.007*** (0.001) 0.005*(0.002) 0.005*(0.002) 0.005
(0.002)
mAPsh100
−0.297*** (0.070) −0.324** (0.113) −0.375*(0.138) −0.387** (0.116)
mAPsh1000
0.214*** (0.040)
0.178*(0.070)
0.187*(0.076)
0.239*** (0.066)
DIGreen
−0.142
(0.083)
0.005
(0.146)
−0.096
(0.140)
0.093
(0.168)
Level
3
Municipality
VarPop0701
−0.001
(0.001)
−0.001
(0.002)
−0.002
(0.002)
−0.002
(0.002)
pAbove65y
−0.006
(0.003)
−0.007
(0.006)
−0.007
(0.006)
−0.003
(0.008)
rUnemployment
−0.018** (0.006)
−0.009
(0.012)
−0.020
(0.012)
−0.008
(0.015)
PopDens
0.000*** (0.000)
0.000** (0.000)
0.000** (0.000)
0.000*(0.000)
Spatial
lags
dVFA
−0.084
(0.119)
DI
−0.031
(0.081)
rAP
−0.002
(0.004)
DIGreen
−0.419
(0.276)
VarPop0701
−0.001
(0.004)
pAbove65y
−0.007
(0.012)
rUnemployment
−0.015
(0.018)
AIC
9674
9580
9323
9346
Log
Likelihood
−4822
−4773
−4638
−4642
Moran’s
I
0.025*** −0.009
−0.008
−0.007
Signif.
codes:
p
<
0.1; *p
<
0.05; ** p
<
0.01-, *** p
<
0.000;
(standard
errors).
To
identify
and
test
for
spatial
relationships
that
might
exist
between
residential
land
transactions
and
to
generate
the
spatial
lags
for
the
selected
explanatory
variables,
a
contiguity
based
spa-
tial
weight
matrix
(SWM)
was
generated.
As
from
the
521
sections,
only
321
register
more
than
three
transactions,
hence
some
iso-
lated
sections
appear
on
the
section
map
(Appendix:
Fig.
A1,
maps
B–D).
In
previous
research,
the
continuity
matrix
at
section
scale
was
identified
as
translating
the
spatial
relationship
among
obser-
vations
best.
By
the
contiguity
matrix,
non-zero
weights
are
defined
between
all
transactions
within
a
same
section
as
well
as
with
the
sections
sharing
a
border
(if
available).
We
consider
that
obser-
vations
are
not
neighbors
to
themselves
and
row-standardize
the
matrix.
Overall
2.24%
non-zero
weights
and
on
average
142.88
links
per
observation
are
counted.
5.
Results
We
first
discuss
the
results
of
the
single
level
model
(Section
5.1)
and
the
related
spatial
tests
(Table
2).
In
Section
5.2,
we
present
the
results
of
the
multilevel
models
with
a
stepwise
introduction
of
random
intercepts
and
slopes,
of
corresponding
spatial
tests
and
of
the
cross-regressive
multilevel
model.
Fixed
and
random
effects
can
be
found,
respectively,
in
Tables
1
and
3.
Municipal
random
effects
are
illustrated
in
Figs.
1
and
2.
Finally,
we
discuss
marginal
effects
in
Table
4.
5.1.
Single
level
hedonic
model
In
the
single
level
model
(OLS
(1)),
the
structural
and
accessi-
bility
measures
in
general
confirm
the
expectations
based
on
the
findings
from
urban
economic
theory.
The
global
effect
for
retail
and
service
diversity
(DI)
is
found
to
be
non-significant.
While
the
gen-
eral
green
diversity
index
(DIGreen)
has
a
negative
impact
though
of
low
significance,
mean
Shannon
land-use
diversity
indices
show
the
expected
signs.
Applying
the
method
suggested
by
Verbeek
(2008),
the
average
predicted
price
is
of
283,064
euros
for
a
typ-
ical
transaction
of
mean
size
and
of
type
other
than
dVFA,
with
all
variables
grand-mean
centered
(except
dVFA).
Moran’s
I
(Table
1)
and
the
Lagrange
multiplier
tests
(Table
2)
confirm
significant
spatial
error
auto-correlation
while
no
signif-
icant
spatial
lag
dependence
is
detected
by
the
robust
LM-test
(Table
2).
This
spatial
error
dependence
is
expected
to
be
accounted
for
by
the
three-level
model
presented
in
the
next
section.
Multi-
collinearity
was
measured
by
variance
inflation
factors
test
(VIF)
and
test
scores
are
all
below
5.
The
null
hypothesis
of
homoskedas-
tic
residuals
was
rejected
by
the
Breusch–Pagan
test,
suggesting
non-constant
variance
of
the
error
terms.
5.2.
Multilevel
models
The
multilevel
models,
accounting
for
the
three-level
nested
hierarchical
structure
of
the
data,
have
been
estimated
by
restricted
maximum
likelihood
(REML),
according
to
Snijders
and
Bosker
(1999)
the
difference
between
the
maximum
likelihood
(ML)
and
REML
method
is
that
the
latter
estimates
the
variance
components
while
taking
into
account
the
loss
of
degrees
of
freedom
result-
ing
from
the
estimation
on
the
regression
parameters,
while
ML
does
not.
We
use
the
“lme4”
package
(Bates,
Maechler,
Bolker,
&
Walker,
2013)
in
R
(R
Core
Team,
2013).
The
significance
lev-
els
of
the
fixed
terms
have
been
computed
using
the
“lmerTest”
package
by
Kuznetsova,
Brockho,
and
Christensen
(2013),
Table
2
LM-test
results
for
OLS
model.
Lagrange
multiplier
test
LMerr
RLMerr
LMlag
RLMlag
Lagrange
Multiplier
test
174.64
96.04
78.62
0.01
p-Value
0.000
0.000
0.000
0.915

106
M.-L.
Glaesener,
G.
Caruso
/
Landscape
and
Urban
Planning
143
(2015)
100–111
Fig.
1.
Random
Intercepts
at
municipal
level.
obtaining
p-values
by
implementing
“Satterthwaite
approxima-
tion”
for
denominators’
degrees
of
freedom.
The
unconditional
model,
identifies
that
7.5%
of
the
total
vari-
ance
in
the
transaction
price
is
located
between
sections
within
municipalities,
while
16%
of
the
total
price
variance
is
between
municipalities
(model
2
(UM)
in
Table
3).
Single-
or
two-level
mod-
els
are
hence
rejected.
The
level-two
ICC
being
68%
suggests
that
mean
section
prices
within
a
municipality
are
alike,
while
the
ICC
for
level-two
relative
to
level-one
indicates
that
transaction
prices
are
not
varying
homogeneously
between
sections
of
a
same
munic-
ipality.
Map
A
in
Fig.
1
illustrates
the
random
intercepts
of
the
UM
at
municipal
scale,
that
is
the
variation
of
the
mean
municipal
price
to
the
overall
intercept.
As
expected
municipal
mean
prices
above
the
overall
intercept
are
observed
for
most
of
the
municipalities
in
the
southern
part
of
the
country,
while
in
the
north
below
average
means
are
estimated
in
general.
5.2.1.
RIM:
Price
variability
partly
explained
The
ability
of
the
fixed
explanatory
variables,
added
in
model
3,
to
account
for
a
significant
part
of
the
price
variability
is
confirmed
by
the
LR-test.
Only
9.1%
of
the
price
variance
is
now
located
at
the
two
higher
levels,
according
to
ICC
for
level-two
relative
to
level-
one.
A
considerable
part
of
between
transaction
variance
remains
unexplained;
which
is
not
surprising
with
regard
to
the
poor
infor-
mation
on
the
structural
transaction
characteristics
available
and
the
aggregated
scale
of
the
contextual
variables.
Only
1.7%
of
the
total
unexplained
price
variance
is
located
between
municipalities.
The
decrease
of
the
level-two
ICC,
indicates
that
most
of
the
vari-
ance
at
the
higher
levels
is
located
between
sections,
suggesting
that
the
explanatory
variables
were
able
to
capture
a
large
amount
of
the
between
municipal
price
variability.
Map
B
in
Fig.
1,
illustrates
the
variation
of
the
municipal
inter-
cept
relative
to
the
overall
intercept
after
including
explanatory

M.-L.
Glaesener,
G.
Caruso
/
Landscape
and
Urban
Planning
143
(2015)
100–111
107
Fig.
2.
Random
coefficients
of
Shannon
diversity.
variables.
Mainly
transactions
located
in
municipality
of
and
around
Luxembourg-city
and
some
regional
urban
centers
are
observed
to
register
higher
variance
from
the
overall
mean.
The
high
coefficient
for
Erpeldange,
located
between
the
municipalities
of
Ettelbruck
and
Diekirch,
together
forming
as
the
Nordstad
(Map
C
Fig.
1),
is
also
most
notable.
All
else
constant,
a
typical
trans-
action
within
Erpeldange
is
on
average
7%
more
expensive
than
the
overall
national
mean.
Explanatory
variables
remain
similar
to
OLS
results
(model
(1)
Table
1),
those
insignificant
remain
insignif-
icant
and
DIGreen
as
well
as
most
socio-economic
variables
turn
insignificant
(Table
1)
in
the
multilevel
model.
To
wrap
up
we
find
that:
(i)
tests
confirm
residual
spatial
dependence
and
heteroskedasticity;
(ii)
the
utility
of
a
three-level
hierarchical
model
is
confirmed;
(iii)
large
proportion
of
price
vari-
ability
is
located
between
transactions
due
to
omitted
structural
variables;
and
(iv)
the
explanatory
variables
capture
an
important
part
of
the
variance.
5.2.2.
FRM:
Spatial
heterogeneity
for
size
and
land-use
diversity
We
are
interested
in
the
non-stationarity
of
neighborhood
amenities,
and
analyzed
random
coefficients
for
them.
Besides,
Table
3
Random
effects.
UM
(2)
RIM
(3)
FRM
(4)
Variance
Level
3:
Municipality ϕ2
00.079
0.005
0.006
mAPsh100 ϕ2
1)
0.501
cov ϕ2
0,
ϕ2
10.044
mAPsh1000 ϕ2
20.077
cov ϕ2
0,
ϕ2
20.020
cov ϕ2
1,
ϕ2
20.132
Level
2:
Sections
in
municipalities 2
00.037
0.020
0.024
lnSize 2
10.062
cov 2
0,
2
1−0.029
Level
1:
Transactions
20.377
0.246
0.225
Total
variance
0.493
0.246
0.475
Level-2
ICC
0.682
0.190
0.197
ICC
for
level
2
relative
to
level
1
0.235
0.091
0.118
since
the
literature
indicates
the
importance
of
spatial
hetero-
geneity
for
plot
size,
we
also
analyzed
this
relationship.
We
report
the
FRM
fixed
effects
in
Table
1
and
the
FRM
random
coefficients
for
the
significant
variables,
i.e.
Shannon
land-use
diversity
and
plot
size,
are
detailed
in
Table
3
and
illustrated
in
Fig.
2.
The
LR-test
indicates
that
including
random
variation
of
plot
size
between
sections
performs
best,
whereas
no
significant
spatial
variation
was
identified
between
municipalities.
Allowing
ran-
dom
variation
of
the
size-price
relationship
within
sections
further
explains
between
transaction
variance
(2).
Random
slopes
for
DIGreen
and
DI,
did
not
lead
to
a
significant
improvement
of
the
model
(Results
are
available
upon
request).
Our
results
related
to
Shannon
land-use
diversity
measures
(mAPsh100
and
mAPsh1000)
support
the
findings
of
Geoghegan
et
al.
(1997).
The
slopes
were
allowed
to
vary
between
munic-
ipalities
(model
4),
which
adds
to
the
overall
explanatory
power.
In
map
C
(Fig.
1)
we
illustrated
the
variance
to
the
over-
all
intercept
of
the
average
estimated
municipal
intercept
of
the
FRM.
Including
land-use
diversity
indices
mitigates
the
positive
variations
of
the
capital-city
Luxembourg,
and
mainly
two
sub-
markets
emerge.
First,
the
municipalities
of
the
Nordstad
positively
stand
out.
Second,
in
the
former
industrial
south,
a
relatively
high
negative
variation
from
the
overall
intercept
is
observed.
In
these
two
segments,
a
typical
transaction
is
valued
differently
by
developable
land
consumers,
which
merits
further
investigation
to
be
related
with
the
polycentric
policy
goals
set
by
at
national
level.
The
fixed
effects
of
the
land-use
diversity
variables
indicate
the
expected
marginal
effects
and
barely
change
from
the
RIM
(model
2).
For
plot
size
and
Shannon
indices
the
results
of
the
global
model
are
mostly
confirmed.
For
the
two
Shannon
indices,
inversions
of
the
sign
of
the
marginal
effect
across
municipalities
are
observed.
On
the
one
hand,
land-use
diversity
in
proximity
to
all
available
plots
is
valued
positively
in
the
Nordstad
munic-
ipalities,
in
the
north-west
and
in
some
municipalities
in
the
south-east
of
Luxembourg,
the
Moselle
valley
region
(Map
A
in
Fig.
2).
Further,
increased
land-use
diversity
in
walking
distance
is
val-
ued
negatively
in
some
of
the
municipalities,
in
particular
in
the

108
M.-L.
Glaesener,
G.
Caruso
/
Landscape
and
Urban
Planning
143
(2015)
100–111
Table
4
Marginal
effects.
OLS
(1)
RIM
(3)
FRM
(4)
Level
1
Transaction/plot
lnSize
(+10%) 6.12%
6.13%
6.08%
dVFA
20.71%
23.83%
25.81%
Level
2
Section
tLUXci −1.15%
−1.30%
−1.35%
tLUXpi −0.31%
−0.24%
−0.29%
rAP
0.68%
0.46%
0.46%
mAPsh100
(0.1) −2.97% −3.24% −3.75%
mAPsh1000
(0.1) 2.14%
1.78%
1.87%
Price
of
a
typical
transaction
283,064
D
280,184
D
277,217
D
former
industrial
south
but
also
in
some
of
the
periurban
munici-
palities
north
of
Luxembourg-city
(Map
B
Fig.
2).
The
covariance
term
(ϕ12)
describes
a
positive
relationship
between
the
ran-
dom
coefficients
of
the
Shannon
diversity
indices;
the
more
a
0.1
increase
in
diversity
in
mAPsh1000
is
valued
positively,
the
weaker
is
the
negative
effect
of
mAPsh100.
Not
allowing
ran-
dom
coefficients
would
have
led
to
wrong
conclusions,
as
there
are
local
variations
in
how
diversity
in
different
extents
is
val-
ued.
The
fixed
effects
remain
almost
unchanged
(Table
1),
and
we
now
discuss
the
marginal
willingness
to
pay
for
the
significant
variables
of
interest
provided
in
Table
4.
According
to
the
fully
random
model
(model
4)
residential
land
consumers
in
Luxem-
bourg
are
estimated
to
be
willing
to
pay
almost
6.08%
more
for
a
10%
size
increase
to
an
average-sized
parcel.
Existing
develop-
ment
plans
are
highly
significant
through
all
models;
consumers
are
willing-to-pay
almost
26%
more
for
a
typical
transaction
with
existing
plans.
An
additional
minute
to
Luxembourg
by
car
lowers
a
typical
transactions’
price
by
1.35%,
while
by
public
trans-
port’s
negative
impact
is
of
0.29%
per
additional
minute.
These
findings
confirm
the
relative
importance
of
individual
transport
over
public
transport
in
consumers’
preferences;
nevertheless
public
transport
has
a
significant
impact
on
developable
land
prices
in
Luxembourg.
The
overall
negative
impact
of
increased
mAPsh100
is
slightly
strengthened
in
model
4,
as
is
the
overall
coefficient
of
mAPsh1000
after
allowing
random
slopes
for
the
land-
use
diversity
indices
between
municipalities.
An
0.1
above
mean
increase
of
the
diversity
indices
has
an
overall
marginal
effect
of
−3.75%
for
close
diversity
and
1.87%
for
diversity
in
walking
dis-
tance.
To
summarize,
we
find
that
(i)
the
marginal
effect
of
size
varies
between
sections
within
municipalities;
(ii)
neither
service
nor
green
diversity
have
a
significant
impact;
(iii)
spatial
market
seg-
ments
around
the
Nordstad
and
the
former
industrial
south;
and
(iv)
we
confirm
spatial
variation
in
the
marginal
effects
of
land-use
diversity.
5.2.3.
CRMM:
MLM
captures
spatial
effects
The
non-significant
Moran’s
I
test
for
the
conditional
residuals
of
the
multilevel
models
(Table
2)
suggests
that
no
spatial
error
dependence
remains
after
accounting
for
the
different
levels.
This
is
confirmed
by
the
cross-regressive
multilevel
model
(CRMM)
sug-
gested
by
Chasco
and
Le
Gallo
(2012).
The
results
of
the
CRMM
estimation
(Model
5
in
Table
2)
show
that
the
fully
random
model
(FRM—3),
as
specified
in
this
case
study,
captures
all
spatial
processes.
Based
on
the
findings
of
Morenoff
(2003),
Chasco
and
Le
Gallo
(2012)
did
not
include
the
spatial
lag
of
all
explanatory
variables
(not
considering
accessibility
and
pollution
variables)
because
of
issues
related
to
multicollinear-
ity.
Similar
observations
were
made
here,
we
could
neither
consider
the
spatial
lags
of
the
random
slope
variables,
nor
those
of
popula-
tion
density
and
the
accessibility
measures.
The
LR-test
confirms
that
the
model
is
not
significantly
improved
by
including
the
spatial
multipliers
conversely
to
what
Chasco
and
Le
Gallo
(2012)
found
in
their
case
study.
In
our
case,
none
of
the
spatial
lags
are
significant,
meaning
that
the
observed
neighborhood
sections’
values
do
not
influence
other
transactions
in
the
neighborhood.
6.
Conclusion
In
this
paper,
we
have
attempted
to
measure
the
effect
of
neigh-
borhood
diversity
of
both
services
and
land-uses
on
developable
land
prices
as
well
as
its
variation
across
space.
We
applied
the
multilevel
approach
to
capture
contextual
effects,
beyond
neigh-
borhood
and
center-periphery
effects.
Our
analysis
confirmed
the
usefulness
of
the
multilevel
approach
with
three
levels
for
our
case
study.
The
RIM
confirmed
that
an
important
part
of
price
variability
is
explained
by
the
fixed
explanatory
variables
and
by
considering
these
three
levels.
Allow-
ing
random
slopes
for
plot
size
and
land-use
diversity
indices
showed
spatial
variation
in
their
marginal
effects
on
land
price
in
Luxembourg.
Parcel
size
is
not
valued
homogeneously
within
municipalities,
suggesting
differentiated
local
planning
policies
within
each
municipality
or
at
least
structural
differences
within
municipalities
that
complement
the
standard
urban
economic
trade-off
(plot
size-commuting
costs)
even
after
controlling
for
municipal
Tiebout
effects
through
neighborhood
services.
The
Shannon
indices
for
land-use
diversity
have
consistently
demonstrated
across
models
positive
value
for
in
walking
distance
and
a
negative
value
in
immediate
proximity,
which
is
in
line
with
literature.
Moreover,
we
observe
spatial
variations
of
these
valuations
across
Luxembourg.
We
observe
that
both
indices
are
valued
positively
in
regions
that
are
particularly
attractive
and
picturesque.
Conversely,
negative
values
were
obtained
for
both
indices
in
the
former
industrial
conurbation,
suggesting
that
the
composition
of
the
diversity
matters
within
neighborhoods,
espe-
cially
in
these
regions
where
a
negative
perception
of
brown
fields
is
likely.
Both
findings
indicate
that
more
importance
should
be
given
to
landscape
contextual
effects
when
assessing
the
effects
of
land-use
proximity.
Although
we
were
expecting
significant
effects
from
green
diversity,
the
significance
disappeared
when
the
multiple
lev-
els
were
considered.
This
is
probably
a
data
aggregation
effect
which
somehow
confirms
previous
findings
that
green
amenities
should
be
considered
at
a
more
local
scale
with
further
geographic
detail.
Similarly,
our
inability
to
capture
the
positive
effect
of
having
a
more
diverse
offer
of
urban
amenities
suggests
that
even
the
munic-
ipal
scale
is
too
small.
This
would
require
further
investigation,
but
is
not
surprising
in
the
Luxembourgish
context
where
service
sup-
ply
is
high
and
car
ownership
is
among
the
highest
in
the
World,
thus
attenuating
the
spatial
distribution
of
service
amenities.
Beyond
our
thematic
contribution,
our
application
shows
that
the
multilevel
approach
is
useful
to
analyze
spatial
heterogene-
ity,
and
comforts
the
findings
of
Orford
(2000)
rather
than
Chaix
et
al.
(2005)
or
Chasco
and
Le
Gallo
(2012),
as
discussed
in
Section
2.2,
in
the
sense
that
it
removes
spatial
auto-correlation
effects.
Our
finding
is
based
on
a
CRMM,
but
caution
should
be
paid
to
this
result
because
of
the
aggregated
spatial
unit
where
our
transactions
were
recorded.
Spatial
multilevel
models
as
suggested
recently
by
Almeida
and
Guimarães
(2014)
or
the
multilevel
model
with
auto-
correlated
error
structure
as
discussed
in
Ren
et
al.
(2013)
could
additional
insights.
Further
research
should
also
consider
endogeneity
effects,
especially
because
we
take
interest
in
neighborhood
amenities
and
the
risk
of
reverse
causation
that
might
exist
between
households’

M.-L.
Glaesener,
G.
Caruso
/
Landscape
and
Urban
Planning
143
(2015)
100–111
109
location
choice
and
the
offer
in
local
public
amenities
can
be
impor-
tant.
Treating
endogeneity
of
residential
decision
with
good
instru-
ments
within
a
multilevel
approach
is
an
interesting
additional
challenge.
Acknowledgments
We
are
grateful
to
Dominique
Peeters,
Luisito
Bertinelli
and
Julie
Le
Gallo
for
insightful
discussions
on
previous
versions
of
the
paper.
We
would
also
like
to
thank
two
anonymous
reviewers
and
the
editor
for
their
comments.
This
research
received
the
financial
sup-
port
of
the
Fonds
National
de
la
Recherche
Luxembourg
(AFR
grant
number:
PHD-09-095).
Appendix
A.
Fig.
A1
and
Table
A1.
Fig.
A1.
Maps
of
main
variables.

110
M.-L.
Glaesener,
G.
Caruso
/
Landscape
and
Urban
Planning
143
(2015)
100–111
Table
A1
Summary
statistics.
Variable
Description
(Unit)
Mean
Min
Max
Expected
Level
1
Transaction
lnPrice
ln
of
price
deflated
to
2007-euros
12.46
9.58
14.87
DV
lnSize
ln
of
plot
size
(are)
1.58
−0.46
3.92
+
dVFA
Development
project
(dummy)
0.19
0.00
1.00
+
Level
2
Section
tLUXci Time
to
Luxembourg-city
by
car
(min)
28.64
4.52
77.73
−
tLUXpi Time
to
Luxembourg-city
by
public
transport
(min)
41.30
8.00
122.00
−
DI
Shopping
and
service
diversity
(index) 0.64
0.00
0.91
+
rAP
Vacancy
rate
(%)
0.11
0.01
0.36
+
mAPsh100
Shannon
Index
in
radius
of
1.29
0.99
1.68
−
mAPsh1000
100/1000
m
around
AP
(index)
1.63
0.85
2.07
+
DIGreen
Green
diversity
(index)
0.57
0.08
0.75
+
Level
3
Municipality
VarPop0701
Population
variation
between
‘01
and
‘07
(%) 9.39
−2.96 36.30
+
pAbove65y
Part
people
above
65
years
(%)
12.67
6.84
20.04
−
rUnemployment
Unemployment
rate
(%)
4.33
2.07
9.92
−
PopDens
Population
density
(hab/km2)
330.58
22.39
2080.35
+
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