Market heterogeneity and the determinants of Paris apartment prices: A quantile regression approach

Abstract

In this paper, the heterogeneity of the Paris apartment market is addressed. For this purpose, quantile regression is applied – with market segmentation based on price deciles – and the hedonic price of housing attributes is computed for various price segments of the market. The approach is applied to a major data set managed by the Paris region notary office (Chambre des Notaires d’Île de France), which consists of approximately 156,000 transactions over the 2000–2006 period. Although spatial econometric methods could not be applied owing to the unavailability of geocodes, spatial dependence effects are shown to be adequately accounted for through an array of 80 location dummy variables. The findings suggest that the relative hedonic prices of several housing attributes differ significantly among deciles. In particular, the elasticity coefficient of the apartment size variable, which is 1.09 for the cheapest units, is down to 1.03 for the most expensive ones. The unit floor level, the number of indoor parking slots, as well as several neighbourhood attributes and location dummies all exhibit substantial implicit price fluctuations among deciles. Finally, the lower the apartment price, the higher the potential for price appreciation over time. While enhancing our understanding of the complex market dynamics that underlie residential choices in a major metropolis such as Paris, this research provides empirical evidence that the QR approach adequately captures heterogeneity among house price ranges, which simultaneously applies to housing stock, historical construct and social fabric.

Full text

Article
Urban Studies
2017, Vol. 54(14) 3260–3280
ÓUrban Studies Journal Limited 2016
Reprints and permissions:
sagepub.co.uk/journalsPermissions.nav
DOI: 10.1177/0042098016665955
journals.sagepub.com/home/usj
Market heterogeneity and the
determinants of Paris apartment
prices: A quantile regression
approach
Charles-Olivier Ame
´de
´e-Manesme
Universite
´Laval, Canada
Michel Baroni
ESSEC Business School, France
Fabrice Barthe
´le
´my
CEMOTEV, Universite
´de Versailles Saint-Quentin-en-Yvelines; THEMA, Universite
´de Cergy-
Pontoise, France
Francois des Rosiers
Universite
´Laval, Canada
Abstract
In this paper, the heterogeneity of the Paris apartment market is addressed. For this purpose,
quantile regression is applied – with market segmentation based on price deciles – and the hedo-
nic price of housing attributes is computed for various price segments of the market. The
approach is applied to a major data set managed by the Paris region notary office (Chambre des
Notaires d’I
ˆle de France), which consists of approximately 156,000 transactions over the 2000–
2006 period. Although spatial econometric methods could not be applied owing to the unavail-
ability of geocodes, spatial dependence effects are shown to be adequately accounted for through
an array of 80 location dummy variables. The findings suggest that the relative hedonic prices of
several housing attributes differ significantly among deciles. In particular, the elasticity coefficient
of the apartment size variable, which is 1.09 for the cheapest units, is down to 1.03 for the most
expensive ones. The unit floor level, the number of indoor parking slots, as well as several neigh-
bourhood attributes and location dummies all exhibit substantial implicit price fluctuations among
deciles. Finally, the lower the apartment price, the higher the potential for price appreciation over
time. While enhancing our understanding of the complex market dynamics that underlie residen-
tial choices in a major metropolis such as Paris, this research provides empirical evidence that the
Corresponding author:
Francois des Rosiers, Business School, Universite
´Laval, Pav. Palasis-Prince, Quebec City, QC G1K 7P4, Canada.
Email: Francois.Desrosiers@fsa.ulaval.ca

QR approach adequately captures heterogeneity among house price ranges, which simultaneously
applies to housing stock, historical construct and social fabric.
Keywords
hedonics, housing sub-markets, market heterogeneity, market segmentation, quantile regression
Received June 2015; accepted July 2016
Introduction
Paris is France’s capital and its most popu-
lous city. However, it is by no means homo-
geneous in terms of neighbourhood, building
and population features. Its growth over the
centuries has resulted from an organic pro-
cess that started from the inner areas (origi-
nally, Lutece) and extended progressively
into the surrounding suburbs that now form
the inner, intramuros Paris, which is the sub-
ject of this paper. Inner Paris, which repre-
sents around 20% of the population in the
Paris region, is divided administratively into
20 boroughs (arrondissements), conveniently
known by their numbers and mostly deli-
neated by Boulevard Pe
´riphe
´rique. The latter
are sequentially grouped, so as to form a
snail-like pattern (see appendix, available
online, Figure A-1), divided into four admin-
istrative precincts, referred to as quartiers.
The inner Paris housing dynamics can there-
fore be analysed on the basis of those 80
neighbourhoods (see appendix, available
online, Figure A-2).
In fact, Paris apartments are highly het-
erogeneous with regard to their price, size,
number of rooms, construction period and
location characteristics. It can be assumed
that all market segments do not follow the
same rationale when it comes to value attri-
butes. For that reason, it is likely that the
shadow price of many housing attributes
varies substantially across product price
ranges. It should be noted that traditional
hedonic models are based on the premise
that the full hedonic price envelope function
is homogeneous (Rosen, 1974). This, how-
ever, does not preclude the existence of dis-
tinct sub-markets. As put by Rosen (1974:
40), who notes that the overall ‘quality’ in
᪈㾱
ᵜ᮷᧒䇘Ҷᐤ哾ޜሃᐲ൪Ⲵᔲ䍘ᙗDŽѪ↔ˈᡁԜ䘀⭘Ҷ࠶սᮠഎᖂ⌅üü׍➗ԧṬ࠶սᮠڊ
ᐲ൪䜘䰘㓶࠶üüˈᒦ䪸ሩᐲ൪кнⲴԧṬ⇥䇑㇇Ҷտᡯ኎ᙗⲴ⢩ᖱԧṬDŽ䘉аᯩᔿ䘀⭘Ҿ
ᐤ哾ൠޜ䇱༴ᦼ㇑Ⲵа྇བྷරᮠᦞˈަѝ 2000-2006 ᒤ䰤བྷ㓖 156,000 ㅄъ࣑DŽ㲭❦⭡
Ҿൠ⨶㕆⸱ᰐ⌅㧧㘼ᰐ⌅䘀⭘オ䰤㓿⍾䇑䟿ᯩ⌅ˈն 80 њൠ⛩Ⲵ㲊ᤏ䟿䱥ࡇݵ࠶䈤᰾Ҷ
オ䰤׍䎆᭸ᓄDŽ⹄ウ⧠㺘᰾ˈࠐњտᡯ኎ᙗⲴ
⴨ሩ
⢩ᖱԧṬ൘࠶սᮠѝᴹ⵰ᱮ㪇ᐞᔲDŽާ
փ㘼䀰ˈޜሃ䶒〟䟿Ⲵᕩᙗ㌫ᮠሩҾᴰׯᇌⲴ྇ᡯᱟ 1.09ˈሩҾᴰ䍥Ⲵ྇ᡯࡉ䱽Ѫ 1.03DŽ྇
ᡯᾬቲǃᇔ޵ڌ䖖սᮠ䟿ԕ৺ࠐњ䛫䟼኎ᙗ઼ൠ⛩㲊ᤏ䟿䜭൘࠶սѝኅ⧠ࠪᇎ䍘ᙗⲴ䳀൘
ԧṬ⌒ࣘDŽᴰˈޜሃԧṬ䎺վˈԧṬ䲿ᰦ䰤㘼к⏘Ⲵ▌࣋䎺བྷDŽᵜ⹄ウаᯩ䶒ঠ䇱ҶᡁԜሩ
ᐤ哾䘉ṧⲴབྷ䜭ᐲտᡯ䘹ᤙ㛼Ⲵ༽ᵲᐲ൪ᵪࡦⲴ⨶䀓ˈаᯩ䶒ᨀ׋Ҷ㓿傼䇱ᦞˈ㺘᰾࠶ս
ᮠഎᖂ⌅ݵ࠶ᦅ᥹ҶտᡯԧṬ㤳തѝⲴᔲ䍘ᙗˈ䘉ᰦҏ䘲⭘Ҿᡯቻᆈ䟿ǃশᶴ䙐઼⽮Պ㚼
⨶DŽ
ޣ䭞䇽
⢩ᖱǃտᡯ⅑㓗ᐲ൪ǃᐲ൪ᔲ䍘ᙗǃᐲ൪䜘䰘㓶࠶ǃ࠶սᮠഎᖂ
Ame
´de
´e-Manesme et al. 3261

the consumption bundle of a complex good
may not necessarily increase with income .
However, in general there is no compelling rea-
son why the overall quality should always
increase with income. Some components may
increase and others decrease (cf. Lipsey and
Rosenbluth, 1971). Be that as it may, a clear
consequence of the model is that there are nat-
ural tendencies toward market segmentation,
in the sense that consumers with similar value
functions purchase products with similar speci-
fications. This is a well-known result of spatial
equilibrium models. In fact, the above specifi-
cation is very similar in spirit to Tiebout’s
(1956) analysis of the implicit market for
neighborhoods, local public goods being the
‘characteristics’ in this case. He obtained the
result that neighborhoods tend to be segmen-
ted by distinct income and taste groups (also,
see Ellickson, 1971).
In the presence of such sub-markets, the abil-
ity of traditional hedonic methods to capture
the true market value of specific bundles of
housing attributes may be questioned.
Unless market heterogeneity is accounted for
in the modelling approach used, unreliable
hedonic prices may be derived for any given
sub-market, since the latter are measured at
the overall mean of the price distribution. As
suggested by our literature review, several
approaches have been used to deal with this
issue. For example, Paris notary house price
indices are based on a series of reference sets
of relatively similar properties (see Clarenc
et al., 2014).
While mean house prices convey a broad
picture of local market structure, they may
be inadequate for providing an in-depth
understanding of how economic agents
belonging to different price segments of the
market value housing attributes. Indeed, the
existence of price segment sub-markets has a
direct impact on real estate prices and rent
dynamics. In order to address that issue, this
paper uses quantile regression (QR) to
identify the implicit price of housing charac-
teristics for different points in the distribu-
tion of house prices. Since QR uses the
entire sample, the problem of truncation
and of biased estimates is avoided
(Heckman, 1979; Newsome and Zietz,
1992). The Paris notary database for the
2000–2006 period, which provides apart-
ment sale prices together with an array of
both structural and neighbourhood descrip-
tors, is used for this purpose.
By using QR, this paper extends the exist-
ing literature on hedonic models in the pres-
ence of market heterogeneity, in line with
Zietz et al. (2008), Farmer and Lipscomb
(2010), Mak et al. (2010) and Liao and
Wang (2012). Its contribution is twofold.
First, it provides new evidence that housing-
attribute pricing may vary, in relative terms,
across quantiles, a conclusion that applies to
both structural and neighbourhood dimen-
sions. Second, it highlights the relevance of
using QR for investigating the price-
formation process in major metropolitan
areas, such as Paris, where market heteroge-
neity is the norm, despite rather strict plan-
ning constraints. Finally, it yields findings
that diverge from mainstream research in
the field with respect to the marginal influ-
ence of unit size on values. Although other
approaches can be used for handling the
issue, the QR approach offers the clear
advantage of circumventing a major con-
straint of hedonic modelling, i.e. market
homogeneity, by estimating multiple coeffi-
cients for housing attributes, depending on
the asset price range.
Literature review
Real estate is all about sub-markets, an asser-
tion about which there is general consensus.
As underlined by Islam and Asami (2009),
there are many ways to define sub-markets,
according to how they will be used in the
regression equation. More often than not,
3262 Urban Studies 54(14)

they are defined as geographical areas based
on either pre-existing geographic or political
boundaries or on socio-economic and/or
environmental characteristics. They may also
be derived from statistical techniques (e.g.
factor analysis, principal component analy-
sis, cluster analysis) or spatial econometrics
(spatial autoregressive models). For instance,
Des Rosiers et al. (2000) use principal com-
ponent analysis to identify sub-markets and
show how it separates influences that would
otherwise be intermingled.
Accounting for sub-markets is essential
for obtaining greater accuracy of hedonic
models and more effectively modelling spa-
tial and temporal patterns present in house
prices. As stated by Goodman and
Thibodeau (2003, 2007), model performance
improves with the number of sub-markets
hence defined.
Emphasising market segmentation,
Goodman and Thibodeau (1998, 2003) turn
to hierarchical linear modelling for delimit-
ing sub-markets and obtain significant gains
in hedonic prediction accuracy, compared
with the market-wide model. In the same
vein, Bourassa et al. (2003) concluded that
price predictions are most accurate when
appraisal-based market delineation is used,
as opposed to sub-markets derived from fac-
tor and cluster analyses. Leishman (2001)
pointed out that housing markets may be
segmented both spatially and structurally,
and may be considered as a set of inter-
related sub-markets. Leishman et al. (2013)
apply multilevel modelling in order to
improve the predictive accuracy.
The development of the geographically
weighted regression approach proposed by
Brunsdon et al. (1998) makes it possible to
generate spatially varying coefficients that
capture local sub-market specificities and
account for spatial autocorrelation (SA).
Following Can and Megbolugbe (1997),
The
´riault et al. (2003) use interactive vari-
ables together with Casetti’s expansion
method to reveal marginal price impacts that
would go unnoticed when only mean esti-
mates are derived. More recently, Biswas
(2012) examines various definitions of hous-
ing sub-markets in the context of foreclo-
sures. He shows how the traditional
approach based on spatial proximity and on
the stock homogeneity assumption, is super-
seded by an approach accounting for both
housing stock heterogeneity and non-
contiguity in space. Koschinsky et al. (2012)
compare the results from non-spatial and
spatial econometrics methods to examine
the reliability of coefficient estimates for
locational housing attributes in Seattle, WA.
They conclude that, while OLS generates
higher coefficient and direct effect estimates
for both structural and locational housing
characteristics than spatial methods, OLS
with spatial fixed effects rank second to spa-
tial methods when SA is taken into
consideration.
Finally, Bhattacharjee et al. (2012) inves-
tigate the sub-market delineation issue
through the dwelling substitutability con-
cept. Their model incorporates both spatial
heterogeneity and endogenous spatial depen-
dence, and shows that house substitutability
is achieved by combining similarity in hous-
ing attributes with similarity in hedonic
prices. In that respect, Pryce (2013) suggests
that the cross-price elasticity concept is most
useful in exploring the degree of substitut-
ability, compared with distance, spatial con-
tiguity or neighbourhood attribute
clustering.
Heterogeneity is one of the main charac-
teristics of real estate. Over the past 40
years, several authors have addressed the
market heterogeneity issue in various ways
(Xu, 2008). As suggested by Bhattacharjee
et al. (2012) and in considering the dwelling
substitutability concept, heterogeneity in
housing attributes can reasonably be
assumed to vary among apartment price
ranges. In that context, QR (Koenker and
Ame
´de
´e-Manesme et al. 3263

Bassett, 1982; Koenker and Hallock, 2001)
reveals itself as a most appropriate device
for capturing heterogeneous utility functions
and for bringing out differences in home-
buyer preference maps. QR is estimated
simultaneously and thus retains all the infor-
mation available from the data set and pro-
vides greater in-depth insight into the effects
of the covariates than would a series of inde-
pendent standard linear regressions (Benoit
and Van den Poel, 2009). QR focuses on the
interrelationship between a dependent vari-
able and its explanatory variables for a given
quantile. QR is of interest when explanatory
factors are expected to exhibit different var-
iations for different ranges of the dependent
variable.
Coulson and McMillen (2007) are among
the first to use quantile regression for
addressing market heterogeneity in housing
research. They use quantile regression to cre-
ate price indices for various housing quan-
tiles. Based on sales from three
municipalities in Chicago, their findings sup-
port theoretical expectations and show coin-
tegration between the supply side and price
indices, with a prevalence of high-quality
units. In addition, their study identifies sig-
nificant variations in how physical attributes
are valued across quantiles. Using 1999–
2000 home sales from the Orem/Provo area
in Utah, Zietz et al. (2008) also find that the
coefficients of some, although not all, vari-
ables vary considerably across quantiles.
Above all, they account for SA and show
that quantile effects largely outweigh SA
effects.
In the same vein, using a data set of
nearly 6000 cross-sectional, intertemporal
(1997–2004) sales from City One, a major
residential project in Sha Tin, Hong Kong,
Mak et al. (2010) apply QR in order to iden-
tify the implicit prices of housing characteris-
tics for different price ranges. The empirical
findings suggest that homebuyer tastes and
preferences for specific housing attributes
vary greatly across different price quantiles.
Among other things, and in line with Zietz
et al. (2008), optimal square footage emerges
as larger for upper quantiles than for lower
quantiles. Higher-priced properties also
command a larger market premium for a
view than do lower-priced properties.
Finally, Liao and Wang (2012) apply quan-
tile regression to Changsha, an emerging
Chinese city. More than 46,000 sales were
recorded in 113 residential developments
over a one-year period, from September
2008 to September 2009. The authors con-
clude, yet again, that the pricing of housing
attributes may vary across their conditional
distribution. The findings initially suggest
that the price of nearby properties has a
greater value impact on high- and low-priced
homes than on mid-priced homes. A clear
upward trend of the quantile effects for floor
area is also revealed.
Farmer and Lipscomb (2010) investigate
the role sub-market competition plays in set-
ting the price of housing attributes, particu-
larly in a context of fixed supply and
evolving homebuyer profiles. Using house-
hold information from both direct stated-
preference surveys and Multiple Listing
Service data, the authors use QR to track
variations in implicit prices for specific attri-
bute bundles in those price ranges where two
sub-markets overlap. The findings support
the hypothesis that, where cross-sub-market
competition is expected, newcomers with
particular needs and preferences are willing
to pay more than average implicit prices for
specific bundles of housing attributes. They
also confirm the relevance of QR for ade-
quately handling the selective heterogeneity
of hedonic coefficients.
Zahirovic-Herbert and Chatterjee (2012)
considered the effects of historic designation
on residential property values in Baton
Rouge, Louisiana. The results support the
well-established notion in the urban eco-
nomics literature that historic preservation
3264 Urban Studies 54(14)

has a positive impact on property values.
Using QR, the authors show that low-end
properties gain most from a historic preser-
vation designation.
Methodology: The quantile
hedonic regression approach
Hedonic theory states that the market price
of a complex, or heterogeneous, good is a
direct function of the utility derived from the
quantity of the nknown attributes it is com-
posed of and results from the market equili-
brium for such attributes. In spite of its
theoretical and methodological limitations
(Rosen, 1974), the hedonic price method has
proved very reliable for isolating the mar-
ginal contribution of market value determi-
nants, time included.
The basic, traditional general form of the
hedonic price equation can be written as:
Log Y=b0+X
n
i=1
biXi+e=Xb+e,ð1Þ
where Yis the sale price; X
i
is the vector of k
housing attributes; b
0
is the intercept; b
i
is
the implicit or hedonic, price of each iattri-
bute; and eis the stochastic error term (the
X
i
may be logged as well, for instance the
unit surface area, as in the log-log model).
Under such an approach, hedonic prices are
usually computed as the mean value of the
parameter estimate distribution, although
the median may also be used for that pur-
pose. However, where it is assumed that the
marginal price of a given attribute changes
over space and/or time, relying on the mean
value of the distribution is no longer ade-
quate and other methods ought to be
applied. This is where quantile regression
comes into play.
The ‘mean’ regression model assumes
that the expected value of variable ycan be
expressed as a linear combination of a set of
regressors X
i
,E(Y|X)=Xb, where brepre-
sents the vector of the variable coefficients.
QR produces different coefficients for each
pre-specified quantile (decile or centile) of
the error distribution. QR allows for raising
such a question for any quantile of the con-
ditional distribution function, thereby gener-
alising the concept of a univariate quantile
to a conditional quantile, given one or more
covariates.
This single mean curve Xbis sometimes
not informative enough and provides only a
partial or overall view of the relationship of
interest. It might therefore be useful to
describe the link between Yand the X
i
’s at
different points of the conditional cumula-
tive distribution of y. QR provides that
capability by using different conditional
quantiles of yaccording to X.
1
They can be
denoted Q
t
(Y|X), where tis a given prob-
ability (0 \t\1).
Without any information on X, the quan-
tile function Q
t
(Y) returns a value of y,
which splits the data into proportions t
below, and (1 2t) above it. Hence Q
t
(Y)is
linked to the cumulative distribution func-
tion of yas follows:
FyQt(Y)ðÞ= Prob YQt(Y)ðÞ=t,0\t\1
ð2Þ
As with the classical regression model that
defines the ‘mean’ of yas a linear function
of the X
i
’s, E(Y|X)=Xb, the quantile
regression model defines the quantile associ-
ated with probability tas Q
t
(Y|X)=Xb.
Hence, there may be an infinite number of
quantile regressions, while there is only one
‘mean’ regression.
Koenker and Bassett (1978) initially
developed this method. QR minimises the
weighted sum of the absolute deviations,
noted S (b
T
|Y,X), with asymmetric weights,
tfor positive residuals and (1 2t) for the
negatives ones:
Ame
´de
´e-Manesme et al. 3265

SbtjY,XðÞ=X
n
i:YiX0
ibt
tYibtX0
i

+X
n
i:Yi\X0
ibt
1tðÞYibtX0
i

ð3Þ
Then, Sis minimised as a function of the
vector b
t
.
Quantile effects lend themselves to a
straightforward interpretation that follows
directly from the hedonic price index estima-
tors. For instance, the marginal effect of X
at the median is b
0.5
, while the marginal
effect at the 90th per centile is b
0.9
.
The database
The database is that of the Paris region
Chamber of Notaries and consists, after fil-
tering, of some 156,000 apartment sales from
Q1-2000 to Q2-2006 for inner Paris. In
France, all property sales have to be regis-
tered by a notary, who collects the realty
transfer fee to be paid to Inland Revenue.
The database is publicly accessible for a fee.
It includes, for each transaction, information
on the sale price, apartment size, floor level,
number of rooms, number of bathrooms,
number of cellars, the construction period,
the presence of a garage, of an elevator, the
type of street (boulevard, square, alley, etc.)
and the date of transaction. Moreover, the
postal code and administrative precinct
information are available for each unit.
They indicate the arrondissement as well as
the district, or quartier, where the asset is
located within the arrondissement. Paris
arrondissements are divided into four dis-
tricts
2
– thereafter referred to as quartiers–
and sequentially numbered so as to form a
snail-like, spiral pattern that extends from
the centre to the periphery. Only second-
hand apartments are considered in the study,
as new dwellings and houses represent a
small share of total transactions for the Paris
Region, with prices and structural attributes
that greatly differ from those of second-hand
apartments.
The main housing attributes (essentially
dummy variables with the exception of the size
descriptor) include apartment size, construc-
tion period of the building, floor level, number
of bathrooms, presence of a lift
3
and street type
(e.g.Street,Avenue,Boulevard,etc.).Time
and spatial trends are accounted for through
26 quarter dummies (Q1-2000 through Q2-
2006) and 80 neighbourhood dummies (quar-
tiers 1 through 80), respectively.
For reasons of conciseness, statistics on
apartment attributes and on sale prices are
not displayed here, but are available online
as an appendix. The most important points
can be summarised as follows:
(1) Mean price and standard deviation are
e226,000 and e242,000, respectively.
(2) Half of the properties sold were built
before the First World War, far exceed-
ing the share this category of units
accounts for in the Paris housing stock
(roughly 30%). This shows the particu-
lar interest in Haussmann-style build-
ings (1850–1913 period).
(3) Some 60% of sales relate to apartments
smaller than 50 m
2
. This is consistent
with the standard two-room Parisian
apartment and with an investment mar-
ket that is driven by small dwellings,
which form its most active segment.
(4) Only 5% of apartments are located
above the seventh floor, inner Paris
buildings usually having between four
and six floors.
(5) More than two-thirds of apartment
sales belong to the peripheral districts
(12th through 20th arrondissements).
This is consistent with their respective
size, which exceeds that of more central
districts (1st to 11th arrondissements).
(6) In contrast with the decile partition for
which, by construction, there is no price
3266 Urban Studies 54(14)

overlap or discontinuity among deciles
(i.e. each decile takes over where the pre-
vious one ends), the price distribution by
size displays pronounced price overlaps.
This emphasises the usefulness of quan-
tile regression based on prices as a mar-
ket segmentation device.
(7) The sales are essentially uniformly dis-
tributed over time, ranging from a min-
imum of 22,100 (2002) to a maximum
of 28,600 (2005). This is even more the
case with regard to quarters, with Q1
through Q3 exhibiting some 40,000
sales, while Q4 displays a somewhat
lower frequency, 35,000 sales (see
appendix, available online).
The reference (included in the intercept) is
an apartment located in ‘Clignancourt’
(quartier 70), in a street-type location (‘rue’),
on the ground floor of a building built
between 1850 and 1913 (Haussmannian
period) with a lift, a cellar and without an
attic room or a garage. Information about
attributes is not always available. When this
problem arises, a variable ‘attribute missing’
has been added to the model, so as to gener-
ate an unbiased estimation of the intercept
(and hence of the other parameters).
Empirical results
Overall model performance and functional
form
Quantile regression findings are reported in
Table 1 for deciles 10, 30, 50, 70 and 90.
Table 1 gives the coefficient estimates with
their statistical significance. The last column
gives the slope of the quantile with its statisti-
cal significance. Most parameters emerge as
highly significant (p-values are predominantly
less than 0.0001, as indicated by three aster-
isks ***). Regarding overall model perfor-
mance, pseudo R-squared statistics pertaining
to deciles are relatively good, with the median
decile R-squared still standing at 0.739.
Model explanatory power also rises with the
price category, from 0.673 (1st decile) to
0.766 (9th decile). The tendency for the equa-
tions to fit better at higher quantiles is proba-
bly due to the heterogeneity of the housing
stock at lower quantiles, which combine pre-
mises in all kinds of areas, either low-quality
or high-quality, except for poorly maintained
apartments. All the associated p-values of the
estimates are reported in the appendix, avail-
able online (Tables A-25 and A-26), as well
as findings pertaining to the other missing
deciles (20, 40, 60 and 80). Finally, and as
discussed below, the relationship between the
selling price and basic hedonic pricing vari-
ables (size, floor, garage, bathrooms) is best
captured using quantile regression.
As is usually the case with hedonic price
models, the log-linear functional form is
used here, with the natural logarithm of sale
price as the dependent variable. Considering
that a semi-log functional form is used for
the model, all dummy variable coefficients
must be transformed, so as to derive the
actual marginal contribution of the variable
to price.
4
For the remainder of the paper,
actual marginal contributions are discussed,
although original regression coefficients are
reported in Tables 1 and A-25 (available
online).
Addressing the spatial autocorrelation
issue
SA is a common source of imperfection in
house price modelling. Essentially, it can
take two forms, i.e. spatial error dependence
or spatial lag dependence. The former is
commonly handled using a weight matrix
approach designed for modelling the spatial
pattern in the error term because of omitted
variables, while a ‘spatially lagged’ depen-
dent variable is generally used to account
for the spatial lag dependence. As geocodes
are not available, the geographical location
Ame
´de
´e-Manesme et al. 3267

Table 1. Regression results – QR estimates.
Quantile level Q10 Q30 Q50 Q70 Q90 Trend and statistical
significance of differences
among quantiles (x2 test)
Parameters
Pseudo R
2
67.3% 71.8% 73.9% 75.5% 76.6%
Intercept 6.7644*** 7.1395*** 7.3706*** 7.5696*** 7.8238***
Size
(size-elasticity of price)
1.0908*** 1.0647*** 1.0532*** 1.0446*** 1.0344*** &***
Q1 2000 reference
Q2 2000 0.0319** 0.0432*** 0.0439*** 0.0383*** 0.0414*** !!
Q3 2000 0.0629*** 0.0756*** 0.0795*** 0.0765*** 0.0766*** !!
Q4 2000 0.0726*** 0.0864*** 0.0829*** 0.0775*** 0.0875*** !!
Q1 2001 0.1070*** 0.1098*** 0.1090*** 0.1017*** 0.0988*** !!
Q2 2001 0.1370*** 0.1352*** 0.1277*** 0.1206*** 0.1163*** &**
Q3 2001 0.1673*** 0.1726*** 0.1627*** 0.1518*** 0.1491*** &*
Q4 2001 0.1658*** 0.1724*** 0.1672*** 0.1551*** 0.1479*** &*
Q1 2002 0.1874*** 0.1934*** 0.1824*** 0.1689*** 0.1569*** &**
Q2 2002 0.2199*** 0.2228*** 0.2092*** 0.1950*** 0.1877*** &***
Q3 2002 0.2852*** 0.2755*** 0.2617*** 0.2459*** 0.2343*** &***
Q4 2002 0.2786*** 0.2875*** 0.2781*** 0.2636*** 0.2555*** &**
Q1 2003 0.3121*** 0.3236*** 0.3100*** 0.2913*** 0.2732*** &***
Q2 2003 0.3535*** 0.3611*** 0.3442*** 0.3268*** 0.3164*** &***
Q3 2003 0.4115*** 0.4108*** 0.3894*** 0.3694*** 0.3537*** &***
Q4 2003 0.4279*** 0.4288*** 0.4166*** 0.4001*** 0.3823*** &***
Q1 2004 0.4540*** 0.4570*** 0.4422*** 0.4237*** 0.4007*** &***
Q2 2004 0.4971*** 0.5042*** 0.4870*** 0.4670*** 0.4492*** &***
Q3 2004 0.5494*** 0.5474*** 0.5300*** 0.5078*** 0.4866*** &***
Q4 2004 0.5638*** 0.5713*** 0.5542*** 0.5351*** 0.5139*** &***
Q1 2005 0.6032*** 0.6017*** 0.5855*** 0.5638*** 0.5464*** &***
Q2 2005 0.6435*** 0.6395*** 0.6205*** 0.5978*** 0.5794*** &***
Q3 2005 0.6939*** 0.6844*** 0.6654*** 0.6515*** 0.6339*** &***
Q4 2005 0.7083*** 0.7096*** 0.6906*** 0.6716*** 0.6550*** &***
Q1 2006 0.7413*** 0.7341*** 0.7124*** 0.6938*** 0.6683*** &***
Q2 2006 0.7557*** 0.7482*** 0.7302*** 0.7046*** 0.6866*** &***
(continued)
3268 Urban Studies 54(14)

Table 1. Continued
Quantile level Q10 Q30 Q50 Q70 Q90 Trend and statistical
significance of differences
among quantiles (x2 test)
Before 1850 0.0235*** 0.0164*** 0.0156*** 0.0206*** 0.0303*** !!
1850–1913 reference
1914–1947 20.0062 20.0123*** 20.0143*** 20.0098*** 20.0070** !!
194821969 20.0032 20.0146*** 20.0198*** 20.0178*** 20.0145*** !!
1970–1980 0.0344*** 0.0135*** 0.0034 20.0005 20.0033 &***
1981–1991 0.0496*** 0.0493*** 0.0466*** 0.0491*** 0.0458*** !!
1992–2000 0.1182*** 0.1079*** 0.1003*** 0.0985*** 0.1018*** !!
Building construction missing 20.0228*** 20.0187*** 20.0141*** 20.0065** 0.0088** !!
No bathroom reference
1 bathroom 0.1495*** 0.0897*** 0.0618*** 0.0456*** 0.0326*** &***
2 bathrooms 0.1415*** 0.0899*** 0.0661*** 0.0582*** 0.0628*** &***
3 bathrooms or more 0.0740*** 0.0471*** 0.0481*** 0.0618*** 0.0973*** !!
Ground floor (bldg with lift) reference
Entresol 0.0954*** 0.0741*** 0.0422*** 0.0450** 0.0414*&*
1st floor 0.1161*** 0.0903*** 0.0702*** 0.0536*** 0.0233*** &***
2nd floor 0.1592*** 0.1290*** 0.1038*** 0.0844*** 0.0497*** &***
3rd floor 0.1780*** 0.1396*** 0.1109*** 0.0890*** 0.0547*** &***
4th floor 0.1771*** 0.1463*** 0.1174*** 0.0963*** 0.0593*** &***
5th floor 0.1915*** 0.1564*** 0.1278*** 0.1097*** 0.0792*** &***
6th floor 0.1814*** 0.1576*** 0.1367*** 0.1263*** 0.1065*** &***
7th floor and more 0.1785*** 0.1577*** 0.1459*** 0.1394*** 0.1281*** &***
Floor missing 0.0865*** 0.0726*** 0.0755*** 0.0720*** 0.0574*** !!
Building without lift 20.0364*** 20.0209*** 20.0193*** 20.0195*** 20.0210*** %*
Lift missing 20.0097** 20.0074*** 20.0073*** 20.0080*** 20.0109*** !!
Duplex 0.0835*** 0.0959*** 0.1060*** 0.1243*** 0.1650*** %***
Triplex 0.0864** 0.1063*** 0.1400*** 0.1473*** 0.1391*** %***
No parking reference
1 parking place 0.0389*** 0.0420*** 0.0459*** 0.0516*** 0.0584*** %***
2 parking places 0.0366** 0.0679*** 0.0857*** 0.0841*** 0.1107*** %**
3 or more parking places 20.0231 0.0068 0.0379 0.0603 0.1358 %***
No attic room reference
(continued)
Ame
´de
´e-Manesme et al. 3269

Table 1. Continued
Quantile level Q10 Q30 Q50 Q70 Q90 Trend and statistical
significance of differences
among quantiles (x2 test)
1 attic room 0.0316*** 0.0424*** 0.0545*** 0.0699*** 0.0846*** %***
2 or more attic rooms 0.0131 0.0376*** 0.0629*** 0.0915*** 0.1177*** %***
No cellar 20.0356*** 20.0187*** 20.0078*** 0.0014 0.0131*** %***
1 or more cellars reference
1 or more balconies 0.0144 0.0224** 0.0204*** 0.0203*** 0.0130 !!
Garden 0.1353*** 0.1570*** 0.1613*** 0.1677*** 0.1958*** %
Mezzanine 0.1219*** 0.1273*** 0.1286*** 0.1239*** 0.1319*** !!
Street reference
Avenue 20.0167*** 20.0024 0.0042*0.0114*** 0.0208*** %***
Boulevard 20.0602*** 20.0560*** 20.0403*** 20.0289*** 20.0142*** %***
Place 0.0290 0.0311** 0.0518*** 0.0640*** 0.0859*** %***
Quay 0.0490*** 0.0790*** 0.0804*** 0.0891*** 0.1098*** %
1 St-Germain-l’Auxerrois 0.4919*** 0.4565*** 0.4040*** 0.3768*** 0.3723*** &***
2 Les Halles 0.3507*** 0.3574*** 0.3314*** 0.3050*** 0.2686*** &***
3 Palais-Royal 0.4475*** 0.4614*** 0.4324*** 0.3980*** 0.3781*** !!
4 Place Vendo
ˆme 0.5381*** 0.4802*** 0.4647*** 0.4318*** 0.4097*** &***
5 Gaillon 0.3881*** 0.3753*** 0.3713*** 0.3310*** 0.3172*** !!
6 Vivienne 0.3191*** 0.2973*** 0.2772*** 0.2663*** 0.2588*** &*
7 Mail 0.2605*** 0.2913*** 0.2724*** 0.2389*** 0.2080*** &***
8 Bonne-Nouvelle 0.1317*** 0.1922*** 0.1863*** 0.1781*** 0.1531*** !!
9 Arts-et-Me
´tiers 0.2482*** 0.2512*** 0.2313*** 0.1946*** 0.1468*** &***
10 Enfants-Rouges 0.3510*** 0.3253*** 0.2979*** 0.2750*** 0.2381*** &***
11 Archives 0.4795*** 0.4769*** 0.4416*** 0.4116*** 0.3805*** &***
12 Sainte-Avoye 0.3680*** 0.3531*** 0.3228*** 0.2732*** 0.2332*** &***
13 Saint-Merri 0.4811*** 0.4316*** 0.3910*** 0.3574*** 0.3310*** &***
14 Saint-Gervais 0.4882*** 0.4830*** 0.4538*** 0.4119*** 0.3633*** &***
15 Arsenal 0.4795*** 0.4583*** 0.4259*** 0.3967*** 0.4047*** &***
16 Notre-Dame 0.7888*** 0.7568*** 0.7460*** 0.7385*** 0.7400*** !!
17 Saint-Victor 0.5766*** 0.5554*** 0.5098*** 0.4626*** 0.4219*** &***
18 Jardin des Plantes 0.5132*** 0.4774*** 0.4366*** 0.3839*** 0.3169*** &***
19 Val-de-Gra
ˆce 0.5870*** 0.5407*** 0.4988*** 0.4571*** 0.4085*** &***
(continued)
3270 Urban Studies 54(14)

Table 1. Continued
Quantile level Q10 Q30 Q50 Q70 Q90 Trend and statistical
significance of differences
among quantiles (x2 test)
20 Sorbonne 0.5819*** 0.5817*** 0.5427*** 0.5111*** 0.4746*** &***
21 Monnaie 0.7139*** 0.6765*** 0.6629*** 0.6215*** 0.5814*** &***
22 Ode
´on 0.7013*** 0.6737*** 0.6769*** 0.6575*** 0.6927*** &**
23 Notre-Dame-des-Champs 0.6317*** 0.6039*** 0.5787*** 0.5418*** 0.5167*** &***
24 St-Germain-des-Pre
´s0.7953*** 0.7452*** 0.7284*** 0.7147*** 0.7369*** !!
25 St.-Thomas-d’Aquin 0.6851*** 0.6719*** 0.6615*** 0.6572*** 0.6691*** !!
26 Les Invalides 0.6370*** 0.6130*** 0.5925*** 0.6080*** 0.6131*** !!
27 Ecole-Militaire 0.5779*** 0.5377*** 0.4979*** 0.4737*** 0.4353*** &***
28 Gros-Caillou 0.5835*** 0.5336*** 0.5058*** 0.4731*** 0.4350*** &***
29 Champs-Elyse
´es 0.5883*** 0.5882*** 0.5952*** 0.6308*** 0.7138*** %*
30 Faubourg du Roule 0.4348*** 0.4133*** 0.3887*** 0.3514*** 0.3218*** &***
31 La Madeleine 0.4137*** 0.4204*** 0.4120*** 0.3752*** 0.3852*** !!
32 Europe 0.3636*** 0.3517*** 0.3226*** 0.2908*** 0.2727*** &***
33 Saint-Georges 0.2436*** 0.2229*** 0.1884*** 0.1485*** 0.0908*** &***
34 Chausse
´e-d’Anlin 0.1824*** 0.1965*** 0.2079*** 0.1922*** 0.1755*** !!
35 Faubourg Montmartre 0.1671*** 0.1595*** 0.1371*** 0.1065*** 0.0652*** &***
36 Rochechouart 0.2011*** 0.1781*** 0.1527*** 0.1103*** 0.0538*** &***
37 St.-Vincent-de-Paul 20.0094 20.0272** 20.0544*** 20.0816*** 20.1243*** &***
38 Porte Saint-Denis 0.0532*** 0.0441*** 0.0268** 20.0056 20.0484*** &***
39 Porte Saint-Martin 0.0894*** 0.0792*** 0.0471*** 0.0135** 20.0382*** &***
40 Hopital St.-Louis 20.0231 20.0367*** 20.0549*** 20.0857*** 20.1295*** &***
41 Folie-Me
´ricourt 0.0866*** 0.1001*** 0.0638*** 0.0347*** 20.0131*&***
42 Saint-Ambroise 0.2132*** 0.1739*** 0.1327*** 0.0850*** 0.0265*** &***
43 La Roquette 0.1973*** 0.1730*** 0.1373*** 0.0943*** 0.0451*** &***
44 Sainte-Marguerite 0.1985*** 0.1684*** 0.1196*** 0.0643*** 20.0024 &***
45 Bel-Air 0.2222*** 0.1714*** 0.1241*** 0.0717*** 20.0023 &***
46 Picpus 0.1824*** 0.1515*** 0.1086*** 0.0667*** 0.0015 &***
47 Bercy 0.1205*** 0.0811*** 0.0592*** 0.0170 20.0379** &***
48 Quinze-Vingts 0.2251*** 0.1856*** 0.1469*** 0.1062*** 0.0568*** &***
49 Salpe
´trie
`re 0.3072*** 0.2807*** 0.2396*** 0.1952*** 0.1429*** &***
50 Gare 0.0176 0.0027 20.0143 20.0418*** 20.0839*** &***
(continued)
Ame
´de
´e-Manesme et al. 3271

Table 1. Continued
Quantile level Q10 Q30 Q50 Q70 Q90 Trend and statistical
significance of differences
among quantiles (x2 test)
51 Maison-Blanche 0.1534*** 0.1370*** 0.1150*** 0.0766*** 0.0276*** &***
52 Croulebarbe 0.3745*** 0.3365*** 0.2951*** 0.2518*** 0.1892*** &***
53 Montparnasse 0.4463*** 0.4167*** 0.3889*** 0.3575*** 0.3144*** &***
54 Parc Montsouris 0.2762*** 0.2407*** 0.2055*** 0.1629*** 0.1146*** &***
55 Petit Montrouge 0.3204*** 0.2692*** 0.2288*** 0.1896*** 0.1369*** &***
56 Plaisance 0.2825*** 0.2427*** 0.2072*** 0.1600*** 0.1022*** &***
57 Saint-Lambert 0.2998*** 0.2505*** 0.2061*** 0.1540*** 0.0940*** &***
58 Necker 0.3831*** 0.3331*** 0.2888*** 0.2475*** 0.2015*** &***
59 Grenelle 0.3900*** 0.3380*** 0.2991*** 0.2514*** 0.2190*** &***
60 Javel 0.3349*** 0.2788*** 0.2371*** 0.1825*** 0.1133*** &***
61 Auteuil 0.3820*** 0.3239*** 0.2807*** 0.2380*** 0.1847*** &***
62 La Muette 0.4690*** 0.4265*** 0.3903*** 0.3524*** 0.3019*** &***
63 Porte Dauphine 0.4597*** 0.4353*** 0.4054*** 0.3749*** 0.3386*** &***
64 Chaillot 0.4650*** 0.4278*** 0.3945*** 0.3660*** 0.3283*** &***
65 Ternes 0.3927*** 0.3534*** 0.3167*** 0.2782*** 0.2197*** &***
66 Plaine Monceau 0.3847*** 0.3535*** 0.3163*** 0.2716*** 0.2222*** &***
67 Batignolles 0.2502*** 0.2307*** 0.1911*** 0.1465*** 0.0916*** &***
68 Epinettes 0.0198*20.0111*20.0404*** 20.0762*** 20.1080*** &***
69 Grandes-Carrie
`res 0.0703*** 0.0715*** 0.0602*** 0.0431*** 0.0349*** &***
70 Clignancourt reference
71 La Gouttes-d’Or 20.2614*** 20.2765*** 20.2889*** 20.3091*** 20.3284*** &***
72 La Chapelle 20.2477*** 20.2618*** 20.2904*** 20.3047*** 20.3237*** &***
73 La Villette 20.2035*** 20.2101*** 20.2259*** 20.2504*** 20.2812*** &***
74 Pont de Flandre 20.1874*** 20.2299*** 20.2497*** 20.2808*** 20.3076*** &***
75 Ame
´rique 20.1188*** 20.1306*** 20.1493*** 20.1721*** 20.1945*** &***
76 Combat 20.0362** 20.0368*** 20.0551*** 20.0896*** 20.1359*** &***
77 Belleville 20.0620*** 20.0795*** 20.1014*** 20.1338*** 20.1731*** &***
78 Saint-Fargeau 20.0021 20.0462*** 20.0855*** 20.1279*** 20.1853*** &***
79 Pe
`re-Lachaise 0.0687*** 0.0297*** 20.0136** 20.0607*** 20.1222*** &***
80 Charonne 20.0113 20.0386*** 20.0601*** 20.0985*** 20.1434*** &***
Notes: Dependent variable: natural logarithm of sale price.
*
:p-value less than 5%; **:p-value less than 1%; ***:p-value less than 0.01%.
!!: no clear trend, &: marginal contribution decreases with price, %: marginal contribution increases with price.
3272 Urban Studies 54(14)

of apartments is used instead. In this sense,
we follow Gregoir et al. (2012), who also use
administrative areas as location dummies
and Zahirovic-Herbert and Chatterjee
(2012), who base location parameters on
census blocks.
5
As mentioned earlier, each
of the 20 Paris arrondissements is an amal-
gamation of four administrative quartiers,
each of which has its own specific features
and price determinants operating at a micro-
spatial level. While a second-best solution,
referring to these 80 dummy variables cap-
tures a large amount of the SA potentially
present in the residuals. Indeed, as shown in
Table A-28 (appendix available online),
regressing the model residuals on the loca-
tion dummies yields R-squared values that
fall below 0.02 for all deciles where the latter
are included in the model, as opposed to val-
ues ranging between 0.35 and 0.38, where
they are not. Such findings corroborate
Koschinsky et al. (2012), as to the relevance
of fixed effect location dummy models for
adequately handling spatial dependence
common in residential transaction prices.
They are also in line with Zietz et al. (2008),
who state that quantile effects largely domi-
nate SA effects. Consequently, it is assumed
that most SA influences are accounted for in
this paper.
As can be seen in Figure 1 for the median
(see appendix, available online, for findings
on other deciles), the (standardised) market
premium assigned to apartments located in
the 18th, 19th and 20th arrondissements
(quartiers 71 to 78) proves to be substan-
tially lower than those assigned to units
belonging to the 5th through 8th arrondisse-
ments (quartiers 20 to 29). In addition, the
premium per quartier decreases with the
price range, although its ranking among
quartiers is somewhat constant across quan-
tiles (see Figures A-7 to A-11, available
online).
Main empirical findings
Apartment size. Starting with the size para-
meter displayed in Figure 2,
6
the findings
tend to confirm the existence of distinct sub-
markets in the Paris apartment market, as
well as the relevance of using quantile
regression to estimate the hedonic prices of
housing attributes. Given our data set, and
in line with other studies using QR, such as
Zietz et al. (2008), Coulson and McMillen
(2007) or Liao and Wang (2012), the quan-
tile effect appears to be very important for
the size parameter. However, in contrast to
previous research,
7
we find that the higher
Figure 1. Standardised neighbourhood premium per Paris quartier.
Ame
´de
´e-Manesme et al. 3273

the price category, the lower the size-
elasticity of the sale price. Indeed, while the
elasticity coefficient reaches 1.09 for the low-
est decile, it is down to less than 1.03 for
upper-end units. Therefore, a 10% incre-
ment in apartment size results in an almost
10.9% price increase for the former, as
opposed to a 10.3% raise for the latter. The
negative slope of the size-elasticity of price
corroborates the fact that size increments
command a substantially higher willingness-
to-pay for smaller, cheaper units, than for
more expensive ones.
8
Such a finding is at
odds with the QR literature, in which an
additional size unit adds substantially more
to relative sale prices (although not necessa-
rily to absolute ones) for higher quantiles.
Orford (2000), in his study on Cardiff,
Wales, also provides empirical evidence of a
positive linear relationship between the aver-
age house price and the hedonic prices of
floor area. Whether the pattern emerging
from this research is generalisable to large
and expensive metropolises or remains spe-
cific to the Paris market, is an issue for fur-
ther research.
Price index. Turning to the price index
(Figure 3), it is worth noting that price
increases are not uniform among deciles and
are clearly inversely related to value. Studies
comparing appreciation rates across price
ranges are scarce, despite abundant literature
on house price index construction, estima-
tion and prediction. A notable exception is
Coulson and McMillen (2007), who high-
light differences in single-family house price
appreciation rates among price ranges. For
our Paris data set, price appreciation over
the 2000–2006 (mid-year) period is 113%
(0.7557) for the lowest decile (Q10), thereby
yielding an annual growth rate of 14.7%. It
declines progressively for higher deciles and
is down to 99% (0.6866, i.e. a 13.3% annual
growth rate) for luxury apartments. Such a
trend is consistent with theoretical
Figure 2. Size-elasticity coefficients of sale price by decile.
Note: Dotted lines indicate 95% confidence intervals.
3274 Urban Studies 54(14)

expectations and rests on the fact that, in a
context of relative housing scarcity, the
lower the apartment price, the more afford-
able it is to homebuyers and the more sus-
tained the demand for such units will be.
Consequently, cheaper units are assigned
greater potential for relative price apprecia-
tion over time, which reflects a catch-up
effect for low-price quartiers.
Floor level. With respect to the floor level
variable, a ground floor apartment located
in a building with a lift serves as the refer-
ence. As expected, the higher the floor, the
higher the price. For the median quantile,
the market premium stands at around 7.3%
for the first floor, 10.9% for the second floor
and rises to roughly 15% for upper floors
(6th and above), which offer a panoramic
view of Paris and its famous mansard roofs.
However, as shown in Figure 4, the pricing
of the floor level attribute is not constant
along the price distribution; interestingly,
the higher the price category, the lower the
premium assigned to a given floor level.
Such a result may seem counterintuitive.
For instance, Mak et al. (2010) find the
opposite, as top floors are usually considered
more prestigious. In that respect, it should
be reiterated that in this paper, regression
coefficients are expressed as percentages and
not as absolute contributions to value.
Consequently, a lower relative marginal con-
tribution may still translate into a larger
absolute price for the attribute, when applied
to upper apartment price tags.
Parking place. Parking in Paris
9
is quite pro-
blematic. While local residents have access
to on-street parking permits that allow
them to park at a small fraction of the
parking fare faced by non-residents, some
households prefer off-street parking (e.g.,
Figure 3. Price index for selected deciles.
Ame
´de
´e-Manesme et al. 3275

those with expensive cars). The latter are
thus assumed to apply to high-value apart-
ment buildings with off-street, indoor park-
ing places, even more so if they are located
in the Central Business District where park-
ing facilities are particularly scarce. This
assumption is confirmed by the regression
findings (Figure 5). At the median, a 4.7%
premium is induced by the presence of one
parking place, which rises to above 8.9%
for two parking slots.
10
Yet again, applying
QR provides additional insights into how
attribute prices are structured. The findings
clearly suggest that the relative price of a
parking place rises as the apartment value
increases. Thus, while the market premium
paid for one parking space ranges from
roughly 4.0% (lower decile) to over 6.0%
(upper decile) of apartment prices, it
reaches 11.7% for two parking places in the
case of high-end units. Unsurprisingly, no
additional premium is assigned to a second
parking spot for low-end (Q10) apartments
whose owners, more often than not, cannot
afford more than one car. In their study on
Hong-Kong, however, Mak et al. (2010)
reach the opposite conclusions, with lower
quantiles commanding a higher premium.
Miscellaneous. Other attributes also yield
interesting results. Regarding the construc-
tion period, the Haussmannian period
(1850–1913) is set as the reference. This vari-
able has a non-monotonic relationship with
price, but displays little variation across dec-
iles. Thus, apartments located in recently
constructed buildings (1992–2000) sell at a
quasi-constant premium of roughly 11%
above Haussmannian prices. Such a pre-
mium can easily be explained by the level of
comfort such buildings provide, a function-
ality in line with the modern way of life and
higher construction standards. By contrast,
those dating from the interwar (1914–1947)
and post-Second World War (1948–1969)
periods sell at a discount ranging between
Figure 4. Floor level (ground floor with a lift as the reference).
3276 Urban Studies 54(14)

0.7% and 2.0% for deciles Q30 and above,
while it is not significant for apartments in
the lowest decile. Finally, pre-1850 units ben-
efit from a ‘historic building’ premium over
and above Haussmannian prices, varying
from 1.6% to 3.1%, depending on the decile.
Other features relating to the unit or its
neighbourhood are also assigned substantial
price premiums or discounts. The presence
of a mezzanine, for instance, commands an
average premium of 13.5%, which proves
constant along the price distribution. While
the presence of a garden also generates a
value increment, it steadily rises with the
price segment, at 14.5% for the cheapest
apartments and reaching 21.6% for the most
expensive ones. Having an apartment located
on a ‘place’ or on a ‘quay’ – as opposed to a
plain street, used as the reference – similarly
exerts a positive and growing influence on
value, as the price of the unit increases. For
a ‘place’ location, and for the first (Q10) and
last (Q90) deciles, the market premium grows
from less than 3% (n.s.) to 9%, whereas it
stands at 5% and 11.6%, respectively, for a
‘quay’ location. The high premium attached
to the latter stems from the view of the river
Seine or of neighbouring canals. In contrast,
being located on a boulevard results in a
price discount that reaches 6% for low-end
apartments, because of the noisy environ-
ment, but which is down to only 1.4% for
high-end ones, considering that amenities
such as trees may, to a large extent, lessen
any inconvenience and because of the social
image of a prestige address.
Conclusion and prospect for
future research
In this paper, the heterogeneity of the Paris
apartment market is addressed. For this pur-
pose, quantile regression is applied – with
market segmentation based on price deciles
Figure 5. Parking place premium by decile.
Note: Dotted lines indicate 95% confidence intervals.
Ame
´de
´e-Manesme et al. 3277

– and the hedonic price of housing attributes
is computed for various prices segments of
the market. The approach is applied to a
major data set, which consists of approxi-
mately 156,000 transactions over the 2000–
2006 period. Although spatial econometric
methods could not be applied because of the
unavailability of geocodes, spatial depen-
dence effects are shown to be adequately
accounted for through an array of 80 loca-
tion dummy variables.
This research provides empirical evidence
supporting the fact that QR estimates add
some useful insight into interpreting the
marginal impact of housing attributes on
property values and clearly demonstrate that
such nuances are overlooked when an OLS
approach, based on mean estimates, is used
instead. The findings suggest that hedonic
relative prices of several housing attributes
significantly differ among deciles, although
discrepancies tend to vary greatly in magni-
tude, depending on the attribute. Among
other findings, the elasticity coefficient of
the apartment size variable, which stands at
1.09 for the cheapest units, is down to 1.03
for the most expensive ones. Similarly, a
majority of housing descriptors, including
several neighbourhood attributes and loca-
tion dummies, exhibits significant implicit
price fluctuations over the price distribution.
Using QR makes it possible to sort out attri-
butes that are assigned a constant, relative
contribution to apartment value, irrespective
of the price segment, as opposed to those
whose marginal influence rises or lessens
with price. The research thus enhances our
understanding of the complex market
dynamics that underlies residential choices
in a major metropolis like Paris, where het-
erogeneity simultaneously operates on the
housing stock, historical construct and social
fabric.
As this research highlights the virtues of
QR as a modelling device for handling het-
erogeneity in housing markets, it also raises
a series of issues that need to be addressed in
future research. First, it would be useful to
replicate the analysis over a longer period of
time to test whether the patterns emerging
for the 2000–2006 period – characterised by
a buoyant real estate market – still hold
through slumps or a bearish market. In par-
ticular, it might be interesting to focus on
price index behaviour, thereby highlighting
investment opportunities for various price
segments of the Paris residential market.
The issues warranting further investigation
include where to invest, when to invest and
which attributes should be focused on most,
depending on the asset price range. Second,
an inter-metropolis comparison of the mar-
ket dynamics at stake in large, international
cities would make it possible to assess
whether price setting patterns obtained for
Paris also apply elsewhere or whether they
are a mere reflection of market features that
are idiosyncratic to France’s capital.
Funding
This research received no specific grant from any
funding agency in the public, commercial, or not-
for-profit sectors.
Notes
1. The QR approach is also known as the L1-
norm method.
2. Thus, the 1st arrondissement comprises quar-
tiers 1 through 4, the 2nd arrondissement of
quartiers 5 through 8, etc.
3. The variable lift is poorly reported and
should therefore be interpreted with care
(see appendix, available online).
4. This is achieved by using the exponential of
the coefficient, minus 1. For instance, a coef-
ficient of 0.1367 (6th floor) yields a marginal
contribution to price of 14.6%. This applies
to all variables in the model, with the excep-
tion of the size coefficient; since the variable
is log-transformed, its regression coefficient
is interpreted as the size-elasticity of price.
5. Gregoir et al. (2012) and Zahirovic-Herbert
and Chatterjee (2012) use a smaller
3278 Urban Studies 54(14)

administrative area (respectively, the land
register unit level and the census blocks, each
corresponding to a few building blocks).
6. Here, the logged sale price is used as the
dependent variable (as opposed to the logged
unit price/m
2
). The ‘Size’ parameter is thus
an estimation of the size-elasticity of price.
7. For instance, Zietz et al. (2008) find that the
price elasticity of square footage emerges as
more than three times as high for upper-
decile properties (0.419), than for those at
the lower end of the spectrum (0.133).
8. It has to be recalled here that price impacts
are expressed in relative terms and that a
higher relative willingness-to-pay for an
incremental unit of living area in a low-end
segment of the market may, and will most of
the time, translate into an absolute price rise
which remains substantially lower than the
one observed for upper-segment properties.
9. Ownership of cars in Paris is comparable
with other European cities such as London or
Berlin (about 300 cars per 1000 inhabitants).
10. Property owners in Paris seldom have gar-
ages at their disposal, which is why the refer-
ence is an apartment without a parking
place.
References
Benoit DF and Van den Poel D (2009) Benefits of
quantile regression for the analysis of customer
lifetime value in a contractual setting: An
application in financial services. Expert Sys-
tems with Applications 36(7): 10,475–10,484.
Bhattacharjee A, Castro E and Marques J (2012)
Spatial interactions in hedonic pricing
models: The urban housing market of Aveiro,
Portugal. Spatial Economic Analysis 7(1):
133–167.
Biswas A (2012) Housing sub-markets and the
impacts of foreclosures on property prices.
Journal of Housing Economics 21(3): 235–245.
Bourassa SC, Hoesli M and Peng VS (2003) Do
housing sub-markets really matter? Journal of
Housing Economics 12(1): 12–28.
Brunsdon C, Fotheringham S and Charlton M
(1998) Geographically weighted regression-
modelling spatial non-stationarity. Journal of
the Royal Statistical Society, Series D (The
Statistician) 47(3): 431–443.
Can A and Megbolugbe I (1997) Spatial depen-
dence and house price index construction.
Journal of Real Estate Finance and Economics
14: 203–222.
Clarenc P, Coˆ te J-F, David A, et al. (2014) Les
indices Notaires-INSEE de prix des logements
anciens. INSEE Me
´thodes No. 128. Paris:
INSEE, pp. 154.
Coulson NE and McMillen DP (2007) The
dynamics of intraurban quantile house price
indexes. Urban Studies 44(8): 1517–1537.
Des Rosiers F, The
´riault M and Villeneuve P-Y
(2000) Sorting out access and neighbourhood
factors in hedonic price modelling. The Jour-
nal of Property Investment and Finance 18(3):
291–315.
Ellickson B (1971) Jurisdictional fragmentation
and residential choice. American Economic
Review 61(2): 334–39.
Farmer MC and Lipscomb CA (2010) Using
quantile regression in hedonic analysis to
reveal sub-market competition. Journal of
Real Estate Research 32(4): 435–460.
Goodman AC and Thibodeau TG (1998) Hous-
ing market segmentation. Journal of Housing
Economics 7(2): 121–143.
Goodman AC and Thibodeau TG (2003) Hous-
ing market segmentation and hedonic predic-
tion accuracy. Journal of Housing Economics
12(3): 181–201.
Goodman AC and Thibodeau TG (2007) The
spatial proximity of metropolitan area housing
sub-markets. Real Estate Economics 35(2):
209–232.
Gregoir S, Hutin M, Maury T-P, et al. (2012)
Measuring local individual housing returns
from a large transaction database. Annals of
Economics and Statistics 107/108: 93–131.
Heckman JJ (1979) Sample selection bias as a spe-
cification error. Econometrica 47: 153–161.
Islam KS and Asami Y (2009) Housing market
segmentation: A review. Review of Urban
& Regional Development Studies 21(2–3):
93–109.
Koenker R and Bassett G (1978) Regression
quantiles. Econometrica: Journal of the Econo-
metric Society 46(1): 33–50.
Koenker R and Bassett G (1982) Robust tests for
heteroscedasticity based on regression quan-
tiles. Econometrica 50(1): 43–61.
Ame
´de
´e-Manesme et al. 3279

Koenker R and Hallock K (2001) Quantile regres-
sion: An introduction. Journal of Economic
Perspectives 15(4): 43–56.
Koschinsky J, Lozano-Gracia N and Piras G
(2012) The welfare benefit of a home’s loca-
tion: An empirical comparison of spatial and
non-spatial model estimates. Journal of Geo-
graphical Systems 14(3): 319–356.
Leishman C (2001) House building and product
differentiation: An hedonic price approach.
Journal of Housing and the Built Environment
16(2): 131–152.
Leishman C, Costello G, Rowley S, et al. (2013)
The predictive performance of multilevel mod-
els of housing sub-markets: A comparative
analysis. Urban Studies 50(6): 1201–1220.
Liao WC and Wang X (2012) Hedonic house
prices and spatial quantile regression. Journal
of Housing Economics 21(1): 16–27.
Lipsey RG and Rosenbluth G (1971) A contribu-
tion to the new theory of demand: A rehabili-
tation of the Giffen Good. The Canadian
Journal of Economics/Revue canadienne d’Eco-
nomique 4(2): 131–163.
Mak S, Choy L and Ho W (2010) Quantile regres-
sion estimates of Hong Kong real estate prices.
Urban Studies 47(11): 2461–2472.
Newsome BA and Zietz J (1992) Adjusting com-
parable sales using multiple regression analysis
– The need for segmentation. The Appraisal
Journal 60(1): 129–133.
Orford S (2000) Modelling spatial structures in
local housing market dynamics: A multilevel
perspective. Urban Studies 37(9): 1643–1671.
Pryce G (2013) Housing sub-markets and the lat-
tice of substitution. Urban Studies 50(13):
2682–2699.
Rosen S (1974) Hedonic prices and implicit mar-
kets: Product differentiation in pure competi-
tion. Journal of Political Economy 82(1):
34–55.
The
´riault M, Des Rosiers F, Villeneuve P, et al.
(2003) Modelling interactions of location with
specific value of housing attributes. Property
Management 21(1): 25–62.
Tiebout C (1956) A pure theory of local expendi-
tures. Journal of Political Economy 64: 416–424.
Xu T (2008) Heterogeneity in housing attribute
prices: A study of the interaction behaviour
between property specifics, location coordi-
nates and buyers’ characteristics. International
Journal of Housing Markets and Analysis 1(2):
166–181.
Zahirovic-Herbert V and Chatterjee S (2012) His-
toric preservation and residential property val-
ues: Evidence from quantile regression. Urban
Studies 49(2): 369–382.
Zietz J, Zietz EN and Sirmans GS (2008) Deter-
minants of house prices: A quantile regression
approach. The Journal of Real Estate Finance
and Economics 37(4): 317–333.
3280 Urban Studies 54(14)