Market Heterogeneity and The Determinants of Paris Apartment Prices: A Quantile Regression Approach Fabrice Barthélémy, Univ. de Cergy-Pontoise, France François Des Rosiers, Laval University, Canada Michel Baroni, ESSEC Business School, France Paper presented at the 2013 ERES Conference, Vienna, Austria, July 3 - 6

Objective and Context of Research This study aims at segmenting the Paris apartment market to better understand the structure of prices over the period through quantile regression. The complexity of metropolitan residential markets makes it most relevant to assume that hedonic prices are not homogeneous over time and space and that various submarkets may be generated based on selected housing attributes. Indeed, while sale prices have globally followed a positive trend for 30 years in Paris, analyzing how housing attributes are being valued by buyers upon sale may lead to useful insights into the proper dynamics of the different market segments. 2

Literature Review – Market Segmentation and House Price Structure Several authors have investigated the heterogeneity-of- attributes and market segmentation issues (Bajic, 1985; Can & Megbolugbe, 1997; Goodman & Thibodeau, 1998 and 2003; Thériault et al., 2003; Bourassa, Hoesli & Peng, 2003; Des Rosiers et al., 2007) as they affect the shaping and interpretation of hedonic prices and question a major assumption of the HP model (Rosen, 1974). In that context, heterogeneity in housing attribute hedonic prices can be addressed through Quantile Regression (Koenker and Bassett, 1982; Koenker and Hallock, 2001 ; Ziets et al.,2008; Benoit and Van den Poel, 2009; Farmer and Lipscomb, 2010; Liao and Wang, 2010). 3

Literature Review – Market Segmentation and House Price Structure Past research suggests that…:  By keeping in all the information available from the dataset, QR provides the analyst with better in- depth insights into the effects of the covariates than would a series of independent standard linear regressions ;  QR is relevant for adequately handling the selective heterogeneity of hedonic coefficients with regard to prices ;  Homebuyers’ requirements and preferences for specific housing attributes vary greatly across different price quantiles. 4

Overall Analytical Approach Step 1: The most significant descriptors are determined by an OLS regression on the transaction prices. Step 2: Quantile regression (performed on deciles and centiles) is applied on selected price segments for testing the relative impact of descriptors. Step 3: Conclusions are drawn on the variability of housing attribute hedonic prices with respect to quantiles. 5

The Database The database (BIEN) is provided by the Chambre des Notaires de France and includes, after filtering, some 159,000 apartment sales spread over a 7 year period, that is from 2000 to Housing descriptors include, among other things:  Building age (construction period);  Apartment size (surface) and number of rooms;  Floor location in building;  Number of bathrooms;  Presence of a garage;  Presence of a lift;  Type of street and access to building (blvd, square, alley, etc.);  Location dummy variables standing for the 20 “arrondissements” and 80 “neighbourhoods” (“quartiers”); 6

Map 1: The Twenty Paris « Arrondissements » Paris “Arrondissements” are structured according to a clockwise, spiral design starting in the central core of the city, on the north shore of the River Seine (Arr. 1) and ending up with Arr. 20, in the north-east area. 7

Descriptive Statistics Number of cases by « arrondissement » and by number of rooms 8

Descriptive Statistics Distribution of cases by period of construction 9 Distribution of cases by floor

Number of cases by year of transaction 10 Descriptive Statistics

11 Year soldMeanMedian Number of Obs.: Dep. Variable: Ln Sale Price R-Square: Root MSE: Main Regression Findings – OLS Transaction year/ Size-elasticity of sale price 2000 Reference Reference **0.0918** **0.1830** **0.3149** **0.4524** **0.5886** **0.7109** - Results are similar using the Mean or the Median - Overall, apartment prices in Paris have experienced a 71% growth over the period - Size-elasticity of sale price is > 1 and averages 1.04 The p-values are less than 1% (*) and 0.01% (**) Size- elasticity **1.0394**

12 Number of rooms MeanMedian Main Regression Findings – OLS Number of rooms / service rooms 1 roomReference 2 rooms * 3 rooms0.0137**0.0092* 4 rooms0.0197**0.0164** 5 rooms0.0217**0.0158* 6 rooms rooms * ** 8 rooms ** 9 rooms service roomReference 1 Service room0.0566**0.0539** 2 Service rooms0.0714**0.0670** 3 Service rooms0.1140**0.1197** 4 Service rooms0.1062*0.1686* 5 Service rooms =0.2734** Number of service rooms MeanMedian - For a similar surface, an additional room commands a premium for 3, 4 or 5 rooms and a discount for more rooms (room size becomes too small) - The presence of “service rooms” increases the price significantly (rental opportunities) The p-values are less than 1% (*) and 0.01% (**)

Main Regression Findings – OLS (median) Other attributes Construction period (Haussmannian as the reference):  Buildings built between 1914 and 1947: 1.8% discount;  Between 1948 and 1969 (post- WWII period): more than 2.5% discount (construction quality);  Most recent buildings (1991 or later): 13% market premium Floor level (Ground floor & Lift as the reference)  As expected, the higher the floor, the higher the price. Thus, the market premium stands at around 5% for the first floor, 8% for the second floor and raises to between 11% and 12% for upper floors (6 th to 9th) Number of bathrooms (One bathroom as the reference):  Second bathroom adds 1.4% to the price;  Units without a bathroom sell at a 5% to 10% discount, depending on the number of rooms Buildings with and without a lift  The absence of a lift leads to a price discount of 2% to 3% compared to the same apartment with a lift 13

Main Regression Findings – OLS (median) Other attributes Parking, Mezzanine & Garden  Market premium of 6% and 12% for one and two parking places;  A mezzanine adds 12%;  A garden adds 15%. Location features  Compared to a ‘street’, a ‘Boulevard’ (-4%) or an ‘Alley’ (-14%) location has a negative impact on prices;  On the contrary, a ‘Place’ (+5%) or a ‘Quay’ (+9%) increases significantly the value of an apartment (mixed effect of unobstructed view and social image) & 8 th arrondissements & 19 th arrondissements

15 Main Regression Findings – Quantile Regression The p-values are less than 1% (*) and 0.01% (**) Parameters 0.1 quantile 0.2 quantile 0.3 quantile 0.4 quantile 0.5 quantile 0.6 quantile 0.7 quantile 0.8 quantile 0.9 quantile Pseudo R Dependent Variable : Natural logarithm of sale price Intercept **7.1372**7.2515**7.3493**7.4459**7.5246**7.6029**7.6906**7.8211** Surface (in log) **1.0585**1.0515**1.0455**1.0395**1.0372**1.0349**1.0322**1.0264**

16 Quantile Regression Findings - Surface-elasticity coefficients of Sale Price by decile

17 Quantile Regression Findings - Floor Level ( Ground floor with lift as the reference )

18 Quantile Regression Findings - Construction period ( Haussmannian period as the reference )

19 Quantile Regression Findings - Bathroom & Toilet ( One bathroom as the reference )

20 Quantile Regression Findings - Basement, Parking places & Balcony

21 Quantile Regression Findings - Miscellaneous features

22 Quantile Regression Findings - Location attributes (Street as the reference)

Conclusion This study provides strong evidence that the QR method allows to bring out marked variations in the magnitude, and even direction, of housing attribute influences on price depending on the price range, which the standard OLS regression method does not. While not all attribute implicit prices are found to vary along the value spectrum, several do: this is notably the case, in this research at least, for the price index, the apartment size, the number of rooms, service rooms and bathrooms, the type of housing unit, the floor level, parking places and some location attributes. 23

Conclusion Among other findings, the elasticity coefficient of the size variable, which stands at 1.07 for the first price decile (cheapest units), is down to 1.03 for units belonging to the ninth one (dearest units). Apartment prices do not evolve at the same pace along the value range, the annual growth rate for lower-priced properties standing at 9.8% over the six year period, as opposed to only 8.9% for luxury apartments. Finally, market premiums (+) or price discounts (-) assigned to some location attributes may also vary widely across deciles, following either an upward (alley-, avenue+) or downward (hamlet+) trend. 24

Discussion Whatever the urban context, specific submarkets may be targeted for commercial marketing, public policy or mortgage lending purposes, in which case a reliable assessment of property values turns out to be of paramount importance. This is where the QR approach, which lends itself to a variety of methodological adaptations, has a clear advantage over the standard OLS method, although it should be viewed as a complement, rather than as a substitute, to the latter. 25