L. Miguel Martínez and José Manuel Viegas

Effects of Transportation Accessibility on Residential Property Values: A Hedonic Price Model in the Metropolitan Area

L. Miguel Martínez PhD Candidate CESUR, Department of Civil Engineering Instituto Superior Técnico Lisbon Technical University Av. Rovisco Pais 1049 - 001 Lisboa, . Phone: +351-21-8418425 Fax: +351-21-840 9884 Email: [email protected]

José Manuel Viegas Professor of Civil Engineering CESUR, Department of Civil Engineering Instituto Superior Técnico Lisbon Technical University Av. Rovisco Pais 1049 - 001 Lisboa, Portugal. Phone: +351-21-8418413 Fax: +351-21-840 9884 Email: [email protected]

The total number of words is 8,389 (5,889 words + 4tables + 6figures)

Submitted to the 88th Annual Meeting of the Transportation Research Board 15 th of November, 2008 L. Miguel Martínez and José Manuel Viegas 1

ABSTRACT

The aim of this paper is to examine the relationship between the availability of transportation infrastructure and services and the pattern of house prices in an urban area, and to assess whether public investment in transportation can really modify residential property values. This study was developed for the (LMA) as part of a broader study that intends to develop new value capture financing schemes for public transportation in the LMA. The paper focuses in three central municipalities (, Lisbon, ) where these effects could be more easily measured due to the existence of a significant variability of public transportation services. The paper tries to determine, using different spatial hedonic pricing models, the extent to which access to transportation infrastructure currently is capitalized into house prices, isolating the influence of three different transportation infrastructures: metro, rail and road. The results suggest that the proximity to one or two metro lines leads to significant property value changes and that the classic hedonic price model (ordinary least squares estimation) leads to similar coefficient values of the local accessibility dummy variables compared to the spatial lag model, thus providing a steady basis to forecast the property values changes derived from transportation investment for the study area in the absence of a significant property values database. L. Miguel Martínez and José Manuel Viegas 2

INTRODUCTION

For decades, there has been considerable discussion about the effects of transportation accessibility on the housing prices. It is well known that a good public transport system provides a high level of access to work and other activities for households, and to customers and employees for businesses. The monetary value of this accessibility will be reflected in the value of a home or a business, in addition to the value of other features such as the specific physical attributes of the building and neighbourhood characteristics. The impact of public transport on property values has been studied from many perspectives, including analyses of different types of systems (e.g., rapid, commuter, light rail), of residential versus commercial impacts, and studies that have attempted to isolate both positive and negative effects. The varied approaches make it difficult to compare the results of one study to another. Further, some of the contradictory results over the years have often been due to differing methods of analysis, data quality, and regional differences. This paper examines the relationship between the availability of transportation infrastructure and services and the house prices in an urban area, trying to assess the impact of public investment in transportation on residential property values. This study was developed for the Lisbon Metropolitan Area (LMA) as part of a broader study that intends to develop new value capture financing scheme for public transportation in the LMA. The available data focuses in three central municipalities (Amadora, Lisbon, Odivelas) where these effects could be more easily measured due to the existence of a significant variability of public transportation services. This study presents several hedonic pricing models to assess the relationship between transportation accessibility and house values, ranging from the classic model to spatial hedonic price models (spatial lag) and including local and systemwide accessibility indicators. The results of the different models are assessed and compared having in mind the need to forecast house prices in subsequent phases of the research project.

LITERATURE REVIEW

In the 1960s, economists like Alonso and Muth developed the theory for determining residential location in the urban land market (1, 2). The theory illustrates a model where a household chooses to locate at a point where its bid-rent curve intersects with the actual one, in which the bid rent curves have a declining gradient with the distance from the residential location to the central business district (CBD). However it might be necessary to consider the effect of other variables such as neighborhood characteristics. The introduction of the hedonic pricing methodology by Rosen (3) led to an easier way of attributing value to different properties’ features. A number of studies have observed the integration of physical, neighborhood and accessibility characteristics of the property in models trying to explain the differences in property values or house prices (4-35). The hedonic price model is a multivariate regression model for housing values, as well as a common robust indirect approach to valuation in that its estimates represent the implied prices that people place on obtaining desirable features of a property and avoiding undesirable ones (20, 36). Most commonly, hedonic price models have used ordinary least squares (OLS) estimation (22, 33, 37-39), but more recently these models have been extended to incorporate L. Miguel Martínez and José Manuel Viegas 3 spatial effects in multiple ways: feasible generalized least square estimation (34) and spatial econometric models (spatial lag and spatial error models) (20, 40). There are several empirical evidences relating the changes in commercial and residential property market values and transport investment. Table 1 presents the information from the Europe, whilst Table 2 does the same for North America. As can be seen from the tables, the evidence is broadly positive with the widest difference being found between the residential and commercial markets. Parsons Brinkerhoff (41) concludes that proximity to rail systems is valued by property owners and there is little support that this proximity can decrease property values. Much of the European research (Table 1) has focused mainly on the residential market, but in the US research (Table 2) where the commercial market has been the main target. Almost uniformly, the impacts are seen as positive, with some very large percentage increases particularly in commercial property values. The enormous variability in (positive) impact points towards either the importance of other factors, or the specificity of results, or the limitations of the methods used – or a combination of all these factors.

TABLE 1 Property value impacts of public transport proximity in European cities.

Case/Location Impact on Impact Source Bremen Office rents +50% in most cases (42) Some localized positive Croydon Tramlink Residential property (43) impacts Freiburg Office rent +15-20% (42) Freiburg Residential rent +3% (42) Greater Manchester Not stated +10% (42) Hannover Residential rent +5% (42) Helsinki Metro Property values +7.5-11% (44) Residential and commercial London Crossrail Positive (45) property Residential and commercial London Docklands LRT Positive (44) property Residential and commercial London JLE Positive (46, 47) property Manchester Metrolink House Prices Unable to identify (48) Montpellier Property values Positive (42) Nantes LRT Commercial property Higher values (42) Nantes LRT Not stated Small increase (42) Nantes LRT Number of commercial premises +13% (44) Nantes LRT Number of offices +25% (44) Nantes LRT Number of residential dwellings +25% (44) Newcastle upon Tyne House prices +20% (42) None-initially negative due Orléans Apartment rents (42) to noise Rouen Rent and houses +10% most cases (42) Saarbr űcken Not stated None (42) Sheffield Supertram Property values Unable to identify (16, 48) Strasbourg Office rent +10-15% (42) Strasbourg Residential rent +7% (42) Tyne and Wear Metro Property values +2% (49) Vienna S-Bahn Housing units +18.7% (44)

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TABLE 2 Property value impacts of public transport proximity in North American cities.

Case/Location Impact on Impact Source Atlanta Office rents Positive (8, 50) Baltimore LRT Not stated Unable to identify (44) Boston Residential property +6.7% (50, 51) Buffalo, New York House prices +4-11% (23) Chicago MTA House prices +20% (52) Dallas DART Commercial rents +64.8% (53) Dallas DART Property values +25% (53, 54) Linden, New Jersey Residential property Positive (55) Los Angeles Property values Higher values (56) Miami House prices +5% (7) New Jersey SEPTA rail House Prices +7.5-8% (57) New Jersey PACTO rail House Prices +10% (57) New York Not stated Positive (58) Pennsylvania SEPTA rail House Prices +3.8% (57) Portland House prices +10% (42) Portland Gresham Residential rent >5% (42) Portland Metropolitan House prices +10.5% (17, 19) Express San Diego Trolley Not stated Positive (44) San Francisco Bay Area Property values Positive (59) BART San Francisco Bay Area +10-15% Residential rent (60, 61) BART +15-26% County Commercial and office property +23-120%% (62) Santa Clara County House prices +45% (18) Santa Clara County Residential rent +15% (25) St. Louis Property values +32% (63) Toronto Metro House prices +20% (29, 44) Washington DC Residential rent Positive (50, 64)

DATA DESCRIPTION

The data used in this study are 2007 cross-sectional real estate data from an online realtor’s database (Imokapa Vector) for Lisbon, Portugal. This database presents the asking price of residential properties on sale during February of 2007 with a total of 12,488 complete records, 70% inside Lisbon’s Municipality. The real estate data contained information on their asking sale price, structural attributes and address. The descriptive statistics of the data is presented in Table 3. The real estate data was geocoded and imported into geographic information system (GIS) transportation analysis network map. All the properties were connected with the road and public transport network in order to measure the several accessibility indicators used. The spatial distribution of asking prices is presented in Figure 1, where it is easy to denote that a great part of the most expensive properties are located near the metro and rail lines. The dependent variable is the advertised asking selling price at which the owner or realtor is offering the property in the market. This can be a limitation to the model because the dependent variable is not directly linked to an equilibrium price, where supply and L. Miguel Martínez and José Manuel Viegas 5 demand have cleared the transaction (65). Other studies that relate public transport accessibility to residential property or land values also have relied on asking prices (11, 16, 24, 64-66).

FIGURE 1 Spatial distribution of property asking prices for the study area

The properties of accessibility to public transport and to the road network were developed using two different types of characterization: local accessibility and systemwide accessibility. Local accessibility indicators were calculated using the network distance to public transport entry points (walking distance using 4 km/h) and to roads considered in Lisbon Mobility Plan 2004 (67) road hierarchy at the various levels (distance in meters). The three different levels of road hierarchy presented represent urban motorways for Network1, urban arterials as Network2 and collector/distributor roads as Network3. These accessibility measures were built using two different approaches. The first approach considers an all-or-nothing influence of proximity to public transport entry points and to the road network, resulting in a set of dummy variables for each public transport mode or line and for each road hierarchy level. L. Miguel Martínez and José Manuel Viegas 6

The second approach considers a continuous decreasing function of impedance of proximity to public transport entry points and to the road network. To model this continuous impedance it was used an inverse logistic function with different parameters for each public transport line and road hierarchy. The inverse logistic function considered is:

1 Y = (1) 1+ exp ()a − b()X max − X where Xmax is an specific parameter of each public transport line or road hierarchy and a and b are calibrated by considering two different point in the curve (e.g. 5 minutes walking distance – Y =0.90, and 15 minutes walking distance – Y =0.10). An example of comparison between both measuring approaches can be assessed in Figure 2, where the main differences are in the values observed for accessibility distances greater than the threshold established for the all-or-nothing measuring approach.

1.0000 0.9000 0.8000 0.7000 0.6000 0.5000 0.4000 0.3000 Accessibilityindicator 0.2000 0.1000 0.0000 0 5 10 15 20 25 30 Accessibility time (min.) Continuous Approach All-or-nothing Approach

FIGURE 2 Calibrated β values of the Gravitational model for Lisbon Mobility Plan 2004

These variables and their descriptive statistics are presented in the local accessibility attributes of Table 3.

The systemwide accessibility indicators were calculated using a gravitational model calibrated for Lisbon’s Mobility Plan survey of 2004. The model equation is (68):

Fij = Oi ⋅ Ai ⋅ D j ⋅ B j ⋅ exp( β ⋅ Cij ) 1 1 (2) Ai = ; B j = ∑[Dk ⋅ Bk ⋅exp( β ⋅Cik )] ∑[Om ⋅ Am ⋅exp( β ⋅Cmj )] k m

L. Miguel Martínez and José Manuel Viegas 7

where Fij is the total flow between zone i and j for each mode, Oi the total number of trips with origin in i, D j the total number of trips with destination in j and Cij is the impedance between zones i and j, measured in travel time between zones. Ai and B j are calibration variables that are needed in a doubly constrained gravitational model calibration. The calibrated β’s for public transport (PT) and private car (PC) are presented in Figure 3, where the difference between the calibrated β’s is very significant (approximately 4 times greater for the private car showing a much greater ease of displacement than in public transport).

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 Exp(-beta.c(k,j)) 0.2 0.1 0 0 20 40 60 80 100 120 140 160 180 200

Accessibility time C ij (minutes)

Beta PC = -0,03420 Beta PT = -0,00833

FIGURE 3 Calibrated β values of the Gravitational model for Lisbon Mobility Plan 2004

A land use database for the study area was then used for the calculation of the accessibility indicator. The D j term of the gravitational model equation was replaced by the land use surface ( Aj ) and standardized using the land use surface of the whole study n area ∑ Aj . The accessibility indicator results then in the following equation: j=1

n A j AccGr i = ∑exp( β ⋅Cij ) ⋅ p(A j ) ; p(A j ) = n j=1 (3) ∑ A j j=1

The descriptive statistics of these accessibility indicators are presented in Table 3. Some neighbourhood attributes for each property were also calculated in order to improve to explanatory power of the models. These variables are an Educational Index that calculates the percentage of undergraduate persons in the population over 20 years old in a 500 radius around the property, and the Entropy Index that measures the mixture of land use types in a radius of 500 m (69, 70). These descriptive statistics of these neighbourhood attributes are presented in Table 3. L. Miguel Martínez and José Manuel Viegas 8

TABLE 3 Descriptive statistics of the variables (N= 12,488)

Variable Description Mean St Dev Price Asking price (€) 223,123.11 145,408.15 Ln_Price Natural logarithm of the asking price 12.17 0.533 Structural Attributes Bedrooms Number of bedrooms 2.393 1.068 House 1 if house 0.027 0.161 Floor Floor number 2.952 2.431 Area Area (sq. meters) 103.789 59.253 Age1 1 if Property age <= 10 years 0.351 0.477 Age2 1 if 10 years < Property age < 50 years 0.327 0.469 Age3 1 if Property age >= 50 years 0.322 0.467 Garage 1 if garage spaces >=1 0.470 0.499 Neighbourhood Attributes Number of undergraduate persons/Population over 20 Educational Index 0.197 0.129 years old (500 meters radius) Entropy Index within a walking distance of 500 meters k Entropy Index pi ⋅ln( pi ) 0.220 0.103 EI 500 = ∑ (69, 70) i=1 ln( k) Local Accessibility Attributes Metro 2MAccess10 1 if walk time to access 2 metro lines <=10 minutes 0.048 0.214 2MAccess = 1/(1+exp(4.394 -0.439 *(20 –walking time))) 0.058 0.163 1MAccess10 1 if walk time to access 1 metro lines <=10 minutes 0.265 0.441 1MAccess = 1/(1+exp(6.812 -0.659 *(17 –walking time))) 0.123 0.240 Road Network1_1000 1 if distance to Network1 <=1000 meters 0.425 0.494 Network1 = 1/(1+exp(8.789 -0.007 *(2000 –access distance))) 0.266 0.351 Network2_500 1 if distance to Network2 <=500 meters 0.438 0.496 Network2 = 1/(1+exp(8.789 -0.013 *(1000 –access distance))) 0.273 0.353 Network3_250 1 if distance to Network3 <=250 meters 0.558 0.500 Network3 = 1/(1+exp(8.789 -0.026 *(500 –access distance))) 0.345 0.367 Rail 1 if walk time to train station < 10 minutes and Azambuja10 0.006 0.078 less than 20% of the distance to CBD Azambuja = 1/(1+exp(4.394 -0.439 *(20 –walking time))) 0.005 0.057 1 if walk time to Lisbon train station < 10 minutes and less Lisboa10 0.014 0.119 than 10% of the distance to the CBD Lisboa = 1/(1+exp(4.394 -0.439 *(20 –walking time))) 0.014 0.094 Nacional10 1 if walk time to Nacional train station < 10 minutes 0.013 0.114 Nacional = 1/(1+exp(4.394 -0.439 *(20 –walking time))) 0.010 0.082 1 if walk time to train station < 10 minutes and less Sintra10 0.028 0.164 than 20% of the distance to CBD Sintra = 1/(1+exp(4.394 -0.439 *(20 –walking time))) 0.029 0.131 1 if walk time to Fertagus train station < 10 minutes and Fertagus10 0.001 0.037 less than 20% of the distance to CBD Fertagus = 1/(1+exp(4.394 -0.439 *(20 –walking time))) 0.001 0.033 1 if walk time to train station < 10 minutes and Cascais10 0.014 0.117 less than 20% of the distance to CBD Cascais = 1/(1+exp(4.394 -0.439 *(20 –walking time))) 0.011 0.078 L. Miguel Martínez and José Manuel Viegas 9

Variable Description Mean St Dev Systemwide Accessibility Attributes Gravitational model accessibility index with β calibrated Gravitational_PT for public transport 0.708 0.058

Gravitational model accessibility index with β calibrated Gravitational_PC for private car 0.493 0.084

MODELING METHODOLOGY

Six different cross-sectional models were developed in this study. We used three different specifications for the accessibility effect (local accessibility all-or-nothing, local accessibility continuous and systemwide accessibility) and two modelling approaches (ordinary least squares regression model (OLS) and spatial lag regression model). Both present a semi logarithmic hedonic specification that is widely used in the property value literature motivated by the fact that it usually produces robust estimates and enables convenient coefficient interpretation. The general structure of the OLS model is:

Ln (P ) = β + β ' X + β ' X + ... + β ' X + ε i 0 1 i1 2 i2 n in i (4) ε ~ N ,0( σ 2 I)

where Pi is the price of house i , X i1... X in are the vectors of the explanatory variables for the price of house i . The dependent variable is given in the natural logarithmic form; thus the values of the coefficients represent percentage change. The specifications used for the OLS models (for each type of accessibility indices) are given by:

' ' ' ' ' Ln(P i ) = α + βBD Beedrooms i + βHS House i + βFL Floor i + β AR Area i + β AG 2 Age 2i + β' Age 3 + β' Garage + β' EducationI ndex + β ' EntropyInd ex + AG 3 i GR i LI i EI i ' ' ' (5) β2MA 2MAccess 10 i + β1MA 1MAccess 10 i + βN1 Network 1_1000 i + ' ' ' ' βN 2 Network 2_500 i + β N 3 Network 3_250 i + βSN Sintra10 i + βCS Cascais10 i + εi

' ' ' ' ' Ln (Pi ) = α + β BD Beedrooms i + β HS House i + β FL Floor i + β AR Area i + β AG 2 Age 2i + β ' Age 3 + β ' Garage + β ' EducationI ndex + β ' EntropyInd ex + AG 3 i GR i LI i EI i (6) ' ' ' β 2MA 2MAccess i + β1MA 1MAccess i + β N1 Network 1i + ' ' ' ' β N 2 Network 2i + β N 3 Network 3i + β SN Sintra i + β CS Cascais i + ε i

' ' ' ' ' Ln (Pi ) = α + β BD Beedrooms i + β HS House i + β FL Floor i + β AR Area i + β AG 2 Age 2i + ' ' ' ' β AG 3 Age 3i + βGR Garage i + β LI EducationI ndex i + β EI EntropyInd ex i + (7) ' ' β PT Gravitatio nal _ PT i + β PC Gravitatio nal _ PC i + ε i L. Miguel Martínez and José Manuel Viegas 10

The spatial lag models general structure is presented in Equation 8.

Ln ( P ) = ρW + β ' + β ' X + β ' X + ... + β ' X + ε i Ln ( Pi ) 0 1 i1 2 i 2 n in i (8) ε ~ N ,0( σ 2 I)

where Pi is the price of house i , X i1... X in are the vectors of the explanatory variables for the price of house i , ρ is the autoregressive coefficient and W the spatial lagged variable in Ln (Pi ) order to a N × N spatial weight matrix.

The specifications used for the spatial lag models are given by:

Ln (P ) = ρW + α + β ' Beedrooms + β ' House + β ' Floor + β ' Area + i Ln (Pi ) BD i HS i FL i AR i β ' Age 2 + β ' Age 3 + β ' Garage + β ' EducationI ndex + β ' EntropyInd ex + AG 2 i AG 3 i GR i LI i EI i (9) ' ' ' β 2MA 2MAccess 10 i + β1MA 1MAccess 10 i + β N1 Network 1_1000 i + ' ' ' ' β N 2 Network 2 _ 500 i + β N 3 Network 3_ 250 i + β SN Sintra10 i + β CS Cascais10 i + ε i

Ln (P ) = ρW + α + β ' Beedrooms + β ' House + β ' Floor + β ' Area + i Ln (Pi ) BD i HS i FL i AR i β ' Age 2 + β ' Age 3 + β ' Garage + β ' EducationI ndex + β ' EntropyInd ex + AG 2 i AG 3 i GR i LI i EI i (10) ' ' ' β 2MA 2MAccess i + β1MA 1MAccess i + β N1 Network 1i + ' ' ' ' β N 2 Network 2i + β N 3 Network 3i + β SN Sintra i + β CS Cascais i + ε i

Ln (P ) = ρW + α + β ' Beedrooms + β ' House + β ' Floor + β ' Area + i Ln (Pi ) BD i HS i FL i AR i ' ' ' ' ' β AG 2 Age 2i + β AG 3 Age 3i + β GR Garage i + β LI EducationI ndex i + β EI EntropyInd ex i + (11) ' ' β PT Gravitatio nal _ PT i + β PC Gravitatio nal _ PC i + ε i

The spatial weight matrix for both spatial lag models was developed assuming constant spatial dependence between properties until a maximum established distance. The maximum Euclidean distance used was 1000 m, resulting in a Moran’s I = 0.144 ( P-value = 0.000)

MODELING RESULTS AND DISCUSSION

Estimation results from the six different models are presented in Table 4. Using the Pseudo R 2 as goodness-of-fit measure (squared correlation between the predicted and the observed values of the dependent variable), we can observe a high explanation of the dependent variable with values ranging from 0.75 and 0.80. Langrange multiplier (LM) tests were also conducted to assess if the omission of the spatial lag on the OLS model was erroneous (i.e H 0 : ρ = 0 ). The LM test statistic is given by (35): L. Miguel Martínez and José Manuel Viegas 11

e'Wy  1 LM =   ⋅ (12)  σ 2  (WXb )' MWXb /σ 2 + tr (W 'W +W 2 ) where

M = common residual maker vector (N × N) in OLS estimation, e = spherical OLS residual vector (N × )1 , σ 2 = e'e / N , b = OLS coefficient vector (K × )1 , tr = trace of the matrix (N × N) .

The LM test is approximately χ 2 distributed with one degree of freedom. As presented in Table 4, the LM test for the local accessibility spatial lag models is significant at α = 01.0 , indicating a proper spatial lag specification, whilst the systemwide accessibility spatial lag model is not significant, indicating that the OLS model in this case is more appropriate. Almost all the independent variables used in the six models are significant at α = 05.0 (Sintra being the exception for both local accessibility spatial lag models), independently of the estimation model and of the proxy accessibility variables used. In addition, the models consistently demonstrate the impact of each independent variable on the natural logarithm of the asking price and a similar magnitude of the coefficients of the structural attributes along the different models. The coefficient estimation for the structural attributes shows that the Area (floor surface) is the attribute with greater impact in the dependent variable (approximately 0.07% increase for a 1% square meter increase), followed by the Age and Bedrooms, which present similar values in all the models. The neighbourhood attributes are the ones that present higher coefficient variation among the estimated models. As expected, the spatial lag term “replaces” some of the explanatory power of the neighbourhood variables and of the constant of the model, although it does not significantly affect the coefficients of the accessibility attributes, as can be seen in the local accessibility models in Table 4. This fact shows the stability of the local accessibility coefficients in the all-or-nothing approach, the significance of the Sintra attribute being the only one affected. The metro accessibility attributes coefficients range in the two models between 5.65% and 6.50% for the accessibility to two metro lines and between 4.25% and 4.28% for the accessibility to a single metro line, showing a significant impact of the metro proximity over the property values. The local accessibility coefficients in the continuous approach present less stability. The metro accessibility attributes coefficients range in the two models between 7.28% and 11.27% for the accessibility to two metro lines and between 4.06% and 5.44% for the accessibility to a single metro line, showing again a significant impact of the metro proximity over the property values. The rail accessibility attributes coefficients in all the local accessibility models illustrate a positive impact for the proximity to the Cascais Line with coefficients ranging L. Miguel Martínez and José Manuel Viegas 12 between 8.40% and 10.55% for the all-or-nothing accessibility measure approach and between 10.16% and 18.83% for the continuous approach; and a negative impact for the proximity to the Sintra Line with coefficients ranging between -4.45% and -1.06% (not significant for the usual significance levels) for the all all-or-nothing approach and between -10.16% and 1.04% (not significant for the usual significance levels) for the continuous approach. These effects might be explained by the perception of lack of security associated with the Sintra Line, which prevents the properties of the nearby areas to take full advantage of the proximity to this high capacity public transport system and the proximity of the Cascais Line to a very expensive residential area in the Southeast area of Lisbon (Restelo neighbourhood). The road accessibility attributes coefficients range in the two models of the all-or- nothing approach between -9.53% and -10.39% for the accessibility road hierarchy 1, between 5.89% and 7.16% for the accessibility to road hierarchy 2 and between -3.77% and - 5.90% for the accessibility to the road hierarchy 3. The road accessibility attributes presents similar impact for the two models of continuous approach with coefficients ranging between -14.13% and -7.98% for the accessibility road hierarchy 1, between 1.33% and 9.64% for the accessibility to road hierarchy 2 and between -1.19% and -4.34% for the accessibility to the road hierarchy 3. These estimations show that the proximity to the road hierarchy 2 (urban ring roads and radial network) is the one that presents a positive impact on the property values, whilst the proximity to the road hierarchy 3 (urban distribution network) and road hierarchy 1 (motorways) present a negative impact. These results can derive from the congestion and noise externalities perceived by the population near road hierarchy 1 and the switch to offices centres of buildings located near road hierarchy 3 in the Lisbon’s city centre, reducing the residential supply in these areas. The results of the local accessibility continuous spatial lag model show the existence of a smaller impact of road network attributes on the dependent variable what might be explained by the significant increase of the SP Lag coefficient of this model in comparison to the all-or-nothing approach spatial lag model. We cannot compare directly the coefficients resulting from the local accessibility continuous models with the all-or nothing accessibility measure models due to fact that the continuous indicators present continuous values between 0 and 1, not being possible to derive a percentage of change directly from the coefficient. The percentage of change on the property selling prices will result from the product between the value of the accessibility indicator and the coefficient of the same indicator, resulting in a property selling prices impact distribution rather than a single value. The systemwide accessibility OLS model presents significant differences in coefficients of the constant and neighbourhood attributes when compared with the local accessibility OLS model. This might be due to the significant correlation of the systemwide accessibility attributes with the neighbourhood attributes (i.e. correlation between Gravitational_TC and Entropy Index is equal to 0.465 and to 0.235 with the Educational Index), which can explain the reduction of the neighbourhood attributes coefficients. This correlation results from the fact that the systemwide accessibility indicators measure accessibility to activities scattered in the study area, which can be positively L. Miguel Martínez and José Manuel Viegas 13 influenced by the presence of a high land use mixture around the property measured by the Entropy Index. We can see easily in Figure 4 that the Gravitational_TC indicator measures simultaneously public transport accessibility and land use activity proximity and their relation. This fact illustrates that is difficult to isolate with the systemwide accessibility indicators the changes in property values derived from transportation infrastructures investment from the neighbourhood land use characteristics.

FIGURE 4 Gravitational_TC indicator spatial distribution for the study area

The systemwide accessibility spatial lag model illustrates also the last statement due to the non significance of the spatial lag model (see Table 4), because the systemwide accessibility indicators can already explain part of the spatial dependence of the property asking price. Using the Akaike info criterion to rank the models, we can consider the local accessibility continuous spatial lag model as the best prediction model followed by the systemwide accessibility OLS model and the local accessibility all-or-nothing spatial lag model. We can thus conclude, from the estimates of the developed models, that the local accessibility models can measure better the isolated effect of transportation investment on L. Miguel Martínez and José Manuel Viegas 14 properties selling prices and that the estimates from the OLS models can be sufficiently accurate in the absence of significant property values database for all the study area (needed for the calculation of the spatial lag model). The spatial distribution of the property prices estimates of the local accessibility continuous spatial lag model is presented in Figure 5 where we can see a similar spatial distribution to the database asking prices (see Figure 1). Figure 6 present the spatial distribution of the estimated residuals, where we can denote sub-estimates and over-estimates scattered along all the study area with some sub-estimates concentrated in the North part of the study area and in the Expo area in the Northeast Lisbon’s border.

FIGURE 5 Property prices estimates of the local accessibility continuous spatial lag model

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FIGURE 6 Unstandardized residuals of the local accessibility continuous spatial lag model L. Miguel Martínez and José Manuel Viegas 16

TABLE 4 Results of the OLS and Spatial Lag Models

Ordinary Least Squares (OLS) ML Spatial Lag Local Accessibility Local Accessibility Systemwide Local Accessibility Local Accessibility Systemwide

all-or-nothing Model continuous Model Accessibility Model all-or-nothing Model continuous Model Accessibility Model Std. Std. Std. Std. Std. Std. Coef. Coef. Coef. Coef. Coef. Coef. Error Error Error Error Error Error SP_LAG_LOGPRICE ------0.4043 *** 0.0121 0.6264 *** 0.0085 0.2968 *** 0.0143 Constant 11.1146 *** 0.0099 11.1073 *** 0.0104 10.4106 *** 0.0369 6.2840 *** 0.1446 3.6777 *** 0.1010 6.8770 *** 0.1743 Structural attributes Bedrooms 0.0357 *** 0.0033 0.0600 *** 0.0032 0.0380 *** 0.0033 0.0396 *** 0.0032 0.0690 *** 0.0029 0.0410 *** 0.0032 House 0.2037 *** 0.0169 0.0838 *** 0.0165 0.2038 *** 0.0166 0.1738 *** 0.0162 0.0818 *** 0.0148 0.2017 *** 0.0163 Floor 0.0156 *** 0.0010 0.0172 *** 0.0010 0.0184 *** 0.0010 0.0169 *** 0.0010 0.0168 *** 0.0009 0.0183 *** 0.0010 Area 0.0069 *** 0.0000 0.0059 *** 0.0000 0.0070 *** 0.0000 0.0067 *** 0.0000 0.0056 *** 0.0000 0.0069 *** 0.0000 Age2 -0.1291 *** 0.0069 -0.1426 *** 0.0070 -0.1415 *** 0.0067 -0.1203 *** 0.0067 -0.1172 *** 0.0063 -0.1360 *** 0.0066 Age3 -0.0851 *** 0.0073 -0.0963 *** 0.0075 -0.0957 *** 0.0072 -0.0820 *** 0.0071 -0.0895 *** 0.0067 -0.0921 *** 0.0071 Garage 0.1205 *** 0.0064 0.1271 *** 0.0066 0.1279 *** 0.0063 0.1189 *** 0.0062 0.1235 *** 0.0059 0.1235 *** 0.0062 Neighbourhood attributes Educational Index 0.9811 *** 0.0202 1.0407 *** 0.0209 0.7638 *** 0.0193 0.7131 *** 0.0219 0.1972 *** 0.0220 0.5932 *** 0.0219 Entropy Index 0.5430 *** 0.0346 0.4231 *** 0.0257 0.2959 *** 0.0347 0.2466 *** 0.0340 0.2422 *** 0.0231 0.2014 *** 0.0344 Local Accessibility Attributes ( all-or-nothing and continuous approach ) 2MAccess10 (2MAccess) 0.0565 *** 0.0130 0.1127 *** 0.0171 -- -- 0.0650 *** 0.0126 0.0728 *** 0.0154 -- -- 1Maccess10 (1MAccess) 0.0425 *** 0.0061 0.0406 *** 0.0114 -- -- 0.0428 *** 0.0059 0.0549 *** 0.0103 -- -- Network1_1000 (Network1) -0.0953 *** 0.0051 -0.1413 *** 0.0074 -- -- -0.1039 *** 0.0049 -0.0798 *** 0.0067 -- -- Network2_500 (Network2) 0.0716 *** 0.0048 0.0964 *** 0.0070 -- -- 0.0589 *** 0.0047 0.0133 ** 0.0063 -- -- Network3_250 (Network3) -0.0590 *** 0.0048 -0.0434 *** 0.0066 -- -- -0.0377 *** 0.0046 -0.0119 ** 0.0060 -- -- Sintra10 (Sintra) -0.0445 *** 0.0151 -0.1057 *** 0.0180 -- -- -0.0106 0.0146 0.0104 0.0162 -- -- Cascais10 (Cascais) 0.1055 *** 0.0245 0.1883 *** 0.0306 -- -- 0.0840 *** 0.0237 0.1016 *** 0.0274 -- -- Systemwide Accessibility Attributes Gravitational_PT ------0.4674 *** 0.0774 ------0.6923 *** 0.0769 Gravitational_PC ------0.8084 *** 0.0546 ------0.4304 *** 0.0561 Pseudo R 2 0.753 0.753 0.764 0.773 0.801 0.772 LM statistic 214.670 *** 2019.366 *** -203.435 Log likelihood -656.08 -886.031 -373.817 -426.742 123.652 -475.535 Akaike info criterion 1344.16 1806.06 771.635 889.483 -211.304 977.07

*** , ** , and * denote coefficient significantly different from zero at the 1%, 5%, and 10% level of significance (two-tailed test), respectively. L. Miguel Martínez and José Manuel Viegas 17

SUMMARY AND CONCLUSIONS

This paper analyses the effect of transportation accessibility on the properties prices as part of a broader study that intends to develop new value capture financing scheme for public transportation in the LMA. Several cross-sectional hedonic price models are estimated based on an online realtor’s database (Imokapa Vector) of property selling asking price. The models account for structural, neighbourhood and accessibility attributes of residential properties, the latest ones structured in two types: local accessibility attributes and systemwide accessibility attributes. The main focus of this study is to develop a framework to forecast house prices and the influence of transportation infrastructure investment in further steps of the research project. The estimated models revealed that:

• The local accessibility hedonic price models developed showed the existence of spatial interactions of sale prices, presenting a spatial autocorrelation with a significant spatial lag. • The local accessibility models present a stability of the local accessibility coefficients estimated, the significance of the Sintra attribute being the only one affected. • The metro accessibility attributes coefficients range in the two all-or-nothing models between 5.65% and 6.50% for the accessibility to two metro lines and between 4.25% and 4.28% for the accessibility to a single metro line, showing a significant impact of the metro proximity over the property values. • The metro accessibility attributes coefficients range in the two continuous models between 7.28% and 11.27% for the accessibility to two metro lines and between 4.06% and 5.49% for the accessibility to a single metro line. • The rail accessibility attributes coefficients illustrate a positive impact for the proximity to the Cascais Line with coefficients ranging between 8.40% and 10.55%, and a negative impact for the proximity to the Sintra Line with coefficients ranging between -4.45% and -1.06% (not significant for the usual significance levels) for the all-or-nothing accessibility measure models. • The rail accessibility attributes coefficients for the continuous accessibility measure models present a positive impact for the proximity to the Cascais Line with coefficients ranging between 10.16% and 18.83%, and a negative impact for the proximity to the Sintra Line with coefficients ranging between -10.57% and 1.04% (not significant for the usual significance levels). • The road accessibility attributes coefficients range in the two all-or-nothing accessibility measure models between -9.53% and -10.39% for the accessibility road hierarchy 1, between 5.89% and 7.16% for the accessibility to road hierarchy 2 and between -3.77% and -5.90% for the accessibility to the road hierarchy 3. • The road accessibility attributes coefficients range in the continuous accessibility measure models between -7.98% and -14.13% for the accessibility road hierarchy 1, between 1.33% and 9.64% for the accessibility to road hierarchy 2 and between - 1.19% and -4.34% for the accessibility to the road hierarchy 3. L. Miguel Martínez and José Manuel Viegas 18

• The systemwide accessibility models presents significant differences in coefficients of the constant and neighbourhood attributes when compared with the local accessibility models. This indicates the difficulty the isolate the accessibility effects from the neighbourhood effects over house prices with these models. • The systemwide accessibility spatial lag model developed is not significant, which indicates that the systemwide accessibility indicators do also explain also part of the spatial autocorrelation.

The coefficients resulting from the local accessibility continuous models cannot be compared directly with the coefficients from the all-or nothing accessibility measure models due to fact that the continuous indicators present continuous values between 0 and 1, not being possible to derive a percentage of change directly from the coefficient. The percentage of change on the property selling prices will result from the product between the value of the accessibility indicator and the coefficient of the same indicator, resulting in a property selling prices impact distribution rather than a single value. Using the Akaike info criterion to rank the models, we can consider the local accessibility continuous spatial lag model as the best prediction model followed by the systemwide accessibility OLS model and the local accessibility all-or-nothing spatial lag model. The main conclusions that can be drawn from the estimates of the developed models are that the local accessibility models can better measure the isolated effect of transportation investment on properties selling prices and that the estimates from the OLS model can be sufficiently accurate in the absence of a significant property values database for all the study area (needed for the calculation of the spatial lag model).

ACKNOWLEDGMENTS

This research is being supported by the Portuguese National Science Foundation (FCT) since 2006. The private company Imokapa Vector has provided support by making available an online realtor’s database. TIS.pt has also provided support by making available the LMA Mobility Survey from 2004, and to the software company INTERGRAPH for the Geomedia Professional 5.2 license.

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