Predicting changes in housing prices from two ...

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Predicting changes in housing prices from two transport investments: A case study of two fixed link projects in rural areas in Norway Øyvind Lervik Nilsen, Corresponding Author Department of Civil and Transport Engineering Norwegian University of Science and Technology/Rambøll Norway 7491 Trondheim, Norway/Fjordgaten 13, 3103 Tønsberg Tel: 0047-45280334 Email: [email protected] Petter Arnesen Department of Safety and mobility, SINTEF S.P. Andersens veg 5, 7031 Trondheim, Norway Tel: 0047-98083886 Email: [email protected] Stig Nyland Andersen Norwegian University of Science and Technology/Norwegian Public Roads Administration 7491 Trondheim, Norway/Askedalen 4, 6863 Leikanger, Norway Tel: 0047-90958569 Email: [email protected] María Díez Gutiérrez Department of Civil and Transport Engineering Norwegian University of Science and Technology 7491 Trondheim, Norway Tel: 0047-47735050 Email: [email protected]

Trude Tørset Department of Civil and Transport Engineering Norwegian University of Science and Technology 7491 Trondheim, Norway Tel: 0047-97038649 Email: [email protected]

(working paper) Word count:

6645 words including references 5663 words excluding references Abstract count: 194 words

Submission Date

26.03.2018

Nilsen, Arnesen, Andersen, Tørset

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ABSTRACT The first signs of increased attractiveness for residential location and population

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growth can usually be seen in a growth in housing prices. Several studies have shown a

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positive relationship between accessibility and housing prices often using hedonic regression

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techniques. However, most of these studies have mainly focused on urban areas and have not

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tested the model’s predictions abilities. This paper will contribute in filling this knowledge

7

gap by investigating the relationship between housing prices and accessibility in a more rural

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context with special emphasis on islands connected by fixed links. By developing spatially

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and non-spatially dependent regression models based on approximately 8,500 actual housing

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sales on the western coast of Norway we test the model’s ability to fit the data set and their

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prediction capabilities. Our results show that the spatially dependent model outperforms the

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non-spatially dependent model for model fitting, while we cannot conclude the same for the

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model’s predictive power. Furthermore, the models show that accessibility to the main

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regional centre seems to be an important part also in a more rural setting. This suggests that

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rural areas that get improved accessibility via transport investments might expect a growth in

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housing prices.

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Keywords: hedonic regression modelling, housing prices, accessibility, fixed link projects


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1. INTRODUCTION

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One main concern with transport investments is to promote infrastructure projects that

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contribute to regional cohesion and economic growth. Many large infrastructure projects have

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been proposed on the very idea that they reduce distances between settlements and trigger

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economic growth making the areas affected more attractive for residential and firm location.

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However, it varies substantially to what degree these projects have had a positive impact on

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population and economic development (Louw, Leijten, & Meijers, 2013; Melo, Graham, &

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Brage-Ardao, 2013; Nilsen, Díez Gutiérrez, Andersen, & Tørset, 2017; Tveter, Welde, &

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Odeck, 2017). Hence, a deeper understanding of how transport investments affect firm and

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residential location is essential. This is a relationship that is seldom taken into account in

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today’s transport planning (Acheampong & Silva, 2015; Waddell, Ulfarsson, Franklin, & Lobb,

12

2007), even though it is of crucial importance in understanding the long-term effects for

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transport investments and of increased interest of policy makers (Vickerman, 2016).

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The first signs of changes in the attractiveness for residential location are usually seen

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in the housing market (Wegener, 2004) . Where people choose to live is highly dependent on

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the real-estate market (Coppola & Nuzzolo, 2011; Ho & Hensher, 2014; Waddell, 2011). The

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real-estate market is influenced by both internal and external housing characteristics. The

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proximity to job opportunities, public amenities, schools etc. are important factors in explaining

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the selling price for a house and the differences between them. The relationship between

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housing prices and accessibility has been verified in a growing number of empirical studies

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often using hedonic regression techniques (Efthymiou & Antoniou, 2013; Á. Ibeas, Cordera,

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Dell’Olio, & Coppola, 2013; Liv Osland, 2010). Hedonic models assume that price is

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determined by the internal and external characteristics of the goods being sold (Rosen, 1974).

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In a real estate market context, this method is appealing as it deals with heterogeneous goods

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such as houses. Even though the methodology is widely used, it has some challenges when it


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comes to spatial autocorrelation and spatial heterogeneity which could lead to biased or

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inefficient parameters (LeSage & Pace, 2009). These issues are often dealt with by using spatial

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econometric techniques such as the simultaneous autoregressive model (SAR), spatial Durbin

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model (SDM) (A. Ibeas, Cordera, Dell’Olio, Coppola, & Dominguez, 2012; L Osland &

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Thorsen, 2013) or geographically weighted regression (GWR) (Gadziski & Radzimski, 2015).

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Several empirical studies have investigated the relationship between changes in

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accessibility and the housing market (Andersson, Shyr, & Fu, 2010; Geng, Bao, & Liang, 2015;

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Mulley, Ma, Clifton, Yen, & Burke, 2016). However, most of these studies are using models at

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a city level mainly focusing on fitting a given data set of housing transactions into the model,

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and not on their predicting performance. A knowledge gap exists in terms of using these kinds

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of models in a more rural context and testing their predictive performance after a transport

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investment is made. These two issues are essential in the modelling of changes in the housing

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market due to large infrastructure projects, and will be addressed in this paper.

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The ability to estimate the increase in real-estate prices from changes in accessibility is

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important for several reasons. Firstly, by developing models for areas that are heterogenous in

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nature, we contribute in the research on using hedonic regression models which mainly have

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been used within homogenous areas (L Osland & Thorsen, 2013) . Secondly, if a proposed

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project significantly increases the real-estate prices in one area, it might trigger development

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effects that might alter the residential location pattern. When these changes are used to

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recalculate the residential location pattern, this might be important input in transport analysis,

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which is highly dependent on accurate population forecasts. Today, population prognoses are

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often treated as an exogenous variable in the transport models. Thus, they are normally not

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depedent of changes in accessibility from transport projects (Ortúzar & Willumsen, 2011). This

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has been the case for transport analysis done on fixed link projects along the Western Coast of

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Norway (Tørset, Nilsen, & Spilsberg, 2013). Thirdly, by testing the models’ predictive power

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on actual transport projects we shed light on their actual use. This is an issue that is scarcely


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studied in the literature, but is essential for practitioners.

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This paper empirically investigates the relationship between accessibility and housing

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prices for two heterogenous counties on the western coast of Norway. By developing spatially

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and non-spatially dependent regression models we shed light on the importance of accessibility

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in a more rural context. How well the models explain the changes in housing prices is then

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tested for two large infrastructure projects and for the counties they are located in. Fixed link

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projects that replace ferries are chosen as infrastructure projects as these projects represent a

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substantial change in accessibility. Thus, potential changes in housing prices should be

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expected.

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The structure of the paper is as follows. Section 2 describes the area studied. Section 3

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describes the methodology, including the estimation of the accessibility measure and the

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hedonic regression models used in the analysis. In Section 4, the results are presented while

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Section 5 discusses the findings. Section 6 summarizes the main findings from our

14

investigation.

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2. STUDY AREA AND DATA

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This paper focuses on two large infrastructure projects on the western coast of Norway.

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The cases are both fixed link projects, involving subsea tunnels replacing ferry services that

20

connect islands to the mainland. Figure 1 shows the two cases studied, including the fixed links.


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Figure 1. Location of cases studied, (a) Eiksundsambandet, (b) Finnfast.

Table 1 describes the characteristics of the connected islands before and after the


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1

opening of the fixed links, while Table 2 describes the two counties. All places experienced a

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growth in traffic volumes to/from the connected islands.

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Table 1: Characteristics of the connected islands

Opening year Travel time to the nearest city before the fixed link (including waiting time for ferry) Travel time to the nearest city after the fixed link Ferry ticket price Toll

Eiksundsambandet 2008 70 min.

Finnfast

50 min.

50 min.

EUR 7 EUR 0 (EUR 8 until 2014)

EUR 8 EUR 17 (EUR 23 until 2011) 1500

Number of jobs that can be reached 16,500 within 45 min, before the fixed link Number of jobs that can be reached 22,000 within 45 min, after the fixed link Traffic the year before the opening 800 (AADT) Traffic five years after the opening 2200 (AADT) Average square meter price before 690 EUR in 2004-2007 (N=103) opening (single unit house) Average square meter price after opening (single unit house) 970 EUR in 2008-2011 (N=158)

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2009 90 min

150,000 400 700 980 EUR in 2006-2009 (N=26) 1230 EUR in 2010-2013 (N=46)

To estimate the changes in housing prices from these two fixed link projects, regression

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models were developed for the counties the fixed links were located in.

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Table 2: Description of the characteristics for the five counties analyzed

County 1 (Rogaland)

County 2 (Møre og Romsdal)

Number of inhabitants

470,000

265,000

Workforce in employment

237,000

132,000

4.7 %

3.4 %

9,400 km2

15,100 km2

Unemployment rate Size 8 9

The two counties, Møre og Romsdal and Rogaland, have relatively low population

10

density (see Table 2). This is especially the case for Møre og Romsdal which only has a few

11

cities in the range of 10,000 – 50,000 inhabitants.


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3. METHOD

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In a hedonic modelling framework, it is essential to distinguish between two categories

5

of attributes. One is the physical attributes of the dwelling and the other is related to the spatial

6

structure of the neighborhood and accessibility to job and recreational opportunities. The

7

housing price will be described by a function of these two factors. In general, the hedonic price

8

function can be written as:

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Pit = f (Dit , A it )

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Equation 1: The general form of the hedonic price function

Pit is the selling price of house i in year t. Dit is the physical attributes of the house i while Ait is its spatial characteristics.

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3.1. Accessibility measure

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The accessibility measure should generally reflect the degree of economic and

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employment opportunities in one area as a function of the distance to and from other nearby

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areas. It should address how accessibility decay with distance, suggesting that areas with many

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activities in close proximity have a higher weight than areas further away. Based on Hansen

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(1959) the generalized cost of travel often appears through a negative exponential function in

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a measure of accessibility. Numerous accessibility measures have been developed after

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Hansen's (1959) pioneering work. In this article an accessibility measure is used based on the

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work of Cascetta (2001) and Nuzzolo & Coppola (2007).

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1

{

Ai = å E aj 1 * exp[a 2 * GCij]

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}

j

2

Equation 2: Accessibility measure

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where the accessibility, Ai, of a given zone i is a proxy of the opportunity of reaching

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activities in other nearby zones j. Ej is the number of jobs within zone j, GC is the generalized

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travel cost of travelling between i and j and α1 and α2 are parameters to be estimated. The

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general travel costs are calculated using time weights from the Norwegian time study (Farideh,

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Flügel, Samstad, & Killi, 2010) between all areas. The travel time includes simplified

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calculations of congestion and waiting time for ferries (half the ferry frequency). These

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calculations were made in the Norwegian transport model (Tørset, Malmin, Bang, & Bertelsen,

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2013). By doing a logarithmic transformation of Equation 2 and using number of trips from

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zone i to j as a proxy for accessibility the parameters α1 and α2 can be estimated using ordinary

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least squares (Coppola, Ibeas, Dell’Olio, & Cordera, 2013) (see equation 3).

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log(TRIPSij) = a1 * log(Ej) + a 2 * GCij Equation 3: Estimation of α1 and α2

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The estimated values of the parameters were for α1 0,18 and for α2 -0,04. The number

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of trips from zone i was obtained from a transport model. The accessibility measure suggested

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in Equation 2 should in principle address the importance of the distance to the central business

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district and more local subcentres/towns, in house price calculation. However, very often these

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two variables are included in addition to the accessibility measure (see (Liv Osland, 2010)) as

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these centres might include other factors not captured by the more general accessibility measure

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(presence of universities, hospitals, cultural facilities etc.).

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The accessibility measure was calculated for 3452 basic statistical units for two

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counties on the Western coast of Norway (see Figure 2). Each of these units included the number


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of jobs within different sectors and number of inhabitants. Statistics Norway produced this data

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set. By combining this information with the generalized cost from the Norwegian transport

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model, it was possible to estimate accessibility measures for each of these statistical units.

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Figure 2: Accessibility for Rogaland and Møre og Romsdal


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The housing data used was on a coordinate level. Therefore, the housing data were

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aggregated to match the transport model zones used to calculate the accessibility measures.

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The same calculated accessibility for all housing sales within each statistical unit was used in

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the development of the regression models.

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3.2. The data used in developing the model

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In total around 2,800 housing transactions were used to estimate the model for Møre

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og Romsdal and 5,700 for Rogaland. These sales were from 2007. The model’s predictive

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performance was then tested on approximately 2,500 housing transactions from 2010 in Møre

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og Romsdal and 5,100 in Rogaland. The housing data were collected from the Land Registry

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and Cadastre, and the data consisted of actual housing sales in the open market. Their detailed

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level made it possible to conduct disaggregated level analysis of each sale. The sales data

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consist of various housing specific variables and x,y coordinates and street name. For each sale,

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the internal and external characteristics were obtained (see Table 3).

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Table 3: Localization and housing attributes

External housing characteristics ACC GC_SUBC GC_RegCen Internal housing characteristics PRICE SIZE GARAGE AGE BATH ROOMS LOT_SIZE HOUSING_TYPE

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Definition Accessibility measure The generalized cost in travelling to nearest subcentre/town by car The generalized cost in travelling to nearest regional centre by car Selling price of house Living area measured in square meteres Number of garages Age of the building Number of bathrooms Number of rooms Lot size measured in square meteres 1=single unit dwelling, 2= semidetached house, 3=Row house, 4=apartment


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3.3. Hedonic regression models

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Spatial data are characterized by spatial autocorrelation and spatial heterogeneity

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(LeSage & Pace, 2009). While spatial heterogeneity refers to the violation of the assumption

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in ordinary least squares (OLS) about constant variance in the residuals, spatial autocorrelation

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is the violation of the assumption about uncorrelated error terms. In a housing market context,

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cross-sectional data from housing transactions often have these issues to overcome, in order to

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get unbiased estimates of the parameters (Liv Osland, 2010).

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To evaluate the inclusion on spatial dependency within the modelling of housing prices

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we will test three models. A simple multinomial linear regression model (MLR) with zero mean

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Gaussian independent noise , used as a baseline and two spatial simultaneous autoregressive

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lag models; the autoregressive error model (SAR) and the spatial durbin model (SDM) (LeSage

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& Pace, 2009). For the regression model we choose the following functional form after some

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exploratory investigation of the data sets:

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log(

_

)= log(

+ =

+

log(GC_RegCen) + )+

log(

sHouse +

)+

log(

log(

)+

_

detHouse + β

)+

log(

_

ℎ+

)+

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Equation 4: functional form of the regression model

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ROOMS were taken out of the model due to high correlation with SIZE. Furthermore, the

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variable GARAGE had to be taken out because many observations were missing.

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The simultaneous autoregressive model (SAR) and the spatial Durbin model (SDM)

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are often proposed as suitable approaches to deal with spatial autocorrelation. By adding the

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average-neighbor values of the dependent variable to the linear model the SAR model deals


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with the issue of spatial autocorrelation (see Equation 5).

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log(

)=

(

+

) + ε

Equation 5: The Simultaneous Autoregressive model (SAR)

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is the internal and external housing characteristics similar to the linear model and

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is the spatial weights matrix that specifies the spatial dependence structure between the

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houses. In this case, houses within the same statistical unit, and neighboring statistical units,

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are assumed to be spatially dependent. Finally,

9

parameter. If ρ is zero, there is no spatial dependency between the observations. Then normal

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MLR can be used. Positive ρ values indicate positive dependency. In the spatial Durbin model,

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the spatial lagging of the explanatory variable,

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means that the characteristics of neighboring houses could have an influence on the price of

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each house in the sample.

is referred to as the spatial correlation

( )

, is also included (see Equation 6). This

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log(

)=

(

)+

W is the spatial matrix and ( )

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while ρ and

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model is equal to the SAR model.

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+

( )

+

Equation 6: The Spatial Durbin model (SDM)

is the internal and external housing characteristics

are spatial autocorrelation parameters. In contrast to the SAR model there is

also a spatial correlation parameter for the independent variables. Thus, if

( )

= 0, the Durbin

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3.4. Evaluation of model predictions

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To evaluate the differences between the spatially independent regression model and the spatial

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simultaneous autoregressive lag models a measure of the predicted residual error sum of


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squares (PRESS) (see equation 6) was estimated. Both the independent and the dependent

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spatial regression models are based on housing transactions from 2007. These models are used

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to predict housing transaction prices for 2010 for the same two counties.

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(pricei - · pricei ) 2 PRESS = åi=1 n n

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Equation 7: Predicted error sum of squares (PRESS)

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is the predicted price for house and pricei is the actual selling price for house

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i. The ability to predict changes in housing prices for areas that experience a significant change

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in accessibility is also tested by isolating PRESS values for the two fixed link projects presented

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in section 2. In additional to the PRESS values, the percentage of estimations with prediction

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error less than 30 % is presented.

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4. RESULTS

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The results from the three different hedonic regression models estimated are shown in TABLE

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4 and TABLE 5. TABLE 4 is for the county of Møre og Romsdal while TABLE 5 is for the

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county of Rogaland. The sign of the coefficient (β) indicate whether the variable will have a

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positive or negative impact on housing prices. For example, an increase in the generalized

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travel cost from the regional centre would decrease the selling price of a house, when all other

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variables are held constant. This is because the coefficient for RegCen is negative. ρ indicates

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spatial autocorrelation in residuals while the Moran I’s values indicate clustering or dispersion

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of the residuals in the model. A statistical significantly positive Moran I value, typically implies

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a tendency of clustering of similar values, while a negative Moran I value means dispersion


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and values close to 0 mean that the residuals are random. The AIC is the Akaike information

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criterion, and it indicates the quality of the model and is helpful in model selection. Lower AIC

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values are usually preferred over high values.

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TABLE 4: Estimated parameters for MLR model, SAR and SDM model, Møre og Romsdal

β 12.65**

MLR S.E 0.08

t-value 159.9

β 7.91**

Constant Internal housing characteristics Log of housing age -0.14** 0.01 -14.24 -0.12** Log of lot size 0.01** 0.01 3.60 0.01** Log of housing size 0.39** 0.02 22.45 0.38** Number of bathrooms 0.03** 0.01 4.29 0.03** Apartment (reference group) Single unit house -0.11** 0.03 -4.39 -0.12** Detached house -0.05** 0.01 -2.88 -0.06** lag. of housing age lag. of lot size lag. of housing size lag. of number of bathrooms lag. of single unit house lag. of detached house External housing characteristics log of accessibility 0.14** 0.00 9.54 0.08** log of generalized cost to regional centre -0.09** 0.00 -7.79 -0.09** log of generalized cost to subcentre/town -0.03** 0.00 -3.16 -0.03** lag. of accessibility lag. of generalized cost to Regional centre lag. of generalized cost to subcentre/town ρ Number of observations, N 2282 Global Morans’I 12.33** AIC 1561 ** Significant at 99 % confidence interval, * significant at the 95 % confidence interval 2

SAR S.E 0.558

z-value 14.18

β 7.13**

SDM S.E 0.73

z-value 9.70

0.01 0.00 0.02 0.01 0.02 0.02

-12.25 3.53 22.01 4.04 -4.84 -3.35

-0.13** 0.01** 0.38** 0.03** -0.11** -0.05** 0.03 -0.01 -0.03 -0.03 -0.08 -0.03

0.01 0.00 0.02 0.01 0.03 0.02 0.03 0.01 0.15 0.04 0.09 0.06

-10.72 3.97 21.82 4.48 -3.87 -2.23 0.81 -1.69 -0.20 -0.82 -0.85 -0.43

0.01 0.01 0.01

-7.65 -3.76 -3.76

0.12** -0.08 -0.05 -0.05 0.02 0.03

0.05 0.06 0.03 0.05 0.08 0.04 0.41** 2282 -0.82 1494

2.43 -1.48 -1.39 -0.87 0.30 0.79

0.35** 2282 1.115 1492


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TABLE 5: Estimated parameters for MLR model and SAR model, Rogaland

β 12.44**

MLR S.E 0.08

t-value 159.9

β 4.96**

Constant Internal housing characteristics Log of housing age -0.06** 0.00 -7.61 -0.02** Log of lot size 0.01 0.00 -0.128 -0.01 Log of housing size 0.53** 0.01 48.89 0.50** Number of bathrooms -0.01 0.01 -0.87 -0.01 Apartment (reference group) Single unit house -0.28** 0.02 -17.91 -0.26** Detached house -0.13** 0.01 -12.12 -0.13** lag. of housing age lag. of lot size lag. of housing size lag. of number of bathrooms lag. of single unit house lag. of detached house External housing characteristics log of accessibility 0.06** 0.00 9.14 0.06** log of generalized cost to regional centre -0.11** 0.00 -23.24 -0.06** log of generalized cost to subcentre/town -0.02** 0.00 -3.32 0.01 lag. of accessibility lag. of generalized cost to regional centre lag. of generalized cost to subcentre/town ρ Number of observations, N 5688 Residuals Morans’I 40.70** AIC 3351 ** Significant at 99 % confidence interval, * significant at the 95 % confidence interval 2

SAR S.E 0.33

z-value 15.22

β 4.25**

SDM S.E 0.36

z-value 11.76

0.01 0.00 0.01 0.01 0.01 0.01

-2.00 -0.98 45.20 -1.25 -17.06 -12.66

-1.48 -0.01** 0.51** -0.01** -0.23** -0.10** 0.02 0.01 -0.23** 0.05** 0.05** 0.01

0.01 0.00 0.01 0.01 0.02 0.01 0.02 NA 0.02 0.02 0.02 NA

-1.71 -5.42 47.86 -2.25 -15.61 -10.18 -1.05 NA -12.03 2.44 2.41 NA

0.01 0.01 0.01

6.68 -10.50 -0.02

0.10** 0.04 -0.01** -0.06** -0.08 0.02

0.03 0.00 0.01 0.03 0.04 0.01 0.62** 5688 4.63 2876

3.97 0.94 -2.27 -2.26 -1.78 1.79

0.51** 5688 5.78** 2958


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1

From TABLE 4 and TABLE 5 the MLR and SAR model gives theoretically correct signs and

2

all coefficients are significant except number of bathrooms and lot size in the model developed

3

for Rogaland. The SDM model show some less significant variables with some unexpected

4

signs. The low and insignificant Morans’I values indicates that the SAR and SDM models

5

explain all the spatial dependency for Møre og Romsdal while there seem to be some spatial

6

dependence left in the SAR model for Rogaland. The results suggest that we need to introduce

7

the extra spatial term in the SDM model to reduce the Moran’s test to be insignificant for

8

Rogaland.

9

In terms of AIC values, the SAR model outperforms the MLR for both counties.

10

Regarding the interpretation of the results it is important that the SAR model considers the lag

11

of the dependent variable, as simultaneous feedback exists because changes in one observation

12

affect the neighboring observations. Therefore, in the case of SAR and SDM models, the

13

estimated parameters should be interpreted as a state of equilibrium in the modelling process.

14

The estimated parameters for SAR models showed similar signs as the MLR model. Moreover,

15

the variables found significant in the SAR model remained the same as in the MLR model.

16

In terms of AIC values, the SDM model outperforms the MLR for both counties. It

17

also seems to have lower AIC values than the SAR model for Rogaland but not for Møre og

18

Romsdal. However, the SDM model has less significant variables than the other two models.

19

The spatial lag of the independent variables was in most cases insignificant. Interestingly, these

20

findings are similar to Ibeas et al. (2012) who also found insignificantly lagged independent

21

variables when using the SDM model for the metropolitan area of Santander.

22

The SDM model does not suggest an increase in model fit for the county of Møre og

23

Romsdal and just slightly for Rogaland, and the lack of significant variables in the SDM model

24

makes the SAR model more suitable for the prediction calculations. Therefore, the SAR model

25

is preferred over the SDM in the future analysis of model predictions in this paper.

26


19

1 2

4.1. How well the models predict the housing sales

3

To evaluate the performance of the MLR and SAR model, we have considered the PRESS

4

statistics on data from 2010. We have considered the whole data set consisting of the whole

5

county, and a subset of the data, corresponding to all housing sales on the islands that have

6

been connected to the main land with a tunnel between the years of the two data sets (2007 and

7

2010). The PRESS statistics are shown in Table 6.

8

Table 6: Prediction calculations, PRESS values and prediction error in % for 2007

Model estimation 2007 Møre og Romsdal (PRESS value) Prediction error less than.. 30 % 20 % 10 % 5% Rogaland (PRESS value) Prediction error less than.. 30 % 20 % 10 % 5% Fixed link projects Eiksundsambandet (PRESS value) Prediction error less than.. 30 % 20 % 10 % 5% Finnfast (PRESS value) Prediction error less than.. 30 % 20 % 10 % 5% 9

MLR

SAR

4.87*10^11

4.72*10^11 (-3.1 %)

72 % 56 % 35 % 19 % 5.85*10^11

72 % 57 % 35 % 20 % 5.41*10^11 (-7.5%)

74 % 54 % 32 % 20 %

76 % 59 % 35 % 21 %

2.60*10^11

2.40*10^11 (-7.7%)

74 % 65 % 42 % 28 % 2.95*10^11

72 % 59 % 33 % 20 % 2.98*10^11 (+1.01%)

N/A N/A N/A N/A

N/A N/A N/A N/A

Table 7:Prediction calculations, PRESS values and prediction error in % for 2010

Model prediction for 2010 Møre og Romsdal (PRESS value) Prediction error less than.. 30 % 20 % 10 % 5%

MLR

SAR

2.24*10^12

2.28*10^12 (+1.8%)

59 % 36 % 15 % 8%

56 % 33 % 14 % 7%


Rogaland (PRESS value) Prediction error less than.. 30 % 20 % 10 % 5% Fixed link projects Eiksundsambandet (PRESS value) Prediction error less than.. 30 % 20 % 10 % 5% Finnfast (PRESS value) Prediction error less than.. 30 % 20 % 10 % 5%

20

1.19*10^12

1.23*10^12 (+3.3%)

68 % 49 % 25 % 14 %

67 % 49 % 26 % 14 %

5.93*10^11

6.42*10^11 (+7.6%)

55 % 29 % 9% 4% 1.64*10^12

51 % 20 % 5% 3% 1.88*10^12 (+12.8%)

N/A N/A N/A N/A

N/A N/A N/A N/A

1 2

The PRESS values on the 2007 data set show better model performance for the SAR model

3

than the MLR for both counties. For the county of Møre og Romsdal the model shows a 3.1 %

4

increase in model fit, while it was 7.5 % for Rogaland. For the two areas connected by a fixed

5

link, the SAR models seem to outperform the MLR for Eiksundsambandet, while the results

6

are similar for Finnfast. However, only 17 observations were available at Finnfast.

7

Interestingly, the MLR seems to outperform the SAR model when it comes to model

8

prediction in 2010. For the county of Møre og Romsdal the values of PRESS show 1.8 %

9

reduction in predictive performance for SAR compared to MLR. This seems also to hold for

10

Rogaland where the SAR models have a reduction of 3.3 % in predicative performance

11

compared to the MLR. The same trend can be seen when isolating the two fixed link projects.

12

Based on the 175 house sales connected to the main land by Eiksundsambandet the predictive

13

performance is reduced with 7.6 % in the SAR model. For Finnfast the predictive performance

14

was 12.8 % lower for SAR than MLR. Even though it is not uncommon for simpler models to

15

outperform more advanced models in terms of prediction it, is a bit surprising, especially since

16

the model fit is better with the more advanced SAR model. In this case, explaining the data and

17

to model the spatial dependence is best done by using SAR, while for prediction purposes the


1

21

simpler MLR model framework cannot be shown to be less useful than SAR.

2

Regarding their ability to estimate the housing prices on the islands before and after

3

the ferry replacement project was built, the models seem to perform better in a situation before

4

the fixed link was built. This seems to hold for the ferry replacement projects in both Møre og

5

Romsdal and Rogaland.

6 7 8

5. DISCUSSION

9

Increased housing prices after a transport investment is usually a sign of increased

10

attractiveness for residential location and an indication of possible population growth in the

11

future. Numerous studies have investigated the relationship between changes in accessibility

12

and housing prices by developing different kinds of hedonic regression models. However, few

13

of these studies have tested the models developed to predict future housing prices after a

14

transport investment is made in a more rural setting. This paper sheds light on how spatially

15

dependent and non-dependent regression models preform regarding both fitting data and

16

predicting housing sales after changes in the transport network is made. Interestingly the spatial

17

regression model preforms the best for model fitting, while for prediction we cannot say that

18

the spatial regression model outperforms the standard linear regression model. Similar results

19

were found in a study by Bourassa et al. (2007) of real-estate transactions in New Zeeland

20

where the MLR outperforms the SAR models in model prediction. However, there are also

21

studies showing that models that deal with spatial heterogeneity outperform MLR in terms of

22

prediction (Füss & Koller, 2016). Thus, further research is needed to give any clear

23

recommendations regarding model selection.

24

The results indicate that both internal and external characteristics are important for the

25

price of a house also in a more rural setting. The price seems to increase with the size of the


22

1

house and accessibility, and decrease with housing age and distance to the main regional centre.

2

This seems to hold across both counties and two of the three models investigated. These

3

findings are in line with earlier studies done within the field (Ahlfeldt, 2013; L Osland &

4

Thorsen, 2013). The results indicate that a reduction in the distance to the regional centre

5

through a transport investment may be associated with an increase in housing prices. Distances

6

to regional centres seem to be more important than subcentres or smaller towns in determining

7

the selling price of a house. To further improve the models, other spatial characteristics might

8

be included such as distances to schools, a dummy for rural lot size, and crime rate (see (Chung,

9

2015; Ho & Hensher, 2014; L Osland & Thorsen, 2013)). However, most areas in Norway have

10

good access to schools and low crime rates, which sugges that these variables might not be of

11

major importance in improving the model in a Norwegian context.

12

The hedonic regression models tested in this paper show the same tendencies as for

13

models that are made for urban, homogenous areas. However, the models developed seem to

14

have a lower predictive power than models that are made for more homogenous areas. As the

15

areas studied in this paper consist of several different labour and housing markets often

16

connected by ferry services it is not surprising. Ferry services are often bottlenecks in the

17

transport network and the inconvenience of being dependent on a ferry is often substantial

18

(Bråthen & Hervik, 1997). Often beyond the waiting time measure used in the calculations of

19

the accessibility and generalized travel cost in this article. Thus, further research is needed

20

regarding the size of the inconvenience cost to obtain better estimates for the impact of ferry

21

replacement projects on housing prices.

22

It is important to this field of research to focus on developing models useful for

23

prediction. In that respect, applying other types of modelling framework could be crucial to

24

obtain good results. Gaussian Markov random fields (GMRF) (see (Rue & Held, 2005)) have

25

been developed to represent spatial dependence and it would be interesting to test that approach

26

within this field. Moreover, as the data set becomes larger, algorithms from the field of artificial


1

23

intelligent (AI) could bring value to such analysis in the future.

2

The results from this investigation show that changes in housing prices may be

3

expected from transport investments also in more rural areas, especially, for projects that

4

substantially reduce the generalized travel cost to regional centres and increase accessibility.

5

This could lead to increased attractiveness for residential location and a population growth.

6

Population prognosis is an essential part of transport analysis and the calculations of transport

7

demand. Ignoring potential population growth from these transport investments could lead to

8

biased traffic calculations, which in turn could affect the decisions regarding road standard and

9

the cost benefit ratio of the projects proposed. In order to obtain indications of the degree to

10

which it affects the population growth and pattern, the housing market model may be included

11

as part of the residential relocation models often used within a Land Use Transport Interaction

12

(LUTI) model framework (Cordera, Ibeas, Dell’Olio, & Alonso, 2018). However, this is

13

outside the scope of this article and left for future research.

14 15

6.

CONCLUSION

16

Many large infrastructure projects are often proposed on the very idea that they reduce

17

distances between settlements and widen the labour market making the areas more attractive

18

for firms and residential location. During the last 30 years, a substantial number of ferry

19

replacement projects have been built connecting people to the main land in Norway.

20

A first sign of increased attractiveness for residential location can usually be seen in

21

increased housing prices. Thus, developing tools that estimate to what degree transport

22

investments increase the housing prices is important to get indications of whether a growth in

23

population might be expected or not. By developing three different hedonic regression models

24

at a county level, this article investigates the ability these models have to predict housing prices

25

after a transport investment is made.


24

1

Our results provide valuable insights into how changes in accessibility in a more rural

2

setting affect housing prices. The results from the models developed, suggest that internal

3

housing and external characteristics do matter in terms of housing prices. The distance to the

4

main regional centre seems to be more important than the distance to smaller towns and

5

subcentres. Thus, areas that experience a major change in accessibility are likely to get an

6

increase in housing prices and attractiveness for residential location.

7

The results from the study show that spatially dependent models seem to outperform

8

traditional non-spatial regression models regarding data fitting. However, this is not found

9

regarding the model’s prediction abilities. The overall prediction abilities seem to be somewhat

10

lower than for similar models developed for more homogenous areas, even though, the same

11

variables seem to be of importance.

12 13

Acknowledgements

14

This research was supported by the Norwegian University of Science and Technology, the

15

Norwegian Public Roads Administration, Rambøll Norway and the Research Council of

16

Norway.

17

18

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