Image source: jaymantri.com, CC0 licensed

What price for “free” on-street parking?

Tiziano Colombo

Supervision: Prof. Dr.Kay W. Axhausen Georgios Sarlas, MSc

Bachelor Thesis Civil Engineering

June 2018 What price for “free” on-street parking? June 2018

Acknowledgements

I would like to thank Prof. Kay W. Axhausen for giving me the possibility to do this bachelor thesis and for the meetings that were very useful in terms of getting the main points of the thesis. An enormous thanks goes to my supervisor Georgios Sarlas for the grand support and help provided each time I needed it, especially for helping me with the statistic software R and with the QGIS software, providing me all the datasets and giving me important and always useful advices on how to proceed. I would also like to thank Thomas Schatzmann for the help provided with QGIS. I would finally thank all the people that supported me in every way possible as my family and my friends.

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Bachelor Thesis

What price for “free” on-street parking? Tiziano Colombo Bergacker 38, 8046 Zürich, Switzerland

Phone: +41-79 194 68 75 E-Mail: [email protected]

June 2018

Abstract

The effect of the different parking categories on the rental price of rental units is quantified with hedonic pricing models. Two models are considered, which use different explained variables: The first describes the net rental price per month, while the second the net rental price per month per square meter. The main parking categories considered are blue zone, non-blue zone on-street parking and private parking. The spatial autocorrelation is taken into account with the SARerror model, with a weight matrix computed on a 100-meter radius and an over the distance inversed weighting, and the GWR model taking into account different neighbourhood depending on the model. All the building related variables increase the price, all the distances from services decrease it. A zone with a high percentage of blue zone parking spaces is likely to have higher rental prices up to the 8% and 0.8 CHF/m2 while if the percentage of private parking is high the rental price can lower down to 20% and 5.85 CHF/m2. Testing the parking categories not relating them to their total number appear to have a very small influence.

Keywords

Free parking; Spatial regression; House pricing; Real estate, Hedonic pricing

Preferred citation style

Colombo, T. (2018), What price for „free” on-street parking?, Bachelor Arbeit, IVT, ETH Zurich, Zurich.

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Table of contents

1 Introduction ...... 7 2 Background ...... 8 2.1 Study area: City of Zurich ...... 8 2.2 Parking in Zurich ...... 9 2.3 Real estate market ...... 11 2.4 Influence of parking on the real estate market ...... 12 3 Hedonic Pricing Methodology ...... 13 3.1 Background ...... 13 3.2 OLS ...... 13 3.3 SAR ...... 14 3.4 GWR ...... 16 4 Case study: Zurich ...... 17 4.1 Data description and analysis ...... 17 4.2 Real Estate Data ...... 20 4.3 Parking Data ...... 28 4.4 Hypothesis...... 33 4.5 Potentially relevant variables tested ...... 34 5 Model results ...... 40 5.1 OLS models ...... 40 5.2 SAR models ...... 45 5.3 GWR model ...... 52 6 Discussion ...... 56 6.1 Comparison between the models ...... 56 6.2 Estimates of the OLS Models ...... 57 6.3 Estimates and lambda of the SAR Models ...... 61 6.4 Estimates of the GWR Models ...... 62 6.5 Limitations of the model and its variables ...... 63 7 Conclusions ...... 64

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8 Literature ...... 65 Appendix ...... 68

List of tables

Table 1: Potentially relevant variables ...... 34 Table 2: Descriptive statistics of potentially relevant variables ...... 37 Table 3: OLS model 1 (log(rent)) ...... 43 Table 4: OLS model 2 (rent per square meter) ...... 44 Table 5: Result of the Moran’I Test ...... 45 Table 6: Result of the Lagrange-multiplier Test for model 1 ...... 46 Table 7: Result of the Lagrange-multiplier Test for model 2 ...... 46 Table 8: SARerror model 1 (log(rent)) ...... 47 Table 9: SARerror model 2 (rent per square meter) ...... 48 Table 10: Comparison between OLS and SARerror ...... 49 Table 11: GWR model 1 (log(rent)) ...... 53 Table 12: GWR model 2 (rent per square meter) ...... 54 Table 13: Comparison between the models ...... 56

List of figures

Figure 1: Subdivision of Zurich in 12 quarters and in 216 statistical zones...... 8 Figure 2: Distribution of on-street parking ...... 10 Figure 3: UBS Swiss real estate bubble index ...... 11 Figure 4: Number of web based housing ads by statistical zone ...... 18 Figure 5: Statistical zone division and names ...... 19 Figure 6: Average monthly gross rent by statistical zone (a) and average rent histogram (b) . 20 Figure 7:Average monthly gross rent per square meter by statistical zone (a) and average rent per square meter (b) ...... 21 Figure 8: Visible square meters of lake by statistical zone ...... 22 Figure 9: Average square meters by statistical zone (a) and average square meter histogram (b) ...... 23 Figure 10: Average number of rooms by statistical zone (a) and average rooms histogram (b) ...... 24 Figure 11: Total built area by statistical zone ...... 25 Figure 12: Residential square meters by statistical zone ...... 26

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Figure 13: Industrial square meters by statistical zone ...... 27 Figure 14: Total on-street parking spaces by statistical zone ...... 28 Figure 15: Blue zone parking spaces by statistical zone ...... 29 Figure 16: Blue zone parking spaces per 120 residential square meter by statistical zone ...... 30 Figure 17: White zone parking spaces by statistical zone ...... 31 Figure 18: Private parking spaces by statistical zone ...... 32 Figure 19: Blue zone par over total parking estimate distribution of model 1 (a) and 2 (b) .... 55 Figure 20: Private parking over total parking estimate distribution of model 1 (a) and 2 (b) .. 55 Figure 21: R2 distribution of model 1 (a) and 2 (b) ...... 62 Figure 22: Parking spaces in car parks by statistical zone ...... 68 Figure 23: Retail and commercial square meters by statistical zone ...... 69 Figure 24: Correlation between log(netrent) and both dist_cbd and log(dist_cbd) ...... 70 Figure 25: Correlation between log(netrent) and both railstkm and railstkmln ...... 71 Figure 26: Correlation between m2miet and both dist_to_hi and log(dist_to_hi) ...... 72

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List of abbreviations

AV Cadastre based data (see Schirmer et al., 2014)

BfS Swiss Federal Statistical Office

ETH Swiss Federal Institute of Technology

GWR Geographically Weighted Regression

IVT Institute for Transport Planning and Systems of ETHZ

OLS Ordinary Least Square

SAR Spatial Simultaneous Autoregressive Model sqm Square meter

TED Tiefbau- und Entsorgungsdepartement, Stadt Zürich

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1 Introduction

The demand of parking spots has always been a major issue in the urban context, since it requires a lot of space that could be otherwise used for other purposes. In Zurich since the “Historic compromise” (Stadt Zürich,2009), the regulation has been strictly regulated to a fixed maximum and minimum, while in most of the other big cities only a minimum is set. But does a maximum of parking spaces influence in some way the rental price of houses and apartments? As it can be easily noticed in most of the residential zones, the on-street blue zones, parking spaces where for a low yearly fee a vehicle can be parked without time limits, seems to be dominant with respect to private parking areas or other types of on-street parking. As stated by Shoup (1997) “A San Francisco study found that requirements for off-street parking increased housing prices by an average of $47,000 and increased the household income necessary to purchase a house from $67,000 annually to $76,000“.

The main purpose of this study is to quantify the impact of the different parking categories on the rental price. The case of Zurich is especially a good study case as some laws about parking and its properties have been already discussed times ago. In addition, the division between the considered types of zone is interesting since in Zurich the diversification between high rental areas and lower ones is smaller if compared with many other cities. To achieve this purpose hedonic pricing methods are used with parking, real estate and demographic data (Páez and Scott, 2004). First a linear regression OLS is applied and subsequently simultaneous autoregressive methods (SAR) are used in order to reduce the spatial autocorrelation correlated issues. Parking is divided into private off-street spaces, blue zones and white zones with all the other less relevant types, in order to isolate the main difference for on-street categories and the private ones.

In chapter 2 and 3 the background of the considered type and the applied methodology are presented in order to give a clearer idea on the topic. Descriptive analysis and hypothesis are presented in chapter 4, while in chapter 5 the models results are presented and subsequently in chapter 6 further discussed.

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2 Background

In this chapter the parking and real estate history of Zurich are presented in order to introduce fundamental concepts for the following chapters.

2.1 Study area: City of Zurich

The focus of this study is put on the city of Zurich. With its 415682 inhabitants in 2016 and a total area of 87.93 square kilometres it is the most populated town in Switzerland (Stadt Zürich, 2017). The city is divided into 12 quarters, that have been divided again into 216 zones in order to increase the study’s precision (Fig.1) and that will be referred at as statistical zones. This subdivision has been chosen in order to give a more detailed analysis since in the quarters there still is the eventuality of big differences, as considering each district by itself seemed too imprecise and it might be that some trends show only on a finer scale of analysis.

Figure 1: Subdivision of Zurich in 12 quarters and in 216 statistical zones.

Sources:

(left picture) Tschubby (2009), https://commons.wikimedia.org/wiki/File:Karte_Stadtkreise_Zürich.png consulted on 23/04/18

(right picture) opendata.swiss (2018), https://opendata.swiss/dataset/statistische-zone1 consulted on 30/5/2018

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2.2 Parking in Zurich

In this subchapter the history of parking in Zurich since the 1970s is briefly introduced for both private and public parking.

2.1.1 Public Parking

In the late 1980's the city of Zurich made an unconventional choice concerning the parking regulation policy (Garrick and McCahill, 2012), but its foundations go back in the 1960’s when a parking minimum was set (a common approach in most American and European cities). In fact, in 1989 a parking maximum was implemented in order to try to avoid a degradation of the urban character of the city. The decision was in line with the public transport policy of the city started in the 1970’s. Later on 1996 as the city tried to end the long discussion about the number of parking spaces and in response to a popular initiative about the topic (Stadt Zürich, 2009). To do so they agreed on the “Historical compromise”, a pact in which the focus was spatially on the city centre and the parking serving the customers and visitors. In fact, the main target was to stabilize the number of those kind of spaces to the one of 1990 and gradually transform the surface parking places into underground parking garages, in order to recover surface and remaking it into more pedestrian-friendly urban space thanks to its requalification. Rental, reserved publicly accessible and private parking and blue zones were not considered by the compromise (further examples of requalification can be found at Stadt Zürich, 2009) To protect residential areas from excessive vehicle emissions, blue zones have been established (Stadt Zürich, 2017). Those are on street parking spaces in which everyone is allowed to park for free for the limited time indicated on the parking sign. The residents can buy an unlimited parking authorization for a yearly 300 CHF fee. A visitor can obtain a daily permission for unlimited parking at the cost of 15 CHF. After 6 pm until 9 am, on Sundays and holidays the blue zones allow anybody to park without fees. The white zones are intended for a short stay (typically up to a maximum of 2-4 hours) and must be paid at the nearby parking meter. The price of the spaces varies from place to place but in comparison is more expensive than the blue zones but still lower with respect to private off-street parking. Usually the pricing period is set to be aligned with business opening times,

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meaning that during the night it becomes a free parking zone (Sarlas, Sinan and Axhausen, 2016).

Figure 2: Distribution of on-street parking

Source: Stadt Zürich (2012), Tiefbau- und Entsorgungsdepartement. Mobilität in Zahlen S17

As it can be seen in Fig. 2, the evolution of the on street parking trends towards the blue zones, with the amount of parking spaces and its distribution remaining stable since 2005.

2.1.2 Private parking

First introduced in 1996 (Stadt Zürich, 1996) and subsequently expanded in 2010 and in 2015, the regulation of private parking is done in an uncommon way. The city is divided into 5 zones based on the main activities exercised there and for each of them a minimum and a maximum of parking spaces is assigned. These values can vary greatly as the minimum required goes from a 0.1 parking space for each 120 square meters in the old town zone to a 0.7 in the suburban zones, while the maximum is between 0.1 and 1.15. The regulation goes on also specifying a maximum for visitors and implementing a minimum for light wheelers. This regulation has been enacted in order to avoid increasing the number of parking spaces and a subsequent rise in attractiveness of the private traffic, in favour of the public transport strategy adopted by the city prior to the parking regulation.

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2.3 Real estate market

Real estate is used not only for living purposes, but also for investment. That can lead to speculations increasing the price beyond the price justified by current local demand.

Figure 3: UBS Swiss real estate bubble index

Data: UBS (2018)

As shown in Figure 3, the prices and the speculation index have constantly risen from 2001 until 2016 with a decrease period due to the sub-prime crisis during the 2006-2008 period. The trend appears to be changed since then as asserted by Credit Suisse (2017), due to multiple factors as the decision in 2015 of the Swiss national bank to retire the decision to keep the exchange rate between CHF and Euro fixed, making the Swiss market less attractive to foreigner investors. Other factors to take in account are the slowdown in the city population growth trend due to a decrease of the immigration to Switzerland.

In Zurich the overall prices are much higher with respect to all the other cities and regions in Switzerland (Comparis, 2016). In fact, the mean rent per 3 or 3.5 rooms amounts to 2324 CHF, while all the other cities are under 2000 CHF. The city is also at the second place if the value considered is the net rent per square meter (29.05 CHF/m2), since Geneva (33.25 CHF/m2) which is first tends to have smaller flats than the average 80 square meters in Zurich. These values reflect the difficulties of finding new building spaces in order to match the houses and apartments demand, as the population increases due to the demographic trend and immigration (Swiss Confederation, 2017) but the zones where it can be built are already

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mostly used. Other important factors to be considered in order to explain the high rental prices are the purchasing power and boom that the real estate market had between the 2000 and the 2016 (Delmendo, 2018)

2.4 Influence of parking on the real estate market

Common sense suggests the free parking means money saved, since you do not pay for it, while paid parking especially in the cities is not seen with favour by the residents, because of course it costs. But the main question is: Is the free parking really free? As Shoup (1999) suggested the money saved has just to be paid by someone else. In the case of a residential zone in fact it will fall on the rental price, so on the inhabitants, while for a shop with free parking the costs will likely be reflected in the price of goods or services (Inci, 2016). Another option is that for the financing of free parking the municipal government could raise the residential property taxes (Litman, 2016). It also must be considered that the space used for parking could have been used to build for other more remunerative purposes and where there is more demand than supply the price will raise and there is a loss in potential gain, eventually translated into the rental prices. The minimum parking requirement when set creates more costs because it often does not reflect the real need of parking and the tenants have somehow to pay for it (London & Williams-Derry, 2013) even if they have no necessity for having it; mostly if the minimum is considered per unit. (Litman, 2016). Private parking on the other hand in an urban context will likely lower the rental price, but only if their presence is based on their real demand and they are not bonded directly to the rental unit, so that the tenant does not have to pay for them if he does not need them (Bakis and al., 2018).

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3 Hedonic Pricing Methodology

3.1 Background

In order to obtain a model for rental prices, hedonic models are used. The price of a good can be considered in two ways: as the price of it by itself or evaluated as the sum of its properties. In reality, the price of a parking can be evaluated over a multitude of factors, not only the parking ones, but also related to its neighbourhood. This approach is the Hedonic Pricing Method. In fact, as suggested by Anselin (1988) and Tobler (1970), all the surroundings exert an influence over a point, but it must be considered that near points have a higher influence and further ones a less considerable one. A spatial analysis requires a good amount of data and spatial explanatory values as such as regional accessibility, proximities/distances and neighbourhood characteristics. The hedonic approach has been used for this purpose since the 1970s’ in the real estate field (Löchl, 2010).

3.2 OLS

The price can be considered as the sum of all the properties of the good, and it can be explained as follow:

P = β0+ β1 X1+β2X2+β3X3++βnXn+ ε (1) or abbreviated in

P = βX + ε (2)

Where P is the price of the good considered (called dependent variable) and it depends on the sum of different characteristics X (called explanatory variables). The parameters β are the weights assigned to each of the characteristics. The ε value is the necessarily random occurring part of the system as it represents the variables that cannot be considered or have been ignored (Woolridge, 2009). β0 is the intercept, which define the price P if all the variables are 0. It could be intended as the fix value of a good has without any of its other elements considered, but in this study it would make no sense to consider a rent of 0 square

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meters or 0 rooms, so it will be evaluated just as statistical parameter. Fixing all explanatory variables but one (let’s assume X1) is then possible to approximate its effect on the price P. It means that for a ΔXn will correspond to a ΔP, so (Woolridge, 2009):

∆P(Xi) = βi∆Xi (3)

This method is used in order to establish an approximate value of βi with an OLS.

Different relation types between P and X other than the linear one can be used, as the most common in the estate market is the log-model, in order to obtain a percentage variation. In fact, from: log(P) = βX + ε (4) a percentage difference shown in (5) can be obtained

%P(Xi) = (100βi)∆Xi (5)

Anyway there are some issues with OLS, one being the price P not taking into account the influence that the surroundings have on it, maybe producing inefficient or biased βi (Charlton and Fotheringham, 2009). As evidenced in (Woolridge, 2009) another issue is the fact that a strong correlation between explanatory variables can exist, leading to multicollinearity. Even if this does not violate the principle of multicollinearity, it appears to lead to a bigger variance of the estimated parameters.

3.3 SAR

To reduce the issues that can present in a linear regression, a SAR is usually used and the bias is decreased, giving a more reliable outcome. It can affect all three levels of a linear regression: the explained variable, the explanatory variables and the error. To achieve a more reliable outcome, the spatial properties of the data and subsequently its influence on the price are taken into account. There are various SAR models, mostly based on the Maximum- likelihood estimators and differentiated by the assumption of where the autoregression will occur and so which component has to be corrected (Hoffer, 2014). Here in the following, four

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of the most used are described.

The SARlag (Spatial simultaneous autoregressive lag model) consider that the auto regression will be present in the response variable and this assumption is integrated as follows:

P = ρWP + βX + ε (6)

Where P is the price, W an n x n spatial weight matrix having n as number of observations and ρ is a spatial autocorrelation parameter. In particular X is the sum of X1+X2+X3 where X1 are observations on the structural characteristics, X2 observations on the neighbourhood characteristics and X3 observations on environmental quality variables (Kim, Phipps and Anselin, 2013). The values β and ε still have the same meaning that they have in (2).

The SARerror method supposes that the autocorrelation lies in the error value and so the model will change as follows:

P = βX + error (7) and error = λWε + u (8)

Where λ is a spatial autoregressive coefficient, u is a vector of i.i.d. errors and all the other terms are defined as in (6) (Anselin, 1999).

The third model, the SAC (Spatial Autocorrelation model), provide a combination of the previous two (Sarlas and Axhausen, 2016) in the form of:

P = ρWP + βX + error (9)

At last the SARmix (Spatial Durbin model) assumes an autocorrelation in the X variables but exclude the error ones and becomes then:

P = ρWP + WXγ + ε (10)

Having γ as another regressive coefficient (Löchl and Axhausen, 2010).

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3.4 GWR

The geographical weighted regression is used to fix an issue occurring while performing the models discussed above, due to the assumption of the homogeneity of the relationship between the observations. In reality they can vary within the study area so it has to be considered the different influence due to the geographical position; this condition is called spatial heterogeneity. To do this the model provide β that consider the characteristics of the point location (Hoffer, 2014) meaning that they might vary between different points. The local GWR model for a point is then described as follows:

P(li)= β0(li)+ β1(li) X1i+β2(li)X2i+β3(li)X3i++βn(li)Xni+ ε (11)

Where with li a specific point given by its coordinates is specified and the ensemble of βn(li) represent the specific relationship around the location li. All the other parameters are still described as in (1). The estimators have the form: T -1 T Β(li) = (X W(li) X) X W(li) P(li) (12) Where P(li) is the vector of the observed values on the location, W is a diagonal matrix weighted on a scheme called kernel (Charlton and Fotheringham, 2009). However, an issue that can arise while performing a GWS is its low reliability due to taking multicollinearity not fully into account since the estimators are evaluated for a specific location.

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4 Case study: Zurich In this chapter the data used in this study are presented. Special focus must be put on the rental prices and parking ones, since they are the main focus of the study and all the others should be then considered with respect to them.

4.1 Data description and analysis

Two sets of data have been used to analyze the real estate market: the first one includes information taken from 2256 web based advertisements regarding rental prices, square meters, number of rooms and many other properties of the advertised apartment or house in the city of Zurich between 2009 and 2010.

The second and third sets, provided by the ITV with data coming from the cadastre (AV) and other sources (more informations can be found at Schirmer et al., 2014), contains all the information concerning every single of the 44782 buildings of Zurich, like the residential square meters built, the industrial square meters built or their function. Another data set furnished by the city of Zurich (more information can be found on Waraich & Axhausen, 2012) provides every parking space in Zurich and its position, including car parks, blue zones, white zones and private parking spaces per building.

Particular attention must be paid on the representation of the plots, since their graduation is based on the quantile method. It means that for every range shown there is the exact same number of zones with that colour. This has been made so that the difference between zones is more clear, but on the other hand the problem is that the highest range is much wider with respect to the others. Furthermore, the areas are often given in square kilometres to render a whole number, since a parking per square meter evaluation does not help in the visualization of ratios. Every time that the word ads or advertisement is used it is referred to a web based advertisement where a price is asked for a rental unit.

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Figure 4: Number of web based housing ads by statistical zone

Data source: Web based housing advertisement (2009-2010)

Since the rental data rely on web based ads it must be considered that not every region is represented and therefore for the descriptive analysis (but not for the OLS or the SAR) the zones represented as white or clear orange (so with less than 7 ads) must be considered carefully while trying to extract a trend from the plots on the houses and apartments properties such as room number. It means that the represented plots could be not completely representative because over or under representation of some zones.

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Figure 5: Statistical zone division and names

Data source: opendata.swiss (2018), https://opendata.swiss/dataset/statistische-zone1, consulted on 30/5/2018

In order to simplify the description of the plots, the zones will be referred to with their above assigned name. In the following plots to ease their reading and evaluation the names are left out. The background map data source is for all maps identical and from now on for simplicity it will not be written, but is for all of them the one cited here above.

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4.2 Real Estate Data

The following maps represent various aspects of the real estate market.

Figure 6: Average monthly gross rent by statistical zone (a) and average rent histogram (b)

(a) (b)

Data source: Web based housing advertisement (2009-2010)

The rent is consistently higher in Unter- und Oberstrasse, Fluntern, Höngg, Enge and Weinegg. Most of them are situated in an elevated position with respect to the lake or the city. In the more peripheral quarters like Affoltern, Seebach or Altstetten, as it can be evinced by looking at the map, the rent is lower. This observation can be explained with the distance to the city centre that implies a longer time to reach the services and the work places that typically are in such central zones, according to the typical distribution models of city sectors. Of course there are some exceptions as it can be seen in the north Affoltern zones and in Albisrieden that can be explained with the lower number of ads with respect to other zones that might result in a too small sample for statistical analysis. For Oerlikon the reason of a higher average can be found in the centrality of “Bahnhof Oerlikon” that allows to reach in very short time practically every zone of Zurich. As it can be seen in the histogram, more than the 65% of the total rent prices lies under the 2000 CHF, mostly between 1600 and 2000. That

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would indicate a major importance of the small rental units, since they are more than three quarters of the real estate market, according to the data. Of course it should be considered that bigger properties are usually advertised in other ways and not on the web, or that often they are private properties usually inhabited for longer with a minor change of tenants or landlords.

Figure 7:Average monthly gross rent per square meter by statistical zone (a) and average rent per square meter (b)

(a) (b)

Data source: Web based housing advertisement (2009-2010)

Compared to Fig.6 there are some evident differences if the rental price is considered per square meter. This is mostly clear for the lake surrounding areas and the city centre. In fact, in the peripheral quartiers this ratio seems very low by virtue of the much larger space that can be built. In support of this point the city centre, Fluntern, Unter- and Oberstrasse have a much higher value compared to areas that had a high rent mean in Fig. 6 like Albisrieden or Hirslanden. Furthermore, the location with respect to the lake seems to play a leading role. The rent per square meter is better distributed with respect to the rental prices, as it has a more normal distributed curve that has its peaks around 18 and 24, under the effective value presented in section 2.3, but that is probably just due to the dataset used.

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Figure 8: Visible square meters of lake by statistical zone

Data source: Web based housing advertisement (2009-2010)

This plot represents the zones with a lake view. As everyone would expect, the better the view over the lake, the higher the rental prices are. The trend appears to be confirmed or even slightly increased for the rent per square meter ratio, especially for the Wollishofen, Enge and Unterstrasse zones. In fact, the regions with lake view are the ones directly on the lake or with an elevated position with respect to the city and oriented towards the lake.

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Figure 9: Average square meters by statistical zone (a) and average square meter histogram (b)

(a) (b)

Data source: Web based housing advertisement (2009-2010)

Looking at the map it can be noticed that the zones where the higher average square meter are found are usually not in residential zones, as there the rental units will probably be smaller, in order to increase their number and so the number of people that can live in the area. The city centre appears to have very small units, probably due to the lack of space and the very high costs per square meter (but they both influence each other) making a large unit unlikely and too expensive. Anyway some marginal zones have high values, because of a higher space availability. The histogram shows that most of the units are between the 40 and the 80 square meters but it could be due to an overrepresentation of these ranges, since usually these are the rental units that are more likely to have more tenants for a brief time, as the bigger ones will probably be considered for a more stable residence and even as a solid investment. More square meters seem to have a direct and remarkable impact on the net rental price, but an inverse impact on the price per square meter, as higher square meter values tend to decrease it.

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Figure 10: Average number of rooms by statistical zone (a) and average rooms histogram (b)

(a) (b)

Data source: Web based housing advertisement (2009-2010)

As it can be seen in the histogram, the typical number of average rooms per apartment is 1, 3 or 3.5, but it must be remarked that the data are from housing advertisement. This detail probably is due again to an overrepresentation of these categories. Looking at the map most of the residential zones tend to have smaller apartments, with some exceptions like Oberstrasse or Enge. It seems that a strong dependence between rooms and rental price can be found, with the city centre as exception for the reason explained for Fig.9

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Figure 11: Total built area by statistical zone

Data source: AV, 2010

This plot shows which parts of the city are the most built up. It should not surprise that the city center and its nearby zones are the most built ones, since in an urban context those zones are the most likely to be built vertically due to the lack of space (meaning more floors) and the rental prices that guarantee an economic return and prestige; therefore, it follows the trend of the rent per square meter. Hardbrücke and Altstetten have as well a high value due to the presence of many towers on their territory.

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Figure 12: Residential square meters by statistical zone

Data source: AV, 2010

The residential zones are of course more concentrated on the middle-outer zones of Zurich, as too far it would require too much time to get there, but in the centre the rental prices per square meter are very expensive and so they will unlikely be used for living. Indeed, the two maps could be considered the negative of each other. This clarify the existing trend of the residential estate market that more square meters decrease the prices per square meter. Anyhow some residential peaks around the lake are used as residential due to the lake view, even if that means higher rental prices.

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Figure 13: Industrial square meters by statistical zone

Data source: AV, 2010

The trend shown in Fig. 12 can be partially applied on this case and be extended for the confront with Fig. 6, as the rental price of an apartment or house will probably be much lower if in the nearby zone there is a high concentration of industries, both for pollution and landscape issues. The Hardbrücke and Altstetten zones lie exactly along the river course and also of the railway, two typical elements of industrial development.

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4.3 Parking Data

In this subchapter the distribution of different parking spaces is presented.

Figure 14: Total on-street parking spaces by statistical zone

Data source: Tiefbau- und Entsorgungsdepartement, Stadt Zürich, 2017

The on-street parking spaces distribution in the city is more or less uniform without significant differences, exception made for the city centre (see section 2.2). In general, the presence of on-street parking spaces appears to have a mixed correlation with the rental prices (Fig. 6 and 7), probably due to the various types of parking included in this statistics.

28 What price for “free” on-street parking? June 2018

Figure 15: Blue zone parking spaces by statistical zone

Data source: Tiefbau- und Entsorgungsdepartement, Stadt Zürich, 2017

The blue zone parking spaces appear to be strictly bonded to the presence of residential zones. As it can be seen from Fig.11 they almost match, meaning that the city has chosen to transform the parking areas near to residential zones in blue ones, to decrease the total costs of the residents and the local pollution. In reality a comparison with Fig. 6 and 7 shows a certain similarity between the two maps. That could lead to the conclusion that blue zones in reality increase the rental prices. The anomaly of the city centre is due to the lack of blue zone parking spaces by the city (See section 2.2).

29 What price for “free” on-street parking? June 2018

Figure 16: Blue zone parking spaces per 120 residential square meter by statistical zone

Data source: Tiefbau- und Entsorgungsdepartement, Stadt Zürich, 2017 and AV, 2010

The trend considered in Fig. 15 relative to the rent appears to be somehow more evident if the number of blue zones is considered by residential area. This leads to the consideration that if there are many blue zone parking spaces and hence more low cost parking possibilities, the rental price will rise. The anomaly on the Friesenberg should not be considered for the reasons previously explained in Fig. 4 commentary.

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Figure 17: White zone parking spaces by statistical zone

Data source: Tiefbau- und Entsorgungsdepartement, Stadt Zürich, 2017

A clear qualitative evaluation on how the presence of white parking spaces affect the rental prices can be done, since the comparison with Fig. 6 and 7 shows as typically their presence result in a lower rent. It could be related to the fact that often in residential zones blue zones are preferred to the white ones and in the city centre they are predominant. In the city centre there is a high number of white parking spaces due to the decision in 1996 to lower the number of parking there and render them paid (Stadt Zürich, 2009) with the “Historic Compromise”.

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Figure 18: Private parking spaces by statistical zone

Data source: Tiefbau- und Entsorgungsdepartement, Stadt Zürich, 2017

The private parking spaces are well distributed over the whole city, but a clear trend can be seen in their presence in the residential zones, since they are likely to be bonded with the presence of houses, and more in general, of rental units meant to be inhabited, as at the end of the day one does not want to lose time on looking for a parking space.

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4.4 Hypothesis

Hypothesis about the influence of some variables can be done. In fact, confronting the presence of private parking spaces it can be argued that they seem to lower the price, as their distribution could be seen as inversed with respect to the rental price and rental price per square unit. It also almost matches the residential area distribution, for which then the same impact prediction can be made, but for other reasons, as there it will probably be a high population density, rendering the rental units higher in number (even if also the demand will probably be higher and it could be argued that this could lead to an increase of the rents) and probably more affordable.

A high presence of blue zone parking spaces on the other hand seem to have the opposite effect, as it could be evinced by confronting Figures 6 and 7 with Figures 15 and 16. This could be caused by the fact that a free service could be paid in other ways.

The white zone presence could lead to a clear increase of the prices and mostly for two reasons: The first is that in the city centre they are the most represented parking category because of the “Historic Compromise” (even if the number of private parking spaces is not much lower there); the second one is the presence of many services, that would be another factor pointing in this direction, as they usually do not have their own parking spaces for customers and they rely on the white zones.

In general, the on-street parking spaces presence seems to increase the prices as they are less expensive than private ones and this could lead the landlords to the conclusion that the tenants could pay more for the rent as they are saving on parking.

33 What price for “free” on-street parking? June 2018

4.5 Potentially relevant variables tested

In this section two tables describing the potentially relevant variables (Table 1) and their descriptive analysis (Table 2) are presented.

Table 1: Potentially relevant variables

Variable Description Unit Origin

Dependent Variable netrent Monthly gross rent [CHF] Web m2miet Monthly gross rent per m2 [CHF m-1] Web

Building related explanatory variables sqm Net living area [m2] rooms Number of rooms [-] Web lift Presence of a lift [Dummy] Web fireplace Presence of a fireplace [Dummy] Web balcony Presence of a balcony [Dummy] Web gterrace Presence of a terrace [Dummy] Web ishouse Building is a house [Dummy] Web builtuntil20 Constructed until 1920 [Dummy] Web built21to30 Constructed between 1921 and 1930 [Dummy] Web built81to90 Constructed between 1981 and 1990 [Dummy] Web built91to06 Constructed between 1991 and 2006 [Dummy] Web [Dummy] Web Location related variables: Structural gr_lakeview Visibility of the lake surface [100ha] IVT gr_lakeview dummy [Dummy] IVT gr_sunshine Sunshine solar exposure [-] IVT gr_slope Land slope [degree] IVT dis_school Distance to the nearest school [100m] IVT dis_CBD_ZH Distance to the CBD of Zurich [100m] IVT dis_Kiga Distance to the nearest Kindergarten [100m] IVT railstkm Distance to the nearest railway station [1 km] IVT dist_to_hi Distance to the nearest highway ramp [100m] IVT acc_pt Accessibility by public transport [Index of acc.] IVT acc_car Accessibility by car [Index of acc.] IVT BZ_50_10 Density1 of blue zone parking spaces within 50 meters [# parking/m2] TED BZ_100_10 Density1 of blue zone parking spaces within 100 meters [# parking/m2] TED BZ_150_10 Density1 of blue zone parking spaces within 150 meters [# parking/m2] TED BZ_200_10 Density1 of blue zone parking spaces within 200 meters [# parking/m2] TED BZ_250_10 Density1 of blue zone parking spaces within 250 meters [# parking/m2] TED BZ_300_10 Density1 of blue zone parking spaces within 300 meters [# parking/m2] TED BZU_50_10 Density2 of blue zone parking spaces within 50 meters [# parking/m2] TED BZU_100_10 Density2 of blue zone parking spaces within 100 meters [# parking/m2] TED BZU_150_10 Density2 of blue zone parking spaces within 150 meters [# parking/m2] TED BZU_200_10 Density2 of blue zone parking spaces within 200 meters [# parking/m2] TED BZU_250_10 Density2 of blue zone parking spaces within 250 meters [# parking/m2] TED BZU_300_10 Density2 of blue zone parking spaces within 300 meters [# parking/m2] TED NB5010 Density1 of non-blue zone3 parking spaces within 50 meters [# parking/m2] TED NB10010 Density1 of non-blue zone3 parking spaces within 100 meters [# parking/m2] TED NB15010 Density1 of non-blue zone3 parking spaces within 150 meters [# parking/m2] TED NB20010 Density1 of non-blue zone3 parking spaces within 200 meters [# parking/m2] TED NB25010 Density1 of non-blue zone3 parking spaces within 250 meters [# parking/m2] TED NB30010 Density1 of non-blue zone3 parking spaces within 300 meters [# parking/m2] TED

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Table 1: Potentially relevant variables (continued)

Variable Description Unit Origin NBU5010 Density2 of non-blue zone3 parking spaces within 50 meters [# parking/m2] TED NBU10010 Density2 of non-blue zone3 parking spaces within 100 meters [# parking/m2] TED NBU15010 Density2 of non-blue zone3 parking spaces within 150 meters [# parking/m2] TED NBU20010 Density2 of non-blue zone3 parking spaces within 200 meters [# parking/m2] TED NBU25010 Density2 of non-blue zone3 parking spaces within 250 meters [# parking/m2] TED NBU30010 Density2 of non-blue zone3 parking spaces within 300 meters [# parking/m2] TED PP5010 Density1 of private parking spaces within 50 meters [# parking/m2] TED PP10010 Density1 of private parking spaces within 100 meters [# parking/m2] TED PP15010 Density1 of private parking spaces within 150 meters [# parking/m2] TED PP20010 Density1 of private parking spaces within 200 meters [# parking/m2] TED PP25010 Density1 of private parking spaces within 250 meters [# parking/m2] TED PP30010 Density1 of private parking spaces within 300 meters [# parking/m2] TED PPU5010 Density2 of private parking spaces within 50 meters [# parking/m2] TED PPU10010 Density2 of private parking spaces within 100 meters [# parking/m2] TED PPU15010 Density2 of private parking spaces within 150 meters [# parking/m2] TED PPU20010 Density2 of private parking spaces within 200 meters [# parking/m2] TED PPU25010 Density2 of private parking spaces within 250 meters [# parking/m2] TED PPU30010 Density2 of private parking spaces within 300 meters [# parking/m2] TED SR5010 Density1 of residential square meters within 50 meters [# parking/m2] AV SR10010 Density1 of residential square meters within 100 meters [# parking/m2] AV SR15010 Density1 of residential square meters within 150 meters [# parking/m2] AV SR20010 Density1 of residential square meters within 200 meters [# parking/m2] AV SR25010 Density1 of residential square meters within 250 meters [# parking/m2] AV SR30010 Density1 of residential square meters within 300 meters [# parking/m2] AV SRU5010 Density2 of residential square meters within 50 meters [# parking/m2] AV SRU10010 Density2 of residential square meters within 100 meters [# parking/m2] AV SRU15010 Density2 of residential square meters within 150 meters [# parking/m2] AV SRU20010 Density2 of residential square meters within 200 meters [# parking/m2] AV SRU25010 Density2 of residential square meters within 250 meters [# parking/m2] AV SRU30010 Density2 of residential square meters within 300 meters [# parking/m2] AV TB5010 Density1 of total built square meters within 50 meters [# parking/m2] AV TB10010 Density1 of total built square meters within 100 meters [# parking/m2] AV TB15010 Density1 of total built square meters within 150 meters [# parking/m2] AV TB20010 Density1 of total built square meters within 200 meters [# parking/m2] AV TB25010 Density1 of total built square meters within 250 meters [# parking/m2] AV TB30010 Density1 of total built square meters within 300 meters [# parking/m2] AV TBU5010 Density2 of total built square meters within 50 meters [# parking/m2] AV TBU10010 Density2 of total built square meters within 100 meters [# parking/m2] AV TBU15010 Density2 of total built square meters within 150 meters [# parking/m2] AV TBU20010 Density2 of total built square meters within 200 meters [# parking/m2] AV TBU25010 Density2 of total built square meters within 250 meters [# parking/m2] AV TBU30010 Density2 of total built square meters within 300 meters [# parking/m2] AV RC5010 Density1 of retail and commercial square meters within 50 meters [# parking/m2] AV RC10010 Density1 of retail and commercial square meters within 100 meters [# parking/m2] AV RC15010 Density1 of retail and commercial square meters within 150 meters [# parking/m2] AV RC20010 Density1 of retail and commercial square meters within 200 meters [# parking/m2] AV RC25010 Density1 of retail and commercial square meters within 250 meters [# parking/m2] AV RC30010 Density1 of retail and commercial square meters within 300 meters [# parking/m2] AV RCU5010 Density2 of retail and commercial square meters within 50 meters [# parking/m2] AV RCU10010 Density2 of retail and commercial square meters within 100 meters [# parking/m2] AV RCU15010 Density2 of retail and commercial square meters within 150 meters [# parking/m2] AV RCU20010 Density2 of retail and commercial square meters within 200 meters [# parking/m2] AV RCU25010 Density2 of retail and commercial square meters within 250 meters [# parking/m2] AV RCU30010 Density2 of retail and commercial square meters within 300 meters [# parking/m2] AV

35 What price for “free” on-street parking? June 2018

Table 1: Potentially relevant variables (continued)

Variable Description Unit Origin Location related explanatory variables: socio- economic hh1_500_12 Density of 1 person households within 500m in 2012 [ha-1] BfS hh2_500_12 Density of 2 person households within 500m in 2012 [ha-1] BfS hh3_500_12 Density of 3 person households within 500m in 2012 [ha-1] BfS hh4_500_12 Density of 4 person households within 500m in 2012 [ha-1] BfS hh5_500_12 Density of 5 person households within 500m in 2012 [ha-1] BfS hh6_500_12 Density of 6 person households within 500m in 2012 [ha-1] BfS hh1_300_12 Density of 1 person households within 300m in 2012 [ha-1] BfS hh2_300_12 Density of 2 person households within 300m in 2012 [ha-1] BfS hh3_300_12 Density of 3 person households within 300m in 2012 [ha-1] BfS hh4_300_12 Density of 4 person households within 300m in 2012 [ha-1] BfS hh5_300_12 Density of 5 person households within 300m in 2012 [ha-1] BfS hh6_300_12 Density of 6 person households within 300m in 2012 [ha-1] BfS hh_05km_12 Households density within 5 kilometers in 2012 [ha-1] BfS hh_1km_12 Households density within 1 kilometer in 2012 [ha-1] BfS hh_300m_12 Households density within 300 meters in 2012 [ha-1] BfS pop_500_12 Population density within 500 meters in 2012 [ha-1] BfS year09 Advertisement of year 2009 [Dummy] Web year10 Advertisement of year 201 [Dummy] Web

1The density here considered is done with kernel density approximation, so regressed and weighted over distance (Rosenblatt, 1956). 2The density here considered is the normal density, so uniform (Park & Bera, 2009). 3With the “non-blue zone” term all the on-street parking spaces that are not blue zone are captured, private parking spaces are not considered

36 What price for “free” on-street parking? June 2018

Table 2: Descriptive statistics of potentially relevant variables

Variable Min Mean Median Max Unit Dependent Variable netrent 530 1938 1640 15000 [CHF] m2miet 10.6 24.67 23.62 53.57 [CHF m-1]

Building related explanatory variables sqm [m2] rooms 20 79.43 73.5 400 [-] lift 1 3.91 3 10 [Dummy] fireplace 0 0.261 0 1 [Dummy] balcony 0 0.022 0 1 [Dummy] gterrace 0 0.399 0 1 [Dummy] ishouse 0 0.016 0 1 [Dummy] builtuntil20 0 0.004 0 1 [Dummy] built21to30 0 0.188 0 1 [Dummy] built81to90 0 0.061 0 1 [Dummy] built91to06 0 0.124 0 1 [Dummy] 0 0.068 0 1 [Dummy] Location related explanatory variables: Structural gr_lakeview 0 338.2 0 2491 [100ha] gr_lakeview_dummy 0 0.332 0 1 [Dummy] gr_sunshine -8.296 -0.485 -0.536 7.517 [-] gr_slope 0 3.603 2.561 18.755 [degree] dis_school 18 317.6 290 1588 [100m] dis_CBD_ZH 140 3399 3647 6653 [100m] dis_Kiga 4 383.5 333 1743 [100m] railstkm 0.022 0.834 0.782 2.329 [1 km] dist_to_hi 57.38 2167.86 1712.25 9287.78 [100m] acc_pt 10.7 11.91 11.96 12.39 [Index of acc.] acc_car 8.977 9.844 9.886 10.3 [Index of acc.] BZ_50_10 0 2.568 0.984 19.459 [# parking/m2] BZ_100_10 0 9.667 8.106 55.448 [# parking/m2] BZ_150_10 0 21.041 19.303 96.383 [# parking/m2] BZ_200_10 0 36.13 34.07 151.86 [# parking/m2] BZ_250_10 0 54.69 52.17 215.78 [# parking/m2] BZ_300_10 0 76.46 73.52 276.84 [# parking/m2] BZU_50_10 0 7.45 6 52 [# parking/m2] BZU_100_10 0 28.3 26 122 [# parking/m2] BZU_150_10 0 60.14 57 234 [# parking/m2] BZU_200_10 0 102.2 97.5 390 [# parking/m2] BZU_250_10 0 102.2 97.5 390 [# parking/m2] BZU_300_10 0 213.2 201 719 [# parking/m2] NB5010 0 0.698 0 15.931 [# parking/m2] NB10010 0 3.052 0.032 50.046 [# parking/m2] NB15010 0 7.077 1.141 100.291 [# parking/m2] NB20010 0 12.49 3.223 132.593 [# parking/m2] NB25010 0 19.473 6.84 163.168 [# parking/m2] NB30010 0 28.083 11.292 201.854 [# parking/m2] NBU5010 0 2.181 0 41 [# parking/m2] NBU10010 0 9.583 1 156 [# parking/m2] NBU15010 0 21.02 6 184 [# parking/m2] NBU20010 0 37.26 14 296 [# parking/m2] NBU25010 0 58.86 25 407 [# parking/m2] NBU30010 0 83.08 40 564 [# parking/m2]

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Table 2: Descriptive statistics of potentially relevant variables (continued)

Variable Min Mean Median Max Unit PP20010 5.285 202.066 183.477 1204.029 [# parking/m2] PP25010 28.32 304.22 279.48 1913 [# parking/m2] PP30010 54.9 424.2 390 2509.9 [# parking/m2] PPU5010 0 43.15 33 313 [# parking/m2] PPU10010 0 155.7 136 1016 [# parking/m2] PPU15010 7 335 298 3237 [# parking/m2] PPU20010 64 565.7 519 3381 [# parking/m2] PPU25010 96 849.5 766.5 4388 [# parking/m2] PPU30010 168 1171 1086 5029 [# parking/m2] SR5010 0 1741 1564 6026 [# parking/m2] SR10010 0 5720 5220 18407 [# parking/m2] SR15010 0 11633 10877 34318 [# parking/m2] SR20010 242.6 19206 18155 52377 [# parking/m2] SR25010 584.7 28256 26652 73160 [# parking/m2] SR30010 1498 38643 36961 97592 [# parking/m2] SRU5010 0 4571 4186 15824 [# parking/m2] SRU10010 0 15460 14419 47052 [# parking/m2] SRU15010 130 31251 29288 86152 [# parking/m2] SRU20010 701 51349 49144 132490 [# parking/m2] SRU25010 3987 74904 72683 199701 [# parking/m2] SRU30010 4367 102410 99587 283107 [# parking/m2] TB5010 0 4522 3479 134620 [# parking/m2] TB10010 1115 16365 12387 136878 [# parking/m2] TB15010 4258 35517 27124 161639 [# parking/m2] TB20010 8656 61139 47408 248549 [# parking/m2] TB25010 13337 92776 72234 356341 [# parking/m2] TB30010 18274 130314 103778 476137 [# parking/m2] TBU5010 0 12661 9763 137010 [# parking/m2] TBU10010 4234 47377 36168 222650 [# parking/m2] TBU15010 11667 101747 79272 422650 [# parking/m2] TBU20010 19587 173166 136848 628870 [# parking/m2] TBU25010 33643 262507 207358 1005268 [# parking/m2] TBU30010 49529 367428 299479 1336240 [# parking/m2] CR5010 0 561.75 201.7 12917 [# parking/m2] CR10010 0 2120.9 1075.3 25831 [# parking/m2] CR15010 0 4693.1 2553.9 53491 [# parking/m2] CR20010 0 8120 4680 87310 [# parking/m2] CR25010 0 12312 7519 130769 [# parking/m2] CR30010 2.05 17313.75 10696.9 185786 [# parking/m2] CRU5010 0 1591 670 22600 [# parking/m2] CRU10010 0 6235 3170 78030 [# parking/m2] CRU15010 0 13559 7808 142280 [# parking/m2] CRU20010 0 22739 14335 235205 [# parking/m2] CRU25010 0 35070 22095 396500 [# parking/m2] CRU30010 35 48647 31400 517680 [# parking/m2]

Table 2: Descriptive statistics of potentially relevant variables (continued)

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Variable Min Mean Median Max Unit Location related explanatory variables: socio-economic hh1_500_12 0.495 22.623 20.478 75.97 [ha-1] hh2_500_12 0.726 11.534 10.963 32.340 [ha-1] hh3_500_12 0.255 4.394 4.239 10.835 [ha-1] hh4_500_12 0.318 3.268 3.831 6.824 [ha-1] hh5_500_12 0.115 1.437 1.407 2.827 [ha-1] hh6_500_12 0.076 0.863 0.777 2.355 [ha-1] hh1_300_12 0.495 22.623 20.478 75.97 [ha-1] hh2_300_12 0.955 13.873 13.369 42.017 [ha-1] hh3_300_12 0.424 5.225 5.128 13.687 [ha-1] hh4_300_12 0.106 3.814 3.678 8.771 [ha-1] hh5_300_12 0.106 1.702 1.662 3.961 [ha-1] hh6_300_12 0 1.039 0.955 3.572 [ha-1] hh_05km_12 1.897 38.351 35.549 106.838 [ha-1] hh_1km_12 0.847 30.549 27.834 74.863 [ha-1] hh_300m_12 3.36 45.24 42.90 74.683 [ha-1] pop_500_12 4.074 75.36 72.747 194.449 [ha-1] year09 0 0.9996 1 1 [Dummy] year10 0 0.0004 0 1 [Dummy]

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5 Model results In this chapter the OLS, SAR and GWR models are presented as used with a clarification on which variables have been used and why. Their results and estimation are then presented and they will be further discussed in chapter 6. All the models have been computed with the aid of the statistical program R.

Two models have been estimated in this study case: One having the logarithm in base 10 of the net rental price as explained variable, which does not include the parking price even if would be available, while the second having the net rental price per square meters.

For all the models a total of 2256 observation have been used.

5.1 OLS models

In order to determine which variables had to be used, four different aspects have been taken into account: Correlation, multicollinearity, heteroscedasticity and significance. In order to control the second z and Wald test have been performed and Wald confidence intervals have been set (Paek 2012), while for the third heteroscedasticity robust standard errors have been computed and confronted with the standard OLS ones (Stock and Watson, 2008).

As significant a p-value up to 0.15-0.2 has been considered, but any value above it has led to the variables to be considered insignificant. Any correlation over 0.5, if inserted in the formula, has been checked also for multicollinearity.

The building year of the apartments has been taken into account in order to see if it influences the rent, as probably the newest and the oldest should have higher prices. The car accessibility has been excluded due to its insignificance, probably due to the presence of the distance to the highway that is likely to already take into account the accessibility by car factor. The is_house and lift dummies, the built81to90 variable, the slope and both distances with school and kindergarten have also been excluded because of insignificance.

The number of rooms of the advertised real estate has been left out due to the high correlation with the square meters, as the two cannot be used together. The square meters have been evaluated to be used in a log form since for big houses the price of the square meter will likely fall in comparison with small apartments. The significance has also increased thank to this adjustment.

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The distance between the rented properties and the railway or the city centre has also been evaluated in a log form since it has to be expected that over a certain distance the impact will likely decrease.

The total build area has been used only to evaluate percentages between a certain use of area and the total built one, as its employment on its own led to multicollinearity problems due to a very high correlation with all the other built area categories.

The year of the advertisement was first meant to be in the model in order to capture the variations of the real estate market, but the analysis showed that of the whole data just 2-3 observation were not made in 2009.

The dummy_lakeview variable has been preferred to the gr_lakeview as most of the observation had no lake view and so a value of 0, making the effective evaluation of the variable much more difficult.

Population and both household density and households evaluated on dimension density could not be used together due to high correlation.

For both blue and private parking spaces density the chosen radius has been set low since the private parking is supposed to be in the building itself or in the close by, while for blue zones a greater impact zone could be considered, but the significance is much higher if they are within a small radius (up to 100-150 meters, but still the lower the radius the more significant the value). The same reasons can be adducted on the evaluation of the on-street parking spaces that are not in a blue zone, especially for white parking, if pays, one wants to be near the activity is about to do, and the free parking granted by shop and restaurant should be within a hundred meters.

Some other variables are the ratio between different kind of built area or number of parking per built area. In these cases, the area has been divided by 120 m2 in accordance to the regulations cited in Chapter 2.2 (Stadt Zürich, 1996).

Every category of parking density should be represented only by one variable of its kind, since including more than one could lead to taking into account twice or more the same influence and also lead to multicollinearity problems. If the same category is represented by

41 What price for “free” on-street parking? June 2018

more variables, they should be included in form of ratio with other variables and of course, with a different radius.

The chosen variables have been then included into a formula that evaluates the linear regression of the tested explained variable with respect to the explanatory ones.

The output gives the estimate, the standard error, t test and based on the it the significance. In addition, the multiple adjusted R-squared that evaluates how much of the dependent variable can be explained by the model. The AIC (Akaike Information Criterion) is a useful tool to compare the different models that estimate their fit, but only relative to each other and the one with the lower value has to be considered the best.

The two models differ to each other in two elements: as already stated above, the explained variable are the log of the net rental price in the first one and the net rental price per square meter in the second one. The second different element is the inclusion of the log of the distance to the highway for the second model, as in the first it was insignificant.

In order to have a better idea of how the parking spaces influence the rental prices, a factor analysis of the parking supply could have been performed, to understand better how the parking market and demand about numbers and hourly use works, but in this study it has not been performed (Sorbara, 2016).

In the next pages the two models and their OLS estimate results are presented.

42 What price for “free” on-street parking? June 2018

Table 3: OLS model 1 (log(rent)) Variable Estimate t-value Sign.

Intercept 4.17200 14.592 *** Dependent Variable log(Rent) Building Related Explanatory Variables log(square meters) 0.82330 103.462 *** Fireplace 0.14560 5.856 *** Balcony 0.03948 5.273 *** Terrace 0.06470 1.930 . Built until 1920 0.06307 5.634 *** Built between 1921 and 1930 0.04086 2.642 ** Built between 1991 and 2006 0.03158 2.147 * Location related explanatory variables: Structural Lakeview dummy 0.11790 12.793 *** log(distance to the city centre) -0.13240 -14.884 *** log(distance to the nearest railway station) -0.02358 -3.433 *** Accessibility by public transport 0.07008 3.249 ** Sunshine solar exposure 0.00670 3.830 *** log(Blue zone parking spaces within 100 meters) -0.01082 -2.918 ** Non blue zone parking spaces within 100 meters -0.00072 -2.731 ** Private parking spaces within 100 meters 0.00009 1.797 . Private parking spaces over total parking spaces within 150 meters -0.22260 -4.285 *** Blue zone parking spaces over total parking spaces within 300 meters 0.12260 2.224 * Percentage of non-residential area within 150 meters 0.07776 2.241 * Location related explanatory variables: Socio-economic Density of population within 500 meters -0.00107 -6.921 *** Adjusted R2 = 0.8849 AIC = -1594 Degrees of freedom = 2236 Significance of the model: *** Sign. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

The model presents an adjusted R2 of 0.8847, meaning that the 88.5 % of the explained variable is due to the explanatory variables chosen. The estimate is the change in percentage of the rent based on a unit change of the variables or a 100% percentage change for the variables considered under logarithmical conditions. The Model assigns a good significance to each variable with the exception of the private parking spaces (its P-value is just above 0.1). For example, doubling the square meters produce an increase of the 82.4% in the rent.

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Table 4: OLS model 2 (rent per square meter) Variable Estimate t-value Sign. Intercept 55.3257 7.274 *** Dependent Variable Rent per square meter Building related explanatory variables log(square meters) -4.4277 -21.133 *** Fireplace 4.0294 6.146 *** Balcony 0.9839 4.989 *** Terrace 1.9603 2.220 * Built until 1920 1.7851 6.055 *** Built between 1921 and 1930 1.0007 2.457 * Built between 1991 and 2006 0.6928 1.788 . Location related explanatory variables: Structural Lakeview dummy 3.0105 12.409 *** log(distance to the city centre) -3.7423 -15.975 *** log(distance to the nearest railway station) -0.5788 -3.203 ** Accessibility by public transport 1.7516 3.084 ** Sunshine solar exposure 0.1423 3.090 ** log(distance to the highway) -0.1845 -1.451 log(Blue zone parking spaces within 100 meters) -0.3248 -3.308 *** Non blue zone parking spaces within 100 meters -0.0219 -3.170 ** Private parking spaces within 100 meters 0.0022 1.734 . Private parking spaces over total parking spaces within 150 meters -5.8271 -4.259 *** Blue zone parking spaces over total parking spaces within 300 meters 2.2139 1.556 Percentage of non-residential area within 150 meters 1.5432 1.691 . Location related explanatory variables: Socio-economic Density of population within 500 meters -0.0315 -7.755 *** Adjusted R2 = 0.4695 AIC = 13164 Degrees of freedom = 2235 Significance of the model: *** Sign. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

According the adjusted R2, this model explains the 46.38% of the rental price per square meter. The two variables considered non-significant have a P-value in the range of 0.10-0.15. The estimates in this model are the unit change of the price per square meter per variable unit or 100% change in case of normally or logarithmical consideration.

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5.2 SAR models

In order to understand which of the SAR models had to be used, the Moran’s I Test has been performed. This test verifies if there is spatial autocorrelation in the neighbourhood matrix within a set radius. A Moran’s I value of 0 means no autocorrelation, while a 1 or a -1 perfect autocorrelation. In this study 100 meters has been chosen after some iterations of the test on different radii (up to 300 meters) in order to find the bigger one to have higher autocorrelation. The neighbourhood matrix has been tested both in a normal form, that means a 1 value if a point is a neighbour and 0 otherwise, and weighted form, where the weight has been set as the inverse of the distance in meters. In case the distance would have been 0, a minimum value of 1/5 has been set (the equivalent of a distance of 5 meters). Here following are listed the results of the Moran’s I test for both models:

Table 5: Result of the Moran’I Test

Neighborhood Matrix Moran’s I Significance

Model 1 normal 0.17712045 *** Model 1 inverse 0.19015381 *** Model 2 normal 0.17397540 *** Model 2 inverse 0.18552907 ***

Subsequently a Lagrange-multiplier test has been performed in order to determine where in the OLS model spatial dependence is and so in what term of the model the autocorrelation could lie. The tested models are 5: two simple Lagrange multiplier tests based on the error dependence and the lagged dependent variable (LMerr/lag), two robust Lagrange multiplier tests weighted on the inverse of the distance based again on the error dependence and the lagged dependent variable (RLMerr/lag) and finally the SARMA, which is the sum of the simple Lagrange multiplier error test with the robust lag one. Larger statistic parameters lead to bigger spatial autocorrelation and so to a smaller P-value (Silvey 1959).

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Table 6: Result of the Lagrange-multiplier Test for model 1

Parameter model Statistic parameter Significance

LMerr 115.71298 *** LMlag 0.01441 RLMerr 115.85561 *** RLMlag 0.15707 SARMA 115.87003 ***

Table 7: Result of the Lagrange-multiplier Test for model 2

Parameter model Statistic parameter Significance

LMerr 111.64013 *** LMlag 8.87292 ** RLMerr 103.26773 *** RLMlag 0.50052 SARMA 112.14066 ***

For both Tables the significance code is the following: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

As result the error values have a much higher significance and even if in model 2 the outcome of LMlag is still significant, a further look at the test on the inversed matrix show that the autocorrelation probably lies on the error term as the parameter is not significant. Following these considerations, the SAR model chosen has been the SARerror. The value of the sum of error and lagged dependent variable dependence is still significant because of the inclusion of the error model. The tables presented in the next two pages are the SARerror model applied to the models 1 and 2.

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Table 8: SARerror model 1 (log(rent))

Variable Estimate t-value Sign.

Intercept 4.22550 12.752 *** Dependent Variable log(Rent) Building Related Explanatory Variables log(square meters) 0.81632 104.458 *** Fireplace 0.13871 5.837 *** Balcony 0.03768 5.183 *** Terrace 0.04863 1.528 Built until 1920 0.05922 5.261 *** Built between 1921 and 1930 0.03137 2.018 * Built between 1991 and 2006 0.04837 3.127 ** Location related explanatory variables: Structural Lakeview dummy 0.11751 11.169 *** log(distance to the city centre) -0.13976 -13.459 *** log(distance to the nearest railway station) -0.02516 -3.143 ** Accessibility by public transport 0.07532 3.051 ** Sunshine solar exposure 0.00634 3.202 ** log(Blue zone parking spaces within 100 meters) -0.01021 -2.514 * Non blue zone parking spaces within 100 meters -0.00061 -2.091 * Private parking spaces within 100 meters 0.00009 1.777 . Private parking spaces over total parking spaces within 150 meters -0.22511 -4.185 *** Blue zone parking spaces over total parking spaces within 300 meters 0.09569 1.533 Percentage of non-residential area within 150 meters 0.04889 1.262 Location related explanatory variables: Socio-economic Density of population within 500 meters -0.00114 -6.382 ***

Lambda λ = 0.2384

AICSARerr = -1698 (AICOLS = -1594) Degrees of freedom = 2234 Nagelkerke pseudo R2 = 0.8911 Significance of the model: *** Sign. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

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Table 9: SARerror model 2 (rent per square meter)

Variable Estimate t-value Sign. Intercept 57.1048 6.5297 *** Dependent Variable Rent per square meter Building Related explanatory Variables log(square meters) -4.6598 -22.6224 *** Fireplace 3.8789 6.1784 *** Balcony 0.9424 4.8790 *** Terrace 1.5662 1.8640 . Built until 1920 1.6748 5.6467 *** Built between 1921 and 1930 0.7876 1.9217 * Built between 1991 and 2006 1.0849 2.6644 ** Location related explanatory variables: Structural Lakeview dummy 3.0253 10.9502 *** log(distance to the city centre) -3.9336 -14.4181 *** log(distance to the nearest railway station) -0.6230 -2.9656 ** Accessibility by public transport 1.8614 2.8700 ** Sunshine solar exposure 0.1348 2.5890 * log(distance to the highway) -0.1821 -1.4988 log(Blue zone parking spaces within 100 meters) -0.3095 -2.8823 ** Non blue zone parking spaces within 100 meters -0.0188 -2.4368 ** Private parking spaces within 100 meters 0.0022 1.6817 Private parking spaces over total parking spaces within 150 meters -5.8945 -4.1622 *** Blue zone parking spaces over total parking spaces within 300 meters 1.3426 0.8352 Percentage of non-residential area within 150 meters 0.9806 0.9635 Location related explanatory variables: Socio-economic Density of population within 500 meters -0.0330 -7.0457 ***

Lambda = 0.2304

AICSARerr = 13065 (AICOLS = 13164) Degrees of freedom = 2233 Nagelkerke pseudo R2 = 0.49279 Significance of the model: *** Sign. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

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Table 10: Comparison between OLS and SARerror

Model 1 OLS Model 1 SARerr Model 2 OLS Model 2 SARerr Variable Estimate Sign. Estimate Sign. Estimate Sign. Estimate. Sign. Intercept 4.17200 *** 4.22550 *** 55.3257 *** 57.1048 ***

Building Related Explanatory Variables

log(square meters) 0.82330 *** 0.81632 *** -4.4277 *** -4.6598 *** Fireplace 0.14560 *** 0.13871 *** 4.0294 *** 3.8789 *** Balcony 0.03948 *** 0.03768 *** 0.9839 *** 0.9424 *** Terrace 0.06470 . 0.04863 1.9603 * 1.5662 . Built until 1920 0.06307 *** 0.05922 *** 1.7851 *** 1.6748 *** Built between 1921 and 1930 0.04086 ** 0.03137 * 1.0007 * 0.7876 * Built between 1991 and 2006 0.03158 * 0.04837 ** 0.6928 . 1.0849 ** Location related explanatory variables: Structural Lakeview dummy 0.11790 *** 0.11751 *** 3.0105 *** 3.0253 *** log(distance to the city centre) -0.13240 *** -0.13976 *** -3.7423 *** -3.9336 *** log(distance to the nearest railway station) -0.02358 *** -0.02516 ** -0.5788 ** -0.6230 ** Accessibility by public transport 0.07008 ** 0.07532 ** 1.7516 ** 1.8614 ** Sunshine solar exposure 0.00670 *** 0.00634 ** 0.1423 ** 0.1348 * log(distance to the highway) - - - -0.1845 -0.1821 log(Blue zone parking spaces within 100 meters) -0.01082 ** -0.01021 * -0.3248 *** -0.3095 ** Non blue zone parking spaces within 100 meters -0.00072 ** -0.00061 * -0.0219 ** -0.0188 ** Private parking spaces within 100 meters 0.00009 . 0.00009 . 0.0022 . 0.0022 Private parking spaces over total parking spaces -0.22260 *** -0.22511 *** -5.8271 *** -5.8945 *** within 150 meters

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Blue zone parking spaces over total parking 0.12260 * 0.09569 2.2139 . 1.3426 spaces within 300 meters Percentage of non-residential area within 150 0.07776 * 0.04889 1.5432 0.9806 meters

Location related explanatory variables:

Socio-economic

Density of population within 500 m -0.00107 *** -0.00114 *** -0.0315 *** -0.0330 ***

Sign. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

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Confronting both OLS with their respective SARerr models it can be noticed that there are not big differences but some significances have a slight variation. The typical variation ranges of P-value change for the values that had it between 0.10-0.15 tends to be a 0.02-0.05 increase, leading to a 0.12-0.20 range. However most of the variables are not affected by this change and for the Built between 1991 and 2006 variable there is a strong increase in significance. The Estimates of model 1 seem to react in a stable way to the passage from OLS to SARerror, especially the Location related structural explanatory variables, while in the Building related explanatory variables the increase of the Built between 1991 and 2006 variable and the decrease of both Terrace and Built between 1921 and 1930 variables has to be considered. In model 2 the variations appear to be much more evident due to the different value range of the explained variable. In reality the percentage changes between OLS and SARerror of model 1 and 2 are very close, with a difference that is often under the 5 percent with some exceptions, as the blue zone parking spaces within 300 meters being halved in model 2 while in model 1 loses only the 25 percent of the estimate. The difference of the AIC between the OLS and SARerr is near -100 for models 1 and 2, meaning an improvement for both.

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5.3 GWR model

The last model performed is the GWR, which as exposed in section 3.4 should resolve or at least mitigate the spatial heterogeneity issue. In our study to understand how many neighbors should be considered as neighborhood, a so called GWR adapt has been used. This value between 0 and 1 indicates the percentage of the surroundings that will be considered as such. In model 1 and 2 the obtained value is 0.9999, indicating that the quasi totality of the nearby observation is taken into account (2255 out of 2256).

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Table 11: GWR model 1 (log(rent))

Variable Min 1. Quartile Median 3. Quantile Max Global Intercept 4.04940 4.10490 4.19110 4.23750 4.27990 4.1717 log(square meters) 0.82040 0.82207 0.82362 0.82678 0.82820 0.8233 Fireplace 0.14495 0.14561 0.14607 0.14672 0.14751 0.1456 Balcony 0.03835 0.03895 0.03986 0.04115 0.04166 0.0395 Terrace 0.05942 0.06281 0.06484 0.06825 0.07107 0.0647 Built until 1920 0.06130 0.06194 0.06241 0.06342 0.06452 0.0631 Built between 1921 and 1930 0.03973 0.03989 0.04057 0.04108 0.04166 0.0409 Built between 1991 and 2006 0.03025 0.03096 0.03149 0.03255 0.03366 0.0316 Location related explanatory variables: Structural Lakeview dummy 0.11587 0.11717 0.11899 0.12000 0.12107 0.1179 log(distance to the city centre) -0.13307 -0.13253 -0.13135 -0.13042 -0.12981 -0.1324 log(distance to the nearest railway station) -0.02415 -0.02366 -0.02322 -0.02303 -0.02278 -0.0236 Accessibility by public transport 0.06196 0.06502 0.06796 0.07341 0.07800 0.0701 Sunshine solar exposure 0.00580 0.00598 0.00625 0.00672 0.00728 0.0067 log(Blue zone parking spaces within 100 meters) -0.01202 -0.01161 -0.01103 -0.01062 -0.01019 -0.0108 Non blue zone parking spaces within 100 meters -0.00078 -0.00075 -0.00072 -0.00070 -0.00067 -0.0007 Private parking spaces within 100 meters 0.00008 0.00008 0.00009 0.00010 0.00010 0.0001 Private parking spaces over total parking spaces within 150 meters -0.24404 -0.23931 -0.22610 -0.21784 -0.21021 -0.2226 Blue zone parking spaces over total parking spaces within 300 meters 0.11472 0.11945 0.12418 0.13034 0.13475 0.1226 Percentage of non-residential area within 150 meters 0.07567 0.07719 0.07844 0.07974 0.08146 0.0778 Location related explanatory variables: Socio-economic Density of population within 500 meters -0.00127 -0.00110 -0.00108 -0.00106 -0.00103 -0.0011 AIC = -1629 R2 = 0.8866 Degrees of freedom = 2233

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Table 12: GWR model 2 (rent per square meter)

Variable Min 1. Quartile Median 3. Quantile Max Global Intercept 52.4811 54.0324 56.0294 57.0740 58.1458 55.3257 log(square meters) -4.4813 -4.4559 -4.4357 -4.3935 -4.3607 -4.4277 Fireplace 3.9945 4.0275 4.7885 4.1253 4.1641 4.0294 Balcony 0.9534 0.9712 0.9952 1.0322 1.0459 0.9742 Terrace 1.8193 1.8966 1.9703 2.0689 2.1382 1.9603 Built until 1920 1.7221 1.7451 1.7671 1.8076 1.8422 1.7851 Built between 1921 and 1930 0.9751 0.9809 1.0018 1.0172 1.0307 1.0007 Built between 1991 and 2006 0.6509 0.6758 0.6930 0.7237 0.7580 0.6928 Location related explanatory variables: Structural Lakeview dummy 2.9722 3.0157 3.0526 3.0759 3.1154 3.0105 log(distance to the city centre) -3.7583 -3.7433 -3.7163 -3.6908 -3.6728 -3.7423 log(distance to the nearest railway station) -0.5873 -0.5755 -0.5698 -0.5641 -0.5611 -0.5788 Accessibility by public transport 1.5357 1.6194 1.6984 1.8414 1.9606 1.7516 Sunshine solar exposure 0.1227 0.1262 0.1322 0.1422 0.1543 0.1424 log(Distance to highway) -0.2269 -0.2116 -0.2024 -0.1941 -0.1841 -0.1845 log(Blue zone parking spaces within 100 meters) -0.3591 -0.3471 -0.3345 -0.3219 -0.3116 -0.3248 Non blue zone parking spaces within 100 meters -0.0238 -0.0228 -0.0220 -0.0214 -0.0206 -0.0220 Private parking spaces within 100 meters -0.0020 0.0021 0.0022 0.0024 0.0025 0.0022 Private parking spaces over total parking spaces within 150 meters -6.4732 -6.3350 -5.9269 -5.7126 -5.4726 -5.8271 Blue zone parking spaces over total parking spaces within 300 meters 1.9998 2.1184 2.2356 2.3933 2.5259 2.2139 Percentage of non-residential area within 150 meters 1.4867 1.5301 1.5742 1.6334 1.6942 1.5432 Location related explanatory variables: Socio-economic Density of population within 500 meters -0.0329 -0.0325 -0.0319 -0.0314 -0.0307 -0.0315 AIC = 13012 R2 = 0.5052 Degrees of freedom = 2232

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The following plots are the spatial distribution of the estimates of some parking variables for both models, each point represent an observation.

Figure 19: Blue zone par over total parking estimate distribution of model 1 (a) and 2 (b)

(a) (b)

Figure 20: Private parking over total parking estimate distribution of model 1 (a) and 2 (b)

(a) (b)

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6 Discussion In this chapter first the models will be confronted when possible and subsequently the estimates and so the impact of the variables will be discussed.

6.1 Comparison between the models

In order to determine if a model is better than another one two values can be taken into account. The first one is the R2, a value that range between 0 and 1 and can be interpreted as the proportion of the explained variable that can be explained through the explanatory ones. It could be said that the higher the number, the better the model is. In reality every variable added to the regression leads to an increase of the R2 so it makes sense only to compare models that differ only in the regression method and not if there are differences in the tested variables (Woolridge 2009). Another way to compare models is to use the AIC value, which is an estimator of the relative quality of models. In fact, for a given set of data it will evaluate the quality of the models relative to each other. As stated in the result chapter, a lower value means a better model (for example an AIC of 130 is better than a 170 one and a -170 is better than a -130. Coming in the next tables both values are presented for the OLS, the SAR, and the GWR.

Table 13: Comparison between the models

Table heading R2 AIC OLS model 1 0.8849 -1594 SARerr model 1 0.8911 -1698 GWR model 1 0.8869 -1633 OLS model 2 0.4648 13164 SARerr model 2 0.4927 13065 GWR model 2 0.4741 13124 The R2 value is higher in the GWR so it should explain better the explained variable. According to the AIC, the SARerr model provides an improvement on both model 1 and 2 of a -100, so both are to be considered better than the OLS. The comparison between the AIC of SARerr and GWR also shows that for both models the SARerr can be considered better; the R2 would also lead to this consideration, even if for the SARerr is a pseudo R2, which is computed in a different way. Anyway these values must be considered carefully for the GWR, as it is locally regressed, while the other two are estimated globally.

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6.2 Estimates of the OLS Models

In this section the estimates of the OLS models, that represent the elasticity of the explained variable are discussed. As already explained in section 5.1, the estimates in model 1 are the change in percentage of the rent based on a unit change of the variables, or a 100% percentage change for the variables considered under logarithmical conditions, while for model 2 they indicate a net unit change of the price per square meter per explanatory variable unit or 100% change in case of normally or logarithmical consideration. A positive sign indicates that an increase of the variable results in an increase of the explained variable, while a negative sign has the opposite effect.

In model 1 a doubling of the square meters leads to a rent increase of the 82 % while in model 2 the estimated change is a decrease of the rent price over square meter of ca. 4.43 CHF/m2. The second value can be explained with the help of the first, as there is not a 1:1 ratio between the price and the square meters, so the bigger the rental unit will be, the smaller the rent price over square meters will be.

The presence of a fireplace increases the price of the 14.56 % and the price over square meter of ca. 4.03 CHF/m2. This is probably due to the fact that a fireplace can be considered a luxury indicator and as other consideration the rental unit could have been recently renovated as its presence is a returning trend of the last years.

The presence of a balcony or a terrace similarly raises the rent as both are an added feature of a rental unit, as they allow to expand the space and they also add the possibility to access the outer environment without leaving the property (as example for a smoker it would be useful). The impact of the terrace is higher as usually it is bigger than a balcony and more useful in terms of living use, and is quantified to a 6.5% with respect to the 4.1% of the balcony on the rental price. For model 2 the estimate of the terrace is even the double of the balcony one (1.78 against 1 CHF/m2).

Another consideration that can be evinced from the estimates is an older rental unit will likely have a higher price of a newer one. In fact, the estimate influx will decrease the closest to our year it gets: If the building year is before the 1921 the estimates are respectively 0.063 and 1.78 for model 1 and 2; if it is between 1921 and 1930 they are 0.041 and 1.00 while for a year of building between the 1991 and 2006 the values lower to 0.032 and 0.69. This could be

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due to the fact that most of the buildings built before 1931 are mostly located near the city centre. They have an historic value and they are more likely in a better position in terms of both view and accessibility. There is also a high probability that an old place has already been renovated, and if it is very old, it could present a fireplace.

All the distances from the locations considered present negative estimates for a 100% increase that for the rent price change vary from the -13.2% of the distance to the city center to the -2.4% of the one from the nearest railway. In model 2 the range goes respectively from -3.74 to -0.58 CHF/m2, and the distance from the highway (present only as explanatory variable of the rent price per square meter) has an estimated impact of -0.19 CHF/m2. This can be easily explained as a high distance means a bigger expense in terms of time, and since time is one the most valuable thing that one can have, the rental unit is less attractive. Anyway this effect tends to mitigate for an increasing distance (in fact the distances were more significant when considered in a logarithmical way. The same considerations (except for the mitigation of the effect) can be made for the accessibility by public transport variable, as its increase results in a spare of time and so in an increase of the rental price and of the rent per square meter, as the estimates show (+7.01% and +1.75).

The lake view presence increase the price as could be easily guessed by an 11.79% for the rental price and a 3.01 CHF/m2. In fact, the consideration is that the view of the lake is evaluated as a pleasant one and so is desirable, so it can be intended as a luxury indicator. The sunshine solar exposure can be read in the same way, but it has a much lesser impact (a 0.67% and 0.14 CHF/m2 increase) that could be due to the difficulty of its quantification.

The density of the population within 500 meters lesser the price of both rent and rent per square meter if its value is high (respectively -0.11% and -0.03 CHF/m2) The consideration is the following: If the density is high the zone considered is likely a residential one, and in such zones the tendency is to build cheaper rental units with less luxury indicators with respect to other ones, but in higher numbers. In fact, even if probably their request is higher the offer is also higher avoiding an increase of the prices due to a lack of units. For the inverse reasons the percentage of non-residential built area within 150 meters raise the price up to a maximum of 8.24 % or to 1.67 CHF/m2 more, for the case that is a zone without any residential area.

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The estimation of the impact of the parking spaces in this study has been considered in two ways for both blue zone and private parking; first by themselves, meaning that their presence alone has been taken into account (in the case of the blue zone under logarithmical conditions), and in a second time their number has been divided per the total number of both on-street and privates parking spaces. The derived percentage has to be considered with a different approach, as it has a maximum of 1 meaning that there are only parking spaces of the considered category. The estimate indicated refers to this condition and sets the maximum of influence of this variable.

For the blue zone related estimators, starting from their density within 100 meters, they resulted to have a negative value that leads to a 1.08 % rent decrease and a -0.32 CHF/m2 each time the value doubles, so the influence appears to be very small. However, if the percentage of the blue zone parking over total parking spaces within 300 meters is considered, we can see that it can increase the price up to a 12.3 % or to a 2.21 CHF/m2, meaning that the residential zones, where the blue zones are more likely to be, will be more affected by this effect. At first, this increase is due to the fact that in order to build blue zones the city gets the money needed by raising the taxes paid by the landlords, and as consequence they increase the rent price to get it back. It could happen that the increase is left there, but since the rental estate market is very dynamic, is probably something else. As stated by Bakis et al. (2018) while referring to the situation of Istanbul, there is a mechanism between private parking and free parking that lead to their influence on the rent just described. The curbside free parking spaces are a privilege given to the residents by the city. But if the privilege falls due to the replacement of the parking spaces into private ones, the prices will decrease without it, as the price of the parking became then unbundled from the rental unit. The private parking regulation is then bonded to a formal market that is based on the demand, and not on a fix fee as for the blue zones, also leading to a decrease in parking usage as one will evaluate more carefully if he really needs a vehicle or if he can find other alternatives as public transport. This means that also the traffic is likely to decrease and decongest the city. In the long term this could still lead to an increase of it because it could then become more attractive having a car and this is the so called direct rebound effect (Sorrell, 2009). Anyway the decrease will first happen in the housing price and after some in the rental prices (but they are likely to not have the same magnitude).

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On the other hand, private parking spaces lead to an opposite reaction of the prices, as if considered by themselves they will increase very slightly the rent (under a 0.01% and 0,002 CHF/m2 for each parking lot), while if the percentage of private parking over the total one is high, it can have up to a 22% decrease of the price and lesser the rent over square meter by 5.83 CHF/m2. This effect is probably due to the private parking spaces being possessed by the landlord, who can make profit out of them and keep the rental prices lower.

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6.3 Estimates and lambda of the SAR Models

The value of the lambdas of the models 1 and 2 are respectively 0.2384 and 0.2340. This would lead to the consideration that the value of the two is almost the same and so the spatial autocorrelation seems to be the same if we consider the rent or the rental price per square meter. The values themselves, with a range within 0 and 1 (where 1 indicates a total spatial autocorrelation) and so it can be interpreted as “the percentage in error that is reduced in predicting the dependent variable by knowing the independent variable” (Paynich, 2013)

Even if the estimates tend to have only minor changes, there are some variation that worth a further discussion. For example, the building year influx changes significantly for the periods between 1921 and 1930, and between 1991 and 2006. In fact, their importance is inversed with respect to the situation presented in section 6.2. The first range of years has a loss in the estimate of about the 24% for both models while the second one has a net increase of about 35%.

The estimates in which the most interest of the study is put are the parking related ones: Looking at them it can be noticed that the parking categories took by themselves have no significant changes, but if the percentages are considered, the private parking spaces have a slight decrease, while the ones of the blue zones over total parking spaces experience an estimate loss of the 22% on model 1 and of the 40% in model 2. Then it can be supposed that this variable is the most affected one by spatial autocorrelation.

All the other variables remain mostly stable, only the ones that had lower significance compared to the others, have a further increase in the P-value of approximately 0.02-0.05.

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6.4 Estimates of the GWR Models

The estimates in GWR are not only calculated for each variable, but also evaluated on their spatial variance. Therefore, is more interesting to consider their spatial distribution over the territory, as represented in section 5.3 in Figures 19 and 20. There are some estimates that experience major differences between the quantile distribution, as for example in model 1 is the case of the public transport accessibility variable, that goes from a 0.062 to a 0.078. Other significant spatial variations of the model are the percentages of the blue zone over total parking (from 0.114 to 0.134) and the private parking one (from -0.244 to -0.210), that as stated in the previous section are the variables suffering more from spatial autocorrelation and more influenced by their location. In model 2 this trend becomes somehow more evident as these two percentage vary in a stronger way, since the second ranges from -6.47 to -5.47 CHF/m2, while the first goes from 2 to 2.52 CHF/m2. An interesting evaluation can be made on the R2 of the models, as it can be seen where the model applies better in the description of the explained variable.

Figure 21: R2 distribution of model 1 (a) and 2 (b)

(a) (b)

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In model 1 the variation is very small even if it has a clear pattern of distribution, as from the west to the east the value increases. On the other hand, the distribution of the R2 squared of model 2 is more interesting as it varies up to a 0.01 and 0.008 with respect to the reported quasi-global one. These are mostly the zones of and around Altstetten, meaning that the models somehow lack variables that could represent the presence of the industries and probably also a better implementation of the residential area would be useful.

The spatial dependence becomes somehow more clear if considering Figure 20.as for both models the distribution seem to be correlated with the distance from the city centre. This could be due to the fact that in the city centre and its surroundings the prices of the private parking spaces are higher (Sinan, 2016).

Regarding Figure 19, it is hard to find out a real explanation on why the distribution shows a decrease of elasticity towards east, but anyway the zones of Altstetten and Hardbrücke are the ones most influenced by a high percentage of blue zones. Maybe this could be due to their both industrial and residential character.

6.5 Limitations of the model and its variables

The models show some limitations on their entirety. They mostly are due to the limited dataset used, because using data of more years than 2009 and some 2010 ones would probably capture the market influence, and of course more data would probably mean a better statistic sample. Taking into account the parking demand would be a further step towards a better understanding of the situation, as only knowing where the parking spaces are but not having any data on their utilization is looking only to the partial situation, and as already stated in section 5.1, a factor analysis of the parking supply could have filled this gap. Another variable that would have been of interest is the fee of the non-free parking spaces and the monthly rent of the private parking spaces, since it is not included on the rental price. The rental price is net so it does not include all the side costs and so it is not the final price that one pays monthly, and this means that the real price could be much higher or some effects could be hidden in the side costs. Another remark has to be done on the usage of the parking variables, as both blue zone and private parking are represented twice, and so the technically could have a double influence on the model output, and they could also influence each other.

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7 Conclusions After performing all the models, it can be stated that the best regression for model 1 is the SARerror as the rental price is more affected by the error term and for model 2 the GWR, indicating that the price per square meter is more affected by the influence of the location. As theorized first in section 2.4 and later in the descriptive analysis chapter, the blue parking zones an all the other “free” parking spaces are all but free. In fact, their price is just hidden somewhere else and in the case of the rental units is on the rental price. On the other hand, the presence of the private parking decreases the price of the rental unit. The mechanism of rivalry between blue zones and private parking and their impact on the market would lead to the consideration that, the parking presence should be related to the request and not to the minimum provided in the city parking regulation, as the costs of all the parking spaces in excess is paid elsewhere and most of time by the tenants, and a parking market regulated on the demand would be more efficient and decrease both traffic and demand itself. The price for parking should also not be included in the rental price in order to render more clear the real cost of a parking influencing the evaluation of a real car need. For car owners it would lead to an increase of parking costs compensated by a decrease on rental prices, while the non-car owners would benefit of the decrease, so there would be no losers, as even the landlords would balance the loss on the rent thank to the private parking costs that increase.

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Appendix

Figure 22: Parking spaces in car parks by statistical zone

Data source: Stadt Zürich, 2017

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Figure 23: Retail and commercial square meters by statistical zone

Data source: Schirmer et al. (2014)

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Figure 24: Correlation between log(netrent) and both dist_cbd and log(dist_cbd)

Data source: IVT

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Figure 25: Correlation between log(netrent) and both railstkm and railstkmln

Data source: IVT

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Figure 26: Correlation between m2miet and both dist_to_hi and log(dist_to_hi)

Data source: IVT

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