Income and Household Location Choice in Switzerland

Zeno Adams∗, Luca Liebi†

June 4, 2021

ABSTRACT

We examine household location choice for eight cities in Switzerland. In line with other stud-

ies for Europe and the U.S., empirical evidence for the income gradient is weak in standard

regression specifications that control for household characteristics and amenities. We pro-

vide a possible solution for this long-standing empirical puzzle and obtain negatively sloped

income gradients that are postulated by the monocentric city model. We show that munici-

pality taxes, a variable with particular spatial variation in Switzerland, play a dominant role

in explaining households’ cross-sectional arrangements. This has significant implications for

policymakers, their local tax rate decisions, and the maximization of the tax substrate.

Keywords: Household location choice, income gradient, consumption amenities, household

characteristics

JEL Classifications: R20, R23, R30

∗University of St. Gallen, Swiss Institute of Banking and Finance, Unterer Graben 21, CH-9000 St.Gallen, Switzerland; Tel.: +41 71 224 7014; E-mail address: zeno.adams@unisg.ch.

†University of St. Gallen, Swiss Institute of Banking and Finance, Unterer Graben 21, CH-9000 St.Gallen, Switzerland; Tel.: +41 71 224 7004; E-mail address: luca.liebi@unisg.ch.

I. Introduction

Since the beginning of the COVID-19 crisis in 2020, house prices and rents in many cities

around the world have experienced a considerable reallocation of real estate demand. In

2020, house prices at the border of the largest cities in Germany rose by 11%, but only by

6% in the centers (The Economist (2021)). The rental index for the 12 largest metropolitan

areas in the U.S. even decreased by 10% in the center but increased by about 5% at the

city border (Ramani and Bloom (2021)). Two major factors can explain the reallocation of

households and the resulting inverted price pattern. First, lockdowns prevent people from

accessing specific amenities in the CBD. As a consequence, city centres lose one of their

most important pull factors. The second factor is the home office effect. Employees can now

considerably reduce commuting time and costs. Opportunity costs of commuting to work

are regarded as a significant force that leads to spatial sorting of income towards the CBD

(Alonso (1964), Mills (1967), Muth (1968)). The pandemic thus served as a reminder of the

importance of commuting costs in determining household location choice.

In this paper, we study household location choice in Switzerland. We rely on a repre-

sentative survey of households (Swiss Household Panel) in eight cities from 1999-2014. We

observe choices on the individual household level and explore the extent to which house-

hold income, amenities, and local variation in the tax rate affect household location choice.

Household characteristics interact in meaningful ways with city amenities and highlight vari-

ation in household preferences for certain amenities.

A persistent finding across empirical studies on household location choice is a positive in-

come coefficient, i.e. income is estimated to increase with rising distance to the employment

centre. This unintuitive finding is consistent across different countries, urban settings, and

time periods. We address this issue with a regression specification that accommodates the

reasons why high-income households move to the city edge: proximity to nature and large

single-family homes that cannot be found in the city. Once the interaction of both driving

factors is adequately specified, the predicted income gradient turns consistently negative for

all cities. To illustrate this point, Figure 1 compares the income gradient estimates reported

in this paper to those found in other studies. Cuberes, Roberts, and Sechel (2019) study

household location choice in the U.K. and Axisa, Scott, and Bruce Newbold (2012) examine

the city of Toronto. All studies shown in this graph use a similar regression setup with

log(distance to CBD) as the dependent variable and log(income) as the main variable of

interest. Typical controls include household characteristics and amenities. Therefore, we

can directly compare our results across the studies shown in Figure 1. A striking empirical

1

regularity is that the majority of income coefficients are estimated to be positive.1 This

stands in contrast to the monocentric city model, which postulates a negative income gra-

dient: households that live close to the employment centre incur lower commuting time and

costs and would therefore prefer living in close proximity to the CBD, everything else equal.

This effect should lead to spatial sorting with high housing costs close to the CBD that are

affordable only to high-income households and with declining incomes as the distance to the

CBD rises (Duranton and Puga (2014)). The positive income coefficients in Figure 1 cannot

be explained by the presence of amenities or household characteristics as these variables are

already controlled for. They are also not confined to a certain city size. The Swiss cities in

our sample are small in an international context, but similar effects have been reported for

other cities that are ten times larger. In this paper, we propose a potential explanation for

this finding. We argue that the income gradient is negative and can be revealed through a

proper regression model specification. This specification needs to incorporate the interac-

tion of the two main reasons for why certain high-income households prefer to locate at the

city border despite higher commuting costs: access to nature/recreation amenities and large

single-family homes that cannot be found in the city.

Although the income gradient is one of the main variables of interest in this study, we

also report a number of relevant findings that contribute to the empirical evidence that has

been collected for other countries. First, we examine household characteristics such as age,

education, tenure, and marital status to accommodate for the variation in household prefer-

ences for living in the city. Second, we examine the extent to which households respond to

the presence of amenities such as eating out, public transportation, and taxes. We find that

a one standard deviation increase in eating out amenities outside the CBD, which equals 50

additional restaurants and fast food places, is estimated to increase the distance to CBD by

30% in Basel and Luzern and by 40% in St.Gallen. A public transportation shock of the

same size has similar effects, increasing household distance to the CBD by 50% in Basel,

38% in Genf, and 11% in Luzern. Additionally, we test for the impact of negative amenities

such as taxes and house prices. We find significant negative coefficients, indicating that a

1% decrease in house prices outside the city centre increases the distance to the CBD on

average by 1.2% in Bern, 0.5% in Luzern, and 2.3% in St.Gallen. Similarly, 1% lower taxes

outside the city centre leads to relocation towards low tax municipalities at the city edge.

A 1% decrease in taxes at the city edge increases the distance to the city centre by 2.5%

1Cuberes et al. (2019) find income coefficients that are even larger than reported in Figure 1 whenusing simple regressions. These coefficients become attenuated and are often statistically insignificant in fullspecifications that include all control variables

2

Figure 1. Reported Income Coefficients in the literatureThis figure plots the estimated income coefficients from a regression of log(distance to CBD) onlog(income) and a full set of control variables. The graph highlights that our estimates are comparableto those found in studies of cities in the United Kingdom (Cuberes et al. (2019)) but are somewhatsmaller than estimates for Toronto (Axisa et al. (2012)).

0 500000 1000000 1500000 2000000 2500000 3000000

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20

City Size [Population]

Inco

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Coeffi

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Aarau

Basel

Bern

GenfLausanne

Luzern

St.Gallen

Zurich

Birmingham

Bristol

Leeds

Liverpool

Manchester

Newcastle

Nottingham

Sheffield

Toronto

Adams and Liebi (2021)Cuberes et al. (2019)Axisa et al. (2012)

in Luzern, 6% in Bern, and 15% in Geneva. These coefficients are both statistically and

economically significant. Households location elasticity with respect to taxes is more than

eight times larger than for house prices. We conclude that taxes are an essential driver of

household location choice in Switzerland. This finding is unique to the specific tax system

in Switzerland is not found in the literature examining other countries.

Finally, we interact household preferences with amenities to account for the fact that not

all amenities are valued by households in the same way. We find that Swiss households

respond stronger to amenities whereas homeowners are less mobile and therefore exhibit a

lower dislocation response.

To summarize, we contribute to the current income and amenity-based sorting literature

that is mainly focused on the United States. Moreover, the majority of existing studies exam-

ine larger aggregate effects. We study location choice for individual households in Switzerland

based on granular municipality level location data. Our work is closely related to Cuberes

et al. (2019), who test the amenity-based sorting model for cities in England. The authors

find no income segregation after controlling for idiosyncratic city and household character-

istics. We test this result for cities in Switzerland and also control for progressive income

taxes at the municipal level unique to Switzerland. Judged from household location choice

3

elasticities with respect to taxes, local tax rates play the most important role for household

location choices. A higher local tax rate increases the municipal tax base but incentivizes

households to move to municipalities with a lower tax burden. This has important impli-

cations for policymakers, their local tax rate decisions, and the tax substrate’s maximization.

The remainder of this paper is structured as follows. In section II we present a brief

overview of the literature in order to place this paper within the body of the existing research.

In section III we provide background and descriptive statistics for the data. We discuss the

empirical results in section IV and extend our main regression along several directions in

order to provide further robustness in section V. Section VI concludes.

4

II. Related Literature

Since the seminal work of Alonso (1964), Mills (1967), and Muth (1968), urban economists

have identified commuting costs as a major determinant of household location choice. A ma-

jor contribution of the monocentric city model is that it provides insights into the city’s

income-distance gradient. Everything else equal, households prefer to live in close proximity

to the CBD to save commuting time and costs. Location incentives are even stronger for

high income households who have higher opportunity costs from commuting. This gener-

ates a spatial demand pattern in which only high income households can afford the higher

housing costs at the city center while lower income households locate towards the city edge.

However, the empirical evidence for this intuitive relationship has so far been disappointing.

Classical studies on urban household location examine America’s spatial income distribution

in metropolitan areas. A well-documented observation for most U.S. metropolitan areas is

that median income actually increases with increasing distance from city the center (Rosen-

thal and Ross (2015)). This spatial income pattern is so prevalent in the U.S. that it has

coined the stylized fact of poor cities and rich suburbs (Jargowsky (1997), Glaeser, Kahn,

and Rappaport (2008), Brueckner and Rosenthal (2009)). After controlling for amenities and

other factors that drive household location choice, this salient income pattern is somewhat

attenuated, but the finding still stands in contrast to the negative income gradient postu-

lated by economic theory. However, local income concentration and spatial patterns remain

an important topic in the literature. Despite a short-term decrease in the local concentra-

tion of poverty in the 1990s, the spatial concentration in the U.S. has surged since 2000 -

even exceeding the peak level of 1990 (Jargowsky (2013)). The observed income segregation

has contributed to the debate to what extent spatial organization of incomes affects poor

households. The consensus argues that there are costs of living in areas with bad schools,

poor transit connections, and few public amenities. Thus, the spatial distribution of income

is subject to an ongoing debate among urban planners and economists.

In contrast to the U.S. literature, studies for European cities find mixed results with large

differences in the sign of the spatial income coefficient. Brueckner, Thisse, and Zenou (1999)

show that in French cities (e.g. Paris, Lyon, Caen, and Nancy), income is typically higher

in the center. Similar patterns to the French case are found in other European, as well as

Latin American cities (Hohenberg and Lees (1995), Ingram and Carroll (1981)). Brueckner

et al. (1999) argue that exogenous amenities lead to a multiplicity of household location

choice patterns across cities. As an example, historical amenities in the city center of Paris

(e.g. Eiffel Tower, Notre-Dame, and Arc de Triomphe in Paris) pull rich households into the

5

center. This effect remarks an opposing force to the effect of lower housing prices in suburbs,

which incentivizes rich households to live further away from the city center. If the CBD’s

amenity advantage is strong enough to overcome the traditional force of commuting costs,

high income households will be located closer to the CBD. The importance of amenities (and

disamenities) on wage and rent gradients has been widely recognized since Roback (1982),

and Rosen (1979). The authors provide a framework that enables to investigate the effect of

amenities on household location choice. If proximity to amenities increases residents’ utility,

they accept lower wages or higher rents as compensation to enjoy these amenities. Thus,

idiosyncratic city characteristics lead to a multiplicity of income-distance gradients across

cities. Despite broad consensus that amenities positively affect household location choice,

studies on the effect of a broad set of amenities are limited. Recent studies exclusively in-

vestigate to what extend a single amenity is valued by households. The positive effect of

specific amenities, such as forests (Hand, Thacher, McCollum, and Berrens (2008)), climate

amenities (Lu (2020)), waterfront access (Lee and Lin (2018)), and ocean views (Rappaport

and Sachs (2003)) have previously been documented. However, only few studies include a

wide range of amenities and household characteristics as determinants for household location

choice. Cuberes et al. (2019) investigate the effect of income while controlling for a large set

of amenities on household location for the eight largest cities in the UK (excluding London).

The authors find no significant relationship between income and distance to CBD for five

cities investigated, when controlling for amenities and heterogenous household characteris-

tics.

The third strand of academic literature focuses on the effect of tax rates on household

location choice. The importance of taxes on household location choice in the U.S. has been

investigated with a special focus on retirees. Academic research has shown that older people

avoid areas with high property taxes (Cebula (1974), Duncombe, Robbins, and Wolf (2001)),

and inheritance taxes (Dresher (1993), Voss, Gunderson, and Manchin (1988)). Duncombe,

Robbins, and Wolf (2003) analyzes census county-to-county migration data for the period

1985–1990. The authors find that from all investigated fiscal variables, income taxes most

strongly influence the migration decisions of retirees. The majority of the U.S. literature

on the effects of fiscal policies on household location choice focuses on state or county level

data. In the U.S., local taxation at the municipality level is very rare with respect to income

taxes but common for property taxes. Overall, most municipalities have no right to increase

income taxes or to impose progressive taxation structures.2 In contrast, most U.S. states

2Only a few states in the US, including Indiana, Maryland, Ohio, and Pennsylvania, impose local taxa-tion.

6

apply a flat tax rate. This may be the reason why most studies on the effect of fiscal policy

on household location choice have been conducted at the state or county level for the US.

Internationally, Switzerland’s taxation system is uniquely designed with progressive tax rates

at the municipal level. The only other country that exhibits a similar taxation system to

Switzerland’s is Belgium. For Switzerland, Schmidheiny (2006) studies the effect of income

tax differentials across municipalities in the Swiss canton of Basel and examines the extent

to which it affects household location decisions. We can confirm the importance of taxes as

an important determinant of household location choice in Switzerland.

III. Data and Descriptive Statistics

We obtain data from three different sources: (1) The Swiss Household Panel for household

characteristics, (2) Fahrlander Partner Raumentwicklung for house prices, and (3) Open-

StreetMap for collecting local amenities. We combine information from municipalities with

data on individual households. We define the dependent variable in section III.A, followed

by a description of all explanatory variables in section III.B.

A. Distance to CBD

The dependent variable measures the straight line kilometer distance of each household

to the CBD. For anonymity reasons, household location is only known at the municipality

level. The distance is measured from the centroid of each municipality where the household

is located. The empirical literature has proposed a number of landmarks that represent the

employment center of a city. Cheshire, Hilber, Montebruno, and Sanchis-Guarner (2018) dis-

cuss the ambiguities when defining the CBD. In our case, the choice between commonly used

locations such as the main railway station or the city hall leads to very similar results since

both tend to be located in the same municipality. We follow the recent literature by defin-

ing the CBD as the coordinates of the main railway station (Cuberes et al. (2019); Nathan

and Urwin (2005)). In many cities in the U.K., railway stations are located in clusters of

commercial activity.3 An alternative identification of the CBD is based on the coordinates

of the city hall (Atack and Margo (1998), Paul, Research, and 1991 (1991), Schuetz, Lar-

rimore, Merry, Robles, Tranfaglia, and Gonzalez (2018)). In Switzerland, the city hall is

3For instance, King’s Cross Station in London introduced its own postal code for all buildings aroundthe main station (The Economist (2014)).A similar situation also holds for Switzerland: The city of Zurich is organized in 12 circles or ”Kreise”. “Kreis1” covers a broader definition of the CBD. The Bahnhofstrasse (”Railway Station Street”) in Zurich is aniconic landmark of commercial activity in Switzerland that features many shops and restaurants (Swissinfo.ch(2016)). As the name suggests, the Bahnhofstrasse starts right next to the main train station.

7

often located close to the main train station. For instance, the city hall in St. Gallen is

located within 100 meters of the main train station. In Zurich, the distance between the

main railway station and the city hall is 800 meters. For Lausanne it is 400 meters. For con-

sistency reasons, we follow the U.K. literature by defining the CBD by the main train station.

Although our empirical results are based on the usual haversine distance, we also provide

evidence of the robustness of our findings with respect to travel distance by car or public

transportation. Differences between these three type of distance measures typically occur

because of topology within a city. For instance, the city of Zurich spans around the lake of

Zurich, the city of Lausanne is built on a steep mountain slope which makes navigation by

car challenging. In both cases, travel distance is likely to be larger than the straight line

distance. However, the correlation between the three types of distance measures is close to

95%, so that our empirical findings remain robust.

Finally, a comment on the size of a typical Swiss municipality is in order. The empirical

literature on U.S. cities examines census tracts, the U.K. literature studies lower spatial

output areas (LSOAs). Figure 2 compares three spatial units that are typical in terms

of surface area and population. Judged from the mean area size, Swiss municipalities are

somewhat smaller than census tracts in the U.S. but larger than LSOAs in the United

Kingdom. In total, Switzerland comprises 2,202 municipalities, each of which belongs to one

out of 26 cantons.

8

Figure 2. Average size of a municipal, census tract, and LSOAThis figure compares the area in square kilometres of a typical municipality in Switzerland, with acensus tract in California and a lower spatial output area in the United Kindom. From left to right thefigure visualizes the municipality Appenzell in Switzerland with an area of 16.88 km2 and a populationof 5,728. The depicted census tract in California has a size of 60.14 km2 and a population of 6,496. TheLSOA in the U.K. covers an area of 4.35 km2, with a population of 1,907. Each of the three spatialunits represents the average size of the corresponding spatial unit.

[CH] Municipal: AppenzellN

0 1 2 3km

[USA] Census tract: 06071008703

0 1 2 3km

[UK] LSOA: E01027950

0 1 2 3km

[CH] Municipal [USA] Census tract [UK] LSOA

Mean Surface Area 17.35 50.97 4.35

Median Surface Area 7.93 1.91 0.47

9

B. Explanatory Variables

This section describes the main drivers of household location choice: household charac-

teristics, amenities, and the unique role of taxes in Switzerland.

B.1. Household Characteristics

We obtain detailed household characteristics from 1999 to 2014 for 16,940 households

from the Swiss Household Panel (SHP). The SHP is an annual panel survey of households

from all regions and across all population groups in Switzerland, with the main objective to

determine social changes in Switzerland (Voorpostel, Tillmann, Lebert, Kuhn, Lipps, Ryser,

Antal, Monsch, Dasoki, and Wernli (2019)). The survey covers a broad range of more than

100 quantitative and qualitative household attributes. The data contained in the SHP range

from socio-demographic, financial, health, and educational household information to qual-

itative interview responses such as the importance of air quality, and potential issues with

noise in the neighbourhood. Due to the broad coverage of the SHP data, it has been used

in a number of previous studies, including the effect of employment uncertainty on fertility

(Hanappi, Ryser, Bernardi, and Le Goff (2017)), the effect of immigration on household dis-

location (Adams and Blickle (2018)), and the effect of attending cultural events on personal

well-being (Weziak-Bia lowolska (2016)). The SHP data is representative of the Swiss popu-

lation and exhibits a high retention rate. On average, each household appears in the survey

for more than six years. For the empirical part of this paper, we can therefore observe the

cross-sectional variation of relevant household characteristics over time. In order to ensure

household anonymity, the exact coordinates for each household location are not included in

the SHP. However, we know in which municipality each household is located.

Panel A of Figure 3 shows the geographical location of our eight cities within 10 kilometers

of the city center. The spatial variation in average income on the municipality level ranges

from CHF 50,000 gross income per year to more than CHF 250,000. The white numbers

in parenthesis show the city population size. Swiss cities are small in a European context.

Zurich is the largest of our cities and has a population of 400,000. We also include the

small city of Aarau with a population of 21,000 for comparison. The advantage of studying

small cities is that the monocentric city assumption is more likely to hold. Identification of

the income gradient will be easier in the empirical part of the paper when cities have one

well-defined center of commercial and social activity. Panel B of Figure 3 focuses on the two

largest Swiss cities, Zurich and Geneva, to highlight the extent of spatial variation in average

income. Although the CBD is characterized by households with relatively high income, some

10

of the highest income municipalities are found towards the city edge and along the lakes. In

the empirical part below, we will control for municipalities with a lake view to account for

this effect.

Figure 3. Spatial Income Distribution and City SizeThis figure shows the spatial distribution of average gross income on the aggregate municipality levelwithin 10 kilometers of the city center. Panel A shows the location of the eight cities used in our sampletogether with city population. Panel B highlights the spatial distribution of household income for Zurichand Geneva.

11

To obtain a first impression of the income gradient, Figure 4 shows the relationship

between annual gross income and distance to CBD for each city. It has become practice in

the empirical literature to plot distance quintiles on the x-axis. We follow this practice to

facilitate comparison with similar studies such as Cuberes et al. (2019). The majority of

our cities show an increasing income gradient. Only Bern and St.Gallen show a negative

relationship. Although these simple scatter plots do not control for amenities and household

characteristics, our fully specified regressions in the empirical part below confirm the first

impression from Figure 4: under standard regression specifications, income gradients are

estimated to be positive or insignificant, contrary to what we expect from economic theory.

This finding is in line with Cuberes et al. (2019) who produce similar graphs for English

cities.

12

Figure 4. Income Gradient for Distance QuantilesThis figure shows the income gradient of eight Swiss cities. We measure distance to CBD at quintiles with the 5th quintile located 10 kilometersfrom the CBD.

13

B.2. Amenities

Although the vital role of transportation costs has long been recognized in the literature,

urban economists are increasingly paying attention to the role of amenities in attracting peo-

ple to cities (Rosen (1979); Roback (1982)). For the empirical part of our paper, we obtain

coordinates for a broad set of amenities in Switzerland from OpenStreetMap (OSM). OSM

was launched in 2004 at the University of London and adopted the peer production model,

which is also used by Wikipedia. In contrast to Wikipedia, however, only registered users can

contribute to the OSM database (Haklay and Weber (2008)). As of today, OSM comprises

over 7 million registered users that are collaboratively editing the world map, making the

data freely available to any user interested in spatial information.4 The fact that the OSM

data is user-generated has raised concerns about quality and geographical accuracy. A wide

range of academic studies have investigated OSM data quality by comparing OSM data to

some reference dataset. ISO 1915 defines six categories to evaluate the internal quality of

a spatial dataset, including positional accuracy, thematic accuracy, completeness, temporal

quality, logical consistency, and usability. Ciep luch, Jacob, Mooney, and Winstanley (2010)

find that for some sites in Ireland, the positional differences between OSM and Google Maps

data can be up to 10 meters. Completeness in the ISO 1915 standards refers to the pres-

ence of features in the spatial data set. Haklay (2010) identifies a bias in the OSM data

coverage for the United Kingdom towards more affluent areas.5 Despite these shortcomings,

the information in the OSM data concerning number and location of amenities is sufficient

for our purpose since we are only interested in the number of amenities on the aggregate

municipality level.6 In addition, the OSM dataset is freely available and provides a powerful

API that enables users to write OSM QL queries to collect id, name, and coordinates for

each amenity in Switzerland.

For our empirical part, we retrieve information from OSM for six categories of amenities:

(i) entertainment facilities, such as art centers, casinos, cinemas, nightclubs, and theatres;

(ii) eating out facilities including restaurants, pubs, bars, biergarten, and cafes; (iii) out-

door recreation such as parks, playgrounds, firepits, and gardens; (iv) public services such

as schools, kindergartens, clinics, dentists, doctors, and hospitals; (v) transportation points

4The crowdsourced spatial database has a current uncompressed size of over 1,323 GB and containsinformation on various amenities. A whole list of all types of amenities can be found online on the officialOSM Wikiwebpage (OpenStreetMap (2020a)).

5see Costa Fonte, Antoniou, Bastin, Estima, Jokar Arsanjani, Laso Bayas, See, and Vatseva (2017) for acomprehensive review on OSM data quality.

6The fact that many large companies such as Amazon, Apple, Facebook, Microsoft, and Deutsche Bahnuse OSM data for routing or navigation purposes suggests that the quality of the OSM dataset is sufficientfor most purposes OpenStreetMap (2020b).

14

including all platforms where passengers are waiting for public transport vehicles; and (vi)

sport facilities such as fitness centers, sport centers, and swimming pools. We aggregate the

number of amenities in each category on the municipality level as of 2020. Moreover, we

control for further geographical points of interest such as lakes and national borders. Lakes

and lake views fulfil an important recreational function, while national borders limit the

extent to which a city can expand its territory. 7

Figure 5 illustrates the number and density of amenities as a function of distance to

the CBD. Panel A shows the number of amenities aggregated over all eight cities. The

city center appears to be not only the center of commercial and social activity, but also a

cluster of all kinds of amenities. Since the amenities in Panel A are all positively related

to household well-being, we expect cities centers to be particularly attractive to households,

everything else equal.8 Panel B of Figure 5 disaggregates Panel A to show the number of

amenities for each city. This view emphasizes the large proportion of eating out facilities

in the total number of amenities and confirms that the presence of all amenities diminishes

with increasing distance to the city center. From Figure 5 we conclude that the number of

amenities decreases quickly with increasing distance to the city center.

7The city of Geneva is spatially constrained by the national border to France and Lake Geneva. Zurich,Lausanne and Luzern are built around lakes. Basel is located at the border to Germany.

8Note that the number of outdoor/recreation amenities may be a bit misleading because the naturalenvironment at the city border does not count as an amenity despite of it’s important recreation role. Infact, it is the lack of nature in the city center that requires the city to provide these amenities in the formof city parks and playgrounds.

15

Figure 5. Number of Amenities and Distance to CBDThis figure shows the distribution of amenities as a function of distance to the employment center foreight Swiss cities. Panel A aggregates over all cities, highlighting that some amenities such as restaurantsand transportation are more frequent than others. Panel B further decomposes the amenities to theindividual city level. Berne is the government center of Switzerland (federal city or de facto capital)which is reflected in the higher number of public services. While transportation and other amenitiesalso occur outside the city center, entertainment and restaurants are strongly concentrated in the CBD.

16

B.3. Taxes

Switzerland’s federalism has led to a unique feature in its tax system. The total tax

burden of households in Switzerland has a distinct spatial variation on the very local level.

The importance of this tax variation is confirmed in our empirical part below, where we

show that taxes are the main driver of household location choice.

According to Art. 3 in the federal constitution, the state has the right to raise taxes. How-

ever, all state taxes must be explicitly listed in the constitution. As of 2019, the federations

income equalled 74 billion CHF. A large part of the federations income is due to indirect

taxes such as the value added tax (VAT), gasoline and other refined products tax, tobacco

tax, and withholding tax. Combined, these indirect taxes account for more than 53% of

the Swiss federations total income (Eidgenossische Steuerverwaltung (2020)). However, the

federation income taxes are of minor relevance when considering the total income tax burden

of a household. Economically, income taxes raised by cantons and municipalities account for

the major share of total taxes paid by households. This generates the strong local variation

of the total tax burden of households.

Switzerland is divided into 26 cantons. Each canton has a supplementary taxation right

and can raise any taxes that are not explicitly under the jurisdiction of the federation. This

leads to significant tax differences between cantons. As an example, the cantons Schwyz

and Obwalden do not tax inheritance, while all other cantons do (VZ VermogensZentrum

(2020)). Similarly, the canton of Luzern does not levy a gift tax. In addition, income tax

rates vary strongly across cantons. Each canton sets a level of income tax and decides on

the tax progression autonomously. The 26 cantons are further subdivided into 2,202 munic-

ipalities. Each municipality sets a so-called income tax shifter. Multiplying the municipal

tax shifter with the cantonal tax rate determines the municipal tax burden. For example,

consider a single household with an annual taxable income of CHF 85,000 (about $93,000)

living in the canton of Zurich. Table I shows the difference in yearly tax burden among two

municipalities within the same canton. One household lives in the municipality of Zurich and

the other in Uitikon. Uitikon is a direct neighbor of the municipality of Zurich and lies only

7.5km to the west. The transit time from Uitikon to the main railway station in the center

of Zurich equals 13 minutes. Both households pay the same amount of federal and cantonal

taxes of CHF 1,884 and CHF 4,945, respectively. However, and despite the geographical

proximity between the two municipalities, the annual tax burden differs by 1,929 CHF. This

stylized example illustrates tax differences across municipalities within a metropolitan area.

Figure 6 generalizes this example to all cantons in Switzerland. The y-axis in this graph

17

Table I Stylized Tax Burden ExampleThis table provides a stylized example of tax burdens within the same canton, but different municipalities. We assumea single household with an annual taxable income of 85,000 CHF. This is equal to the mean annual taxable income of asingle household living in Zurich as of 2020.

Zurich (canton: Zurich) Uitikon (canton: Zurich)

Taxable income 85,000 CHF 85,000 CHF

Federal tax 1,884 CHF 1,884 CHF

Cantonal tax 4,945 CHF 4,945 CHF

Municipal tax 5,885 CHF 3,956 CHF

Total tax 12,738 CHF 10,809 CHF

shows the annual tax burden for a married, single-income household with two children and

an annual gross income of CHF 150,000. First, there exists a considerable variation of income

tax burdens across municipalities within the same canton. Second, income taxes also strongly

depend on the corresponding canton, with the canton of Zug exhibiting on average lowest

tax rates. For instance, the two children household described above would have an annual

tax burden of 3.5% when living in Baar in the canton of Zug but would pay almost five times

more or 15.9 % when living in Les Verieres in the canton of Neuchatel. From this section on

local tax variation in Switzerland, we conclude that taxes are likely to play a major role in

household location choice.

18

Figure 6. Tax Rate Distribution for Cantons and MunicipalitiesThis figure shows the spatial distribution of annual income taxes across all Swiss municipalities. Taxesare calculated for a married, single-income household with two children and an annual gross incomeof CHF 150,000. The lowest tax burden occurs in Baar in the canton of Zug, with a tax burden of3.46% of gross income. The highest tax burden results in Les Verieres in the canton of Neuchatel, witha tax burden of 15.94% of gross income. The data is obtained from the federal tax administration(”Eidgenossische Steuerverwaltung”)]

An

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[CH

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15000

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19

IV. Empirical Models and Results

A. Benchmark Regressions

To compare our empirical findings with those reported in the literature for other coun-

tries, we start with a benchmark regression that has become standard in the household choice

literature. We highlight the municipality level tax rate as an important driver of household

location choice. We then extend the benchmark specification to include interaction terms

between household characteristics and amenities. The interaction regression highlights the

variation in household preferences for different amenities and helps to explain spatial segre-

gation of homeowners and tenants.

We begin with the benchmark regression specification of household location choice:

log(Di,j,k,t) = α + β · log(Ii,j,k,t) + γ1Aj,k + γ2Hi,j,k,t + γ3Tj,k + εi,j,k,t (1)

where Di,j,k,t is the kilometer distance of household i, in city j, located in municipality

k, in year t. As in Cuberes et al. (2019) we locate the employment center in the vicinity of

the main railway station and measure distance as the straight-line geographical distance by

default. However, we will also present alternative distance measures below. Annual gross

income is denoted by I and measured on the individual household level. The regressor matrix

A contains two positive amenities, eating out and transportation, as well as house prices,

all measured on the municipality level.9 H is a set of household characteristics and includes

age, number of children, years of education, marital status, and other indicator variables

denoting whether a household is a homeowner, is unemployed, or native Swiss. We treat the

municipality level tax rate T as a separate variable to highlight it’s importance for our study.

Equation 1 is estimated using pooled OLS. Some variables such as gender are time-invariant

while other variables such as age change for all households similarly over time. This prevents

us from using household or year fixed effects. Table II shows the regression estimates for the

benchmark specification in Equation 1.

From economic theory, we expect a negative relationship between household income and

distance. Households living closer to the CBD enjoy shorter commuting times on average.

These benefits put upward pressure on house prices for those households located in close

proximity to the CBD. Spatial sorting of incomes happens since not all households will be

9Other amenities that we have collected such outdoor amenities and public services are excluded in thisspecification due to mutlicollinearity.

20

able to afford the high house prices and rents. Except for Zurich, all income coefficients are

either positive or insignificant. For instance, a 1% increase in household income increases

distance to CBD in Basel on average by 0.084%. To put this effect into economic context, a

household living 5km away from the CBD and experiencing a 50% increase in gross income

would move 210 meters further away from the CBD.

21

Table II Household Location Choice RegressionThis table shows individual city regressions of log(distance to CBD) on log(income), a set of household characteristics, and selected amenities. The number of householdsNi varies by city and are observed over 16 years from 1999 to 2014. The coefficients are estimated with pooled OLS since some variables are time invariant (gender) orchange every period for all households (age). Standrad errors are robust to unknown form of heteroscedasticity (Long and Ervin (2000)).

Dependent variable:

log(distance to CBD)Aarau Basel Bern Genf Lausanne Luzern St. Gallen Zurich

(1) (2) (3) (4) (5) (6) (7) (8)

log(Income) 0.133∗∗∗ 0.084∗∗∗ 0.005 −0.005 0.004 0.069∗∗∗ 0.047 −0.008∗∗

Age −0.001 0.001 0.004∗∗∗ 0.002∗∗ −0.0005∗∗∗ −0.002∗ −0.003∗ −0.0004∗∗

Kids 0.065∗ 0.079∗∗∗ 0.021 0.077∗∗∗ 0.010∗ 0.066∗∗ 0.361∗∗∗ 0.022∗∗∗

Education [Years] −0.018∗∗ −0.007∗∗∗ −0.012∗∗∗ 0.005 −0.002∗∗∗ 0.002 −0.022∗∗∗ −0.003∗∗∗

Female 0.118∗∗∗ −0.034∗∗ −0.036∗∗ 0.015 −0.010∗∗ 0.065∗∗∗ −0.217∗∗∗ −0.009∗∗

Married −0.023 −0.036∗∗ 0.083∗∗∗ −0.036 0.026∗∗∗ 0.143∗∗∗ 0.140∗∗∗ −0.013∗∗

Homeowner 0.261∗∗∗ −0.047∗∗ 0.041∗∗ 0.232∗∗∗ 0.025∗∗∗ 0.297∗∗∗ 0.303∗∗∗ 0.003

Unemployed −0.051 0.045∗∗ −0.036∗ 0.030 0.006 0.033 −0.119∗∗ 0.004

Swiss 0.132∗∗∗ −0.034 0.155∗∗∗ −0.036 0.024∗∗∗ 0.069 0.562∗∗∗ 0.010

Eating Out 0.194∗∗∗ 0.303∗∗∗ 0.015∗∗∗ 0.003 0.010∗∗∗ 0.307∗∗∗ 0.411∗∗∗ −0.149∗∗∗

Transportation 0.071∗∗∗ 0.498∗∗∗ 0.075∗∗∗ 0.382∗∗∗ 0.003 0.114∗∗∗ 0.027∗∗∗ 0.090∗∗∗

log(Tax) 1.657∗∗∗ −7.422∗∗∗ −6.715∗∗∗ −15.318∗∗∗ −5.519∗∗∗ −2.571∗∗∗ −5.509∗∗∗ 1.730∗∗∗

log(House Prices) −1.041∗∗∗ −0.390∗∗∗ −1.275∗∗∗ −0.103∗∗∗ −0.019∗∗∗ −0.492∗∗∗ −2.327∗∗∗ −0.041∗∗∗

Lake −2.275∗∗∗ −0.314∗∗∗ 0.136∗∗ −0.137∗∗∗

Border −0.121∗∗∗ 0.150∗∗∗

(Intercept) −2.193 78.238∗∗∗ 84.924∗∗∗ 151.294∗∗∗ 56.516∗∗∗ 31.259∗∗∗ 85.078∗∗∗ −13.403∗∗∗

Observations 1,681 2,556 1,752 2,511 5,175 1,830 1,989 4,571R2 0.373 0.763 0.620 0.870 0.352 0.553 0.577 0.986Adjusted R2 0.368 0.761 0.617 0.869 0.351 0.549 0.574 0.986

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

22

The positive income coefficient estimates are in line with findings from other countries

including the U.K. (Cuberes et al. (2019)), Canada (Axisa et al. (2012)) and the U.S. (Rosen-

thal and Ross (2015)). The size of most coefficients suggest that the economic income effect

is generally economically small. Thus, income is not an important driver of household lo-

cation choice once household characteristics and amenities are controlled for. Looking at

household characteristics, native Swiss households, families, homeowners, and older house-

holds tend to live further away from the city center. In contrast, more educated households

prefer living closer to the city center. In this specification, we only include eating out ameni-

ties (restaurants and fast food) as well as transportation amenities (number of bus or train

stops). Although we have also collected other amenities such as public services, sport, and

entertainment amenities, these are all highly correlated among each other. The reason is

that amenities are only available on the municipality level for the most recent year. While

the supply and composition of amenities in a city change rather slowly over time (Duranton

and Puga (2015)), this setting introduces multicollinearity in our model so that we focus on

eating out and transportation amenities. We further weight the amenities by distance prior

to entering them into the regression model. This set of compound variables is motivated by

the nature of the dependent variable: since we measure household location choice relative to

a reference point (the city center), we should expect households to respond to amenities that

lie far away from the CBD. For instance, an increase in amenities in municipality k, which is

located close to the city center should only have a small effect on household location choice

given that amenities are highly concentrated in the CBD.

In contrast, an increase in amenities at the city edge should have a much larger impact as the

CBD no longer has the unique feature of offering amenities. Given that households would

no longer have to commute to the city center to enjoy these amenities we expect a positive

coefficient for distance weighted amenities. This seems to be generally the case for eating

out and transportation amenities: a one standard deviation increase in eating out amenities

outside the CBD, which equals 50 additional restaurant and fast food place, is estimated to

increase the distance to CBD in Basel by 30% in Basel and Luzern, and by 40% in St.Gallen.

A shock in transportation of the same size has similar effects.

We also test for the impact of two negative amenities: house prices and taxes. While house

prices are an important control variable that captures a variety of latent local factors, taxes

take a special role in this study as its regional variation is particularly large. We find a

strongly negative coefficient, indicating that lower taxes outside the city center leads to relo-

cation towards low tax municipalities at the city edge. For instance, a 1% decrease in taxes

at the city edge increases the distance to the city center by 2.5% in Luzern, 6% in Bern,

and 15% in Luzern. These coefficients are both statistically and economically significant.

23

Households location elasticity with respect to taxes is more than 8 times larger than the

house price elasticity. We conclude that taxes are an important driver of household location

choice in Switzerland a finding that seems to be unique to the Swiss data and is not found

in the literature examining other countries.

Figure 7 illustrates the level of R-squared when the variables labelled on the x-axis are

sequentially added to the regression. For instance, log(income) alone has little explanatory

power. Adding household characteristics improves R-squared only moderately. A regression

model with all 9 household characteristics from log(income) up to nationality explains less

than 20% of the variation of household’s distance to CBD. In contrast, adding amenities to

the regression strongly improves the R-squared for all cities. Sequentially adding variables

has the disadvantage that the ordering of the variables is not taken into account. For in-

stance, if we switch the position of eating out with log(taxes), the increase in R-squared is

quite similar. However, the improvement of R-squared is robust over ordering and Figure

7 can illustrate that amenities appear to be more important for explaining the variation in

household location than household characteristics.

Figure 7. R-Squared Response to Sequentially Adding VariablesThis figure plots the level of R-squared when the variables labelled on the x-axis are sequentially addedto the regression. The regression specification is according to Equation 1.

0.0

0.2

0.4

0.6

0.8

1.0

R-s

quar

ed

log(

Inco

me)

Age

Kid

s

Educa

tion

Fem

ale

Mar

ried

Hom

eow

ner

Unem

plo

yed

Sw

iss

Eat

ing

Out

Tra

nsp

orta

tion

log(

Tax

)

log(

Hou

seP

rice

s)

Lak

e

Bor

der

Household Characteristics AmenitiesLausanne

Aarau

Basel

24

The benchmark regression specification in Equation 1 is useful for comparing the findings

in this study to those reported for other countries. An interesting direction for expanding

this analysis is to include interaction terms between household characteristics and amenities.

For instance, entertainment amenities such as clubs and bars are likely valued differently by

young singles than by families. A household may also have different preferences concerning

outdoor amenities, public services, and public transportation. To highlight these differences

in amenity preferences, we first construct an amenity index that will be interacted with

each household characteristics. The reduction of the set of amenities to one index allows

for a compact regression specification and reduces the number of interaction terms from

40 (5 amenities times 8 characteristics) to just 8 (1 amenity index times 8 characteristics).

The amenity index Aj,k is computed as the first principal component from the following

5 amenities: “Entertainment”, “Eating Out”, “Outdoor/Recreation”, “Public Services”,

and “Transportation”. This first principal component explains between 55% for Aarau and

Luzern and 98% for Lausanne and can therefore be considered as a representative amenity

variable.

log(Di,j,k,t) = α + β · log(Ii,j,k,t) + γ1Aj,k + γ2Hi,j,k,t + γ1Aj,k · γ2Hi,j,k,t + γ3Tj,k + εi,j,t (2)

Table III shows the results for the interaction model of Equation 2. The coefficients

and the model’s explanatory power seem to be robust to the extended specification and the

income elasticity is of similar size. However, a number of significant interaction terms indi-

cate that the extent to which households value the presence of certain amenities varies with

household characteristics. To illustrate this further, Figure 8 compares the economic size of

the interaction terms. Panel A on shows the dislocation response from a one standard devi-

ation increase in amenities. In most cities, households respond to an increase in amenities

at the city edge by increasing their distance to the city center. The response is particularly

large in Geneva, but is also sizeable for Basel, Luzern, and St.Gallen: a one standard de-

viation increase in amenities at the city edge (equal to 50 additional amenities) increases

the distance to the city center by around 50%. While panel A shows the variation across

cities, panel B emphasizes the differences in household characteristics. For instance, Swiss

and female residents show a stronger response to amenities than married households and

homeowners. A possible explanation for this finding is that these types of households have

higher social and pecuniary moving costs and are therefore less mobile than other households

in the sample. In contrast, the preference for amenities does not seem to vary strongly across

25

age, and education.10

From the empirical findings in this section, we conclude that households respond strongly

to the presence of amenities and taxes when making household location decisions. However,

not all households value amenities in the same way. Income is not an important determinant

of household location choice, which contradicts the economic theory. A possible explanation

would be that the cities examined in this study are relatively small in a global context and

are well connected by public transportation. Some of the city centers studied here can be

reached within 30 minutes by train from the city edge so that commuting costs are within

a range that is acceptable to most households. However, Cuberes et al. (2019) conducted

a similar study for larger cities in the U.K. and report similar income coefficients. Another

explanation would be that the monocentric city model is not an accurate description of

the cities studied here. However, the Swiss cities examined in this study generally have

a well-defined employment center that encompasses the main train station, offices, and a

walkable historical town center that includes shops and other commercial activities. In the

next section, we provide a possible solution to this problem.

10Note that a one-unit increase in age and education is measured in years. However, even a sizeableincrease of 20 years in age or 5 years in education does not result in large interaction terms.

26

Table III Household Location Choice Regression with Interaction TermsThis table shows individual city regressions of log(distance to CBD) on log(income), a set of household characteristics, and an amenity variable that is estimated fromthe first principal component of individual amenities “Entertainment”, “Eating Out”, “Outdoor/Recreation”, “Public Services”, and “Transportation”. The proportionof the variance that is explained by this principal component is shown in the lower part of the table. The number of households Ni varies by city and are observed over 16years from 1999 to 2014. The coefficients are estimated with pooled OLS since some variables are time invariant (gender) or change every period for all households (age).Standard errors are robust to unknown form of heteroscedasticity citeLong2000UsingModel).

Dependent variable:

log(distance to CBD)Aarau Basel Bern Genf Lausanne Luzern St. Gallen Zurich

(1) (2) (3) (4) (5) (6) (7) (8)

log(Income) 0.147∗∗∗ 0.094∗∗∗ 0.020 0.073∗ 0.005 0.075∗∗∗ 0.038 −0.019∗∗

Age −0.002 −0.001∗ 0.003∗∗∗ 0.001 −0.002∗∗ −0.003∗∗∗ −0.006∗∗∗ −0.001

Amenities −0.444 0.519∗∗∗ 0.005 1.060∗∗∗ −0.025∗∗∗ 0.521∗∗∗ 0.250∗∗∗ −0.393∗∗∗

Kids −0.093 0.056∗∗ 0.005 0.243∗∗∗ 0.076∗∗∗ 0.068 0.423∗∗∗ 0.045∗

Education [Years] −0.034∗∗∗ −0.015∗∗∗ −0.029∗∗∗ −0.008 −0.015∗∗∗ −0.015∗∗∗ −0.039∗∗∗ −0.008∗∗

Female 0.119∗∗∗ −0.051∗∗ −0.067∗∗ −0.310∗∗∗ −0.061∗∗∗ 0.114∗∗∗ −0.311∗∗∗ −0.115∗∗∗

Married −0.041 −0.012 0.191∗∗∗ 0.119∗∗ 0.122∗∗∗ 0.227∗∗∗ 0.164∗∗∗ −0.071∗∗∗

Homeowner 0.439∗∗∗ 0.004 0.142∗∗∗ 0.532∗∗∗ 0.094∗∗∗ 0.511∗∗∗ 0.430∗∗∗ −0.051∗∗

Unemployed −0.042 0.048∗∗ −0.036 0.080 −0.033 0.097∗∗ −0.201∗∗∗ 0.031

Swiss −0.023 −0.036 0.234∗∗∗ 0.259∗∗∗ 0.038 −0.148∗ 0.791∗∗∗ 0.109∗∗∗

log(Tax) 2.006∗∗∗ −7.281∗∗∗ −6.646∗∗∗ −13.798∗∗∗ −3.513∗∗∗ −2.871∗∗∗ −7.037∗∗∗ 0.863∗∗∗

log(House Prices) −1.183∗∗∗ −0.458∗∗∗ −1.224∗∗∗ −0.261∗∗∗ −0.028∗∗∗ −0.561∗∗∗ −2.365∗∗∗ −0.289∗∗∗

Amenities*Age 0.008∗∗∗ 0.006∗∗∗ −0.0001 0.004∗ 0.0002∗∗ 0.003∗∗ 0.003∗∗∗ 0.0003∗∗

Amenities*Kids 0.411∗∗∗ 0.034 −0.004 −0.120 −0.009∗∗∗ −0.023 −0.171∗∗∗ −0.002

Amenities*Education 0.022 0.022∗∗∗ 0.008∗∗∗ 0.015 0.002∗∗∗ 0.032∗∗∗ 0.025∗∗∗ 0.0002

Amenities*Female −0.031 0.025 0.018∗∗ 0.241∗∗∗ 0.007∗∗ −0.093∗∗ 0.092∗∗∗ 0.009∗∗∗

Amenities*Married 0.021 −0.057 −0.051∗∗∗ −0.226∗∗∗ −0.014∗∗∗ −0.246∗∗∗ −0.089∗∗∗ 0.010∗∗∗

Amenities*Homeowner −0.590∗∗∗ −0.063∗ −0.042∗∗∗ −0.263∗∗∗ −0.011∗∗∗ −0.478∗∗∗ −0.158∗∗∗ 0.030∗∗∗

Amenities*Unemployed −0.016 −0.051 0.007 −0.088 0.004 −0.100∗ 0.049∗ −0.007∗∗∗

Amenities*Swiss 0.593∗∗∗ 0.029 −0.053∗∗∗ 0.085 −0.004 0.226∗∗ −0.250∗∗∗ −0.009∗∗

(Intercept) −3.486 77.755∗∗∗ 83.566∗∗∗ 136.309∗∗∗ 36.938∗∗∗ 35.407∗∗∗ 100.880∗∗∗ −1.254

Observations 1,681 2,556 1,752 2,511 5,175 1,830 1,989 4,571R2 0.451 0.753 0.633 0.509 0.344 0.604 0.568 0.944Adjusted R2 0.445 0.751 0.629 0.505 0.342 0.600 0.563 0.944Variance of Prin. Comp. 55% 70% 83% 66% 98% 55% 83% 85%

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

27

Figure 8. Visual Comparison of Amenity Interaction TermsThis graph visualizes the amenity-household interactions from Table III. The upper graph shows thedislocation response from a one standard deviation increase in amenities. Households in Geneva respondmore strongly to an increase in amenities outside the CBD, while the response in Zurich and Lausanneare very small. The lower graph compares the interaction terms for different household characteristics.It shows that Swiss households and households with a female head appear to value amenities more whilehomeowners are less respondent.

(a) City Variation in Amenity Interation Terms

Household Dislocation to One S.D. Increase in Amenities

Aarau

Basel

Bern

Genf

Lausanne

Luzern

St.Gallen

Zurich

-1.0 -0.5 0.0 0.5 1.0

Amenities*AgeAmenities*KidsAmenities*Education

Amenities*FemaleAmenities*MarriedAmenities*Homeowner

Amenities*UnemployedAmenities*Swiss

(b) Comparing the Size of Interaction Terms

Comparison of Interaction Terms

Amenities*Age

Amenities*Education

Amenities*Female

Amenities*Homeowner

Amenities*Kids

Amenities*Married

Amenities*Swiss

Amenities*Unemployed

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

AarauBasel

BernGenf

LausanneLuzern

St.GallenZurich

28

B. Negative Income Gradients

The empirical results presented so far indicate a positive or insignificant income gradient

for cities in Switzerland. Although this result is in line with studies for other countries in

Europe, it contradicts the way spatial sorting is predicted by urban economic theory. In this

section, we present a possible solution to this problem.

In practice, regression models are usually specified to provide an intuitive economic inter-

pretation. Although this approach has clear advantages, it will also mask a number of more

complicated interactions between variables. We argue that the income gradient is probably

negative as predicted by theory but that the true relationship has so far been undetected

because it requires a complex interaction of three variables that govern why high-income

households sometimes locate at the city edge: (1) distance to the CBD, (2) access to na-

ture, and (3) a preference for large single-family homes. The city center is characterized by

apartments and a densely populated area. Access to nature and spacious homes can only be

found at the city edge. Once household preferences for distance to the employment center,

access to nature, and spacious houses are jointly controlled for, we expect a negative income

gradient as predicted by economic theory. Therefore, we estimate a regression with a triple

interaction term consisting of distance to CBD, the presence of nearby nature/recreation

amenities, and the number of rooms of the property occupied by a household.

Incomei,t = α + β′ · distancei,t × roomsi,t × outdoori,t + εi,t (3)

which can be expanded to

Incomei,t = α + β1 · distancei,t + β2 · roomsi,t + β3 · outdoori,t+

γ1 · distancei,t · roomsi,t + γ2 · distancei,t · outdoori,t + γ3 · roomsi,t · outdoori,t+

δ1 · distancei,t · roomsi,t · outdoori,t + εi,t (4)

The multiplicative specification in this equation prevents an intuitive interpretation of the

marginal effects of the regressors. However, a visualization of the predicted nature between

income and distance is instructive. To obtain predicted values of income for increasing levels

of distance, we employ the following approach:

1. Estimate the triple interaction Equation (4).

2. Fit the number of rooms on distance to CBD using second or third order polynomials

29

when statistically significant:

Roomsi,t = f(distancei,t) + εi,t (5)

3. Based on the results from the regression in equation (5), predict the number of rooms

with increasing distance.

4. Estimate a regression of outdoor amenities on distance using higher order polynomials

when necessary as before:

Outdoori,t = f(distancei,t) + εi,t (6)

5. Based on the results from the regression in equation (6), predict the number of outdoor

amenities with increasing distance.

6. Predict the relationship between income and distance based on equation (4) and taking

the predicted behavior of the number of rooms (equation (5)) and the presence of

outdoor amenities (equation (6)) into account.

Figure 9 shows the estimated income gradient for all eight cities using the approach

described above. The red dashed line shows the income-distance relationship based on

the multiplicative interaction specification of Equation (4). For comparison, the black line

shows the income gradient when income is regressed on distance alone instead of the triple

interaction specification. This linear specification generates the income gradient with the

opposite sign that is typically reported in many household location choice regressions in

the literature. The findings in Figure 9 suggest that income is not a function of distance

alone but that the interaction between distance, outdoor amenities, and luxury homes is

necessary to uncover the nature of the income relationship of Swiss households. We expect

that this specification will also yield negative income gradients when tested on other cities in

Europe. We conclude that the income gradient appears to be downward sloping as predicted

by the theory but that empirical evidence for this effect requires careful specification of the

regression model.

30

Figure 9. Income Gradient and Distance to CBDThis figure depicts the results from linear and multiplicative regression for each city. The linear modelis represented by the solid black line.

(a) Aarau

2 4 6 8 10

50000

100

000

150

000

200

000

2500

00

Distance to CBD [km]

AnnualGross

Income[C

HF]

LinearMultiplicative

(b) Basel

2 4 6 8 10

20000

04000

006000

008000

00

Distance to CBD [km]

AnnualGross

Income[C

HF]

LinearMultiplicative

(c) Bern

2 4 6 8 10

050

0000

1000

000

1500

000

Distance to CBD [km]

Annual

Gross

Income[C

HF]

LinearMultiplicative

(d) Genf

0 2 4 6 8 10

010

0000

020

0000

030

0000

0

Distance to CBD [km]

Annual

Gross

Income[C

HF]

LinearMultiplicative

(e) Lausanne

3 4 5 6 7 8 9

020

0000

6000

0010

0000

0

Distance to CBD [km]

Annual

Gross

Income[C

HF]

LinearMultiplicative

(f) Luzern

2 4 6 8 10

020

0000

4000

0060

0000

8000

00

Distance to CBD [km]

Annual

Gross

Income[C

HF]

LinearMultiplicative

31

(g) St.Gallen

2 4 6 8 10

0200

000

400

000

600

000

Distance to CBD [km]

AnnualGross

Income[C

HF]

LinearMultiplicative

(h) Zurich

2 4 6 8 10

01000

000

2000

000

300

000

0400

000

0

Distance to CBD [km]

AnnualGross

Income[C

HF]

LinearMultiplicative

V. Robustness Checks

One of the main topics in this paper is the empirical estimation of the income gradi-

ent. In the following, we assess the robustness of our results along three dimensions. First,

we examine the sensitivity of the income gradient when the city edge is placed at various

points along the distance scale. Second, we evaluate the extent to which the income gradient

depends on the inclusion of control variables from the set of household characteristics and

amenities. Finally, we examine whether the choice of a specific distance measure affects our

empirical findings.

The majority of the Swiss territory is occupied by the Alps. Thus, cities in Switzerland

are concentrated in a dense urban area on the alpine plateau. In addition, the average city

size is small in an international comparison. We decided to place the city edge at 10km from

the city center. Although this cut-off is to some extent arbitrary, it reflects the trade-off

between adequately covering the city’s land surface and including regions that belong to a

neighboring city. In this section, we will therefore assess the sensitivity of the income gradi-

ent for different distance levels at which municipalities are no longer considered to be part

of the city edge. Figure 10 shows the income gradient estimated from a simple regression

of log(distance) on log(income) for different cut-off points and averaged over all cities. The

average income gradient is fairly robust for different cut-off values. Using 10 km as in our

32

analysis or 30 km has little effect on the estimated income coefficient.11

Only very short distances of 5 km, which are still close to the city center seem to affect the

coefficient estimates. From Figure 10 we conclude that choosing a specific cut-off value is

not likely to drive our empirical results.

Figure 10. Sensitivity of Income Coefficient to Distance Cut-Off ValueThis figure shows the sensitivity of the income coefficient with respect to the cut-off value for the cityedge. Each bar shows the result from a simple regression of log(distance) on log(income), averaged overall eight cities and for a given distance. The benchmark cut-off value used throughout the paper is10km. The graph shows that the coefficient estimate for income is relatively stable between 0.08 and0.1 for typical distances used in the literature.

5 5.9 7.6 9.3 11 12.8 14.5 16.2 17.9 19.7 21.4 23.1 24.8 26.6 28.3 30

Ave

rage

Inco

me

Coeffi

cien

t

0.00

0.02

0.04

0.06

0.08

0.10

The second robustness test concerns the sensitivity of the income coefficient to the inclu-

sion of control variables. In their study of cities in the United Kingdom, Cuberes et al. (2019)

conclude that “there is no systematic relationship between income and household distance

to the city centre, once neighbourhood amenities and other household characteristics are

taken into account”. We present evidence of a similar effect for Swiss cities: the size of the

income coefficient declines once controls are added to the regression. Finally, we examine

the impact of using different distance measures. While the haversine distance has become

standard in the literature, we can also test whether our results respond to driving distance

or travelling distance based on public transportation. We address both issues in Figure 11 .

11Cuberes et al. (2019) use a cut-off value of 40 km. Since our cities are smaller and located in closeproximity, a 40 km cut-off value would lead to overlapping city borders of Zurich – St.Gallen, and Geneva –Lausanne.

33

The y-axis measures the estimated income coefficient. As before, we use a simple regression

of log(distance) on log(income). Each point represents the coefficient estimate for one city

where the three distance measures are highlighted using different symbols. The x-axis shows

how the regression specification is expanded by first adding household characteristics, then

amenities, and finally the interaction between both sets of variables. These control variables

are sequentially added. The estimates in column three include income, household charac-

teristics, and amenities. The fourth column includes all variables from the previous column

plus interaction terms.

Figure 11. Income Coefficients with Control variablesThis figure shows the estimated coefficient from distance to CBD on income. Three different distancemeasures are used as the dependent variable: driving distance by car, straight-line haversine distance,and distance by public transportation. Each point in the plot represents the estimated coefficientfor a specific city. The points in the first column are from a simple regression of log(distance) onlog(income). The second column shows the same income coefficients when household characteristics areadded as control variables. The third column shows the estimated income coefficient when householdcharacteristics and amenities are added as control variables (full model).

Est

imat

edC

oeffi

cien

tfo

rIn

com

e

-0.1

0.0

0.1

0.2

Income + H.H. Characteristics + Amenities + Amenities*Char

Driving Distance Haversine Distance Public Transport Distance

The results in Figure 11 confirm a finding in the European and U.S. literature: the income

coefficient in a simple regression of log(distance) on log(income) is positive but declines

once household characteristics and amenities are added. What initially appears to be an

income effect can be to some extent explained by household preferences for certain amenities.

34

Another finding from this graph is that the choice of distance measure has no substantial

effect on the main results in this paper. The empirical analysis in this paper was conducted

using the haversine distance, but other alternatives produce very similar results.

VI. Conclusion

We present an empirical analysis of household location choice in Switzerland. Our find-

ings add to the few existing studies for European cities. Our analysis of Swiss cities differs

from studies for other European cities like in Cuberes et al. (2019). Swiss cities are small

in a European context, are located in close proximity, and are well connected by an effi-

cient public transportation network. Despite these specific characteristics, we can confirm

the findings from other studies concerning the relationship between income and distance

to the city center. In simple regressions of distance on household income, income tends to

increase with distance to the CBD. This result stands in stark contrast to predictions by

urban economic theory. Standard regression specifications that include household character-

istics and amenities as control variables yield mostly positive but economically small income

coefficients. Instead, amenities appear to be a more important driver of household location

choice. In particular, we find that households respond sensitively to municipality level taxes,

a variable with strong regional variation and special importance in Switzerland. We also

provide evidence that amenities are not all valued in the same way.

Importantly, we provide a possible solution to the income gradient problem. We propose

a multiplicative regression specification that jointly controls for the main reasons why high

income households choose to locate at the city border despite higher commuting times: the

presence of spacious houses, distance to the city center, and the presence of nature. Once

these three variables are properly modeled, the income gradient is strongly negative as pre-

dicted by the monocentric city model. We expect this specification to lead to similar results

for other European cities.

Future research on this topic is likely to take the rising practice of working from home

into account. Recent studies that examine urban growth during the Covid-19 pandemic

of 2020-2021 already show a reallocation of housing demand towards the city border, an

observation with strong implications for the spatial sorting of household income.

35

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VII. Appendix

Table A1 Variable descriptionThis table provides an overview of the dependant variable and all explanatory variablesof interest.

Variable Variable description

Dependent VariableLinear distance to CBD Linear distance (meters) from household to the CBD using the Haversine

formula.Car distance and time Google Maps API was used to estimate the distance and time by car

from the centroid of each municipal to the CBD.Transit distance and time Google Maps API was used to estimate the distance and time by public

transportation from the centroid of each municipal to the CBD.

Explanatory Variables

Household CharacteristicsAnnual gross income Annual gross income in CHF from all sources.Age Age of the household head.Kids Number of kids living in the household.Education [Years] Number of years spent at school or UniversityFemale =1 if head of household is female; zero otherwise.Married =1 if head of household is married; zero otherwise.Homeowner =1 if head of household is a homeowner; zero otherwise.Unemployed =1 if head of household is unemployed; zero otherwise.Swiss =1 if head of household is Swiss; zero otherwise.

AmenitiesTax Municipal tax shifter.House prices House price index at the municipal level obtained from Fahrlander Part-

ner Raumentwicklung.Entertainment Total number of art centers, casinos, cinemas, nightclubs, and theatres

in a municipal.Eating out Total number of restaurants, pubs, bars, biergarten, and cafes in a mu-

nicipal.Outdoor Total number of parks, playgrounds, firepits, and gardens in a municipal.Public services Total number of schools (kindergarten, primary, middle, and secondary

schools) and health facilities (clinic, dentists, doctors, and hospitals) ina municipal.

Transportation Total number of platforms (place where passengers wait for the publictransport) in a municipal.

Sport Total number of fitness centers, sports centers, and swimming facilitiesin a municipal.

Lake =1 if the municipality borders on a lake; zero otherwise.National border =1 if the municipality borders on a national border; zero otherwise.

41