Housing patterns and school choice in school segregation

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M

ASTER

T

HESIS

Housing patterns and school choice in

school segregation

Author: Efi Athieniti Supervisor: Dr Michael Lees Co-Supervisor: Dr Willem Boterman

A thesis submitted in fulfilment of the requirements for the degree of MSc Computational Science

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Declaration of Authorship

I, Efi Athieniti, declare that this thesis titled, “Housing patterns and school choice in school segregation” and the work presented in it are my own. I confirm that:

• This work was done wholly or mainly while in candidature for a research de-gree at this University.

• Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated.

• Where I have consulted the published work of others, this is always clearly attributed.

• Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work.

• I have acknowledged all main sources of help.

• Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed my-self.

Signed: Date:

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“The greatest thing by far is to have a command of metaphor. This alone cannot be im-parted by another; it is the mark of genius, for to make good metaphors implies an eye for resemblances.”

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UNIVERSITY OF AMSTERDAM

Abstract

MSc Computational Science

Housing patterns and school choice in school segregation

by Efi Athieniti

School segregation, often measured as the uneven distribution of pupils of dif-ferent socioeconomic and ethnic backgrounds, is associated with socioeconomic in-equalities and unequal opportunity, and is becoming a central policy concern in the Netherlands.

Ethnic segregation in schools in Dutch cities is high, and consistently higher than the residential segregation observed in the surrounding school neighbourhood. This difference is often attributed to individual behaviour in parental school choice. In this report, an agent based model to understand the discrepancy between school and residential segregation is proposed. Using the same individual ethnic prefer-ences for school and residential choice, we find that the level of school segregation is systematically higher when compared to the school segregation level in a con-trol case of integrated residential distributions. It is suggested that systemic effects, which emerge from the combination of residential segregation and school choice could explain the difference observed in residential and school segregation.

We conclude that cause and effect in parental school choice behaviour, residential patterns and school segregation are complex and interconnected even in contexts with freedom in school choice.

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Acknowledgements

I would like to thank my supervisor Dr Mike Lees, for his valuable guidance and advise on the technical side of agent based modelling. Without his confidence in my contribution to the project, it would not have made it into one of the projects I am most proud of. I would like to thank the Institute for Advanced study for hosting me. My deepest gratitude to Dr Willem Boterman, for the knowledge and inspiration he gave me about the topic of segregation and the importance of urban geography. Eric Dignum, Thomas van Der Ween and Nigen van Herwijnen who through countless meetings enabled me to be critical about my work and made the project more fun than work. Natalie Kastel, Bas Chatel and Fiona Lipperta who helped me look at different perspectives. And lastly, to my family and friends for the immense, continued and unconditional support.

I thank everyone again for helping me complete a project which made me push myself in areas I did not explored before.

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List of Figures

1.1 School segregation against residential segregation level in 22 munici-palities in the Netherlands. The segregation index is the dissimilarity index for the 3 minorities Surinamise, Turkish and Moroccan vs. the

Native dutch (taken from [3]) . . . 3

2.1 Factors in parental school choice summarised in the literature . . . 9

2.2 The neighbourhood studied in [14] . . . 10

2.4 Agent’s Payoff Profile [29] . . . 12

2.5 Agent’s neighbourhood definition in the Schelling models (a) Spatial model (b) Aspatial bounded neighbourhood model . . . 13

2.6 Tolerance schedule in Schelling bounded neighbourhood model . . . . 14

2.7 Figure taken from [25]. The sensitivity of the school-neighbourhood index, variable neighbourhood index and school segregation index to ethnic preference, f is shown (Threshold of satisfaction, Tu=0.40) . . 17

3.1 The main processes modelled are parental school choice and parental residential choice. The residential choice is made considering the eth-nic composition of the agents’ neighbourhood. The school choice is driven by two factors, the ethnic composition of the agents’ neigh-bourhood, and minimising the distance to school. . . 20

3.2 Artificial grid, size: 100×100. There are two types of agents, blue and red. The yellow marks indicate the school positions, and the white lines indicate the neighbourhood boundaries. . . 20

3.3 Agent’s local neighbourhood definition: a combination of Moore and the fixed school neighbourhood . . . 22

3.4 Variable segregation index with radius=3 . . . 26

4.1 School and neighbourhood segregation index for different values of f α = 1, b = 1, Tu = 0.75. Fixed parameter values are shown in Table 4.1. . . 30

4.2 Residential patterns at different values of b, the weight of bounded to local variable neighbourhood in agent’s choice (a) b=0 (b) b=0.2 (c) b=0.8, Tu=0.75, radius=3 . . . 32

4.3 Number of red and blue agents in each neighbourhood, b = 0.20, Tu =0.75, radius=3 . . . 32

4.4 Parameter sweep for the neighbourhood segregation index and mixed residential segregation index against parameters (a) b (b) radius Tu = 0.75 . . . 32

4.5 Parameter sweep for the school segregation index against f for differ-ent values of α, fr=0 c=2, Tu=0.75 . . . 34

4.6 Parameter sweep for the school segregation index against α fr = 0 fs =0.7, c=2, . . . 34

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4.7 Parameter sweep for (a) Mixed Residential Segregation fr =0.7, radius=

3, b = 0.15 (b) School Segregation index fs = 0.7, fr = 0 against Tu

c=2, Tu =0.75 . . . 35

5.1 (a) School segregation index when fr=0 (green dotted line) and fr=

fs (blue line) as f is varied. (b) The ratio of the school segregation

index between the two simulations in (a). radius=3, b =0.15, c=2, Tu =0.75 . . . 37

fs (blue line) as α is varied. (b) The ratio of the school segregation

index between the two simulations in (a). radius=3, b =0.15, c=2, Tu =0.75 . . . 38

fs (blue line) against (a) radius (b) Tu radius = 3, b = 0.15, c = 2,

Tu =0.75 . . . 39

5.4 (a) School segregation and residential segregation (b) Ratio of resi-dential segregation to school segregation, for different values of mean ethnic preference f radius=3, b=0.15, α=0.25, c=2, Tu=0.75 . . . 40

5.5 Ratio of School Segregation to residential segregation (here measured with the Mixed residential segregation index). radius = 3, b = 0.15, c=2, Tu =0.75 . . . 41

5.6 Ratio of School Segregation to residential segregation, blue line: School Segregation index / Mixed residential segregation index, purple line: School segregation index / Neighbourhood segregation index. (a) b (b) radius . . . 42 5.7 Proportion of neighbourhood minority and majority agents that travel

> 3x the minimum distance to school (a) fr = fs, (b) fr = 0 fs = 0.7,

r=3, b=0.2, Tu=0.75, mean from 6 simulations . . . 43

49figure.caption.161

A.2 Parameter sweep for (a) the mixed neighbourhood segregation index and (b) mixed neighbourhood segregation index against ethnic pref-erence, f at different values of radius b=0.15, Tu=0.75 . . . 49

A.3 Parameter sweep for (a) the mixed neighbourhood segregation index and (b) neighbourhood segregation index against ethnic preference, f at different values of b b=0.15, radius=3 . . . 50 A.4 Parameter sweep for the school segregation index against ethnic

pref-erence, f at different values of (a) Tu(α = 0.25) and (b) α (Tu = 0.75)

fr =0 . . . 50

A.5 Parameter sweep for the school segregation index against ethnic pref-erence, f at different values of (a) Tu (al pha = 0.25) and (b) α (Tu =

0.75) fr = fs, b=0.15, radius=3 . . . 51

A.6 Parameter sweep for the school segregation index (green line) and the mixed neighbourhood segregation index (red line) at at f = fr = fs,

and school segregation index at ( fr=0) (blue line) for parameters (a)

f (b) α (c) b (d) radius (e) Tu. . . 52

A.9 Ratio of School Segregation to residential segregation (here measured with the Mixed neighbourhood segregation metric. radius= 3, b= 0.15, α=0.25, Tu=0.75 . . . 54

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List of Tables

3.1 Segregation indices and spatial unit . . . 27

3.2 Model parameters and description . . . 27

4.1 Fixed parameters and selected values . . . 30

4.2 Free parameters and range of values for residential choice . . . 31

4.3 Free parameters and range of values for school choice . . . 33

4.4 Free parameter, Tuand value for the nominal parameter set. . . 35

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1

Chapter 1

Introduction

1.1 School segregation in the Netherlands

Education has been identified as the key to long-term economic growth across the developed Western world [7]. Besides educational attainment being one of the main factors associated with social position and life chances, schools are the first social system an individual experiences. School environments expose students to a variety of social norms which can promote cohabitation and social cohesion1. The education system is therefore at the heart of policies for ensuring equal opportunity, decrease in socioeconomic (SE) inequalities and generally fostering social integration.

In the Netherlands, at least primary and secondary school education is widely available to pupils from different socioeconomic backgrounds. Despite this, school segregation, the uneven distribution of pupils of different socioeconomic and ethnic backgrounds is a prominent phenomenon across the country, and especially in the larger Dutch cities with diverse populations. Generally assumed to hamper the po-tential success in social cohesion, school segregation is becoming a growing policy concern in the Netherlands.

1.1.1 Why ethnic segregation is emerging as a policy issue?

Until the 1950s, segregation in the Netherlands was mainly driven by religion. Seg-regation has emerged as a policy issue more recently when ethnic segSeg-regation started to rise. This is a result of the combination of two recent phenomena, the secularisa-tion2_{of Dutch society together with the influx of guest workers and ethnic migration}

from the dutch colonies in the 1960s and 70s [19]. After the economic boom of the 1950s and 1960s, guest workers from Turkey and Morocco and the Dutch colonies of Suriname and Antilles were invited by the Dutch government to fill a shortage in labour jobs. The integration of guest workers into Dutch society was a minor policy concern until the 1980s when another wave of migration occurred through a pro-cess of family reunification and marriage and family immigration from Surinam that peaked in the 1970s after the country became independent. These processes led to a significant shift in socio-economic and ethnic residential demographics and more recently school populations, especially in the larger Dutch cities of Amsterdam, the Hague, Rotterdam and Utrecht.

In light of this emerging as a policy topic, several studies have attempted to as-sess the effects of segregation of ethnic minorities in Dutch in society.

1_{The extent of connectedness and solidarity among groups in society} 2_{The historical process in which religion loses social and cultural significance}

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1.1.2 Effects and policy in segregation

Segregation in schools has been known to jeopardize social integration of different groups of pupils. Certain certain levels of segregation would reduce the opportuni-ties of minoriopportuni-ties to participate in society at the required level [8]. Other issues can be administrative, and only arise when segregation is too high resulting in the so called ‘black’ schools. These schools sometimes come with a disproportional amount of practical problems because of a large number of non-Dutch students and have thus been a concern to the city of Amsterdam [9]. In addition, being undesirable by the general public they are being forced to shut down. Other studies have also shown that mixed schools enhance the respect for cultural differences.

In most cases, the different studies on segregation evolve their research based on the assumption that neighbourhood outcomes are associated with social position and life chances [13]. Some potentially ‘positive’ aspects of segregation are less anal-ysed in literature [8]. These arguments specifically refer to residential segregation and are mainly advantages from the perspective of the ‘minority’. For example, spa-tial concentrations of immigrants can help when starting their life in a new country. More generally ethnic neighbourhoods are regarded as facilitating the conservation of cultures.

Even though segregation in schools is widely recognised as a social issue, seg-regation policies to deal with the segseg-regation in schools have been limited. In the Netherlands freedom of school choice is a constitutional right, and specifically, un-der the article 23, schools based on any faith or pedagogical principle can be founded and receive state funding. This makes direct intervention in parental choice almost impossible. Some attempts to deal with it in the past, include busing which aims to enable students from less privileged areas to access schools outside their neighbour-hoods. Others were more direct, like the policy of admit by analogy, to ensure, that a certain quota for each ethnic group is not exceeded. However, the effectiveness of such measures depended on the cooperation from parents and the school boards and was hard to sustain.

1.2 School Segregation levels

Segregation levels in schools in the Netherlands are being closely monitored in the last decade. To this end different approaches have been adopted. These include measurements like the dissimilarity index, which quantifies segregation in terms of unevenness of different social groups across different schools. Several studies have extended the focus on comparing the ethnic composition of schools with neighbour-hood demographics [18], [19], [3]. These studies have different objectives, at the first level understanding the impact of neighbourhood demographics on the parental choice and therefore ‘disentangling’ the contribution of the different processes in the levels of school segregation. And secondly, understanding the role of geogra-phy in the segregation in schools, for example when the supply of different types of schools is differentially distributed in low and high-privileged neighbourhoods [5]. 1.2.1 School and residential segregation trends

In the study in [3] the school segregation index in primary schools was calculated across 22 municipalities. Ethnic segregation in schools was found to be generally high, with the Hague, Amsterdam and Rotterdam, the cities with high ethnic mix,

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1.3. Research Question 3

FIGURE1.1: School segregation against residential segregation level in 22 municipalities in the Netherlands. The segregation index is the dissimilarity index for the 3 minorities Surinamise, Turkish and

Mo-roccan vs. the Native dutch (taken from [3])

among the highest. The next part of the study focused on the comparison of neigh-bourhood segregation and school segregation trends. In figure1.1, taken from the same study, the relationship between the school segregation level and the segrega-tion level in the surrounding neighbourhood is shown. A strong correlasegrega-tion was found between the school and neighbourhood segregation index. In addition, in the majority of the municipalities the school segregation was found to be higher than the neighbourhood segregation.

A previous study in [18] attempted to assess the number of schools that are sig-nificantly more segregated than the surrounding neighbourhood. Here the authors analysed the segregation levels of the individual schools using two types of data: the percentage of ethnic minority pupils per school and the percentage of ethnic mi-nority children reciting in the postcode district of a school. From the total number of districts across different municipalities they extracted 40 that have both ‘segregated’ schools which are both ‘White’ and ‘non-White’.‘White’ and ‘non-White’ schools are identified as schools were the percentage of the ethnic minority in the school was ±23% higher than in the postcode district of the school. From the 163 schools in the 40 districts, 103 were found to be segregated.

The above trends are persistent over the last decade with school segregation re-maining higher than residential segregation and the problem of segregated schools being a concern for the Ministry of Education in the Netherlands.

1.3 Research Question

The trends observed when comparing the school and residential segregation, pose a question which is highly discussed in the sociological literature on the topic of

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school segregation:

Why is the difference between residential and school segregation levels observed and what causes it?

Some proposed explanations are attributed to the individual factors that affect the residential and school segregation in different ways. Residential and school seg-regation are correlated but the dynamics of housing and school choice, also have their own specific mechanisms. Residential segregation could arise from ethnic spe-cific choices but also indirectly from socioeconomic factors in the housing market. School choice on the other hand is affected by neighbourhood demographics, but also the school landscape, the supply of schools and parental choice [5].

The larger school and residential segregation, however, is not limited to the Dutch context. In a review paper [27], more geographical contexts where there is freedom in school choice, were found to have a higher school segregation compared to the residential segregation in the surrounding neighbourhood. However, they find that the mechanisms behind this are highly contextual. They are specific to the choice system and among others, the existing socioeconomic geographies of the neighbourhoods involved.

The broader objectives of this report is to identify and test generic mechanisms that can lead to this observation using computational modelling.

1.3.1 Computational models to understand the dynamics

As mentioned above, three key factors are found to critically influence school segre-gation: neighbourhood demographics, parental school choice and the school land-scape. The parental choice for schools is a complex decision made with a set of at-tributes that include the quality of the school, the atmosphere and the socioeconomic and ethnic composition [3]. While these factors determine parental choice, they are also determined by parental choice. The composition of the schools is determined by the neighbourhood demographics and parental school choice. As the author in [3] concludes, there is a continuous feedback loop in which “Choice leads to patterns and patterns influence choice”. Cause and effect between parental choice and outcome is complex and interconnected. Methods and tools from the field of complexity science and computational modelling will be used to understand the dynamics.

The use of complexity science and computation in segregation was first demon-strated by Thomas Schelling, [26] using an agent based model. The model came to be one of the most widely known and used models in segregation literature to ex-plain segregation dynamics. In the simplest version of the model there are two types of agents. They have a specific threshold, F, for the number of neighbours of their own group, and make moves to find sites to satisfy this threshold. Collecting seg-regation measures at the end of the agents’ moves, it was found that the proportion ‘like’ neighbours the agents ended up, with was significantly higher to their indi-vidual preference F. With this result the phenomenon of segregation as an emergent property of the social system was established: “there is no simple correspondence of individual incentive to collective results”.

1.3.2 Gap in agent-based models for school choice

Schelling’s results have promoted the use of agent based models to demonstrate residential segregation of ethnic groups in real cities and promote understanding of

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1.4. Hypothesis 5 individual behaviour. School choice has been mainly examined with discrete choice models in literature, but agent based models to understand choice are limited. It is this gap that this report aims to fill.

By placing agents and schools on an artificial grid the individual’s behaviour for residential and school choice will be explicitly modelled. In this way the impact of residential segregation patterns, the relative supply of schools and the individual’s school choice on school segregation will be studied to discern individual behaviour from systemic effects.

1.4 Hypothesis

The study in [4] found that ethnic diversity is a concern for middle-class parents in ethnically mixed, gentrified areas3. It is argued that while gentrifiers celebrate multiculturalism in their neighbourhood, when they become parents the diversity of the neighbourhood might be perceived as a threat. Middle class parents often travel outside the neighbourhood for a school because they are not happy with the ethnic composition of the local schools. However, a big group from the parents interviewed has shown tolerance or even a preference for their children to attend schools with a ‘fair representation of the society’, but argue that they could not find this type of mixed school. The schools in these areas are regarded as quite ‘segregated’ by Dutch middle class parents. [4].

Clearly there is a mismatch between the global neighbourhood demographics and school, and between the desires of parents’ and what is observed in the macro scale in schools. In this report an alternative explanation for the mismatch observed will be offered and tested. Assuming, that there are ethnic preferences for one’s own group, both for the school and the residential choice, the additional sorting happening in schools, after the existing neighbourhood sorting will lead to higher segregation in the school. The hypothesis that will be tested is the following:

Systemic effects from the combination of neighbourhood segregation and school choice amplify school segregation

If systemic effects exist then an increase between school and residential segrega-tion would exist even when individual ethnic preferences for schools is the same as for residential choice.

1.5 How to approach the research question using ABM

Task 1: Develop an agent based model to simulate the dynamics of school and residential choice

Task 2: Establish a method to compare school and residential segregation

Task 3: Execute experimental plan to test whether systemic effects drive school segregation higher than residential

To answer the research question an agent based model will be implemented to simulate the school and residential choice. Without taking into account other po-tentially segregating factors eg. economic prices in housing, and keeping the ethnic preferences for schools and neighbourhoods the school and neighbourhood choice

3_{Gentrification: The process by which wealthy or affluent individuals in the middle class displace}

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will be executed. Firstly the residential choice patterns will be established and after that the school choice patterns. The measure of the residential and school segrega-tion index and a comparison of the two indices will be made at the end of the run. By keeping the ethnic preference in school and residential choice the same, we can es-tablish whether the higher school segregation can be observed even when the agents do not explicitly seek it.

1.6 Report overview

This report will be structured as follows. In Chapter 2, firstly a literature overview of the mechanisms involved in residential and school segregation will be presented. Secondly, an overview of current methods of agent based models used in residential choice will be given which will aid in implementing the model of this report. In Chapter 3 the agent based model of school and residential choice will be described. The agents and processes involved, the different parameters, and the measures of segregation that will be used will be defined. In Chapter 4, a calibration and sen-sitivity analysis of the residential and school model will be made to set the values of the nominal parameter set that will be used in the main experiments. The main experiments to examine the hypothesis proposed will be presented in Chapter 5.

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7

Chapter 2

Literature study

Explanations for existing patterns of segregation typically focus on three poten-tial mechanisms. Firstly, from practices of organisations and institutional barriers. Secondly, driven by individual choice: the preference for living among one’s own group. And thirdly, the corollary of other modes of segregation, for example racial differences in economic resources [6].

In the context of segregation in primary schools in the Netherlands, where school choice is free, any institutional barriers are weak. Segregation literature focuses on segregation processes arising from parental choice. Parental choice in itself is found to be interconnected with spatial patterns: the residential segregation at the school neighbourhood level and the local supply of schools [3].

In this literature study, firstly the factors that drive parental choice for a primary school will be studied. A discussion of potential segregation processes arising from these choices is made.

In the second part of the study an overview of models for residential choice and school choice and the patterns of segregation observed are presented. The goal of this section is to provide the background on current models and methods that will be the basis of the residential and school choice model of this study. It aims to in-troduce notations and concepts used in agent based and segregation models: the individual agent’s utility function, global measures of segregation, tipping points and transitions to segregation.

2.1 Parental Choice and Segregation

2.1.1 Parental School Choice

The findings of two studies, [18] and [4] examine the motivations behind the parental choice, in order to track down potential segregation processes. In [18] the authors carried out a survey on 931 parents from neighbourhoods with ‘White’ and ‘non-White’ schools and investigate the factors parents consider when they accept or re-ject a school. The study in [4] focuses on the white middle-class parents in Amster-dam, and analyses the socio-spatial strategies adopted by 24 parents. Both studies find parental choice for schools to be ‘socially and ethnically motivated’.

Firstly, we note that sub-groups of parents that span different socioeconomic di-mensions are revealed when analysing parental choice: White, ethnic minority, non-Western (eg. Turkish, Moroccan), high and low educated, high and low class or economic status. It is observed that the groups can adopt different factors in their choices and the weighting of the factors can also differ.

Ethnic specific choices seem to emerge from for all groups but at different de-grees. The authors referred to the preference for schools from their own background as a ‘match between home and school’. Dutch parents expressed their preference for

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this by going for schools with ‘people like us’. The socioeconomic composition of the school is also a concern. In the study in [4], one of the parent expressed their worry about schools with a lot of lower class parents. Another, factor shown to matter to ethnic minority parents is the attention given to difficulties in learning dutch. The authors in [18] also asked the parents for reasons to not choose a school and a few types of schools seem to be avoided by both native-Dutch and ethnic minority par-ents. ‘Non-White’ schools seem to be regarded as unsuitable by both. Other reasons were poor academic standards in the school and the school having a bad reputation. ’School quality’ and ‘School atmosphere’ were mentioned by different groups, but the way these are perceived is variable between parents of different groups. School quality is often associated with the class and ethnic or racial composition of the school population. Other parents, measure school quality in terms of ‘the school climate, order and discipline’ or the success of the pupils after they leave the school. The average test scores (CITO) are also used as a proxy for the academic standard of the school which mostly reflect the achievement of the school population rather than the school itself. Researchers agree that school atmosphere includes a num-ber of things that are hardly quantifiable, for instance, the state of school buildings and facilities, the environment and staff. Lastly, some parents have preferences for religious schools, which can also produce differentiation between different ethnic groups. Inclination, for specific school denominations like Montessori is also mainly observed in particular subgroups like highly educated parents.

Apart from school composition preferences, the distance to school is consistently found to be among the most important factors for all parents. It is especially im-portant among lower educated parents, but decreases as the level of education of the parents increase. Especially for the middle class parents, distance becomes a secondary factor when they cannot find a ‘suitable’ school in the vicinity.

Choice dynamics and segregation

The literature study revealed a number of factors playing a role in parental choice in-cluding school ethnic composition, school quality, the distance to school, and school atmosphere that also vary in weight according to parents educational attainment, ethnicity or socioeconomic class. A diagram of the different factors is shown in Fig-ure2.1. The processes of ethnic segregation from parental choice, could be broken down into three themes:

• Segregation of ethnic groups because of preferences to be with their own • Segregation because of heterogeneity in choice among the different groups • Segregation of one ethnic group because of correlations with another

dimen-sion eg. socioeconomic class

The themes of ‘match between home and school’ seem to be directly connected to ethnic segregation processes. Heterogeneity, in choice is another factor that can produce segregation. Specifically, ethnic minority parents seem to favour schools with attention given to difficulties in learning dutch. Such heterogeneity in prefer-ence could indirectly lead to minorities favouring certain types of schools that native Dutch don’t go for. The way school quality is perceived is also highly dependent on social and ethnic composition of the schools. Differences in perceived quality by dif-ferent groups could lead them to make difdif-ferent choices. Lastly, ethnic segregation of minorities can emerge from correlations of the ethnic dimension with socioeco-nomic class. If race and income are highly correlated (for example if minorities are

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2.1. Parental Choice and Segregation 9

FIGURE2.1: Factors in parental school choice summarised in the lit-erature

poorer on average than Dutch nationals), ethnic segregation will be higher than if race and income were uncorrelated [6].

2.1.2 Parental residential choice and the creation of ethnically mixed ar-eas

This section studies the choice mechanisms behind the growth of ethnically mixed areas in the Netherlands and the patterns of residential segregation. The main find-ing, is that while ethnically mixed areas are generally attractive, they consist of sub-clusters of ethnically homogeneous groups.

Residential choice is driven and affected by a combination of economic factors, housing prices and regulations in the housing market in the Netherlands. Like in school segregation, residential segregation mechanisms by institutional barriers are less applicable. The main mechanisms are explained by either individual choice to live with one’s own group or the corollary of other modes of segregation, like segregation by class.

From the 1990s immigrants continuously moved to urban renewal areas that were less favoured by the Dutch. There, they found suitable dwellings for large families which were restored in the urban renewal process [2]. At the same time, separation is reinforced by a preference of people for living with their own ethnic group. This process described as ethnic drift, influences both ethnic minority resi-dential choices and Dutch nationals and can lead to the resiresi-dential clustering pat-terns observed in ethnically mixed or gentrified areas within the Dutch cities.

The mechanisms of creation, growth and spatial patterns in ethnically mixed areas are driven partly by urban renewal plans and ethnic specific choices. By mod-elling and measuring moving flows between neighbourhoods for different ethnic

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groups, the research in [1] shows that the the largest moving flows are to ethnically diverse neighbourhoods. But within these neighbourhoods there is positive correla-tion to moving there, if their own ethnic group is also present. Another sociological study [14] looked into the perception of the neighbourhood in socially mixed areas with a focus on class and ethnicity. The results indicate fragmentation within the eth-nically diverse neighbourhood and highlight that the perception of neighbourhood for different people is variable. Geuzenveld is a typical case of a poor neighbour-hood where urban renewal was used to alter the social mix. Originally, the area was built to house labourers working in nearby port facilities. In the 1990s urban regeneration sought to diversify and improve the social mix new housing was con-structed. This divided the neighbourhood into 4 sub-regions which are socially and ethnically different: A: new mixed housing, B: new high rise housing with mainly middle-class native dutch residents. C: original construction multi housing, mostly poor and migrant families. D: original construction: single-family housing, with ageing working class residents.

When the residents in each area were asked to draw what they perceived to be ‘their neighbourhood’ on the map, considerable differences in perceptions of neigh-bourhood boundaries were observed. The maps in Figure ?? visualise the fault lines created by the residents’ perceptions. Specifically, most dutch middle-class resi-dents, only consider the new areas as part of their neighbourhood, and they tend to view the overall area’s social composition negatively. Also residents from C, the poorer migrant families, generally draw smaller perceived neighbourhoods com-pared to the new areas.

These results show evidence for the growth of ethnically diverse areas but at the same time highlight their uniqueness in terms of spatial patterning. Albeit globally diverse, the fragmentation of the residents creates social fault lines withing these areas. High fragmentation and disconnect could also lead to aversion of the resi-dents in the different sub-areas to the use of the shared neighbourhood amenities like schools.

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2.2. Models for residential and school choice 11 2.1.3 Summary of residential and school choices

The studies summarising residential and school choices in ethnically diverse areas, show that preferences for their own ethnic group is a major driver. In addition dif-ferences in the perception of the neighbourhood for different groups can lead to sub-clustering within larger areas and affect the behaviour of agents for school choice.

While recognising the complexities of the emergence of ethnic segregation be-cause of interrelations between the different factors of choice and dimensions of segregation, two main factors are isolated for the objectives of this thesis. The be-haviour of ethnic groups to be with their own ethnic group within neighbourhoods and schools.

In addition, by including the effect of minimising the distance to school, the aim is to explore the extent to which residential segregation contributes to the overall segregation levels and affects the school choice in ethnically diverse areas.

In the next section of the literature, different methods that incorporate such pref-erences in the agents’ residential and school choice will be studied.

2.2 Models for residential and school choice

The mismatch between the individual and the collective

Schelling’s model was the first agent based model used to describe segregation pro-cesses driven by agent’s behaviour. In the specific study an inductive approach is adopted to explore the dynamics of segregative behaviour.

In the general dynamics of the model there are two groups of agents, black and white and specify their ethnic preferences with a preferred ‘ratio’ for like neighbours. The analysis of the outcomes of the agent’s behaviour is first done using simple inductive rules. For example, if the two groups have equal proportion, if any of them insists on being a local majority the only mixture that will satisfy them is complete segregation. If whites want 3/4 and blacks 1/3 it will also not work. Only if they have a sum of less than 1 it can work, but even so integration is found to not be easily guaranteed.

This type of analysis revealed that the individual behaviour is nonlinear with respect to the collective outcome. It promoted the use of agent based models, which allow the definition and experimentation with agent’s behavioural rules, and their relation to collective outcomes.

2.2.1 ABMs for residential segregation

The agent based models used so far for residential segregation models mainly ex-pand on the simplified version of Schelling’s model by adding more residential choice factors, more realistic behaviour for the agents or adopt analysis methods from game theory and evolutionary game theory to explore the robustness of the results from simulation.

Evolutionary Game Theory and the utility function

After Schelling’s findings in the study in [29], Zhang formalised Schelling’s model using evolutionary game theory. The segregation state, S is shown to be the stochas-tically stable state (SSS), and it is argued that it is the only long-run outcome if the agents’ preferences are biased towards their own group. It was also shown that it is the SSS even when agents have integrationist preferences.

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FIGURE2.4: Agent’s Payoff Profile [29]

This was done using a utility function that maps the proportion of like neigh-bours in the neighbourhood to the utility and is asymmetric. The utility function, shown in Figure2.4grows linearly as the number of like agents increases until the optimal fraction n, and then linearly decreases when the number of like neighbours is 2n. Agents of two types, black and white, are reciting on an N×N lattice graph. Each agent has a local neighbourhood of size 2n. Agents move to increase their utility by switching positions. This value represents a penalty on utility if the neigh-bourhood is 100% homogeneous of one’s own type.

The analysis of segregation results is then embedded in a game-theoretic frame-work to solve the model analytically and predict the global pattern from the spec-ified utility function. To do this, the potential function of the game is defined: the degree of exposure between the members of the two ethnic groups. Using the poten-tial function and a special case of the theorem in [28]: In general, in any potenpoten-tial game with the log-linear revision rule, the set of all the states that maximise the potential func-tion is stochastically stable. Since the set of segregated states, S maximise the potential function, then segregated states will be observed in the long-term.

In summary, this paper and other related studies [Young1993], [21] showed that even if all individual agents have a preference for integration over homogeneity with their own group, myopic best-response dynamics will lead to segregation. Even though powerful for demonstrating the robustness of results predicted with compu-tation and simulation, evolutionary game theory constrains the configuration and behaviour of the agents for mathematically tractability. In [29] the agents are lim-ited to switching places when two of them agree for the move, instead of being autonomous.

Neighbourhood definition in residential choice

In Schelling’s study two types of segregation models were introduced a spatial and a compartmented model. In the most common version of the spatial model, which has been used as a basis for residental segregation models, agents are placed and have a local vision for their neighbourhood. In the aspatial ‘compartmented’ model agents either are in or out of a compartments and do not have a specific location in it.

Continuous neighbourhood model

In the spatial model, agents distribute themselves in an area in accordance with preferences about the composition of their local surrounding neighbourhoods. The agents move with the following rule: if an individual is discontent with his own neighbourhood moves to the nearest cell where the surrounding neighbourhood meets his preference ratio. An individual’s neighbourhood is defined as the Moore neighbourhood, the 8 immediate cells surrounding them.

The need for a segregation measure is immediately identified - concentration, clustering or sorting, to analyse the patterns observed. A simplistic measure is used: the average proportion of neighbours of like or opposite colour.

In the computation of the model, the individuals move until they reach satisfac-tion, for example 1/2 of their neighbours as their own. Schelling notices that, even though agents move to obtain 1/2 of their neighbours, when all agents have finished their movements they have on average 5/6 of their neighbours as their own. There is exaggerated segregation resulting from individual dynamics.

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2.2. Models for residential and school choice 13 In further experiments, the intensity of demand for like neighbours was varied and finds that segregated patterns already emerge when individuals need a 1/3 of their own in their neighbourhood, and that the segregation measure is non linear with respect to the individual demands. This finding is explained as follows: ‘An increase in the demand for like neighbours does three things. First it increases the number that will be initially discontent. Secondly it increases the like-color den-sity that results from each movement. And third, the greater the demands the more movement is induced by by those that move in the neighbourhood of those who were originally content. These three effects compound together to make segregation a rapidly rising function’.

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FIGURE2.5: Agent’s neighbourhood definition in the Schelling mod-els (a) Spatial model (b) Aspatial bounded neighbourhood model

Bounded neighbourhood model

The bounded neighbourhood model is an aspatial model, which is compartmented. The agents are either in or out of a common neighbourhood. They now evaluate the colour ratio within the whole neighbourhood instead of their immediate sur-rounding. This model works like when people are assigned to organization units, for example choosing a church or a school. Their is no spatial connection between the units or between the agents within them. Firstly, it is shown that if everyone has more than 0.5 ratio of their own then the compartment will be filled only with whoever came in first but only one type of equilibrium is stable: either everyone in the compartment is white or everyone is black.

The behaviour of the agents is such that an individual will be happy to enter or stay in the compartment as long as the ratio of opposite color their color does not exceed some limit. This ratio is refered to as tolerance. The tolerance schedule, is represented using the cumulative frequency distribution to allow different indi-viduals in a group to have different tolerances. In this schedule (Figure2.6)o ut of 100 whites, the 75 are happy with a maximum of 0.5 ratio of black to white in their neighbourhood, 50 whites are happy with a maximum of 1:1 ratio of black to white and 25 are happy with 1.5 ratio.

For this tolerance schedule there are only two equilibria: the fully black or fully white for each of the neighbourhood blocks. Making the tolerance schedule steeper allows more whites to be tolerant to a higher number of black to whites. This adds the mixed equlibrium to the system but whether this equilibrium will be approached depends on the initial conditions and rates of movement in the neighbourhood.

Summary of the Schelling segregation modelsThe dynamics of two types of models have been described and analysed, a spatial and a compartmented model. The dynamics of the two models are clearly different, in the compartmented model,

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25 50 75 100 2

1

Number of whites upper limit for

ratio of black to

whites

FIGURE2.6: Tolerance schedule in Schelling bounded neighbourhood model

the agents’ order of entering matters and the equilibrium depends on the shape of the tolerance schedule. The spatial model dynamics resemble those of residential choice. An agent’s neighbourhood has overlap with another agent’s neighbour-hood next to them. The bounded model would more closely resemble dynamics in a school where the agents evaluate the school as a whole and there are no corre-lations between schools. The two models can serve as a basis for the residential and school choice model in this report.

Complex segregation patterns observed in real cities

Schelling’s and Zhang’s models have given important intuitions on the segregation dynamics observed. However, their abstraction makes them sometimes unsuitable to explain real life dynamics and generally need to be adapted to become applica-ble. The authors in [17], identified that the spatial segregation patterns described by Schelling’s model are lacking the qualitative components of residential patterns in real cities. They observe that in Tel-Aviv there are areas of different levels of group homogeneity, like areas inhabited fully by one group and others areas seemingly mixed with both groups at different ratios. The approach taken is common in mod-elling complex systems: what is the microscropic or agentic behaviour that could lead to the complex patterns observed in real cities? They showed that inhomo-geneous residential patterns can be obtained with small asymmetries in the utility function of the agents of the different groups.

The authors propose a new segregation metric the C−index, which is calculated using an algorithm to identify different kinds of mixed patterns of segregation, ie. landscapes where three types of areas coexist: areas homogeneously red, areas ho-mogeneously blue and areas mixed with red and blue agents. By varying three free parameters: β: Fraction of blue agents, FB: tolerance threshold of Blue agents and

FG: fraction of Green agents, they show that mixed segregation patterns can only

exist for a certain intersection in the parameter space of these parameters.

Another study in [20] showed that showed that the size of radius of residen-tial choice matters in the transition to segregation and in the residenresiden-tial patterns established. A larger radius in agent’s choice can cause delay in the transition to segregation, with respect to the ethnic preference parameter. Also a small radius for the agents’ vision exacerbates the disconnect between the agent-intent and model outcome.

Both the quality of residential patterning, the size of clustering with respect to school neighbourhoods can make a difference in the dynamics observed in the school choice, therefore these ingredients will have to be specified in the model to obtain realistic residential patterns.

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2.2. Models for residential and school choice 15

ABMs for residential choice - Conclusion

The summary of residential choice models revealed a number of themes im-portant in residential dynamics. Firstly, the mismatch between the individual and collective preferences is highlighted by Schelling’s agent based model. Observed segregation in neighbourhoods and schools can be highly nonlinear to the agent’s behaviour. In addition observed outcomes can depend qualitatively (eg. spatial pat-terning) and quantitatively (segregation index) by model choices like the definition of agent’s neighbourhood: bounded or continuous and the radius of choice. These choices can affect the results observed and therefore they need to be made with sup-ported literature. Sensitivity analysis will aim to explore the robustness of results due to choices made for the model in this report.

2.2.2 Models in school choice

In choosing appropriate models for school segregation the main dynamics in school segregation need to be identified. As described in the literature the segregation in schools is affected by choices of parents, housing patterns and the geographi-cal supply of schools. In the model parents can be seen as agents making a choice among available options in their areas based on their individual preferences. The most widely used models are data-driven discrete choice models. In discrete choice models (DCM) individuals make a choice from a selection of discrete alternatives yj which are dependent on a set of decision factors xj. DCM statistically relate the

choice made to the attributes of a person and the attributes of the alternatives avail-able to the person.

Data-driven models

In [22] a discrete choice modelling approach is taken. The purpose of the paper is to analyze the determinants in secondary school choice in Amsterdam and uses conditional and mixed logit models to predict school choice of parents.

The motivation behind the study has a slightly different focus from segregation trends. The authors try to establish the importance of school quality in school choice. Nevertheless, the model does provide a formulation on how a discrete choice model can be used to scrutinize factors in parental school choice. The formulation of the discrete choice model is as follows. A student is assumed to choose a school that maximizes their utility. The utility for a student i choosing school, s in year t:

Uits=Vits+eits (2.1)

where Vitsand eitsis the observed and unobserved portion of utility respectively. eits

is assumed to be iid extreme value in which independence means the unobserved utility for one alternative is unrelated to the unobserved utility of another. After a qualitative analysis and discussion on potential indicators for school choice, they include 3 types of factors: student-school combination factors xits, school specific

factors wts, and student specific factors zit. For the student-school combination

fac-tors the distance to school was included. For the school specific facfac-tors the school quality score as published in the Trouw magazine was used. For the student specific factors among others was the ethnicity of the students. Probability, pitsthat student

i in year t chooses school s:

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By estimating the coefficients of the different factors the authors are able to anal-yse the relative importance of factors in school choice. Firstly, the authors find that the distance to school is the strongest predictor of school choice. Secondly, they find that students prefer schools where graduating students have higher exam grades, a ‘measure’ of school quality, and lastly where their primary schools peers go. The model demonstrates the application of discrete choice models for school choice. However, the model does not take explicitly the spatial dimension into account or residential segregation into account. In the absence of data, agent based models are more suitable to test the relation of residential segregation patterns and agent’s choice.

Agent based models in school segregation

A reasonable path for the research of school segregation modelling would be to ex-plore whether techniques and conclusions from agent based residential choice mod-els can be applied to school choice. This approach has been adopted by [25] where the authors apply an agent based model for school choice to study school segrega-tion and compare the results to known residential segregasegrega-tion dynamics.

Addition of distance in school choice to ABM segregation models

The Schelling model of residential segregation is adapted by combining two pref-erence arguments in modelling parents’ school choice, prefpref-erences for the ethnic composition of a school and preferences for minimising the travelling distance to the school. To do this the Cobb-Douglas utility function is used for school choice:

U=Pα_D(1−α) _(2.3)

where P is the ethnic preference, and D is the nearness to school. The ethnic prefer-ence, P(x)is a function that maps the proportion of like neighbours, x, to utility and is adopted from [29]. The utility for ethnic preference is maximum when the number of like neighbours is equal to the optimal ethnic preference parameter, f .

At every step of the simulation agents are randomly chosen and make a decision to change their location. In the decision function the current residential location, or school is compared against a satisfaction threshold, Tu. If dissatisfied, an agent

considers moving to another location or change school.The agent then evaluates all schools or residential sites in a random order and moves to the first where the re-quirements are satisfied.

Main findings and conclusion: The hypothesis is that when parents prefer nearby schools this may curb tendencies towards self-organised school segregation. This is, if the initial distribution of households across geographical space when mak-ing a school choice is ethnically integrated. To explore this result, the level of param-eter α is changed in steps of 0.2. For the paramparam-eter space explored ( f =0.7, Tu=0.4),

integrated regimes can be sustained for α between 0-0.8, but in high α > 0.8 segre-gation can emerge in the same way as in residential models.

The sensitivity of the above result to the ethnic preference parameter f is ex-plored, by varying fa and fb, the ethnic preference of the minority and majority

group independently. Figure2.7 shows this for α = 1 and α = 0.5. For α = 0.5 the preference for nearby schools suppresses the effect of f . For all combinations of fa, fb segregation remains very low. In addition to this result a comparison of the

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2.2. Models for residential and school choice 17 [width=]figures/flacheresults1.jpg

FIGURE 2.7: Figure taken from [25]. The sensitivity of the school-neighbourhood index, variable school-neighbourhood index and school seg-regation index to ethnic preference, f is shown (Threshold of

satisfac-tion, Tu =0.40)

index and the variable neighbourhood index is made. A comparison with the vari-able neighbourhood index shows that it responds more smoothly to f . The school neighbourhood index is mostly unresponsive to f . This is because segregation in the micro-scale of radius=1.5 is enough to satisfy the agents locally that larger clusters that would affect the school neighbourhood index are less likely to be formed.

In summary the authors conclude that parents’ preferences for nearby schools may be an important factor in tempering for school choice the segregation dynamics known from models of residential segregation. A suggestion for further research is to explore the extent to which school segregation observed are mainly due to resi-dential segregation rather than the Schelling dynamics.

The contribution of this first comparison of school and residential segregation in-dices underlines that they respond differently to the ethnic preference f . This makes a direct comparison of the two less straightforward and highlights that specific val-ues of f will make a difference in the valval-ues we obtain between the two.

2.2.3 Residential segregation patterns and school choice

Agent based models provide a way to test the theory and a way to combine school and residential choice. The models shown in this section vary from differential equa-tions, discrete choice models and ABMs.

The impact of residential segregation patterns on school choice and consequences on school segregation has not been studied with computational models. Agent based models can model the spatial distribution of housing explicitly and provide a direct interpretation of the spatial connection to school segregation. They can be used to explore mechanisms of the impact of residential patterns on agent’s choices. A combination of an agent-based model where the agents behaviour is governed by a discrete choice function will give the ability to directly model the school choice factors of distance and ethnic preferences, and understand their impact in combina-tion to the spatial patterns, in segregacombina-tion in schools.

The model in [25] will be extended to perform computational experiments of the school choice when there are residential segregation patterns. In this way the effect of residential patterns on school choice can be explored under different scenarios.

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19

Chapter 3

The residential and school choice

agent based model

In this section the agent based model for residential and school choice are described following the ‘ODD’ (Overview, Design concepts, and Details) protocol [16] for agent based models. Firstly, the spatial setup of the household and school agents on the artificial grid will be described. Following that, the residential and school choice utility for the agents will be defined, and their behaviour towards maximizing their utility. Finally, an overview of the simulation process of the residential and school choice will be given before presenting the results.

3.1 Model purpose

The aim of the agent based model is to test whether having the same ethnic prefer-ence for the residential and school choice, can produce higher levels of school seg-regation compared to residential segseg-regation. The hypothesis is that compounding effects from existing neighbourhood segregation patterns can produce higher segre-gation in schools compared to residential segresegre-gation levels.

In order to do this, the sensitivity of the residential and school segregation index to the ethnic preference parameter f will be measured and compared. For this rea-son, other potentially segregating factors, for example, economic prices in housing for the residential model, or factors like school quality for the school choice model will not be included. The objective is to compare the baseline segregation level for the two models when only ethnic preferences are considered, and are equal: ethnic preference for the school choice, fsis equal to the ethnic preference for residential

choice fr.

The main processes of the model are summarised in Figure3.1.

3.2 City and agents

The artificial city is a two-dimensional N×N square lattice. There are two types of household agents, red and blue, and the population ratio is 50:50. The param-eter density, d, controls the density of the agents on the grid. There are 16 neigh-bourhoods on the lattice and 16 schools each in the centre of the neighneigh-bourhoods as shown in Figure3.2. In this way a one to one mapping of neighbourhoods to schools is established.

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FIGURE3.1: The main processes modelled are parental school choice and parental residential choice. The residential choice is made con-sidering the ethnic composition of the agents’ neighbourhood. The school choice is driven by two factors, the ethnic composition of the

agents’ neighbourhood, and minimising the distance to school

FIGURE3.2: Artificial grid, size: 100×100. There are two types of agents, blue and red. The yellow marks indicate the school positions,

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3.3. Agent’s objectives 21

3.3 Agent’s objectives

The agents make two types of choices: residential and school. For the school choice they rank schools based on distance and ethnic composition, and for residential choice they rank residential sites based on the neighbourhood ethnic composition. They move to increase their utility for those choices. The definition of the agent’s utility and method of choosing sites is described below.

3.4 Agent’s attributes and behaviour

3.4.1 Agent’s attribute, fi

All agents have an optimal ratio for like neighbours fiwhich is static throughout the

simulation. fi is determined by drawing from a truncated normal distribution with

mode f , and standard deviation σ, and upper and lower bounds of [0,1]. The agents have the same fr = fs = f , unless stated otherwise.

3.4.2 Ethnic preference, P

Each agent computes their level of satisfaction at a current school or residential site using a utility function. For the residential satisfaction this depends only on the composition of the neighbourhood of the agent, specifically the proportion of like agents, x.

The utility function, for ethnic preference is taken from [29]. The function is asymmetric, it is maximum when the number of neighbours is equal to the optimal ratio, x = fi and there is a penalty for homogeneity with one’s own group

deter-mined by the parameter M. P(x, fi, M) = ( _x fip x≤ fip M+(p−x)(1−M) p(1−fi) (3.1)

3.4.3 Residential Choice Utility

The residential choice is made to maximise the utility for ethnic preferences in the agent’s neighbourhood:

Ur =P(x, fi, M) (3.2)

Neighbourhood perception in residential choice

The next model choice to be made is to define the neighbourhood the agents con-sider when selecting a residential site. Residential segregation models typically use the a Moore or Von-Neumann neighbourhood. This is in line with the definition of the neighbourhood in the spatial model described in [26] (see section2.2.1). Another option for the definition of agent’s neighbourhood is the bounded neighbourhood model also defined in [26]. However, in this model the ’bounded neighbourhoods’ behave like independent organizational units, since the agents evaluate the compo-sition of each bounded neighbourhood separately.

In Dutch cities the demographic patterns consist of ethnically heterogeneous neighbourhoods that have within them smaller clusters of more concentrated ho-mogeneous groups (from socioeconomic and ethnic backgrounds). In addition, the

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FIGURE3.3: Agent’s local neighbourhood definition: a combination of Moore and the fixed school neighbourhood

boundaries of neighbourhoods are sometimes not well defined resulting in neigh-bourhoods having a continuous boundary.

As discussed in the study in [14] agents have variable perceptions for their neigh-bourhood. Within a larger neighbourhood, agents sometimes associate themselves with a smaller portion of the larger spatial unit. In order to incorporate this in the model, the combination of two types of neighbourhoods will be evaluated by the agents: the fixed, bounded, neighbourhood and the variable (Moore) neighbour-hood around their location on the grid.

This leads to the agents evaluating the ethnic composition of the sum of the two neighbourhoods for each potential residential site before making a selection. A pa-rameter, b is used to weigh the composition of the fixed neighbourhood, xboundedand

1−b to weight Moore neighbourhood xMoore.

x= b×xbounded+ (1−b) ×xMoore (3.3)

This neighbourhood definition allows for the fact that agents choose a neigh-bourhood to live in because of certain global characteristics in it (for this model this is just the global ethnic composition) and a specific location within the neighbour-hood based on their immediate neighbours.

3.4.4 School choice utility

The school choice utility, Us, is defined in [25] to combine the utility for ethnic

com-position and the distance from residential location to.

U=Pα_D(1−α) _(3.4)

where 0 < α < 1 is the parameter which controls how much weight is put on the

distance minimisation, D relative to the ethnic preference, P. A value of α=0 means only distance considered and α=1 means only ethnic preference is considered.

Di,j, represents the nearness to school. It is a function of disti,j, the Euclidean

distance between an agent, i and a school j, and is normalised with respect to distmax,

the maximum distance between two points on the grid. Di,j =

(_dist

max−disti,j

distmax if disti,j ≤distmax

0, otherwise (3.5)

distmax =

√

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3.5. Process overview 23 3.4.5 Behavioural rule

The core dynamic of the model is that agents move at every iteration towards max-imizing their individual utility until they reach a satisfaction threshold Tu. The rule

is the same for residential and school choice and it is summarized in1. In the first it-eration an initial configuration is randomly chosen. In each successive itit-eration, the agents are chosen sequentially in a random order and their satisfaction is evaluated against a satisfaction threshold, Tu. If not satisfied, the agent can make a move using

a behavioural logit rule.

All candidate empty residential sites or schools are evaluated and assigned a probability using Equation3.6 [15]. This means their assigned probability is pro-portional to the improvement the agent will obtain in the new site compared to the current state. In reality, agents move greedily to improve their state, but with some noise because of insufficient information or a mistake, so moving with the behavioural logit rule allows these mistakes to happen. The behavioural logit rule which ensures that the model is independent from initial conditions since every state is accessible by every state for finite t>0.

Pr{move}(i) = 1

1+e−∆uj/t (3.6)

The agent chosen moves to the school or residential site, j with a probability Pr{move}that depends on the utility gain ∆uj. The scalar t also referred to as the

temperature is used to determine the relative importance of the random part to the deterministic part of the utility function.

Algorithm 1Behavioural rule

Initialization: Agents choose a new site at random

for each model step, s do for each agent, a do

if satis f action(a) <T then

utilities, u_j= calculate utilities;

new site = choose new site from Pr(uj)

end end end

3.5 Process overview

In order to answer the research question the residential choice model is simulated first. In the simulation all agents are created and are assigned an ethnic preference, fi. The agents are moved at every step in a random order using the behavioural rule

described above. Once the residential choice is ran then the school choices are made. The school and residential segregation values are collected at the end of the run. The parameters values remain fixed during each run of the model. The core idea is that the agents have the same preference for like neighbours, fi, for their residential

choice and school choice. This will allow the comparison of the sensitivity of the school and segregation index to ethnic preference.

Housing patterns and school choice in school segregation

M

T

Housing patterns and school choice in

school segregation

Declaration of Authorship

Abstract

Acknowledgements

Contents

List of Figures

List of Tables

Chapter 1

Introduction

1.1

School segregation in the Netherlands

1.2

School Segregation levels

1.3

Research Question

1.4

Hypothesis

1.5

How to approach the research question using ABM

1.6

Report overview

Chapter 2

Literature study

2.1

Parental Choice and Segregation

2.2

Models for residential and school choice

Chapter 3

The residential and school choice

agent based model

3.1

Model purpose

3.2

City and agents

3.3

Agent’s objectives

3.4

Agent’s attributes and behaviour

3.5

Process overview