Segregation by choice? School choice and segregation in England

ABSTRACT

School choice can segregate schools by academic ability, income or ethnicity, but is this because of households’ choices, or constraints in access to good schools? We examine whether segregation is by choice, finding that households’ school choices are segregating in most areas. Through counterfactual simulation, we find that implementing a policy of ‘neighbourhood’ schools would, in contrast, reduce segregation in most areas, under the assumption that each household’s location is fixed. Policymakers require further evidence to weigh up the effects of school choice systems on sorting across schools and neighbourhoods, relative to potential efficiency benefits of school choice.

KEYWORDS:

• School choice
• segregation
• neighbourhood allocation

1. Introduction

School choice – broadly defined as any system in which parents’ preferences over schools partly determine allocation to school – has theoretical benefits: increasing competition between schools drives productivity (Friedman 1955; Hoxby 2003) and freedom of choice promotes equality of access to ‘good’ schools (Cantillon 2017). There is long-standing concern, however, that allowing households school choice will increase school segregation between groups of different social class, income level and ethnicity, that may be problematic for educational outcomes (Guryan 2004; Reber 2010; Hanushek et al. 2009; Lutz 2011; Johnson and Rucker 2011; Billings, David, and Deming 2014) and wider outcomes such as crime (Billings, David, and Deming 2014; 2019). It is also likely to be problematic for society, as integrated schools ‘offer the opportunity to enhance intergroup relations’ (Burgess and Platt 2021) and pro-social behaviour (Rao 2019).

This paper focuses on whether school segregation is by choice, rather than due to constraints in school access or residential segregation. This is important, because to design policies to reduce segregation ‘knowledge about its driving forces is indispensable’ (Oosterbeek 2021). We use data from parents’ submitted school choices, under-explored due to their recent availability. This improves upon using school allocations, as these are the product of school choices and assignment to school, considering school over-subscription criteria and capacity constraints.

Consider an example of a high-attaining state school that has few low-income pupils, neighbouring a low-attaining state school with the reverse. This segregation could be due to households’ preferences: preferences for a peer-group ‘like us’ (Clark, Dieleman, and de Klerk 1992; Schneider and Buckley 2002; Karsten et al. 2003; Elacqua, Schneider, and Buckley 2006; Noreisch 2007; Byrne 2009; Hastings et al. 2009; Bunar 2010; Saporito 2003; Abdulkadiroğlu, Agarwal, and Pathak 2017; Glazerman and Dotter 2017), the ‘right mix’ (Byrne 2006; Hollingworth and Williams 2010; Vowden and James 2012) or for distance over academic quality (Weekes-Bernard 2007; Hastings et al. 2009; Burgess et al. 2015; Borghans et al. 2015; Glazerman and Dotter 2017; Beuermann et al. 2018; Harris and Larsen 2019; Walker and Weldon 2020; Abdulkadiroğlu et al. 2020; Bertoni, Gibbons, and Silva 2021). Alternatively, this could be driven by constraints in access: all households could prefer the high-attaining school, but if places are rationed by distance to the school and prices rise accordingly (Black and Machin 2011; Nguyen-Hoang and Yinger 2011), only the higher-income households are able to gain admission through residential sorting. In England, around 15% of households each year are not admitted to their first-choice school because of capacity constraints (Burgess, Greaves, and Vignoles 2019), with this percentage higher in urban areas. Using the current allocation of pupils to schools to infer the role of preferences in driving segregation is therefore problematic: segregation could be driven by differences in preferences or differences in constraints across groups.

We provide the first evidence on whether segregation is by choice in a national school choice environment where school choice is not typically constrained by academic ability. Using national administrative data for England, we find that school choices are segregating across most Local Authorities (LAs). A counterfactual exercise that allocates all pupils to their first-choice school, removing all constraints in access, leads to equally highly segregated schools than the current allocation in most areas. This is true for segregation by ethnic group, income deprivation and prior-attainment. In contrast, a counterfactual that assigns pupils to their closest school reduces segregation across all groups in most areas. This final finding would be reversed if only a small percentage of households changed their residential choice in response to such a reform, however.

England is an excellent laboratory to study the functioning of school choice. The right for parents to express a preference for their child’s school has been enshrined since the 1988 Education Reform Act. School choices are collected by a central authority and the allocation mechanism used to assign pupils to schools is truth-revealing. National, complete and high-quality data on each pupil in a state-funded school is collected by Government, including their school choices. We exploit the variation in density, ethnic and social composition of LAs to explore how school choice may or may not contribute to segregation in different areas.

A significant body of qualitative research across fields studies households’ school choices. Choices are often driven by the reproduction of cultural capital (Ball, Bowe, and Gewirtz 1995; Reay and Ball 1998; Ball 2003; Butler and Robson 2003; Bridge 2006; Byrne 2006) as the middle-classes fear the ‘destructive and contaminating effects of going to the local comprehensive’ (Reay and Lucey 2004).

This process leads to ‘white flight’ from some schools (Reber 2005; Noreisch 2007; Baum-Snow and Lutz 2011; Vowden and James 2012) and consequently segregated ‘idealized’ and ‘demonized’ schools (Reay and Lucey 2004) while working-class households are traditionally characterised as ‘disconnected’ choosers (Gewirtz, Ball, and Bowe 1994). Research focusing on the interaction between class and ethnicity has also shown preference against ‘white’ schools for some ethnic minority households to avoid the possibility of racism/bullying and enhance community (Reay and Lucey 2004; Byrne 2009; Weekes-Bernard 2007; Bunar 2010).

One may suppose, therefore, that observed levels of segregation in England’s schools are through choice, but in fact there are also ‘structural constraints on the choices available to parents in economically deprived areas’ (Weekes-Bernard 2007). This is because over-subscribed schools must choose a way to ration places, that is often by proximity. Admission to a school at the top of the local hierarchy, dependent on a ‘fragile equation of colour, ethnicity and social class’ (Reay and Lucey 2004) therefore typically depends on parents’ willingness and means to afford higher property prices in the desirable catchment area. This is one of the ‘circuits of schooling’ identified by Ball, Bowe, and Gewirtz (1995). Burgess et al. (2011) and Hamnett and Butler (2011) describe how school catchment areas limit access for economically disadvantaged households, who have only the illusion of choice to over-subscribed schools. Hamnett and Butler (2013) conclude that ‘distance-based rationing of supply of school places in the face of high demand serves to reinforce and reflect existing patterns of residential social segregation and to indirectly undermine the principles underlying the policy of greater school choice’.

Previous empirical research has used either event analysis or counterfactual simulation to study segregation under school choice. In a meta-review of research, Wilson and Bridge (2019) conclude that ‘school choice is associated with higher levels of segregation of pupils between schools’, remarkably consistent across school choice systems and contexts.

In the former strand of research, the consensus is that introducing school choice has not led to markedly higher segregation between social groups in England (Allen and Vignoles 2007; Goldstein and Noden 2003; Gorard and Fitz 2000; Noden 2000) or German primary schools (Schneider et al. 2012; Makles and Schneider 2015).

Elsewhere worldwide, school choice is typically related to increases in segregation across schools. In Chile, by ability (Hsieh and Urquiola 2006); New Zealand and the US by race (Ladd and Fiske 2001; Bifulco and Ladd 2007), Sweden by ability and family background (Söderström and Uusitalo 2010; Böhlmark, Holmlund, and Lindahl 2016) and South Korea by ability (Oh, Jung, and Sohn 2019).

In the latter, counterfactual, strand of research, segregation is typically found to decrease under ‘neighbourhood’ allocation to schools (Allen 2007; Taylor 2009; Östh, Andersson, and Malmberg 2013; Bernelius and Vaattovaara 2016; Glazerman and Dotter 2017; Boterman 2019) although Harris and Johnston (2020) find that school intakes generally reflect the surrounding neighbourhoods. Glazerman and Dotter (2017) find that a neighbourhood schools policy would decrease segregation by race but increase segregation by income.

Our paper builds most closely on Allen (2007), who assesses the allocation of pupils in earlier administrative data for England, relative to counterfactual simulations. Allen (2007) concludes that where pupils sort into non-proximity schools it tends to increase segregation by ability and income. The difference between the current and counterfactual simulations is largest in urban areas, presumably as pupils have a more diverse choice set of schools within a reasonable commuting time. We extend this analysis by using administrative data on households’ school choices in addition to allocation to explore the role of preferences relative to constraints.

Recent work studying Amsterdam is the first to quantitatively isolate the effect of parents’ school choices (preferences) on segregation. Using administrative data from the secondary school match, Oosterbeek (2021) find that 70% of school segregation (within school tracks) is driven by preference heterogeneity across groups. In Amsterdam, pupils are free to choose any school that offers their ability track. As Amsterdam is relatively small and school density is high, the authors suggest that residential segregation should not necessarily be a main driver of school segregation. The results may not therefore generalise to cities without free school choice, larger cities, or cities with less developed public transport.

The next section describes the system of school choice in England in more detail, followed by our data and methodology. The results follow, including robustness checks. The final section provides discussion, including possible policy options to reduce segregation, and our conclusion.

2. School choice in England

School choice is England is broadly defined as ‘open enrollment’ as opposed to ‘opt-out’ (see Wilson and Bridge 2019). That is, households are not assigned to a default school that they can opt out from (as is common in the US, Scotland, and some areas in Germany) and instead can submit preferences for any preferred school(s), locally or further afield. This is like the system in many European countries – for example Sweden and the Netherlands – New Zealand, and South America – Chile and Brazil (Wilson and Bridge 2019). Butler and Hamnett (2007) characterise the English education system as sitting between ‘a choice-driven North American model of educational allocation and a more geographically driven allocation model traditionally favoured in Europe’.

Parents in or entering the English state education system provide a ranking of their preferred choices of school on a form that is submitted in a centralised system to their LA. All government-funded schools, including faith, selective and academy schools participate in this common system. Applications made to private schools are not coordinated, although parents can apply to both private and state schools simultaneously. The process is the same for primary and secondary schools.

Depending on the LA, parents can provide up to three to six choices of school in rank order, with three being the mode (Table 1). Parents may apply to school(s) outside their LA by ranking the school(s) on the application form submitted to their home LA.¹ The number of choices parents can make therefore depends on the restriction of their home LA.

Table 1. Summary statistics on 115 Local Authorities.

	Min.	1st Qu.	Median	Mean	3rd Qu.	Max.
Pupils:
# pupils	303	1,807	2,537	3,157	3,484	12,935
% white	3	47	80	68	91	97
% FSM	13	25	34	34	41	70
% high KS2	23	36	39	39	43	52
Allocations:
% at nearest	19	35	45	45	54	81
% at 1st preference	66	81	89	88	95	99
% 1st pref. is nearest	19	35	45	45	54	81
Schools:
# Schools	4	11	15	18	20	80
% faith school	0	11	18	19	25	67
Mean % 5+ A*-C	39	53	57	56	60	71
LA:
# choices on list	3	3	3	4	6	6
Rural	0	0	0	0.13	0	1
Urban city and town	0	0	0	0.36	1	1
Urban conurbation	0	0	1	0.51	1	1
School density	0.01	0.03	0.09	0.15	0.22	0.86
Market tightness	0.86	1.05	1.15	1.16	1.26	1.70

Source: Author’s calculations from national preference data and the National Pupil Database. School characteristics from publicly available information provided by the Department for Education and collection of secondary school admissions criteria.

Note: ‘Fair-banding’ means that at least 20% of schools in the LA select pupils according to an academic test to have a equal balance of academic ability in the intake. An LA is classified as ‘rural’ if at least one third of schools are classified as ‘rural’. An LA is classified as ‘town’ if the modal school is classified as ‘urban city and town’ and less than one third of schools as ‘rural’. An LA is classified as ‘city’ if the modal school is classified as ‘urban conurbation’ and less than one third of schools as ‘rural’. ‘School density’ is the number of schools per km2 (/1,000,000). ‘Market tightness’ is the ratio of places available at the LA to number of applications received. This measure is calculated from publicly available data from the Department for Education.

A set of published school admissions criteria are used where a school is over-subscribed. Typically, these include: whether the child has a statement of special educational need, whether the child is looked-after by the LA; whether the child has a sibling at the school already; the distance of the family home from a school; and less commonly, the faith or aptitude of a child (Burgess, Greaves, and Vignoles 2019). Each child is allocated to their highest ranked school where they are admitted according to the criteria of each school. This allocation is done using an algorithm (student optimal stable allocation, see Pathak and Sönmez 2013). If a pupil is not allocated to any preferred school, they are assigned to a school with spare capacity (that is by definition less popular).

The algorithm used is weakly truth-revealing, meaning that parents can do no better than by reporting their true preferred schools, although the short list implies that low probability schools may be omitted (Haeringer and Klijn 2009; Calsamiglia, Haeringer, and Klijn 2010; Fack, Grenet, and He 2019). Theoretically, the first school choice should not be strategic, as parents’ need for a ‘safe school’ (to avoid being unassigned) can be satisfied using the lower ranked choices. Fack, Grenet, and He (2019) show that non-trivial application costs can induce non-truthful application behaviour, however. Unfortunately, we therefore cannot rule out that parents’ ‘skip the impossible’ (as coined by Fack et al. [2019]) for their first school choice. Parents may also have erroneous beliefs that imply that some preferred schools are omitted from the submitted choice list. For this reason, we treat the list of chosen schools as ‘stated’ preferences rather than necessarily parents’ true underlying preferences.

Parents may consider transport provision when making school choices. There are official regulations from the Department for Education regarding school transport, which in general provides free transport if the ‘nearest suitable school’ is sufficiently difficult to access by foot.² This could in principle restrict parents’ school choices, although in practice, described later, most parents choose a school that is not their closest.

This system leads to a level of segregation in England’s schools that is around the middle of OECD countries, typically lower than countries where selection by ability is the norm (Jenkins et al. 2008).

3. Materials and methods

3.1. Data

Data on each household’s secondary school choice(s) covers the whole cohort of pupils seeking admission to any English state secondary school in the school-year 2014/2015. Access to these data was provided by the Department for Education, through the National Pupil Database (NPD) application process.

We derive the closest, or neighbourhood, school from pupils’ home location. We calculate the straight-line distance between home and school rather than travel distance, as this is most relevant for school admissions and most computationally feasible. The data include the following pupil-level characteristics that we use to study segregation: eligibility for Free School Meals (FSM) in any of the last six years, a binary variable as a marker of poverty; ethnic group, that we group into White British and non-White British; prior-attainment according to performance in nationally set and externally examined assessments at the end of primary school (KS2). This measure is grouped into the top 20% of prior-attainment and bottom 80%. These are coarse measures, that miss subtlety across the distributions of socio-economic status and prior-attainment, and across ethnic groups. Taylor (2018) shows that there is a meaningful proportion of children ‘who could be described as disadvantaged’ who are not recorded as eligible for FSM, for example. Hobbs and Vignoles (2010) show that FSM children are more likely to be in low-income households than non-FSM children, but between 50% and 75% of FSM children are not in the lowest income households. Additionally, FSM does not capture a broader definition of social class that is shown to influence the process of school choice in other contexts (see for example Boterman [2021]).

Our sample excludes 15 LAs that have a middle school system, where pupils enter secondary school at age 13 rather than age 11. We also exclude 21 LAs where at least 10% of schools are selective – that accept pupils according to performance on an entrance test. We also exclude schools in other LAs that have a selective admissions policy (163 in total). This is to focus our analysis on schools and LAs that operate a non-selective admissions policy, so that our findings are generalisable to non-selective settings.

Table 1 shows the descriptive statistics for our final sample at the LA-level, for the 115 LAs remaining. The population of students is all students who didn’t choose and weren’t allocated to a Special school (catering for children with special educational needs) or selective school. The median LA has 80% of secondary school pupils that are white, 34% FSM and 39% high prior-attainment. In the median LA, 89% of pupils are assigned to their first-choice school, although there is wide variation across LAs, with the minimum at 66% and maximum at 99%. In the median LA, 45% choose their closest school as first-choice, and 45% attend their closest school. Again, there is variation across LAs, from 19% to 81%.

These data are supplemented with area-level characteristics, such as pupil composition, school density (schools per km²), spare capacity (the ratio of total school places to total applications), rural/urban category, and whether the LA allocates pupils according to ‘fair-banding’ where an equal proportion of pupils from across ability bands is admitted to the school. This policy variable is binary, defined according to whether at least 20% of schools in the LA operate fair-banding, and was collected as part of a wider project on secondary schools’ admissions criteria led by Simon Burgess at the University of Bristol.

3.2. Measuring segregation

A common measure of segregation is the Index of Dissimilarity (D) (Duncan and Duncan [1955]). For two disjoint sub-groups of the population indexed by t ∈ {0,1} representing, for example, white and minority pupils, and G non-overlapping geographical units (for example neighbourhoods or schools), the index is defined as. $D={\displaystyle \frac{1}{2}\sum _{g=1}^G\left|{\displaystyle \frac{n_{g.0}}{N_0}-{\displaystyle \frac{n_{g.1}}{N_1}}}\right|}$where n_g,t is the number of group t in unit g, and N_t is the total population of group t across all units. At the LA level, N₀ would be the total population of White pupils in the LA, for example.

If D takes its maximum value of 1, this implies that no two members of different sub-groups share the same geographical unit or school. At its minimum value of 0, D implies that the empirical distribution of each sub-group is identical to that of the other. The index has an intuitive interpretation as the proportion of either of the groups who would have to move between geographical units (for example schools) to equalise the spatial distributions of the two groups.

Although popular in the segregation literature, D is known to be upward-biased for finite samples. This problem is especially acute when numbers of one or both groups are small in some geographical units. To address this, we use the bias correction method in Allen et al. (2015), described in Appendix A.

3.3. Counterfactual simulation

Segregation under first-choices is calculated using each household’s first-choice rather than actual school in the measure of D. School capacities are allowed to vary, with popular schools expanding and unpopular schools contracting. By removing capacity constraints, this simulation isolates the effect that parents’ school choices (interpreted as preferences) have on school segregation. We discuss caveats to this interpretation in section 4.5.

An advantage of D as a measure of segregation is that it is additive, that means that the observed D and D resulting from the counterfactual estimates can be differenced. For example, post-residential sorting would be $D_{\left[alloc\right]}-D_{\left[nearest\right]}$. To assess the degree to which D reflects post-residential rather than underlying residential segregation, we compute segregation under an additional simulated scenario in which all children attend their nearest school. In this scenario, all segregation is residential, so the difference between the actual measured levels of segregation, and the levels measured under this counterfactual indicates the extent of post-residential segregation.

This method is very similar to that described by Allen (2007). The main difference is that way that school capacities are treated in the counterfactual. To treat school capacities as exogenously fixed, Allen uses a ‘Boston’ matching mechanism where some pupils are therefore allocated to schools far away. In contrast, we remove fixed capacities, so each pupil is allocated to his/her nearest school: the de facto catchment area of each school is its Voronoi neighbourhood.

4. Results

Figure 1 presents the distribution of segregation of secondary schools across LAs in our sample. The first column shows segregation by FSM. The second column shows segregation by prior-attainment and the third by ethnic group. Each row represents a different school choice environment. From top to bottom: current allocation, allocation by first-choice, and allocation by nearest school.

Figure 1. Distribution of segregation indices for 115 LAs in England. Source: Author’s calculations from national preference data and the National Pupil Database. Note: The first column shows segregation index (D) by Free School Meals status; the second column by Key Stage 2 prior-attainment (top 20% vs bottom 80%); and the third column by White/non-White. The first row shows the observed allocation. The second row shows the counterfactual allocation to first choice school. The third row shows the counterfactual allocation of students to their nearest school. The vertical line shows the mean of segregation in each panel.

4.1. Segregation under current allocation

The current distribution of segregation in England’s secondary schools is shown in the first row of Figure 1. The average level of segregation by FSM is around 0.21: 21% of pupils would have to be re-allocated across schools for there to be an even spatial distribution across schools within the LA. This is slightly lower than found for the cohort of pupils entering secondary school in 2000 (Allen 2007). There is variation in segregation across LAs, with some having levels of segregation around zero and some close to 0.4. The inter-quartile range is narrow, however (0.10, Table 2). The average segregation by prior ability is lower, with a mean of 0.14. Recall that this sample excludes selective schools and LAs with at least 10% of selective schools. (Segregation by prior ability would therefore be higher if these schools were included.) The interquartile range is also narrower than for FSM (0.06). In contrast, the average segregation by ethnic group is higher (0.28) and has a wider distribution (inter-quartile range 0.19). Some LAs have levels of segregation close to zero while others are around 0.6, meaning that over half of pupils would have to re-allocated across schools for there to be no segregation within the LA.

Table 2. Distribution of dissimilarity indices of 115 Local Authorities.

	Min.	1st Qu.	Median	Mean	3rd Qu.	Max.
Dissimilarity indices:
DFSM, allocated	0.00	0.16	0.22	0.21	0.26	0.37
DFSM, pref.	0.00	0.17	0.21	0.21	0.24	0.37
DFSM, near	0.02	0.13	0.19	0.18	0.23	0.37
DKS2, allocated	0.02	0.11	0.14	0.14	0.17	0.26
DKS2, pref.	0.01	0.12	0.14	0.14	0.17	0.25
DKS2, near	0.02	0.08	0.10	0.11	0.14	0.26
Deth, allocated	0.01	0.19	0.26	0.28	0.38	0.60
Deth, pref.	0.05	0.19	0.26	0.28	0.36	0.61
Deth, near	0.02	0.16	0.25	0.27	0.36	0.61
Dissimilarity differences:
DFSM,pref – DFSM,alloc	−0.08	−0.02	−0.00	−0.01	0.00	0.04
DFSM,near – DFSM,alloc	−0.16	−0.06	−0.02	−0.03	0.00	0.10
DFSM,pref – DFSM,near	−0.12	−0.01	0.02	0.02	0.05	0.15
DKS2,pref – DKS2,alloc	−0.05	−0.00	0.00	0.00	0.02	0.07
DKS2,near – DKS2,alloc	−0.14	−0.05	−0.03	−0.03	0.00	0.07
DKS2,pref – DKS2,near	−0.07	−0.00	0.03	0.03	0.05	0.17
Deth,pref – Deth,alloc	−0.13	−0.01	0.00	0.00	0.02	0.13
Deth,near – Deth,alloc	−0.36	−0.04	−0.01	−0.01	0.03	0.17
Deth,pref – Deth,near	−0.18	−0.03	0.01	0.01	0.05	0.31

Source: Author’s calculations from national preference data and the National Pupil Database. ‘Min.’ refers to the minimum value across Local Authorities, ‘1st Qu.’ to the 25th percentile, ‘3rd Qu.’ to the 75th percentile, ‘Max.’ to the maximum value.

England’s secondary schools are therefore more segregated by ethnic group than income deprivation, and least segregated by prior-attainment (excluding the selective system). A high level of segregation by ethnic background is consistent with earlier research, dis-aggregated by ethnic group (Burgess, Wilson, and Lupton 2005). The cause may be the interaction between class and race in white middle-class school choices (Byrne 2009) and ‘tipping points’ in the acceptable percentage of ‘other’ students (Noreisch 2007; Vowden and James 2012) but could also reflect active choices by non-White ethnic groups. For example, Burgess, Greaves, and Vignoles (2019) and Walker and Weldon (2020) show, using the nationally representative data we employ here, that the school choice patterns of non-White households are consistent with active engagement in the school choice process and ‘ambitious’ school choices consistent with valuing school quality. Households from the non-majority ethnic group in England may also seek a safe and respectful place for their child, free of bullying (Weekes-Bernard (2007); Bunar (2010)) and low teacher expectations (Weekes-Bernard (2007)). Harris and Johnston (2020) also explore the interaction between ethnic and socio-economic segregation, finding that, for some groups in some LAs, apparent ethnic segregation has ‘underlying socio-economic causes’.

The current level of segregation across LAs is correlated with several observable LA characteristics (Table 3). These vary across groups. The percentage of White students in the LA is negatively correlated with segregation by FSM, but positively with segregation by ethnic group. Segregation by ethnic group is higher where there is a higher proportion of non-White pupils, even conditional on geographical characteristics such as school density and market tightness. Segregation by ethnic group is lower in London than other regions, conditional on these other factors.³

Table 3. Correlates with dissimilarity indices in 115 Local Authorities.

	FSM	KS2	Ethnicity
Fair-banding	−0.036	−0.013	−0.049
	(0.030)	(0.023)	(0.056)
More than 3 choices	−0.002	−0.011	−0.022
	(0.018)	(0.014)	(0.033)
Urban city and town	0.069***	0.035*	0.051
	(0.019)	(0.015)	(0.036)
Urban conurbation	0.075**	0.042*	0.100*
	(0.023)	(0.018)	(0.044)
London	0.030	0.004	−0.174**
	(0.027)	(0.021)	(0.052)
School density	−0.139	3.800	−0.729
	(8.668)	(6.843)	(16.482)
Market tightness	−5.475	0.074	14.169
	(4.196)	(3.313)	(7.980)
% FSM	−0.011	−0.082	−0.120
	(0.089)	(0.070)	(0.169)
% White	−0.149**	−0.015	0.429***
	(0.047)	(0.037)	(0.089)
% Low KS2	0.061	0.169	0.654*
	(0.154)	(0.122)	(0.293)
% Religious schools	0.100	0.054	0.067
	(0.058)	(0.046)	(0.110)
N	115	115	115

Source: Author’s calculations from national preference data and the National Pupil Database. School characteristics from publicly available information provided by the Department for Education and collection of secondary school admissions criteria.

Note: ‘Fair-banding’ means that at least 20% of schools in the LA select pupils according to an academic test to have a equal balance of academic ability in the intake. An LA is classified as ‘rural’ if at least one third of schools are classified as ‘rural’. An LA is classified as ‘town’ if the modal school is classified as ‘urban city and town’ and less than one third of schools as ‘rural’. An LA is classified as ‘city’ if the modal school is classified as ‘urban conurbation’ and less than one third of schools as ‘rural’. ‘School density’ is the number of schools per km2 (/1,000,000). ‘Market tightness’ is the ratio of total school places to total applicants at the LA level.

Other variables have a similar effect across categories. For example, as in Allen (2007) urban LAs have higher segregation relative to rural LAs.

Several area-level characteristics are notably uncorrelated with the current level of segregation, however, such as whether households are permitted to express more than three school choices.

4.2. Segregation under first choice allocation

The distribution of segregation across LAs would change only marginally if all pupils in England were assigned to their first-choice school rather than the actual allocation. The second row of Figure 1 shows the distribution for segregation by ethnic group, FSM and prior-attainment. The distributions for FSM and prior-attainment are very similar to the distributions under the current allocation. For example, the mean level of segregation for FSM is 0.21 under both the current allocation and simulated allocation using first-choice school. For prior-attainment, the mean level of segregation remains at 0.14 (Table 2). The inter-quartile ranges are also almost identical. The mean and inter-quartile range for segregation by ethnic group are also largely unchanged, although the shape of the distribution is altered, with weight moving from the very lowest to slightly higher levels of segregation. These patterns are perhaps unsurprising given the high percentage of households that are allocated to their first-choice school. At the mean in our sample, 88% of households are allocated to their first-choice school, so the first-choice counterfactual would be affected by only 12% of households.

The lower panel of Table 2 shows the distribution of the difference in segregation between current and simulated allocations across LAs. There is no difference in segregation by ethnic group, FSM or prior-attainment for the majority of LAs: the mean, mode and median are close to zero in each case. There are LAs where allocating all pupils to their first-choice would increase or decrease segregation, however, up to around 0.13. The interpretation is that constraints on admission to first choice school in some LAs change the proportion of pupils that would have to change schools to equalise the distribution of pupils by around 13%.

At face value, these results suggest therefore that segregation from school choice is a result of parents’ preferences rather than any constraints in accessing preferred schools. Whether this is true depends on whether parents’ school choices reflect their true preferences, or whether, instead, parents’ stated choices are influenced by other factors such as the probability of admission to each school. We return to this in section 4.5.

4.3. Segregation under proximity allocation

In contrast, the distribution of segregation across LAs changes when all pupils are assigned to their closest school. The mean level of segregation typically decreases: by prior-attainment, 0.11 under neighbourhood assignment compared to 0.14 under the current allocation; by FSM, 0.18 compared to 0.21; by ethnic group, 0.27 compared to 0.28 (Table 2).

At the LA-level, moving to neighbourhood schools would reduce school segregation in most LAs. This is most obvious for segregation by prior-attainment and FSM, where the mean difference across LAs is −0.03: moving from a system of school choice to neighbourhood allocation would reduce segregation (the proportion of pupils that would need to move schools to equalise the distribution) by 3% in the mean LA. The magnitude of this effect for FSM is equivalent to moving from the median of the distribution to the 35th percentile. For prior-attainment, moving from the median to the 26th percentile. The distributions are also wide, with segregation increasing in around 24%, 22% and 36% of LAs under the neighbourhood allocation compared to the current allocation, for FSM, prior-attainment, and ethnic group, respectively.

These results imply that, overall, school choice exacerbates rather than reduces school segregation arising from residential segregation. This does not take into account that residential choices are endogenous pupil assignment, however. This has two (related) implications. First, that under the counterfactual neighbourhood assignment, parents’ residential choices may be more segregating. For example, parents’ choice of residential neighbourhood becomes even more important when it entirely determines access to schools. Second, that under the current assignment, parents’ residential choices may be more integrating. The current level of neighbourhood segregation may be endogenous to the current school choice environment, as school choice allows some households to choose school and residence independently. Both possibilities are discussed in section 4.5.

4.4. Where does school choice exacerbate segregation?

This section explores the circumstances where allocation by first-choice exacerbates or reduces segregation, presenting results from a multivariate regression with the difference in segregation under the first-choice allocation and current allocation ($D_{\left[pref\right]}-D_{\left[alloc\right]}$) as the dependent variable. The interpretation of $D_{\left[pref\right]}-D_{\left[alloc\right]}$ is the difference in sorting due to school choices when admission constraints are removed. The current allocation, D_[alloc], is included as a covariate, as the current allocation is likely to reflect some structural features of the LA that cannot be captured by other observable characteristics. A negative coefficient means that the covariate lowers $D_{\left[pref\right]}-D_{\left[alloc\right]}$, that is equivalent to decreasing segregation under the first-choice allocation relative to the current allocation. The first three columns of Table 4 show that the coefficient for D_[alloc] is negative for each category, and significant for the first two columns: when households face a more segregated school system, their first school choices tend to be less segregating.

Table 4. Correlates with the difference in dissimilarity indices under alternative counterfactuals in 115 Local Authorities.

	Preferences and current allocation			Nearest school and current
	FSM	KS2	Ethnicity	FSM	KS2	Ethnicity
D. Allocation	−0.082*	−0.104*	−0.039	−0.277**	−0.347***	−0.235***
	(0.035)	(0.040)	(0.029)	(0.085)	(0.075)	(0.055)
Fair-banding	0.025*	0.022*	−0.010	−0.016	−0.021	−0.029
	(0.010)	(0.010)	(0.016)	(0.026)	(0.018)	(0.032)
More than 3 choices	−0.003	−0.001	0.007	0.010	0.003	−0.008
	(0.006)	(0.006)	(0.010)	(0.015)	(0.011)	(0.019)
Urban city and town	0.003	0.004	−0.001	0.013	0.010	0.021
	(0.007)	(0.006)	(0.011)	(0.017)	(0.012)	(0.020)
Urban conurbation	0.012	0.007	−0.009	0.005	0.004	0.044
	(0.009)	(0.008)	(0.013)	(0.021)	(0.014)	(0.025)
London	0.001	0.008	−0.033*	−0.025	0.017	−0.036
	(0.010)	(0.009)	(0.016)	(0.024)	(0.016)	(0.031)
School density	−3.838	−6.684*	1.677	1.321	−3.711	−4.395
	(3.052)	(2.791)	(4.810)	(7.463)	(5.186)	(9.258)
Market tightness	1.719	0.247	−1.859	2.311	2.941	1.595
	(1.490)	(1.349)	(2.364)	(3.643)	(2.507)	(4.550)
% FSM	−0.021	0.053	−0.018	−0.111	0.002	−0.253**
	(0.031)	(0.029)	(0.049)	(0.076)	(0.053)	(0.095)
% White	−0.013	0.006	0.017	0.012	−0.010	0.088
	(0.017)	(0.015)	(0.029)	(0.042)	(0.028)	(0.055)
% Low KS2	0.075	0.026	−0.009	−0.043	0.022	0.597***
	(0.054)	(0.050)	(0.088)	(0.133)	(0.093)	(0.169)
% Religious schools	0.008	−0.017	−0.046	0.030	−0.051	0.034
	(0.021)	(0.019)	(0.032)	(0.050)	(0.035)	(0.062)
N	115	115	115	115	115	115

Source: Author’s calculations from national preference data and the National Pupil Database. School characteristics from publicly available information provided by the Department for Education and collection of secondary school admissions criteria.

Note: ‘Fair-banding’ means that at least 20% of schools in the LA select pupils according to an academic test to have a equal balance of academic ability in the intake. An LA is classified as ‘rural’ if at least one third of schools are classified as ‘rural’. An LA is classified as ‘town’ if the modal school is classified as ‘urban city and town’ and less than one third of schools as ‘rural’. An LA is classified as ‘city’ if the modal school is classified as ‘urban conurbation’ and less than one third of schools as ‘rural’. ‘School density’ is the number of schools per km2 (/1,000,000). ‘Market tightness’ is the ratio of total school places to total applicants at the LA level.

Geographical characteristics of the LA are typically not correlated with the dependent variable. Two exceptions are first, in London, allocation by first-choice lowers segregation across ethnic groups relative to the current allocation. Second, allocation by first-choice lowers segregation by prior-ability (relative to the current allocation) when school density is higher.

One policy characteristic of the LA is correlated with the difference between current and counterfactual segregation. Areas with fair-banding have higher segregation by FSM and prior-attainment under the first-choice allocation relative to the current allocation. Fair-banding means that parents have a positive probability of admission to a larger set of schools. This result could therefore suggest that when given more freedom to choose schools, households make choices that lead to higher segregation. This suggestion is tentative, however, as the effect of other factors that would theoretically act in a similar way, like parents having more than 3 choices, are close to zero.

In summary, there are no clear or universal characteristics of LAs that are correlated with school choices that are highly segregating or desegregating. The strongest relationship is between the current level of segregation in the LA, that is correlated with first-choices being desegregating relative to the current allocation. Other than that, policy options have the clearest correlation. Where parents have more freedom in their choices (through fair-banding) their choices appear to result in slightly more segregation for some groups.

In the final three columns of Table 4, the dependent variable is $D_{\left[near\right]}-D_{\left[alloc\right]}$, and again, D_[alloc] is an important covariate. Unsurprisingly, the nearest-school counterfactual is more desegregating (relative to the current allocation) where schools are currently more segregated.

There are few other policy or geographical characteristics that affect the change in segregation between counterfactuals. The coefficient for fair-banding is negative but not significant. This could reflect lower residential segregation in LAs with fair-banding, or more segregating choices/allocations in these LAs. Segregation by ethnic group decreases in the neighbourhood allocation relative to the current allocation where the LA has a higher percentage of FSM pupils and increases with a higher percentage of pupils with low prior-attainment.

Overall, there is an emerging (but tentative) pattern that LAs that currently allow parents more freedom in their school choices are more segregated under first-choices and less segregated under neighbourhood assignment. This strengthens the case that households’ preferences affect the current level of segregation in England’s schools in addition to schools’ capacity constraints, rather than solely by schools’ capacity constraints.

4.5. Robustness

Throughout, we have assumed that school choices reflect parents’ true preferences for schools. This is justified in part by the truth-revealing allocation mechanism used to assign pupils to schools in England. The restricted list length for school choices means that parents may rationally be strategic in their school choices, omitting schools with zero/low probability of admission (Haeringer and Klijn 2009; Calsamiglia, Haeringer, and Klijn 2010; Fack, Grenet, and He 2019). If so, then school choices do not map perfectly to preferences, but instead incorporate constraints (through the expected probability of admission) to some extent.

To explore this, we first interpret the results that school choices are segregating (and neighbourhood allocation desegregating) where households’ school choices are currently less bound by residential location. These are areas for which a meaningful proportion of schools allocate pupils according to prior ability, equalising the distribution (fair-banding LAs). Across these areas where it is most likely that school choices to equate to preferences, school choices generally lead to more segregation relative to the current allocation.

A limitation of all counterfactual studies to date is that households’ location is fixed, rather than responsive to changes in school assignment mechanisms. Local school quality currently informs households’ residential decisions as admission is often implicitly tied to location, for example through ‘catchment areas’ or distance. A substantial body of literature finds that house prices, indicative of demand, respond to local school quality (Black 1999; Leech and Campos 2003; Bayer, Ferreira, and McMillan 2007; Gibbons and Machin 2008; Fack and Grenet 2010; Gibbons, Machin, and Silva 2013; Machin and Salvanes 2016). Exploring the variation in this response, He (2017) finds heterogeneous effects across cheaper and more expensive school districts and Cheshire and Sheppard (2004) show the house price premium is responsive to the ‘suitability’ of potential homes for families and local constraints in the supply of housing.

How would households’ choice of neighbourhood change if it were explicitly (rather than implicitly) tied to school choice? Theory suggests that households’ location responds to changes in school admission policies (Nechyba 2000; Epple and Romano 2003; Bayer, Ferreira, and McMillan 2007; Ferreyra and Marta 2007; Calsamiglia, Martínez-Mora, and Miralles 2015, 2020). This has been confirmed through empirical work using changes in school choice environments over time (Thrupp 2007; Baum-Snow and Lutz 2011; Brunner, Cho and Reback 2012; Chakrabarti and Roy 2015). The re-introduction of school zones (catchment areas) in New Zealand indicates that residential segregation is likely to increase in response to neighbourhood schooling (Thrupp 2007). Baum-Snow and Lutz (2011) find a strong migration response of White households in response to desegregation policies in the US, while Reber (2005) estimates that ‘white flight’ reduced the effects of desegregation plans by about one-third.

We find that neighbourhood allocation decreases income (FSM vs non-FSM) segregation compared to the current allocation by 3% at the mean. This implies that, for the mean LA, more segregating residential choices of 3% of non-FSM households would reverse this finding. This seems modest, given the findings in the literature.

A related limitation is that households may respond to a change in school admissions policies by exit to the private sector (Clotfelter 1976; Clotfelter 2001; Reardon and Yun 2003; Reber 2005; Saporito 2013; Saporito and Sohoni 2007; Söderström and Uusitalo 2010; Baum-Snow and Lutz 2011; Calsamiglia and Güell 2018; Calsamiglia, Fu, and Güell 2020) that is one method of admission to a preferred school (Butler and Robson 2003; Rangvid and Schindler 2007; Maloutas 2007; Cordini, Parma, and Ranci 2019; Bonal, Zancajo, and Scandurra 2019; Nielsen, Skovgaard, and Andersen 2019; Boterman 2021). Again, for the mean LA, a relatively small exit response by more affluent households would reverse the finding that neighbourhood assignment is desegregating.

Like previous counterfactual analysis, we can therefore conclude that neighbourhood allocation would decrease segregation in schools if households have no endogenous responses. Incorporating households’ changes in residential location and exit to the private sector is likely to mean that neighbourhood allocation is no longer desegregating, as in empirical studies of real-world cases.

Finally, our results are similar in an alternative specification where no density correction is applied to the Dissimilarity Index and where schools outside the LA are not aggregated to a single ‘outside option’ (not shown due to space constraints).

5. Discussion

Segregation in schools between different groups of pupils has been shown to have negative short-term and long-term consequences. This paper extends previous research to explore whether, under a system of school choice, segregation is by choice. This is important, as different policies are required to address segregation depending on the cause: driven by parents’ preferences, or constraints in accessing their preferred school. Using national administrative data for England, we find that school choices are segregating across most Local Authorities. Allocating all pupils to their first-choice school, removing all constraints in access, leads to equally highly segregated schools than the current allocation in most areas. This is true for segregation by ethnic group, income deprivation and prior-attainment.

A potential limitation to these results is the interpretation of the first-choice as reflecting parents’ preferences. Despite the truth-revealing assignment mechanism used in England, the short list length (between three and six across England) may induce strategic school choices if households ‘skip the impossible’ where there is no chance of admission (Fack, Grenet, and He (2019)). Our interrogation of the data suggests that this is not the case: school choices are more segregating in areas where school choices are less constrained by a geographically based probability of admission, suggesting that segregation is, to some extent, by choice.

In our second counterfactual, following Allen (2007), we find that ‘neighbourhood’ schooling – where all pupils are assigned to their closest school – reduces segregation relative to the current allocation in most Local Authorities. At face value, this implies that removing school choice would integrate schools. However, interpretating this finding requires careful consideration of the school and neighbourhood choices made by parents in both counterfactuals.

First, parents’ residential choices might be more integrating under school choice than neighbourhood assignment. For example, Boterman (2021) finds that free school choice in Amsterdam has allowed neighbourhood integration, as parents need no longer move to gain admission to their preferred school. (See also Rangvid and Schindler (2007) and Rangvid (2009) for Copenhagen, and Söderström and Uusitalo (2010) for Stockholm.) In contrast, residential sorting is particularly strong in areas where location largely determines school admission, such as Finland (Bernelius and Vilkama 2019) and Paris (Oberti and Savina 2019). For example, higher income households that choose to live in more integrated neighbourhoods under free school choice may decide to sort into more segregated neighbourhoods around ‘good’ schools to gain admission in a neighbourhood system.

Given the likely residential responses, a ‘neighbourhood’ policy would therefore be likely to lead to increased sorting across neighbourhoods, which in turn might have detrimental effects, such as lower well-being, education, and employment outcomes. Theoretically, outcomes for the minority or disadvantaged group could be reduced due to neighbourhood/peer effects and increased spatial mismatch between workers and jobs (Boustan 2012). The causal effect of residential segregation is difficult to establish empirically (Manski 1993; Durlauf 2004), although experimental evidence suggests that randomly assigning households to less disadvantaged neighbourhoods leads to wide-ranging benefits to households (Katz, Kling, and Liebman 2007; Ludwig et al. 2013; Chetty, Hendren, and Katz 2016). Reducing residential segregation may be a positive externality resulting from school choice, that would be reversed by returning to a neighbourhood schools policy. Returning to a neighbourhood schools policy may change segregation at the school-level by little, while increasing segregation at the neighbourhood level, with potentially adverse consequences for more disadvantaged groups.

Alternative policies for increasing equality of access and reducing segregation in schools should be considered, such as the introduction of fair-banding, marginal lotteries or quotas. Fair-banding, where an equal proportion of pupils from across ability bands is admitted to the school, could be expanded across England, as considered by Hamnett and Butler (2011) and Hamnett and Butler (2013). Hamnett and Butler (2013) state that fair banding ‘appears to have much to commend it in terms of overcoming the role of distance-based allocational systems’, although Weekes-Bernard (2007) notes the potential for parents (particularly those with English as an Additional Language) to misunderstand fair banding as a selective, 11 + style, admissions test.

There are other non-geographical admissions arrangements, such as lotteries for over-subscribed schools. This policy has been trialled in Brighton and Hove (see Allen, Burgess, and McKenna 2013) and was vehemently opposed by residents in formerly desirable catchment areas. Local pressure meant that the lottery became district-wide rather than LA-wide, with ‘district’ arguably gerrymandered to retain segregation between higher and lower attaining schools.

These political problems are noted by Hamnett and Butler (2013) as a significant barrier to implementation. Parents may also be opposed to the uncertainty created by lotteries (Vowden and James 2012) and mourn the loss of local schools that serve as a community for many parents, particularly of primary school age children (one reason for attaining the ‘right mix’ of children is to form friendships with the ‘right mix’ of parents). Burgess, Greaves, and Vignoles (2020) consider the feasibility of ‘marginal ballots’ – where a substantial proportion of school places would be allocated as normal, and the remaining places would be reserved for a random draw among unaccepted applicants – and a simple priority for disadvantaged families, or reserved places for applicants from less well-off backgrounds. Burgess, Greaves, and Vignoles (2020) state that:

Our personal view of the evidence is that there is much to recommend a marginal ballot approach, with perhaps 10% or 20% of places reserved for non-priority applicants. However, how the ballot is communicated to potential applicants is also key to avoid a rejection of a “postcode lottery” approach which is perceived to be a major problem in other public services.

For all potential policy reforms to school admissions under school choice, careful consideration would need to be given to ‘tipping points’ or ‘white flight’ from the area or from the state sector entirely (Reber 2005; Noreisch 2007; Baum-Snow and Lutz 2011; Vowden and James 2012), that could lesson integration overall. Considering this, Vowden (2012) states that:

Even a relatively modest reform – such as a controlled choice system designed to ensure that the proportion of children eligible for free school meals in every Hammersmith & Fulham primary school fell between 25 and 50% – might prompt a significant exodus of middle-class parents from the local state system. The most popular schools in the study area had lower proportions than that, and for many respondents this was an important part of their appeal.

Evidence suggests that segregated school systems have particularly detrimental effects for those in ‘Minority’ schools. In the US, some of these disadvantages stem from the local financing of schools, and so the effects of segregation on pupils’ educational outcomes could be partially offset by compensatory resources to schools (Billings, David, and Deming (2014); Gamoran and An (2016)). Progressive funding in England, enhanced by the Pupil Premium, is therefore likely to mitigate the effects of segregation, although broader outcomes such as social cohesion are unlikely to be resolved by additional funding. Researchers and policymakers must combine efforts to study the causes and consequences of segregation in schools.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Access to these data was provided by the Department for Education, through the National Pupil Database (NPD) application process. These data are available to ONS Approved Researchers through the Secure Research Service.

Notes

1 The proportion of pupils that apply to a school outside their home LA varies across regions, from 4% in the North East to 21% in London. The full distribution is as follows: North East: 4%; East: 5%; Yorkshire: 5%; South East: 6%; North West: 7%; South West: 7%; East Midlands: 7%; West Midlands: 10%; London: 21%.

2 Secondary school aged pupils are eligible for free school transport if they attend their ‘nearest suitable school’ and that school is at least three miles from their home, or there is no safe walking route to that school, or the pupil has a special educational need, disability or mobility problem that prevents them from walking to school (DfE (2022)). Pupils from low-income families have slightly more generous free transport provision: if they attend one of their 3 nearest suitable schools, which is between 2 and 6 miles from their home, or, a school between 2 and 15 miles away chosen because of the family's religion of belief (DfE (2022)).

3 The negative coefficient for London has a larger magnitude than the positive coefficient for Urban, implying that the net effect is lower segregation by ethnic group in the capital city.