Quasi-markets, school diversity and social selection: Analysing the case of free schools in England, five years on

The opening of new state schools by non-state actors has intensified debates about social selection and inequality in quasi-markets. This article examines the case of England, where the government allows anyone to apply to open a new 'free school', arguing this will improve social equity.
 Using data from the National Pupil Database for all 325 free schools established between 2011/12 and 2015/16, we analyse whether the students attending free schools are representative of their local neighbourhoods. We develop the first analysis of whether the specifics of who opens and provides
 a free school impacts on who attends the school. We also analyse whether opening a free school has an impact on neighbouring schools. We find that free schools are located in areas with above-average deprivation but admit intakes that are more affluent than the average for the neighbourhoods
 from which they recruit. This is particularly the case for primary free schools, which also recruit students with above-average prior attainment. There is no evidence that free schools become more representative as they admit additional year groups. Significantly, we find that all categories
 of free school providers have opened schools whose populations are more affluent than their neighbourhoods, with the exception of academy chains. We also find that the opening of a free school leads to a concentrated loss of pupils at the closest school, except in cities, but we do not identify
 an impact on the student composition of neighbouring schools. Discussing the reasons for this, we conclude that free schools are socially selective and reproduce socio-economic inequalities.


Introduction
Free schools are part of an ongoing policy agenda to liberalize the 'supply side' of the school quasi-market in England, by allowing non-state actors to open and govern new state schools. Introduced in 2010 by the then coalition government to satisfy a Conservative Party manifesto pledge, free schools are established through a unique 'demand-led process' in which potential providers -including 'teachers, charities, parent groups, faith organisations and others' (DfE, 2010: 58) -are encouraged to apply to central government for the right and state funding to set up a new school. Free schools can be opened without local demographic need for new school places, where there is evidence of 'parental demand' (though critics have raised objections concerning the evidence required to demonstrate parental demand in the application process; see National Audit Office (2013: 7) and McInerney (2016: 1)). The Conservative governments elected in 2015 and 2017 have committed to increasing the number of free schools, with the aim to open 900 by 2020 (DfE, 2015), arguing that free schools will increase parental choice, create new competitive pressure on existing schools and contribute to greater equity, not least because the people and organizations opening free schools would be 'motivated by the desire to make a difference in disadvantaged areas' (DfE, 2010: 59). Five years on, following the opening of the first five waves of free schools, Nicky Morgan, the then Secretary of State for Education, argued that 'Free schools are the "modern engines of social justice" helping "break the cycle of disadvantage"' (DfE, 2015: 1).
Despite these policy claims, there is widespread concern that free schools will exacerbate social selection (NUT, 2013;Stokes, 2014) and reproduce social inequality (Coldron et al., 2009). Social selection by socio-economic status has been found to reduce the educational and occupational aspirations of disadvantaged students (Gorard and Smith, 2008). In countries where there is greater socio-economic segregation between schools, there are wider inequalities in student outcomes by socio-economic status and no beneficial effect on average student attainment (OECD, 2003). While free schools are not allowed to select students by ability, they could become socially selective in a number of ways. Free schools with a faith designation are allowed to select half of their students using faith criteria. Parents opening free schools can prioritize the admission of their own children. All free schools are able to determine their own admission policies, within the constraints of a national admissions code (DfE, 2014). This allows schools to create prioritized catchment areas (instead of using a simple distance measure) as an oversubscription criterion and to select 10 per cent of their students by aptitude, determined by a test, in specific subject specialisms (performing arts (including music), visual arts, modern foreign languages, sport, design and technology and information technology) (DfE, 2014b). Perhaps most significantly, the people and organizations opening free schools can choose to locate their schools in more advantaged areas or develop a school ethos and curriculum that proves more attractive to particular parents, including by socio-economic class and/or ethnicity (Hatcher, 2011;Walford, 2014;Higham, 2014a).
These concerns regarding social selection were partly borne out by two early analyses of free school intakes, which used fairly small amounts of data concerning the first three waves of openings. Green et al. (2015: 921) found that while free schools had in fact been located in areas of 'somewhat above average disadvantage', they admitted fewer pupils eligible for free school meals than did neighbouring schools. Morris (2015: 1) reported that, while Wave 1 free schools 'underrepresented poorer children every year', Waves 2 and 3 provided 'a more mixed picture'. Both studies argued for further research into free school student composition, and there is a number of compelling reasons for doing so now. First, the intakes of free schools may be changing over time, both as new annual waves are established and as earlier waves admit new year groups. There is preliminary evidence, for instance, that the longer a free school is open the greater the likelihood that local parents and pupils express a preference to attend it (EPI, 2017). Second, there is no evidence to date on whether there is an impact on student intake from who opens a free school. This is despite evidence that the profile of those who open free schools is changing over time (Higham, 2017).
Drawing on admissions data from the 325 free schools opened in the first five annual waves between 2011/12 and 2015/16, this paper develops the following analysis. First, to investigate whether free schools are socially selective, we analyse which students attend free schools and whether they are representative of the neighbourhoods from which free schools recruit, in terms of socio-economic status, ethnicity and prior attainment. Where possible we employ a methodological approach similar to Green et al.'s (2015) to enable comparison. Second, to consider the influence of the non-state actors who have opened free schools, we analyse whether the profile of those who open a particular free school is associated with whether that free school is socially selective or not. We refer to the actors opening free schools as 'school providers', reflecting the government's policy on 'liberalizing the supply side' of the school quasi-market. This includes policy aims to roll back local government from school governance and to make who provides state schools 'contestable', which concerns both the opening of new schools by non-state actors and 'creating the possibility that new providers can be brought in to replace those who are not performing adequately in running a service' (IPPR, 2001: 44). Third, to examine the wider intended aims of free school policy on competition, we analyse whether the opening of a free school has a discernible impact on neighbouring schools in terms of the number and composition of the student populations they admit.

Social selection in school quasi-markets
The current policy framework for school quasi-markets in England has origins in the 1988 Education Reform Act (ERA). The ERA introduced open enrolment and per capita funding to place schools more directly into competition with one another. Schools received greater control over finance and an option to opt out of local authority governance. City Technology Colleges (CTCs) enabled businesses to open secondary schools with support from central government. Although only 15 CTCs opened, the ERA (1998: 110) allowed the Secretary of State for Education to 'enter into an agreement with any person' to open a CTC, and this now provides the legal basis for opening free schools (the 2010 Academies Act having modified the wording of the 1998 Act to allow the Secretary of State for Education 'to enter into Academy arrangements with any person', with free schools having the same legal status as academies (Wolfe, 2011), see below). The overall logic of the ERA was that choice and competition would develop incentives for institutional diversity and improvement, and that inequalities would reduce as disadvantaged families gained more choice and unpopular schools faced the threat of closure. Since 1988, successive attempts have been made to achieve these aims. Demand-side reforms have seen the government appoint choice advisors to support low-income families in making school choices (Exley, 2013) as well as ever more school performance data for parents (Ozga, 2009). Supply-side reforms have sought to promote institutional diversity by allowing existing schools to convert to new statuses (e.g. convertor academies) and non-state actors to take over existing schools where they are judged to be 'inadequate' or 'coasting' (e.g. as sponsored academies). Academies are schools that are legally independent of local authorities and sign a funding agreement directly with central government. They are operated by academy trusts, which have the legal basis of companies limited by guarantee with charitable status. In December 2017 there were 2,009 sponsored academies and 4,890 convertor academies in England, compared with just over 20,000 mainstream, maintained state schools.
Despite the dominance of these ideas there is little evidence to support the claim that choice and competition lead to improvement (Whitty, 2008). Rather, there is evidence that segregation can increase. Analysing primary schools in London, for instance, Gibbons et al. (2006: 9) found that segregation increased as competition intensified, both by socio-economic status and 'with high-and low-ability pupils more segregated in schools that face more competition'. Waslander et al. (2010) argue that competition may need to exceed a certain threshold before schools respond to it. When they do, external responses such as marketing, public relations exercises and covert selection are to be expected as schools seek to control the size and composition of their student body. Schools may also try to shape enrolment by making internal changes such as introducing student tracking systems and/or (extra-)curricular options that appeal to particular parents. These responses interact with parental choice, which often includes middle-class strategies to 'escape from class "others"' (Ball, 2013: 16), but also wider class and ethnic solidarities, where for instance poorer parents may also choose schools that reproduce social ties over higher-attaining alternatives (Burgess et al., 2015). One consequence is that schools are commonly organized into local status hierarchies. As school status is closely related to student population composition, this creates incentives for social selection (van Zanten, 2009).
The interaction of choice and competition varies locally, however, and is one of a range of influences on social segregation. Government policies on school accountability (which often dovetail quasi-market reforms) influence social selection (Woods et al., 1998). Residential patterns around schools reflect deeper, historical socio-economic class inequalities (Simon, 1999). Trends in any one indicator of segregation are also influenced by national changes in the student population measured by that indicator -where this alters student distribution across schools. Gorard et al. (2013) argue, for example, that since eligibility for free school meals (FSMs) is influenced by economic up-and downturns, when the economy worsens FSM segregation is likely to decrease as more families will be officially living in poverty and this may well spread FSM eligibility across more schools. Gorard et al. (2013) argue that these population changes have a significant influence on national measures of socio-economic segregation.
A consistent school-level finding, however, is that specific forms of institutional diversity are associated with social selection. Allen (2007) reports that in most parts of England secondary schools are more segregated than their neighbourhoods, but that this is most pronounced where more students attend grammar, voluntary aided or foundation schools. Grammar schools select students by attainment, voluntary aided schools by (mainly Catholic) faith and foundation schools act as their own admission authorities. Coldron (2015) argues that schools that act as admission authorities are more likely to use complex admission criteria, uneven banding and/or be reluctant to accept hard to place children. New regulations in 1998 sought to reduce these practices by requiring schools to comply with an admissions code, which to some extent reduced social stratification across schools (Allen et al., 2012). The code was, however, weakened from 2010, alongside a rapid increase in the number of schools that are academies, which also act as their own admission authorities (Coldron, 2015). While the early (pre-2006) sponsored academies often replaced disadvantaged schools, the majority of (post-2010) academies are convertor academies that admit on average markedly fewer students eligible for FSMs than the national average. For Gorard et al. (2013: 193), this confirms that state-funded school diversity 'is almost inevitably a cause of further segregation'.
A key question is whether free schools will conform to these trends. Waslander et al. (2010) argue for a distinction between new 'start-ups', such as free schools, and existing schools that change status in response to diversity reforms. Neoclassical economic theory, Waslander et al. suggest, assumes that start-ups will help quasi-markets work more equitably by allowing entry for non-state actors committed to equity goals and/ or by stimulating choice and competition, particularly where start-ups are allowed to create or add to an over-supply of places. Evidence from two countries where start-ups opened during the 1990s does not, however, provide support for these assumptions.
In Sweden, Wiborg (2010) argues, 'free schools' increased socio-economic and racial segregation, including by being overrepresented in urban, affluent and gentrifying localities. In America, different states have different policies. Logan and Burdick-Will (2015) report that charter schools have increased racial segregation in Philadelphia and Texas but may have reduced it in Chicago. Lubienski et al. (2009) report that in Detroit, Washington, DC and New Orleans, even when the stated mission was to serve poorer students, both for-profit and (over time) not-for-profit charter schools tended to adopt locations on the outer edges of poorer areas, to try to attract more aspirational parents. Waslander et al. (2010: 57) conclude that, while there is limited evidence across the Organization for Economic Co-operation and Development (OECD), in practice startups often choose locations strategically to be 'close to "desirable" pupil populations'. However, policy rules and regulations, they argue, could be used to 'provide incentives to tone down or even reverse these preferences'.
In England, there are no decisive rules on location. Free schools can open in response to 'parental demand' rather than demographic need for places alone, and so can in principle create or contribute to an over-supply of places. In practice it is unclear what proportion of free schools have opened in areas of need or over-supply. After being found to have used funds ring-fenced for urgently needed new places to build free schools in areas without need, the government committed to publish the proportion of free schools opening in or adjacent to areas of forecasted need. Across the first five waves, the DfE (2014) projected this would exceed 75 per cent. As the NAHT (2016: 1) argued, however, the creation of a free school satisfying this measure is 'not the same as a coordinated and measured approach … to create school places exactly where they are needed'.
There is a specific application process, run and determined by central government alone, through which free schools have to be opened. Anyone can apply, although free schools cannot be run directly for profit, to preach hatred or teach creationism as science. To apply, proposers have to set out an educational vision, curriculum and staffing plans, provide evidence of parental demand and detail their capability to establish and govern a school. Once open, free schools are legally the same as academies and so independent of local government. Free schools receive initial startup funds, but then the same recurrent funding as other state-funded schools. They are held accountable by central government against the same inspection framework and performance indicators as other schools. There is no single official definition or explanation of the word 'free' in 'free school'. In part this word is borrowed from Swedish free schools (Friskolar) policy, although there are significant differences between the Swedish and English policies (Wiborg, 2015). In English policy texts, 'free' is associate with the fact that free schools 'aren't run by the local council. They have more control over how they do things' (DfE, 2017: 1).
In this context, this article addresses three research questions. First, are students attending the first five waves of free schools representative of their local neighbourhoods? Second, is who provides a free school associated with whether free schools are socially selective or not? Third, does the opening of a free school have a discernible impact on neighbouring schools, in terms of their number or composition of students?

Method to analyse free schools
To develop this analysis we take data from the National Pupil Database (NPD) for England, a termly census of all pupils in state-funded schools containing basic demographic and attainment information. We analyse the standard age 4 (Year R -reception year) and age 11 (Year 7) intakes into primary and secondary schools, respectively, for the years 2011/12, 2012/13, 2013/14, 2014/15 and 2015/16. This allows us to study the intake patterns for the cohorts of pupils attending the free schools that opened in September 2011September , 2012September , 2013September , 2014September and 2015 Our analysis also uses data from the School Capacity Survey (SCAP), a statutory annual survey through which the Department for Education collects data from local authorities on the number of places in and the number of pupils admitted into all state-funded schools. We look, again, at the standard admission years (Years R and 7) in 2012, 2013, 2014 and 2015. This allows us to study the number of students admitted by free schools in 2011, 2012, 2013 and 2014 and compare this to each school's published maximum Pupil Admission Number. The 2016 SCAP data had not been released at the time of this analysis, which means we could not conduct this analysis for Wave 5 free schools.
To develop this analysis in relation to our first research question, we calculate three indicators of demographic profile for every school and neighbourhood in England, following Green et al. (2015). The first indicator is the percentage of students eligible for FSM, which we use as a proxy for socio-economic disadvantage. While we acknowledge the weakness of this proxy in some respects (see Hobbs and Vignoles, 2010), and recognize that socio-economic disadvantage is influenced by the intersection of a range of factors, including 'income, parents' education, social class, marginalisation and negative segregation' (Cederberg et al., 2009: 12), recent government analysis shows that FSM eligibility at least is strongly associated with students who make poor progress at school (Allen, 2017). The second indicator is the percentage of students of white British ethnic background, which we use as a proxy for ethnic diversity. The third indicator is prior attainment. For primary schools, we use the mean score on the Foundation Stage Profile (FSP) of the Year R intake. For secondary schools, we use the mean Key Stage 2 (KS2) scores of the Year 7 intake. In both cases we standardize the scores for each cohort to give a mean of zero and standard deviation of one.
In order to measure the demographic profile of the neighbourhoods in which free schools have been set up, we must also define neighbourhoods around schools. We again follow Green et al. (2015) by assigning a lower layer super output area (LSOA; a geographical area with an average population of 1,500 people, defined at the national level by the Office for National Statistics) to a free school's recruitment neighbourhood if one child who lives there currently or previously attended the free school. As Allen and Burgess (2013) have shown, using this approach allows the recruitment neighbourhood of a school to comprise irregular and even noncontiguous spaces, if that is how historically recruitment has taken place. Using one student admitted to a free school from a LSOA is a low threshold, so we performed a sensitivity analysis in Table 3 (below) by raising the threshold to two pupils. We found that this did not change the analytical inference. Specifically, on FSM eligibility there was never more than a two-percentage-point change in the neighbourhood profile, and all cohort-years (of which there are 30 in the table across secondary and primary schools) continue to show that the neighbourhood FSM eligibility is higher than the free school's. On prior attainment, there was never more than a 0.04 s.d. change in the neighbourhood profile. There was also little change in the frequency with which free schools are reported to have higher-attaining intakes: 25 out of 30 using two students per LSOA, versus 27 out of 30 using one per LSOA.
To analyse who provides free schools, our second research question, we develop a categorization of the individuals and organizations that govern all 325 free schools in Waves 1 to 5. To determine which category a free school is assigned to, we use data on who originally proposed the school and on who serve as members and directors of the resulting free school trust (who have the right to appoint the majority of governors) -most commonly the original proposers and current trust members are one and the same, though in a small number of cases free schools have been closed by government, due to financial irregularities or an 'inadequate' Ofsted inspection, and then often reopened by a new provider. Our analysis uses data on who was providing the schools in December 2016, generated from a review of each provider's online presence, local media and documents published by the DfE, the local authority and the New Schools Network, a charity that aims (with government support) to help proposers develop applications. This analysis triangulated a minimum of three documentary sources for each school. This follows the approach employed by Higham (2014a) to analyse the providers of free schools opened in the first three waves (see Higham (2014a) for a detailed discussion of the characteristics of each resulting free school provider category).
Since the opening of free schools is not random, we face difficulties in measuring their impact on neighbouring schools, our third research question. Our estimation approach involves drawing data from as far back as 2008/09, i.e. before the launch of the free schools programme, to measure both levels and historical changes in school intakes at all schools across the country. We then use the more recent data, up to 2015/16, to measure how much intakes at schools neighbouring free schools change after they open, compared to all other changes in intakes across the country. This is known as a difference-in-difference estimation approach, because each neighbouring school's pupil roll and FSM proportion is compared to both their historical figures and changes at schools in areas where free schools did not open. In these school panel data regressions, following Green et al. (2015), a school fixed-effect dummy accounts for starting points in the size and composition of schools, time dummy variables account for national trends in pupil roll sizes and FSM take-up, and we also control for changes in deprivation and pupil population at a more local level. (This is generally at the local authority level, though we group together very small local authorities such as those in London.)

Findings
We set out the findings of the analysis by first outlining several key characteristics of the free schools that opened in Waves 1 to 5. We then examine who attends mainstream free schools, including who has provided them, before considering whether free schools have a discernible impact on neighbouring schools.
In Table 1 we count the number of free schools that opened in the first five waves by provider category. Of the 325 free schools to open, 146 were primary schools, 111 secondary schools and 68 were non-mainstream 'other' free schools. 'Other' free schools include special, alternative provision and 16-19 free schools, which have been opened by state schools and charities in particular. We note that we do not include 'other' free schools in our subsequent analysis, which focuses on mainstream schools.  Notes: (i) The figures include all free schools as well as those that have since closed. In the 'other' category we include special schools, alternative provision and 16-19 free schools. Throughout this article we do not treat studio schools or university technical colleges as free schools.
(ii) 'FE/HE' indicates providers operating further education or higher education institutions. 'Sponsored' free schools are the result of a parent or community group asking a separate organization to propose -or sponsor -a free school on their behalf. The governance of the free school is usually controlled by the sponsor, but is sometimes shared with the local group.
To date, sponsored free schools have most commonly been opened by educational services organizations (Higham, 2014a).
(iii) We differentiate between academy chains, which are groups of schools controlled by private not-for-profit companies, including philanthropists and educational consultancies, which hold similarities to charitable management organizations in the USA (Glatter, 2017), and state schools, which typically involve a single existing school opening a free school in the same or different phase, or an existing consortium of schools working to open a free school collectively. In practice, both academy chains and state schools use the legal vehicle of a multi-academy trust to open free schools. We have chosen to retain this differentiation following Higham (2014a), however, as it recognizes an empirical difference in who governs free schools.
There have been changes in the balance of provider categories over the first five waves of free schools. In the first wave of opening, the majority of providers could be classified as belonging to 'civil society' (i.e. parent, teacher, faith or charity groups). By the last wave we analyse (2015 openings) that the majority of providers were existing educational institutions (i.e. state schools, academy chains, independent schools and FE/HE institutions -see Higham (2014a) for a discussion of the reasons for and implications of these changes.) Overall, to date, free schools have been opened most frequently by existing state schools, faith groups, parents and academy chains. Over a fifth of mainstream free schools have chosen to have a religious designation. Figure 1 shows that free schools are not more religious than existing state schools, but the type of religious designation is materially different. Existing state schools are overwhelmingly Anglican or Roman Catholic, reflecting the historical role of the Church of England and the Catholic Church in opening and maintaining schools (Lawson and Silver, 1973). By contrast, a majority of free schools are being set up to serve other Christian and other religious communities, including the Jewish, Muslim and Hindu faiths. We note that the Conservative government announced plans in 2016 to end the restriction whereby faith free schools can designate a maximum of 50 per cent of places for students who fulfil faith requirements. This may influence the balance of faith free schools in the future, including as the Roman Catholic Church has been unwilling to open new schools under the 50 per cent restriction, as it expects Catholic schools to give first priority to Catholic applicants (Catholic Diocese of Southwark, 2015).

Figure 1: Religious denomination of free schools
In terms of the size of student intake in free schools, Figures 2 and 3 show the pupil roll for each of the five waves of free schools in secondary and primary schools respectively. In both cases, across the first five waves, the size of the programme peaked at Wave 3 (the 2013/14 cohort). For each wave of openings, the pupil roll was somewhat smaller in its first year than it was in subsequent years. This is particularly the case for secondary school openings.  We can also compare the size of the pupil roll in Year 7 (the admission year for secondary schools) and Year R (the reception admission year for primary schools) to each school's published admission number. This allows us to observe how successful free schools are in filling their places each year after opening. We note that this data was not available for the 2015/16 wave at the time of the analysis. Figure 4 reveals that secondary free schools in the 2012, 2013 and 2014 cohorts typically filled less than three-quarters of their spaces in their first years of opening. Figure 5 shows that primary free schools were more likely to be full or nearly full on opening, except for the 2014 cohort of free schools. Across both phases, the first wave of 24 free schools that opened in 2011 was notably more successful in attracting students than each subsequent wave.  We also found that the category of the free school provider was associated with whether free schools were successfully filling their intake places (available from authors). Free schools set up by teachers, state schools and independent schools generally have full cohorts by the second year after opening. By contrast, about half of those opened by academy chains, charities or faith groups still fail to fill half of their places in their second intake cohort.
We now analyse the student intake of free schools. We compare the social, ethnic and attainment profile of free schools to their neighbourhoods and to England as a whole. As discussed in the method section, we define a neighbourhood as all LSOAs where at least one child attends a free school in that year. The reach of free schools across England is now considerable: 15 per cent of LSOAs now have at least one Year 7 pupil going to a secondary free school, and the equivalent figure for Year R in primary free schools is 11 per cent. We can observe no evidence that as a free school matures, the number of recruitment neighbourhoods falls. We can observe, however, a clear phase difference in whether free schools recruit from a wider area than the national average for state schools. As Table 2 sets out, we do this by distinguishing between free schools opened in more rural areas, towns and cities, so as to account for population density. For the Year 7 intake into secondary schools, we find no evidence that free schools are recruiting from a wider area in comparison to the national average. For the Year R intake into primary schools, however, we find that free schools are recruiting from a wider than average area.   Note: all statistics calculated using pupil data and so weighted for school size.

Rebecca Allen and Rob Higham
London Review of Education 16 (2) 2018 In terms of student composition, Table 3 shows free schools' intake and free schools' recruitment neighbourhood statistics for FSM eligibility, the proportion of white British students and the mean prior attainment at intake. Both primary and secondary free schools have opened in areas of higher than average ethnic diversity, with a substantially lower proportion than the national average of students who are white British. Across all waves, the percentage of free school pupils who are white British is broadly similar to the recruitment neighbourhood.
In terms of prior attainment, we find that both primary and secondary free schools are located in areas with a lower attainment profile than the national average. However, the foundation stage profile recorded at Year R in primary schools shows that primary free schools have had higher-attaining intakes than their recruitment neighbourhoods in all five waves of openings. The first wave of secondary free schools also had intakes that were attaining higher than their recruitment neighbourhoods, but this has not been true for subsequent waves of secondary free schools.
The proportion of FSM-eligible students at free schools is further illustrated in Figures 6 (secondary school) and 7 (primary school). The patterns need to be interpreted against the background of falling FSM eligibility nationally (light grey line), as the economy began to recover after the 2008 financial crash, but also in relation to changes in benefit rules under public sector austerity. Overall, free schools have had a lower proportion of FSM eligibility than their recruitment neighbourhoods in every year of every wave. The one exception is secondary free schools in the third year of Wave 3, where the FSM proportion was the same as their neighbourhoods. Primary free schools in particular are more affluent than their recruitment neighbourhoods and this is especially the case in the first and third waves (2011 and 2013 cohorts). It is also true that secondary free schools are more affluent than their recruitment neighbourhoods, but this difference is more significant for the first wave of free schools (2011 cohort) than it has been for more recent waves. When compared to the wider decline in FSM eligibility both nationally and in their recruitment neighbourhoods, there is no evidence that in the years after opening free schools either decrease or increase their percentage of FSM eligible students.  We also analyse student FSM eligibility by free school provider category. Figures 8  and 9 show how the free school and neighbourhood FSM eligibility proportions compare for each provider category. For primary schools, it is notable that all provider categories have set up free schools that are more affluent than their neighbourhoods, except for those set up by academy chains. For secondary schools, it is again the case that all provider categories have set up free schools that are more affluent than their neighbourhoods, except for charities and academy chains. The differences in FSM eligibility are again smaller for secondary than primary free schools, and it is only those secondary free schools provided by independent schools that have a significantly lower FSM proportions than their neighbourhoods. It is also important to note that the number of schools in some of these categories is very small (see Table 1), so inferences about how provider category is associated with composition of pupil intakes need to be treated carefully. This is particularly the case for secondary schools opened by charities, for which there are only two cases.
We also look at the direct impact of free schools on the size and social profile of their nearest neighbouring schools. We do this in a panel data regression that models changes in the number of pupils and in the FSM proportion for each non-free school from 2008/09 onwards. As described, we use wider area control variables to account for any underlying demographic changes in the area.
The first column of estimates in Table 4 reports how the opening of a primary free school is associated with changes in pupil roll at the nearest school, the next two nearest, fourth to sixth nearest and the seventh to tenth nearest. We distinguish again between free schools opening in cities, towns and more rural areas. In more rural areas, the opening of a primary free school is associated with a fall of 5.4 pupils in the Year R intake at the nearest school. It is also associated with a fall of 3-4 pupils at other neighbouring schools that are not the nearest. We can observe no impact on pupil rolls in towns and cities.  The third column of estimates reports how the opening of a secondary free school is associated with changes in pupil roll in neighbouring schools. In more rural areas, the opening of a secondary free school is associated with a fall of 16 pupils (i.e. half a form class) in the Year 7 roll at the nearest school, with no discernible impact on schools further away. In towns, a free school is also associated with a fall of 16 pupils at the nearest school, with other neighbouring schools losing 2 to 3 students. In cities we do not identify an impact on the closest secondary school. We can observe, however, that other neighbouring schools in the city lose between 4 and 7 pupils after the opening of a secondary free school. Finally, the second and fourth columns of estimates show that the opening of a free school is not associated with a material change in the proportion of students eligible for FSMs in neighbouring schools.

Discussion
In the context of quasi-market supply-side liberalization reforms in England, we have presented new data on 'start-up' schools (Waslander et al., 2009 Our first research question asked whether students attending the first five waves of free schools are representative of their local neighbourhoods. We have shown that free schools have developed recruitment neighbourhoods that are above average in terms of deprivation and have higher than average ethnic diversity. We have also shown, however, that free schools do not admit a representative proportion of students eligible for FSMs. Free schools do have a similar proportion of students who are white British to their recruitment neighbourhood, but their intake is more affluent. These findings are broadly consistent with two earlier studies of the first three waves of free schools. As we have shown, this is because free schools have not become more locally representative as they have admitted additional year groups and because later waves of free schools have continued to be more affluent than their local neighbourhoods. Morris (2015) for instance argued that the first wave of free schools 'underrepresented poorer children' but Waves 2 and 3 provided 'a more mixed picture'. It is true that secondary free schools in Wave 3 were then (in their first year) and have continued to be the most inclusive free schools to date, but this has not been replicated in Waves 4 and 5. We have also shown that there is an important difference between primary and secondary free schools. Primary schools are notably more affluent and have a higher prior attainment profile than their recruitment neighbourhoods. Secondary free schools are also more affluent than their recruitment neighbourhoods, but this is more significant for the first wave of free schools than it has been for more recent waves.
Our second research question asked whether who provides free schools influences whether free schools are socially selective or not. There has been a range of concern about parents in particular setting up their own free schools with, as Boffey (2011: 1) reported, arguments that free schools will be: 'established by 'sharp-elbowed, well-off parents' in affluent areas for middle-class children'. Our analysis shows that parents have indeed set up free schools that are unrepresentative of their recruitment neighbourhoods. However, rather than parents in particular, it is in fact free schools set up by all categories of provider that are socially selective in terms of FSM eligibility, with the exception of academy chains (and two charity providers in the secondary phase). There is again a difference between providers of secondary schools, who tend to have opened schools that are less socially selective, and providers of primary schools whose schools are notably more affluent in terms of FSM eligibility (expect for academy chains).
There are several potential reasons for this recurring phase difference. The aims of secondary free school providers could be different to those operating primary schools, with for instance greater interest in serving disadvantaged communities. However, given the consistency of phase differences across all provider categories (except for charities), it is likely that different or additional factors are at work. Student recruitment for example into secondary free schools may be different to primaries, for which we have some evidence. We have shown secondary free schools are less likely to be full, which means primary schools are more likely to have used oversubscription policies and less able (regardless of willingness) to admit mid-year admissions, including of hard to place students. We have also shown that whereas secondaries free schools do not recruit across a greater number of LSOAs than schools on average, primary free schools do, which means they have attracted parents willing to travel further to schools. Nationally, students eligible for FSMs travel less far to schools than do non-FSM-eligible students, including when distance to the nearest school is controlled for (DCSF, 2008: 111). Both these findings suggest student recruitment has been empirically different in primary and secondary free schools.
In this context, the case of academy chains is intriguing. The majority of free schools opened by academy chains (30/39) are primary schools, but they do not conform to the wider trends by phase. Rather, primary free schools provided by academy chains are representative of their local neighbourhoods in terms of FSM eligibility. Further, half of academy chains still fail to fill half of their places in their second intake cohort. This is despite significant contemporary demand for primary school places and claims by the think-tank Policy Exchange (Porter and Simons, 2015: 40-41) that academy chains are most likely to set up free schools in areas of basic need for new places. Clearly there is a need for further research here, which we discuss below.
Our third research question asked whether the opening of a free school had a discernible impact on neighbouring schools. We have analysed the number of students admitted into neighbouring schools and found an impact on, specifically, the nearest primary schools in rural areas and the nearest secondary schools in rural areas and towns, which were shown to lose half a class of students. There was also a smaller impact on neighbouring (but not the nearest) secondary schools in cities, suggesting the impact is more dispersed in cities, potentially as a result of greater population density. In comparison to Green et al. (2015) -who have found no impact from free schools on student rolls, except with third-wave secondary schools -our findings suggest that the impact may have increased over time, but since we used a refined measure of population density, we have not made a direct comparison.
We have also analysed the student composition of neighbouring schools in terms of FSM eligibility but found no evidence of impact. Our findings are consistent here with Green et al. (2015), showing that the lack of impact on FSM eligibility in neighbouring schools has continued as early waves admitted further years of entry. This finding does not rule out individual free schools having a significant compositional impact on one or more neighbouring school, but there is at present no discernible impact from free schools overall. As Green et al. noted, this lack of compositional impact is an interesting finding to set next to the observation that free schools admit intakes that are more affluent than their neighbourhoods. This may be because, as we have shown, primary free schools recruit over a wider area and/or because a significant proportion of secondary free schools are not full, but further analysis is needed.
It is useful, finally, to consider these findings in relation to three common arguments about why free schools may be socially selective, so as to also highlight areas for further research. The first is school location. Waslander et al. (2009: 57) conclude that 'start-up' schools tend to locate strategically so as to be 'close to 'desirable' pupil populations'. Our analysis suggests that this may not have occurred to the same extent in England, as free schools have developed recruitment neighbourhoods with above-average deprivation and higher than average ethnic diversity. Identifying school sites has also been reported as a common challenge for providers, so there may have been fewer possibilities for strategic choice of location, particularly in London where building density and prices are constraining factors (NAO, 2013). A more detailed analysis of location is needed, however. This might usefully analyse whether (and if so how) school location influences the socio-economic geography of student recruitment. We also need a closer analysis of where free schools have created or extended an oversupply of places and where they have met a need for new places, as this may be an important influence on social selection.
The second thematic area is provider category. Higham (2014b) has critiqued the government application process, arguing that it risks diverting resources to advantaged actors. Our research has shown that all categories of providers are socially selective in terms of FSM eligibility (except for academy chains) and this appears to offer support to Higham's argument that actors who really want (in the words of the government) 'to make a difference in disadvantaged areas' have found it difficult to gain government approval for their application (DfE, 2010: 59). Further research on providers' aims is clearly needed here, however. This might seek to understand the extent to which social selection is intentional or not, or -as we recognized the challenge of undertaking such research -whether providers who have evidently taken local equity and inclusion seriously fare better in recruiting intakes that are locally representative.
The third thematic area is school admissions in the context of parental choice. There has been concern that free schools' admission policies will be socially selective, even where they adhere to the 2012 Admissions Code (Morris, 2014;Stokes, 2014). This adds further weight to the argument that schools should not be allowed to become their own admissions authorities (Coldron, 2015). Further research on local admissions and parental choice is needed, however. This might analyse, for instance, whether specific types of free schools are more or less attractive to particular groups of parents, including in terms of the educational aims of free schools. We also need a closer analysis of parents' socio-economic status and ethnicity -as a limitation of this article is that we have used FSM eligibility and percentage of students that are white British as proxies.

Conclusion
We have shown that free schools that opened in the first five annual waves, between 2011/12 and 2015/16, have been socially selective in terms of students' social economic status. Located in areas of above-average deprivation and substantially above-average ethnic diversity, free schools have admitted a representative proportion of local students who are white British, but their intakes are more affluent than the neighbourhoods from which they recruit. We have shown that this is particularly the case for primary free schools, which also recruit students with above-average prior attainment. There is also no evidence that as free schools admit additional year groups, they become more representative of their neighbourhoods.
We have also developed the first analysis of whether the profile of the provider of a free school impacts on who attends the school. We have shown that it is not only parent-led free schools but also all categories of providers that have opened schools that are more affluent than their neighbourhoods, with the exception of academy chains. This highlights the persistence of social selection. We cannot comment from our data on whether this social selection was intentional or otherwise on the part of free school founders. We can, however, state that, in terms of the intakes of the first five annual waves, free schools in England join a growing list of market-based school diversity reforms that reproduce socio-economic inequalities through social selection.