This is an Accepted Manuscript of an article published by Taylor & Francis in Education Economics on 18 Jan 2021, available online: http://www.tandfonline.com/10.1080/09645292.2021.1874878 .

1         Introduction

This paper studies access to Britain’s private schools over recent decades. The relevance of this issue lies in its potential implications for educational inequality and, hence, social and economic mobility. In Britain, private schools[1] propel a narrow sector of the population through high-quality education towards successful careers in elite positions (Elliot Major and Machin, 2018).

In some countries, private schools have little or no resource advantage over state-run schools – an example is Germany (DESTATIS, 2016). Moreover, in many countries only small or zero effects of private schooling on student academic outcomes are reported (e.g. Elder and Jepsen, 2014, Pianta and Asari, 2018,  for the US; Nghiem et al., 2015 for primary schooling in Australia; Agasisti et al. (2016) for Italy). However, Britain is distinctive: the socio-economic divide between private and state school children is among the highest in the developed world (OECD, 2012, Table B2.3); and its private schools, funded by exceptionally high fees, have a very substantial resource advantage over state schools (Green and Kynaston, 2019). Significant effects on educational attainments at both primary and secondary levels have been found over the past 50 years (e.g. Halsey et al., 1980; Feinstein and Symons, 1999; Dearden et al., 2002; Sullivan and Heath, 2003; Malacova, 2007; Parsons et al., 2017; Henderson et al., 2020), consistent with the evidence of the effects of large resource gaps and peer effects on academic achievement (e.g., Sacerdote, 2011; Lavy et al., 2012; Antecol et al., 2016).

There are considerable labour market advantages associated with Britain’s private schooling (Macmillan et al., 2015; Crawford et al., 2016; Green et al., 2017; Belfield et al., 2018). Recruitment to the upper echelons of power in British business, politics, administration and media continues to be tied to private schools (Reeves et al., 2017; Sutton Trust and Social Mobility Commission, 2019). The labour market premium for private schooling increased for earlier generations growing up in the 1960s to 1980s (Green et al., 2012). Considering the persistent ability of private schools to access high-ranking universities (Jerrim et al., 2016) and that the higher education premium has grown more dispersed (Lindley and McIntosh, 2015; Naylor et al., 2016; Lindley and Machin, 2016), there is little reason to expect a break in the trend. Many private schools have become more internationalist in their orientation, both admitting more international students and channelling more British pupils into pathways towards a global upper echelon of universities; such a global outlook has the potential to open up worldwide job market opportunities with high earnings expectations (e.g. Weenink, 2008; Kenway and Fahey, 2014).

Even though only about 9 per cent of adults have ever been to a private school, the British private school sector is, therefore, a significant pathway through which some families obtain long-term advantages for their children. An appreciation of the, possibly changing, extent to which participation in Britain’s private education is unequal and exclusive to those with higher income and wealth should thus provide a highly relevant contribution to the understanding of educational and economic inequality. While high fees make it self-evident that Britain’s private schools are more accessible by high-income families, we know little about the extent to which participation is income-concentrated, or how that concentration might be changing, or the extent and distribution of bursary provision, or how the role of family income and wealth may affect access.

This paper contributes to the, as yet small literature on private school participation in several ways. First, we document the concentration of private school participation in family income and how it has changed since the 1990s. We find that attendance is highly income-concentrated, but not so much that there are not some in the low-income deciles attending private school. We also find that the concentration ratio is quite stable over time, though there is a modest drop in the last period analysed (2011-2017). Second, we also document that, for many, regional private school fees have become unaffordable out of family income; the change is starker for those on lower incomes. The presence of low-income families at private schools, despite the lack of affordability, point to either bursaries or family wealth. Third, therefore, we also document the distribution of bursaries. We find that the distribution of bursaries is overall progressive, their value linked to financial needs, though with no evidence of substantive change; yet most low-income private school families do not receive bursaries.

The low frequency of bursaries and declining affordability suggest an important role of longer-term financial family resources. In aggregate, the private wealth-income ratio in 21st century Britain is substantially higher than in the 1980s and 1990s despite the losses following the 2008 financial crisis (Atkison, 2018; Piketty and Zucman, 2014). Our fourth contribution, therefore, is to estimate the marginal effects of family income using a pseudo-panel with cells defined by the region of residence and by grouped income deciles. Our models find a substantive, potentially non-linear income effect. It is positive and substantial for those in the top income decile, and insignificant for those below.  Fifth, we estimate the marginal effects of projected housing wealth (a large fraction of total wealth) on private school access among home-owning families. We find a significant positive association of home value with private school access, which is, as the income effect, stronger for families in the top income decile.  

In Section 2 we describe the British system of private schooling and consider potential expectations about trends in the income concentration of participation, the role of family resources in private school choice and the distribution of fee-assistance through bursaries and scholarships. Sections 3 describes our empirical model and the primary data source, the Family Resources Survey. Our findings are presented in Sections 4 and 5. In our conclusion, Section 6, we note the implications of our findings for the schools’ policies on bursaries and for the government’s policies on social mobility.

2         Access to Private Schooling in Britain

2.1        The British private school sector

One in eleven schools in Britain is private. Notwithstanding some heterogeneity, private schools are generally considered elite institutions, reflecting both the social composition of their pupil intake, their resources and the destinations of their alumni (Maxwell and Aggleton, 2015; Reeves et al., 2017). On average, the fee income from families with children in private day schools exceeds the income from the state provided to maintained schools by a factor of around 2.5 or more, depending on education stage; when supplemented by private schools’ endowments of physical and financial wealth, the per-pupil resource gap becomes at least three (Green and Kynaston, 2019). 

With these resources, British private schools can specialise in small class sizes, with a pupil-teacher ratio, at 8.5, less than half that of state-maintained schools in 2016 (ISC, 2019, p. 25), and offer a broader education including more sports and a much wider range of extra-curricular activities. Facilities are typically generous and well-equipped, although there is some heterogeneity across private schools in respect of resources, as well as, for example, in their size, pedagogical approaches, boarding facilities or religious denomination. This private-state resource gap is typically much higher than in many other countries, though data are scarce. In Germany, for example, where schools have a legal obligation to accommodate families regardless of income, there is a financial resource gap of
-5.3 per cent at upper-secondary level (DESTATIS, 2016). In Australia, the resource advantage is 30 per cent for non-sectarian private schools and -5 per cent for private religious schools (ACARA, 2019), though there is considerable fee variation linked to their pupils’ social background (Lye and Hirschberg, 2017). The United States has in recent years become another exception where non-sectarian private schools, though relatively small in number, deploy a teacher-pupil ratio twice that in public schools, while the Catholic private schools have a small resource advantage (Broughman et al., 2019).

Private schools are managed and governed autonomously, though three-quarters of them are registered as charities and must thus comply with charity law; doing so qualifies them for a small amount of public subsidy through tax relief. Though they are not required to follow the National Curriculum, their pupils usually enter the same national exams that state secondary school pupils take, these being the gateway to university and other post-secondary education. Since the start of the 1980s, private schools’ resources have transformed. With the cessation of the Assisted Places Scheme that ran from 1981 till 1997 (Whitty et al., 1998), neither schools nor potential pupils receive direct public subsidies except for small government programmes targeted at vulnerable children in foster care or those qualifying for the UK’s Music & Dance Scheme in specialist schools.

There are notable regional variations in the availability of private schools. In England’s North East, for example, there were 1.2 private schools per 10,000 pupils while in the South East and Greater London the figures were 3.6 and 3.8 private schools, respectively (DfE, 2018). In Wales, there were 1.5 private schools per 10,000 pupils in 2017/2018 (Welsh Government, 2018) and in Scotland, the figure stood at 1.4 private schools per 10,000 pupils (Scottish Government, 2018). Although boarding is an option for the very affluent, region-specific differences in the provision of private education will likely correlate participation.

Since the 1980s, the average participation rate in private education has remained stable at around 7 per cent of all school pupils in England (DfE, 2018). Yet private schools now operate in a different environment from the one they faced in 1980. The external economic and social context has changed substantially through wider access to higher education, rising ‘value’ of education credentials, increased income and wealth inequality, and the emergence of a global elite in a globally connected world. Approximately 5 percent of the pupils in Britain’s private schools have non-British parents living abroad (Ryan and Sibieta, 2011).

2.2        Inequality of access and the determinants of private school choice

Broader economic developments are likely to have affected the extent and distribution of private school participation in contrasting ways since the 1990s: the pull of the (aforementioned) potentially increasing benefits; the increasing costs; changes in the provision of means-tested bursaries; changes in income and wealth inequality and in the relationship between family income and wealth – especially given increases in housing wealth and potential wealth transfers within the extended family.

The costs of private schooling have risen considerably (Ryan and Sibieta, 2011; Parsons et al., 2017). By 2018 the average annual fee before any extras had reached £14,280 for day school and £33,684 for boarding school: in real terms about 60 per cent above the figures for 2000, and three times the 1980 fees. Meanwhile, while income inequality has fallen a little since its peak in 2001[2], the rising wealth-income ratio may have enabled some lower-income families to gain better access to private school than before. Fee reductions for some students are also potentially important. Across a range of countries, access to means-tested student aid has influenced the distribution of college enrolment depending on the degree to which credit constraints bind (Nielsen et al., 2010; Fack and Grenet, 2015). In Britain, the Assisted Places Scheme (Whitty et al., 1998) – through which the state had funded, at its height in 1998, 8.5 per cent of places at private schools – was ended in 1997 and fully phased out by 2004. Spurred by the requirements of the Charities Act 2006, provision of means-tested bursaries expanded. The Independent Schools Council (ISC), the umbrella association of UK private school groups covering about 80 per cent of private school pupils, reported in 2019 that around 28 per cent of pupils received some financial assistance from the schools, up from 19 per cent in 1998. Fee discounts, typically small reductions for siblings or for teachers’ children, were the most common form of financial support (13.2 per cent of students), followed by scholarships (10.8 per cent) and means-tested bursaries (7.8 per cent) (ISC, 2019).  Only one per cent of pupils attend for free. Schools provide discounts for a range of reasons, including to influence the school’s academic standing and associated peer effects, price discrimination to increase revenue, and a measure of corporate social responsibility (Wilde et al., 2016). While scholarships are allocated based on academic or cultural/sporting abilities, the award of means-tested bursaries often also entails academic or other ability selection. In total, the bursaries amount to about four per cent of private school turnover. 

With these developments pulling in different directions, it is not possible to state whether access to private school would have widened or narrowed over time. Either way, the developments also point to the need for a good understanding of the effects of income and wealth on private school choice. Two earlier studies of private school choice in Britain have found that current income enters non-linearly; that other socio-economic background indicators are also important; and that demand is sensitive to price with an estimated elasticity of -0.26 for private school choice at age 7 (Blundell et al., 2010; Dearden et al., 2011). Complementing these, sociological research has found a mix of motivations and some ambivalence among parents choosing private schooling; emphasising roles both for traditional attitudes and allegiances and for an instrumental approach to choosing private schooling as a way to gain access to high-ranking universities and rewarding careers (Fox, 1985; Ball, 1997; West et al., 1998; Foskett and Hemsley-Brown, 2003). The socially exclusive peer group is seen as a positive attraction for some families and a negative factor for others. Anders et al (2020) demonstrate the importance of family values, while also showing the influence of location and of permanent income.

Educational choices are likely to be taken for a long horizon, given the costs of switching between sectors. In Britain, school sector choices generally happen at key ages: seven, eleven (sometimes 13) and 16. Given the magnitude of the investments, the choice of school sector will be affected by long-term financial family resources (Chevalier et al., 2013; Carneiro and Ginja, 2016). Wealth gains may influence school choice either through life-cycle wealth effects or by relaxing credit constraints through additional collateral (Cooper, 2013). In general, there is a positive association of household net worth with total educational achievement in Britain (McKnight and Karagiannaki, 2013).  About two-thirds of total private wealth (except pensions) is held in property (ONS, 2018). Home value gains may thus have the potential to influence household decisions, including around educational choice. In general, housing wealth has been found to correlate with consumption, individual health, fertility, and labour supply (Dettling and Kearney, 2014; Fichera and Gathergood, 2016; Burrows, 2018; Disney and Gathergood, 2018). Lovenheim and Reynolds (2013) find that housing wealth gains change students’ chances to access flagship universities in the US. Although with notable regional heterogeneity, residential real estate prices have more than doubled in real terms since 2000 across England (HM Land Registry, 2018b). At the same time, equity withdrawal expanded, particularly over the early 2000s (Reinold, 2011). It, therefore, appears appropriate to consider the role of family wealth either in property or financial assets in addition to income to study private school access.

In light of the above, our empirical description and analysis address these questions: How has the family income concentration of private school attendance been changing in Britain? Who receives bursaries: how large are they and are they progressive in their distribution? What are the effects of family income? What is the correlation of housing wealth with private school access?

3         Data and Variables

3.1        Data

Our primary data comes from the Family Resources Survey (FRS) and the Households Below Average Income (HBAI) programme. The FRS is a continuous series of annual cross-sectional random probability surveys of private households in the UK. Since its launch in 1994, it has collected information on household composition, economic activity, income and broader financial resources from all adults in around 25,000 households up until 2010 and a sample of around 20,000 respondent households per year after that (DWP, 2018a, 2018b). We consider data from survey waves since 1997 for families in Great Britain (excluding Northern Ireland) with dependent children aged 5-15 years (the years of compulsory primary and secondary schooling). We further restrict the sample to families with family heads in the age bracket 25-64 years to avoid confounding from transitions into and out of the labour market.

As part of the household grid, FRS queries survey participants “What type of school or college does [name] attend?” From the responses, we derive private school attendance as a dummy that distinguishes children in private schools (defined as any school where at least some pupils pay fees) from children in state-maintained schools. Because the focus is on mainstream primary and secondary schools, we remove observations on special schools and on those few who have moved on to non-advanced further education.[3] In all, the analytical sample includes information about 154,529 children from 96,915 families.

3.2        Measuring income and home value

FRS is the primary data source for income conditions of British households. FRS includes detailed questions about families’ current income from all sources.  As part of the HBAI programme, the Department for Work and Pensions (DWP) re-weights and imputes very high incomes to compensate for under-representation and under-reporting in the raw data at the top of the income distributions. Although not without issues, the procedure goes some way towards reconciling the survey data with data from income tax records (Burkhauser et al., 2018a, 2018b). All monetary variables are in 2017/18 prices. Under the assumption that all family members benefit equally from total disposable income, we equivalise total net income by dividing it by the square root of family size, i.e. the combined number of adults and dependent children in the family.

In addition to current family income, FRS asks a set of questions about households’ housing tenure, the number of bedrooms in the accommodation, the type of accommodation (detached, semi-detached, terraced, flat, others), the council tax band for owner-occupiers, and, for mortgaged home-owners (86% of all owner-occupiers in the survey), the purchase price and purchase year. Early waves of FRS up until 1995/96 included a question for mortgaged home-owner to estimate the price their property would fetch if they were to sell. Data quality concern let to the removal of the survey question from wave 1997/98 onward. Thus, to examine the role of housing wealth for private school access, we impute a plausible current home value for all owner-occupier families from the information in the survey. We estimate a hedonic Poisson regression model of the initial purchase price on the number of bedrooms, type of accommodation, council tax band, and purchase year in the sample of mortgagors separately for each government region over the survey waves 1997/98-2017/18. The estimated coefficients are used to predict the current property value for each owner-occupier household in FRS from 1997 onward.  Averaged by survey year, government region, and property type, there is a very strong correlation (r=0.98) of the projected home value with average property prices published by the HM Land Registry (HM Land Registry, 2018a). For the subsequent analysis, we deflate the projected home value to 2017/18 prices.

Furthermore, FRS also includes information on financial awards (scholarship, bursary, grant or similar award) for education for children in secondary education or above. From this information, we construct an indicator variable whether a child in lower secondary education receives any bursary/ scholarship and if so, the total annual value deflated to 2017/18 prices.

Besides these variables, we also use information about the region of residence, the number of adults in the family, the age of the family head, housing tenure, the socio-economic class of the parents, and the parents’ age when leaving full-time education.

4          Empirical Model

To test the relationship of financial family resources with private school access, we draw on a set of common assumptions which imply a structural relationship between both (e.g. Becker and Tomes, 1994; Acemoglu and Pischke, 2001; Solon, 2004). Parents care about their children’s future life chances and decide whether to enrol their children at a private school. The decision is assumed to be non-separable over time, reflecting typical school choices at the beginning of primary and secondary school, respectively. Because credit markets are imperfect, parents cannot borrow against their children’s future human capital returns. Since there is no public loan scheme that could help to secure credit, private school access will depend on families’ private access to financial resources through income and capital markets. For wealthy, high-income families who are not credit constrained in their decision to send their children to private school, additional financial resources may not affect the private education decision; except if private education has characteristics of a consumption good. However, for families who are credit constrained a rise in lifetime income or wealth is predicted to increase the likelihood of investing in private education. In addition, we assume that there is a third group of income-poor parents who face an affordability constraint, namely that lifetime consumption is constrained to be above a certain minimum. For all in this group, the decision is the corner solution of non-participation, even in response to marginal increases in income or wealth. Additional wealth can raise private school access by relaxing credit constraints through a collateral effect or by easing the lifetime budget constraints.

Our econometric model builds on these assumptions:

(1)

Demand for private school education for children of family i, , is a function of the natural log of permanent family resources,  (income or home value), a set of control variables with an influence on financial family resources and private school access, region-by-year effects, , and a family-specific taste shifter for private education, , which can include expected returns from private school education. The region-by-year effects control for common factors that influence all families within regions and years. The effect of financial family resources on private school access is given by . The term  is unobserved and possibly correlated with financial family resources  and school choice. Thus, a cross-sectional analysis will potentially lead to biased estimates.

Moreover, while private school choice will depend on longer-term resources such as permanent income, survey data measures current income. The gap between measured current and family permanent income can be either transitory shocks to family income or measurement error. If ignored, this gap will attenuate the estimated income effect.

To solve both issues, we construct cohorts that we track through repeated cross-sections to estimate a fixed-effects model (Deaton, 1985). By aggregating the family decision to the cohort level, we derive the following model:

(2)

where is the proportion of privately educated children for all  children in family cohort  at time . Similarly,   are the average permanent family resources of cohort  at time , respectively. Because region and period effects are assumed to be the same for all cohorts who live in region  at time ,  remains unchanged.

Since the families who form the cohorts in the sample will differ for each year,  is time-variant. Following the literature around pseudo-panels, we can treat  as an unknown fixed parameter with  if sample sizes for each cohort are sufficiently large (e.g. Deaton 1985; Verbeek 2008). Similarly, with sufficiently large numbers of observations within cohorts, the measurement error in family resources approaches zero if there is no time-variant cohort component to measurement errors (Antman and McKenzie, 2007). For income,  is, therefore, closer to the concept of permanent income,  will pick up common trends that affect all families within a region.

Families are grouped into mutually exclusive cohorts, c, based on family income decile and region of residence. In pseudo-panel analyses, there is a trade-off between cohort size and the number of observations in the panel. We distinguish between families with incomes in the tenth decile, in the seventh to the ninth decile,  in the fourth to the sixth decile, and families with incomes at or below the third decile across eight British regions (North East and Yorkshire, North-West, the Midlands, East of England, Greater London, South East, South West, and the combined devolved nations of Scotland and Wales). Income deciles were derived in the sample of all non-pensioner households in Great Britain separately for each survey wave. The derived 32 cohorts are tracked over the 21 cross-sections of FRS 1997-2017. Table A1 in the online appendix gives mean cohort sizes. 

We arrive at the following baseline estimation model:

(3)

The model identifies family resource effects, for income and for home value, on school access through variations in  conditional on income rank, region and region-period effects. The family income effect, , is identified from differential income growth over the income distribution within regions. Likewise, the home value effect  is identified from the differential growth of home values across family income ranks within regions.  As in Acemoglu and Pischke (2001), families’ rank in the income distribution is thought to control for their unobservable characteristics. Because private school fees are high and credit markets are imperfect, we will also test if  or differ across grouped income deciles.

Like with any other method, there are some caveats. First, pseudo panels can be sensitive to the definition of the constituting cohorts. Thus, we also look at cohorts-based on region and socio-economic class instead of income rank. Second, the within estimator can be imprecise without enough time variation in the dependent and independent variables. Although there is within variation in cell-average income, home values, and private school participation, it is conceivable that with finite samples, some cohorts contribute little information to the parameter estimates. To assess the importance of unobserved heterogeneity and sources of variation,  we also estimate more restrictive models with   and pooled period effects Third, while the within estimator conditions out time-invariant unobserved characteristics, estimates will be biased in the presence of omitted time-variant variables that affect family resources and private school demand. For example, the analysis of home values on private school participation is limited to the self-selected group of homeowners. If the percentage of home-owning families with children remained the same within cohorts, the fixed effects would condition out the unknown selection mechanism. However, homeownership has started to slip after 2007 from 68 per cent to 58 per cent, which suggests possible changes in group selection as well.  Ideally, we would instrument for self-selection. In the absence of a convincingly exogenous time-varying instrument, the set of time-variant control variables,   , can help to assess the magnitude and direction of the bias. But even if the parameter estimate for    is biased upward, it can still document how changing access to permanent private financial resources may facilitate private school access.

5         Documenting the Income Concentration of Private School Participation and Bursary Provision.

The main aim of this section is to document, for the first time, the extent to which private school participation is family income concentrated, and whether this concentration is changing. In addition, we describe the extent of bursary provision and its correlates; if large enough and income-progressive, bursaries might be expected to modify the link between family resources and private school participation.

5.1        Income Concentration

Figure 1 plots participation in private schooling after 1997 against the percentile rank of net equivalised weekly family income for families with children in the 5-15 age range. It shows the extent to which participation is especially skewed at the very top of the income distribution. At the 100th percentile, half of the children go to private school. At the 95th percentile, however, this proportion is much lower, with only 15 per cent of children in the private sector. While still much greater than the average, it is striking that only a minority of the affluent families in the top 5 per cent are paying for private education.[4]

Figure 1 also shows that there is a non-zero – albeit very low – private-school participation among low- or middle-income families, for whom full fees would be difficult or impossible to cover out of current income alone.

A key question for policy discourse is whether access to private school has been widening. Table 1 summarises the income concentration of children in the private sector over the periods 1997-2003, 2004-2010 and 2011-2017. The top panel reports the participation rate in private education across the income distribution. Consistent with Figure 1, around a quarter of five children in the top-income decile went to a private school. This proportion and the overall participation rates have remained very stable since 1997. Only the bottom third of the income distribution increased their participation slightly from 1.2 per cent to 2.1 per cent over the study period. Despite this improvement, children from top-decile families remained around twelve times more likely to access private education than those with family incomes below the 4th decile in 2017.

Figure 1: Income concentration of private school participation, 1997-2017

Note: Participation of 5-15-year-olds in private schools in Great Britain by equivalised net family income percentile rank across all non-pensioner households. Equivalised using the square root of family size. The chart is restricted to families with income at or above the 5th percentile.

Target: Families with 5-15-year-old children in Great Britain. Source: HBAI, 2018. FRS 1997/98-2017/18.

The bottom panel gives the income concentration index of private school attendance. This index encapsulates the inequality of private school uptake over the whole distribution.[5] Index values can range from -1 (all private school concentrated among the poorest) to +1 (all concentrated among the richest). A value of 0 would indicate the absence of income inequalities in private school choice. The trend in the index summarises the descriptive findings in the rest of the table. The estimates confirm the substantial pro-rich income concentration of private school participation. This income concentration remained remarkably stable until the early 2010s then shows a statistically significant drop in the latest period.

Table 1: Private school participation across the net income distribution of families with children at private school and concentration index, 1997-2017

 1997-20171997-20032004-20102011-2017
 Income Rank (decile)
10th0.264
(0.007)
0.268
(0.011)
0.265
(0.011)
0.260
(0.013)
7th – 9th0.055
(0.002)
0.059
(0.003)
0.056
(0.003)
0.051
(0.003)
4th – 6th 0.017
(0.001)
0.018
(0.001)
0.018
(0.001)
0.017
(0.002)
<4th0.015
(0.001)
0.012
(0.001)
0.014
(0.001)
0.021
(0.002)
 Concentration Index
 0.528
(0.007)
0.560
(0.011)
0.542
(0.012)
0.486
(0.013)

Weighted concentration index of private school attendance for families in Britain with children aged 5-15 years between 1994 and 2017.  The proportion of children in private schools by net equivalised family income rank across all non-pensioner households in Great Britain. Standard errors in parentheses.

Table 2: Family financial resources and the relative costs of private education relative, 1997-2017

  Income RankTotal
<4th4th – 6th7th – 9th10th
Equivalised Weekly Net Income (in £)1997142
(0.8)
260
(0.9)
419
(2.0)
1007
(42.7)
293
(3.7)
2017194
(1.9)
321
(1.2)
515
(3.3)
1279
(93.5)
405
(10.6)
Growth rate (%)1.83
(0.1)  
1.19
(0.0)  
1.14
(0.0)  
1.35
(0.5)  
1.92
(0.2)
Projected home value (in £1,000)199794.9
(2.2)
102.9
(1.7)
142.4
(2.4)
244.1
(9.7)
124.3
(1.5)
2017242.4
(9.4)
250.4
(7.2)
338.7
(8.4)
582.1
(28.9)
321.6
(6.4)
Growth rate (%)2.55
(0.1)
7.17
(0.4)
6.89
(0.4)
6.92
(0.8)
7.94
(0.3)
The ratio of annual average regional day school fees to mean equivalised net family income (in %)199796.3
(0.60)
53.2
(0.23)
33.4
(0.19)
14.2
(0.60)
47.3
(0.59)
2017130.0
(1.74)
79.4
(0.48)
50.5
(0.42)
21.3
(1.58)
63.4
(1.66)
Δ33.6
(1.84)
26.3
(0.53)
17.1
(0.46)
7.1
(1.69)
16.1
(1.76)
The ratio of annual average regional day school fees to mean projected home value wealth (in %)19977.5
(0.17)
7.0
(0.11)
5.1
(0.08)
3.0
(0.11)
5.8
(0.07)
20175.3
(0.18)
5.2
(0.13)
4.0
(0.09)
2.4
(0.11)
4.1
(0.07)
Δ-2.2
(0.25)
-1.8
(0.17)
-1.1
(0.12)
-0.6
(0.16)
-1.7
(0.10)

Mean equivalised weekly net family income in 2017/2018 prices. Mean projected home value based on the accommodation type, the number of bedrooms, and region and survey year. Home values for owner-occupiers. Regional average day school fees from annual ICS census 1997/2017.  Standard errors in parentheses.

The comparative stability in both the rate and the distribution of private school participation contrasts with trends in the ‘affordability’ of private education out of family income. The first panel of Table 2 shows the rises of incomes between 1997 and 2017, while the second panel shows the rises in home value, at each income decile. Overall, the growth rate was about two per cent per year. Within income groups, family income rose fastest at the bottom and the top of the income distribution. Home value increased substantially more than family incomes. Average home value expanded 2.6-fold from £124,300 in 1997 to £321,600 in 2017, an increase of almost eight per cent per year. Top-income families saw the largest absolute rise in projected home value, but the relative gains were fairly even across the top two-thirds of the family income distribution. The smaller figure for lower-income families could indicate some degree of spatial segregation. Nonetheless, the average home value among low-income owner-occupiers in 2017 approached figure for top-income families two decades earlier. Given this strong growth, housing wealth gains may have contributed to family resources for private education among homeowners.

The third panel then shows the substantively declining affordability of school fees relative to net family income: from 14 per cent to 21 per cent at the top decile, and from 96 per cent to 130 per cent for those in the bottom third. Indeed, by 2017, only those in the top decile could send children to private school without spending more than half their income per equivalised family member. The last panel shows, however, that affordability in relation to home value, for owner-occupiers, improved significantly.

If housing wealth were associated with private school access, we would expect lower-income families with privately educated children to own relatively more valuable property. Table 3 breaks down the ratio of projected home value over annual equivalised net family income by income decile for children in the private sector and in state schools for owner-occupiers. As expected, the figures show a substantially higher housing wealth-to-income ratio for children in the private school sector. The private-state gap is especially large for families at the bottom of the income distribution; which further indicates that families with children at private schools may be able to draw on other resources than income.

Table 3: Ratio of family housing wealth to annual equivalised net income by children’s school type in Britain, 1997-2017

  Income RankTotal
<4th4th – 6th7th – 9th10th
Home value to income ratioState20.1
(0.17)
12.0
(0.06)
10.5
(0.05)
7.2
(0.13)
11.2
(0.06)
Private59.4
(3.56)
24.1
(0.93)
16.6
(0.41)
7.8
(0.26)
10.7
(0.29)
Δ39.3
(3.56)
12.1
(0.93)
6.0
(0.41)
0.6
(0.28)
-0.5
(0.30)

The ratio of mean projected family home value wealth to mean annual equivalised net family income across 96,812 children in owner-occupier families in Britain in FRS, 1997-2017. Robust Standard errors in parentheses

5.2        Bursaries and scholarships

Bursaries or scholarships may have offset some of the fee rises. About 4 per cent of school turnover is spent overall on bursaries, while 1 per cent of pupils receive full bursaries and go free (e.g., ISC, 2018, 2019). We know, however, little about the distribution of financial support among private school families. Using the FRS data, Table 4 shows the proportion of pupils in lower secondary education at private schools who receive bursaries or scholarships and the average value of financial support, split by family income deciles. Throughout the period, around 15 out of every 100 pupils received direct financial support. Significantly, for all those below the top decile, a large majority – four out of five children – receive no grants or bursaries. Evidently, this source of funds does not account for private school participation in this group. The value of financial support was around £4,900 in 2011-2017, little changed from earlier periods, and thus a smaller fraction of the fees.

Table 4: Frequencies and value of bursaries/scholarships by income rank for the periods 1997/2003, 2004/2010 and 2011/2017

 Income rank1997-20032004-20102011-2017Δ
% in private secondary schools in receipt of grants/ bursaries10th 9.4
(1.6)
13.2
(1.9)
10.0
(2.0)
0.6
(2.8)
7th – 9th13.2 (1.9)14.8 (2.1)18.3 (2.7)5.1 (3.3)
≤6th22.9
(2.5)
17.0
(2.5)
20.1
(2.7)
-2.8
(3.7)
Total14.8
(1.1)
14.8
(1.2)
15.3
(1.5)
0.5
(1.9)
The average annual value of grants/ bursaries per supported student (in £ at 2017/2018 prices)10th 4,091
(822.1)
3,822
(572.5)
2,992
(587.0)
-1099
(1010.1)
7th – 9th4,512
(593.2)
4,479
(623.7)
5,095
(724.5)
584
(936.3)
≤6th5,470
(595.7)
5,887
(815.0)
6,240
(928.2)
770
(1102.9)
Total4,863
(378.6)
4,687
(397.1)
4,935
(489.6)
71
(618.9)

Note: Base population comprises students aged 11-15 years; standard errors in parentheses.

Both the allocation and the value of bursaries are, as expected, progressive with respect to parents’ incomes. Nonetheless, even at the 10th decile, around ten per cent of students received financial aid. It is conceivable that these are scholarships, that eligibility is not only tested against income, or that schools are not fully informed about parent’s financial circumstances. Relatively large standard errors make it difficult to draw confident conclusions about the changing degree of progressiveness. Nevertheless, there is a suggestion of a decline in the allocation of bursaries to low-income families in the middle period, which follows the cessation of the Assisted Places Scheme, and recovery thereafter. 

To analyse who received bursaries or grants we ran separate multivariate analyses (see Table A2 in the online appendix). These show that economic needs matter more for the amount awarded than for the likelihood of receiving an award. Higher levels of material deprivation and a family head who is out of work are individually and jointly associated with the annual value of bursaries. Consistent with the descriptive patterns, these associations have not changed significantly over time. Overall, the data could not support claims that the private school sector has widened access for students from low-income families through more generous financial support.

6         Analysis of Income and Wealth Effects

Given that the affordability of fees out of income is in question for all but the top- income decile, and that bursaries distribution and values are far too small a scale to explain much of the participation, we now turn to analyse the effects of cell-wide average family resources in the pseudo-panel described above. 

6.1        Family income effects

First, we consider family income effects in the whole sample; Table 5 reports our main findings. In column (1), we condition only on a set of period dummies. The coefficient of the family income effect is 0.122.  However, this estimate does not account for family background effects related to income rank and regional differences. In column (2), we thus add panel fixed effects (income rank-period dummies). The estimated income effect drops slightly to 0.118, which indicates that private access may be more about the money rather than relative income rank. 

Column (3) give the headline estimate based on equation (3). Despite panel fixed effects and the controls for region-period effects, the coefficient of log mean family income is substantial at 0.116. In other words, a 10 per cent increase in family income is associated with 1.16 point rise of private school participation. Out of the 24-point participation gap between children from the top decile and the bottom third of the income distribution, income can roughly explain 22 points (0.116×LN(1,279/194)).

Our conceptual framework suggests that income effects may be heterogeneous across the income distribution. Therefore, column (4) estimates income effects for each income bracket. According to the estimates, marginal income effects on private school participation are largest for the most affluent families in the 10th top decile, where the estimate is 0.118. For families below the top income decile, increases in cell-average income might not raise private school access. The coefficients are near zero and statistically insignificant, albeit with large standard errors. Although an F-test of equal income effects across income-deciles does not reject the null hypothesis (F(3,31)=1.88, p=0.153), there is overall no evidence of a very affluent group that are unaffected by income – a finding similar to that of Acemoglu and Pischke (2001) in respect to college attendance in the US. Adding a set of time-variant control variables to the estimation model in columns 5 and 6 increases the estimated effect of income slightly and leads to a rejection of a homogenous effect across the income distribution, but does not alter any of the substantive conclusions.

Further robustness tests with a pseudo-panel based on socio-economic class instead of income deciles lead to similar conclusions: Income affects private school access, and the point estimates are larger for families at the top of the socio-economic hierarchy. Table A3 in the appendix summarises the key findings.

Table 5: Income effects on the probability of attending private school from pseudo-panel fixed effects regressions, 1997-2017

 (1)(2)(3)(4)(5)(6)
Ln mean family income0.122***
(0.016)
0.118**
(0.038)
0.116**
(0.033)


0.121***
(0.032)


Ln mean family income #      
(10th income decile)





0.118**
(0.034)


0.123***
(0.033)
(8th – 9th income decile)





0.026
(0.062)


-0.007
(0.070)
(6th – 7th income decile)





-0.006
(0.050)


-0.032
(0.054)
 (≤5th income decile)





0.040
(0.036)


0.034
(0.044)
FENOYESYESYESYESYES
PeriodYESYESYESYESYESYES
Region # PeriodNONOYESYESYESYES
Time-variant controlsNONONONOYESYES
R20.6400.8250.8630.8640.8690.870
F(constant income effect) – p-value   0.153 0.029

Estimates from a pseudo-panel of 672 cells of eight aggregate regions, four grouped income decile of pupils’ family income, and 21 survey years. The dependent variable is the proportion of students aged 5-15 years in private schools within cells derived from the FRS, 1997/1998-2017/2018. The underlying population are all children aged 5-15 years in Great Britain. Columns (5) and (6) control for the with cell proportion of family heads under 35 years, the proportion over 55 years, the share of single parents and the proportion of families where at least one parent left full-time education at the age of 21 or higher. Heteroscedasticity and autocorrelation robust standard errors in parentheses. Clusters at region-income ranks level. * p < 0.05, ** p < 0.01, *** p < 0.001.

6.2        Housing wealth

Given that our descriptive analysis earlier pointed at a potential role of housing wealth for private school access,   we next assess how changes in housing wealth, through home price changes, correlate with private school participation. This is done for owner-occupier families, for whom we imputed current home value.

Table 6 presents coefficients for the relationship of imputed home value with private school attendance over the period 1997-2017. Column (3) has the key finding from an estimation of equation (3): a 10 per cent appreciation of projected home value for owner-occupier families raised private school participation by 1.84 points. Compared with column (1), the addition of panel fixed effects and region-period effects did not reduce the estimated home housing wealth.

Columns (4) estimates separate home value effects by family income band. As before, income deciles are based on the family income distribution across all non-pensioner households in Great Britain in each wave. The housing wealth effect is again highest for families at the top of the income distribution. But unlike for family income, there is evidence for a positive housing wealth effect across the distribution. The inclusion of time-variant controls, in columns (5) and (6) reduce the estimates slightly without changing any of the substantive points.

Robustness tests in the alternative pseudo panels confirm the positive and substantial effect of home value on private school access for owner-occupier, especially at the top of the socio-economic class distribution, respectively. However, the headline estimate is about half the size at 0.093 points (Column 3, Table A4 in the online appendix).

Table 6: The effects of home value on the probability of attending private school from pseudo-panel fixed effects regressions, 1997-2017

 (1)(2)(3)(4)(5)(6)
Ln mean home value0.175***
(0.028)
0.094**
(0.028)
0.184***
(0.026)


0.157***
(0.029)


Ln mean home value #      
(10th income decile)





0.211***
(0.030)


0.186***
(0.032)
(8th – 9th income decile)





0.180***
(0.029)


0.150***
(0.032)
(6th -7th income decile)





0.179***
(0.031)


0.150***
(0.033)
 (≤5th income decile)





0.179***
(0.026)


0.147***
(0.028)
FENOYESYESYESYESYES
PeriodYESYESYESYESYESYES
Region # PeriodNONOYESYESYESYES
Time-variant controlsNONONONOYESYES
R20.5350.8060.3250.8610.8620.863
F(constant home value effect) – p-value   0.088 0.048

Results from a pseudo-panel of 672 cells from 8 regions, four grouped income decile of pupils’ family income and 21 survey years. The dependent variable is the proportion of students aged 5-15 years in private schools within cells derived from the FRS, 1997/1998-2017/2018. The underlying population are all children aged 5-15 years from owner-occupier families. Columns (5) and (6) controls in addition for the proportion of family heads under 35 years, the proportion over 55 years, the share of single parents, and the proportion of families where at least one parent left full-time education at the age of 21 or higher. Heteroscedasticity and autocorrelation robust standard errors in parentheses. Clusters at region-income ranks level. * p < 0.05, ** p < 0.01, *** p < 0.001.

Finally, Table 7 reports the estimated income and home value effects from a combined model of family resources in the sample of homeowners.  The table reports pseudo-panel estimates based on income bands in columns (1) to (5) and based on socio-economic class in columns (6) and (7). The income effect in the pooled pseudo-panel for this group (column 1) is similar to the estimate in column (1) of Table 6. With the addition of home value (column 2), panel fixed effects (column 3) and period-region dummies (column 4), the income effect drops to 0.036 and fails to reach statistical significance at common levels. By contrast, the estimated effect of home value remains substantial. It appears that it is the access to permanent wealth, measured by home value, rather than current family income that determines private school access in the group of owner-occupier families. The robustness tests in columns  (5) and (6) supports this conclusion.

Table 7: The effects of home value and income on the probability of attending private school from pseudo-panel fixed effects regressions, 1997-2017

 (1) Income bands(2) Income bands(3) Income bands(4) Income bands(5) Income bands(6) NS-SEC(7) NS-SEC
Ln mean home value 0.098***
(0.024)
0.084**
(0.028)
0.174***
(0.027)
0.145***
(0.029)
0.084***
(0.017)
0.083***
(0.016)
Ln mean family income0.112***
(0.017)
0.070***
(0.010)
0.049*
(0.020)
0.036
(0.019)
0.039*
(0.017)
0.019
(0.013)
0.020
(0.013)
FENONOYESYESYESYESYES
PeriodYESYESYESYESYESYESYES
Region # PeriodNONONOYESYESYESYES
Time-variant controlsNONONONOYESNOYES
N67267267267267211751175
R20.5660.6560.8090.8610.8630.6690.670

Pseudo-panel estimates. Columns (1) to (5) are based on 672 cells from eight regions, four grouped income deciles and 21 survey years. Columns (5) and (6) use seven socio-economic classes and eight regions to follow 56 cohorts over 21 years. The dependent variable is the proportion of students aged 5-15 years in private schools within cells derived from the FRS, 1997/1998-2017/2018. The underlying population are all children aged 5-15 years from property-owning families with a mortgage. Heteroscedasticity and autocorrelation robust standard errors in parentheses. Clusters at region-income ranks level. * p < 0.05, ** p < 0.01, *** p < 0.001.

7         Conclusions

Access to private schools in Britain matters, given the success these schools have in incubating future elites, and the ongoing academic and public discourse surrounding social mobility. The fees have risen much more than income, to the extent that the costs for just one child have become more than half of net family income per family member for all but the highest income decile, while the ratio of housing wealth to fees has changed little. The degree of income concentration is high, despite a small fall in the recent period: the income concentration index is 0.49 over 2011-2017. For comparison, access to regular after school activities such as sports clubs is associated with an income concentration index of 0.08. A small proportion of non-income-rich households do attend private school. Bursaries and grants, though income progressive and related to need, are relatively low in value and distributed to only one in five of families outside the top decile; they cannot, therefore, account for more than a minor share of the participation of these non-income-rich families. However, among homeowners, non-rich families with privately educated children have much greater housing wealth than families with children in state schools. Other factors, including parental values and location (distance from good quality state schooling), are also found to be significant determinants of private school choice (Anders et al, 2020); being steady over time, these factors are likely to affect the choices of those able to afford the fees through either income or wealth.

Following these descriptive findings, we have deployed pseudo-panel methods to estimate that the income effect of a 10 per cent income rise on private school access is a 1.16 percentage point rise in participation; outside the top-income decile, the estimated effect is statistically insignificant. The impact of a 10 per cent rise in housing wealth is for a 1.84 percentage point rise in participation for homeowners. Considering the low participation outside the top-income decile, these effects are substantial.

These results contribute further understanding to debates about social mobility trends in Britain (Elliot Major and Machin, 2018). The exclusiveness of access, and its comparative stability over more than two decades of social and economic change, is arguably one reason for the lack of progress over social mobility. The data on bursaries and scholarships have shown how little they can have contributed to any change. The importance of the strong link between wealth and private schooling underpins other recent research showing how family wealth affects success in adult life (Fagereng et al., 2018). 

While these results are the first to show the importance of family wealth for access to high-quality education in Britain, they may underestimate the role of family resources. With our data, we have only been able to examine one, albeit substantial, component of family wealth. Other elements, such as the wealth of family relatives, especially grandparents, are likely to be very important. Family resource surveys typically do not observe transfers within the extended family, and one recommendation for the future is that survey designers consider ways in which this information could be collected. In the case, resources within the extended family have gained in importance, the here estimated home value effect is likely to proxy some of it.

The estimates imply that the future demand for private schooling will be linked to trends in wealth, as well as the growth of top incomes. If relative wealth inequality continues to increase as it has done in recent decades, our findings point to, if anything, a prospect of even more exclusivity in private school access. That trend will be exacerbated if, in particular, homeownership continues its downward trend while home values continue to rise. In that light, we can conclude that policies to improve social mobility should include as a key objective the opening up of private school access to wider sections of the population. Externally-imposed reforms such as removing the schools’ charitable status, taxing school fees, focusing ‘contextual admissions’ to universities on school-type, or integrating private schools either partially or entirely with the state sector aim to reduce demand.[6] Internally driven reform focuses largely on an expansion of means-tested bursaries. Our analysis supports that hitherto bursaries have been income progressive, though too small and scarce to affect the overall exclusivity substantially. Though rising wealth inequality and fees might make this an uphill struggle for fund-raisers, greatly expanded bursary provision not linked to academic selection could make a difference. Means-tested bursaries would need to expand considerably in reach and scale, and the selection criteria should include a strong focus on family wealth, not just income. Whether such internal-driven change is feasible remains uncertain.

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[1] Throughout this paper ‘private schools’ are fee-paying schools; elsewhere these are also variously termed ‘independent schools’, ‘prep schools’ at primary level, and confusingly ‘public schools’ in the case of the more prestigious secondary schools.

[2] https://preview.tinyurl.com/zo5m7du

[3] While the school type question has remained unchanged throughout, the wording of the response option underwent a minor change, from “Any PRIVATE school (prep or secondary)” before the 2002/2003 wave to “Any PRIVATE/Independent school (prep, primary, secondary, City Technology Colleges)” thereafter. This coincided with a significant increase in the estimated private school participation rate from 3.4 percent in 2001 to 4.4 percent between in 2002. Yet a simple pooled OLS regression of private school participation on income decile interacted with period dummies with data from 2001 and 2002, revealed no significant period-income rank interaction effects. The null hypothesis of no joined differences could not be rejected at p=0.70 (F=0.71). We judge that this change is unlikely to seriously bias the trend analysis of private school access. To check, we find that restricting the analysis to the years after 2002 does not make any significant difference to the findings.

[4] The chart is restricted to families with income at or above the 5th percentile. Income data becomes more unreliable at the very bottom of the distribution (Brewer et al. 2016).  

[5] The concentration index is a bivariate generalisation of the Gini coefficient, and there is a theoretical literature that examines the properties of different definitions and their relation to different concepts of inequality (e.g., O’Donnell et al., 2016).

[6] https://www.privateschoolreform.co.uk/our-publications.

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