Schooling in London

OFSTED published their annual report last week. In common with the recent White Paper ‘Education Excellence Everywhere’ the report emphasised geographical differences in the quality of schools arguing that higher attainment among children in London, and particularly among those from disadvantaged backgrounds, is due to the higher quality of schools in the capital. The improvement in children’s education in London is likely to have more than one cause. The emphasis placed on school quality by policy makers and some researchers has always seemed odd, however, because although there is certainly a link between school quality and education outcomes, all of the evidence is that schools are less important than families as a determinant of children’s education outcomes. As a rough rule of thumb between 20 percent of the variability in education outcomes is usually found between schools meaning that if all children went to the same school the overall variation in education outcomes would only go down by 20 percent. In contrast, around 50 percent of variation in children’s education outcomes is between families. In other words, family characteristics are much more important than schools as a factor influencing variation in children’s education outcomes.

This matters for our understanding of geographical differences in education in England because there are important differences in family characteristics between children in London and in other areas. In particular, children in London are more likely than those in other areas to live in families where an adult has a degree-level qualification. The figure below shows the proportion of adults in families with children who have a degree-level qualification using data from the 2011 Census (table DC5106EW) and the percentage of KS4 pupils in receipt of free school meals for local authorities in England in 2012. The figure shows that most local authorities in London are distinguished from other local authorities by the combination of a high proportion of pupils in receipt of free school meals and a high proportion of the adult population living in families with children who have a degree-level qualification. The combination of high proportions of children in receipt of free-school meals and a highly educated adult population might seem unusual but reflects the relatively low employment rates in London, including for adults with high qualifications (see Kaplanis 2010). Rather than reflecting an improvement in schools, another way of looking at the relatively good education outcomes of disadvantaged children in London is therefore to see children’s outcomes as a reflection of geographical differences in the characteristics of disadvantaged families with disadvantaged families in London being more likely to have high qualifications than in other areas. While I wouldn’t argue that this interpretation is conclusive it at least fits in with researchers view of processes in cities as generating inequalities rather than reducing inequalities for disadvantaged groups.

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How about change over time. Is it possible to also explain changes in the attainment of children in London over the last decade in terms of changing family characteristics? The figure below shows the variation in the proportion of the population between 16 and 64 years of age who have a level 4 qualification using data from the Annual Population Survey. Although this is the qualifications of all adults and not only those in families with children, the figure shows that over the last decade the proportion of the workforce with a degree-level qualification has risen by over 15 percentage points in London in comparison to less than 10 percentage points in other regions. It seems possible therefore that the increase in the proportion of the adult population with high qualifications has been a factor in improving children’s education outcomes in London. The marked rise in adult qualifications in London is linked to wider processes of economic change as well as to the greater opportunity in cities to use skills and to major investments in infrastructure in London which have made the city more liveable for families. From a policy perspective this cautions against simply assuming that schools across the country will be able to reproduce the increase in attainment seen in London over the last decade. The tendency for cities to have high proportions of highly qualified adults is weak for cities in England outside of London and, in consequence, it is unlikely that other cities in England will be able to reproduce the recent improvement in schooling seen in London.

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The English Baccalaureate

I have read several newspaper articles recently about either the withdrawal of subjects from those being offered by exam boards or the decline in the number of pupils taking, what are usually termed, creative subjects, such as Art. Both changes have been attributed to the introduction of the EBACC (or English Baccalaureate) in 2010. The EBACC is a performance measure published in the DFE school performance tables, rather than a qualification, and is awarded when pupils get a grade C or above in the GCSE subjects: English, maths, the sciences, geography or history and a language. The government has argued that the EBACC provides the right educational foundation for the vast majority of pupils. Schools have responded to the EBACC in the intended way and the proportion of pupils with entries in all EBACC subject areas has risen from 23.8 percent in 2011/12 to 36.3 percent in 2014/15. The intention is that all pupils should be taking the EBACC subjects at GCSE by 2020.

The EBACC has been criticised, however, for limiting pupil’s opportunity to study a wider range of subjects and for forcing pupils to take subjects that they struggle in. The characteristics of pupils taking the EBACC have certainly changed since its introduction. The figure below shows the variation in the proportion of pupils with high and with average KS2 attainment entered for the EBACC at the school-level from 2011/12 to 2014/15. The figure shows that since 2011/12 the number of schools in which the majority of pupils with high KS2 ability were entered for the EBACC has risen markedly with around 50 percent of schools now entering at least 75 percent of their most able pupils. EBACC entry rates have also risen for pupils with average KS2 ability but it remains rare for schools to enter pupils with low KS2 ability for the EBACC. Although schools are targeting their most able pupils for entry to the EBACC, the overall proportion of EBACC entries from pupils with high ability has actually fallen from 66.4 percent in 2011/12 to 56.8 percent in 2014/15. Unsurprisingly therefore the proportion of pupils entering the EBACC who are successful fell from 73.9 percent in 2011/12 to 63.0 percent in 2014/15.

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In order to understand whether the fall in the proportion of pupils with EBACC entries who are successful can be explained by changes in the ability of pupils, we can use the same decomposition methods that have been developed to study wage inequalities. This involves estimating two OLS regression models, in this case for 2012 and 2014, with the proportion of pupils taking EBACC subjects who are successful as the dependent variable and school characteristics as independent variables. The school characteristics from the DFE performance tables that I can use are the percentage of pupils with EBACC entries who had high KS2 ability, the percentage in receipt of free school meals and the share of pupils with EBACC entries. We then use the OLS results to compute the difference in the mean proportion of pupils achieving the EBACC as: EBACC2012 – EBACC2014 = α2012 + β2012 * X2012 – α2014 + β2014 * X2014. If we then add and subtract a counterfactual outcome calculated using the coefficients from the 2012 model and the school characteristics from the 2014 model (α2012 + β2012 * X2014), the achievement gap can divided into a portion due to differences in explanatory characteristics in the two years, or, β2012 * (X2012 – X2014) and a part due to differences in model coefficients, or, α2014 + (β2012 – β2014) * X2014. This shows that around 50 percent of the change in average EBACC achievement can be explained by the change in the characteristics of entrants with the remaining 50 percent is due to change in model coefficients.

It is also interesting to look at how the explained and unexplained components vary in importance in explaining the change in achievement at different percentiles of the distribution of achievement (using methods describe here). The drop in EBACC pass rate varies from 4.4 percentage points (38.1 vs 33.7 percent) at the 10th percentile to 8.7 percentage points at the 90th percentile (89.1 vs 80.4 percent) of the achievement distribution and the figure below shows the variation in the proportion of the gap due to each component. The figure shows that change in the characteristics of pupils entering the EBACC is the most important explanation for the change in achievement at the top of the distribution while changes in the model coefficients are more important at the bottom of the distribution. We can interpret this as showing that at the top of the distribution schools are no longer able to achieve very high EBACC success rates by being selective in the pupils they enter. At the bottom of the distribution EBACC success rates have fallen largely because of the change in the constant in the regression model reflecting a fall in average school achievement unrelated to any of the characteristics included in the model.

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Gender Pay Gaps

I listened to a discussion on the news recently about a report on the gender pay gap from Deloitte. It is the first time I have heard a discussion of differences in pay between men and women that didn’t refer in some way to discrimination. Rather, the report came to the conclusion that to close the gender pay gap women need to earn more. Why didn’t I think of that!! Using data on the pay of recent graduates the report showed that women who had degrees in STEM subjects received the same median pay as men. If more women studied these subjects the gender wage gap would therefore close.

Differences in the characteristics of men and women are not the only factor contributing to the gender pay gap, however. The pay gap between men and women can be understood as being partly due to differences in the characteristics of men and women, such as occupation and industry, but also partly due to differences in the rates of pay between men and women who have the same characteristics. The difference in pay between men and women with the same characteristics is sometimes termed the adjusted pay gap and captures the effect of gender discrimination (plus the effect of other differences between men and women that we don’t know about). See here for a review article of the methods from the NBER in all the gory details.

Whether discrimination is an important factor in the pay gap is therefore something that we can look at empirically and the figure below shows the hourly pay (excluding overtime) of men and women between 25 and 59 years of age using data from the Labour Force Survey from 2012 to 2014. Overall, average pay was £15.48 per hour for men and £12.37 per hour for women while the corresponding figures for median pay were £12.82 for men and £10.16 for women, a gap of around 20 percent. Decomposition results show that around a third of the gap in mean pay between men and women can be explained by differences in male and female characteristics including age, region, highest educational qualification, industry and occupation. The remainder either reflects discrimination or the effect of characteristics, such as labour force experience, that we haven’t been able to measure using the LFS. While changing the characteristics of women to be more like those of men would reduce the gender pay gap, paying men and women with the same characteristics the same rate of pay would seem to be a much more significant factor in the unequal pay of men and women.

wagesiiAlthough decomposition techniques were originally developed in economics in an attempt to explain differences in mean pay between groups, the article from the NBER describes their recent development to statistics such as quantiles. This allows us to look at whether differences in the characteristics of men and women have different importance in explaining the pay gap at different positions in the pay distribution. Looking at how the explained and unexplained portions of the pay gap vary across the distribution shows that differences in characteristics are more important at the bottom of the pay distribution than at the top. In my quick look at this using the LFS, differences in the characteristics of men and women seem to explain less of the pay gap at top of the distribution than at the bottom. The results in Table 4 of the NBER article show the same result. The slightly counter intuitive conclusion therefore is that the more you earn as a women the less likely you are to be receiving equal pay.

Are Teachers the Cause of Educational Inequalities in England?

Recently policy makers have argued that improving the standard of teaching is key to improving children’s educational attainment in those schools which have the lowest levels of performance on national tests. Datasets which contain information on both teacher characteristics and pupil outcomes are rare, however. Whether the quality of teaching is a major factor in the low levels of education in some schools has therefore not been an easy question for researchers to answer, at least directly. Researchers have been able to use routinely collected administrative data, such as the National Pupil Database, to examine the relative importance of schools in explaining differences in children’s educational achievement. The overall finding from this work has been that schools only account for around ten to fifteen percent of the observed variation in children’s achievement. In other words, if all children went to the same school we would expect the variation in children’s achievement to be lower but a significant amount of variation would still exist. The emphasis placed on improving the quality of teaching as a means of increasing educational achievement in the lowest performing schools therefore seems slightly surprising.

A further indication that the main factors causing differences in children’s educational achievement are outside of schools comes from socioeconomic differences in children’s development when they first start school. In England, children’s education is divided into stages with the Early Years Foundation Stage (EYFS) covering the period from birth to age 5 years. The EYFS profile summarises children’s attainment at the end of their reception year in primary school in terms of characteristics which play a central role in learning (e.g. creating and thinking critically). Children who achieved at least the expected level of learning in each area are assessed as having a good level of development. The figure below shows the relationship between the proportion of children who have a good level of development in each local authority in England and the proportion who are eligible for free school meals using data from the Department of Education. The regression line (in blue) shows that as the proportion of children receiving free school meals in each local authority increases there is a fall in the proportion achieving a good level of development. In the local authorities with the lowest proportion of children in receipt of free school meals around 65 percent of children achieved a good level of development while in those areas with the highest proportion of children receiving free school meals only 55 percent of children showed good development at the end of their reception year.

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I am not trying to argue that teaching is unimportant in learning but only question whether differences in teaching are important in causing differences in educational attainment in the population. The idea that the quality of teaching has a key role in causing differences in educational achievement might seem persuasive because most of us would probably have had one or two school teachers who we thought were really great and one or two, perhaps, who we thought were not so good. In considering the effect of teaching on children’s achievement we need to distinguish, however, between the impact of teaching on the level of attainment of the individual child and the impact on the level of attainment in the population. The importance of high quality teaching in explaining the overall pattern of children’s achievement depends both on the degree to which high quality teaching raises educational achievement and the overall proportion of high quality teachers in the teaching workforce. Although having a high quality teacher may have a strong effect on an individual child’s learning, it seems unlikely that the number of high quality teachers are sufficient to explain overall differences in educational achievement in the population. Rather, it seems likely that the impact of teaching is likely to have the most significant impact on the learning of children who have teachers of average quality simply because of the larger number of teachers in this group. This implies that rather than focusing on initiatives, such as Teach First, which aim to increase the numbers of high quality teachers in schools, strategies which try to increase educational achievement by raising teaching quality should aim to improve the quality of teaching across the entire profession. We should acknowledge, however, that few interventions are likely to significantly change the structure of educational inequalities in England on their own. Improvements in the quality of teaching are certainly worthwhile but are unlikely to significantly reduce inequalities in educational achievement without accompanying changes in the socioeconomic situation faced by many families.

Regional Differences in University Admissions in England

In England, the proportion of young people who go to university after completing their A levels varies significantly across regions. In particular, figures from HEFCE show that the proportion of young people from London who enter university is significantly higher than in other regions. At the student level studies have shown that the most important factor influencing admission to university is level of educational achievement. It seems unlikely, however, that variation in the level of educational achievement can entirely explain the higher likelihood of entering university for young people who live in London. The figure below shows the relationship between the proportion of young people going to university and the proportion of school children with 5 GCSEs at grade A to C including English and Maths for parliamentary constituencies in England using data for 2011. The regression line shows that there is a significant positive relationship between participation in higher education and levels of prior achievement. There is significant variation around the regression line, however, suggesting that factors other than prior achievement might be important in influencing the proportion of young people in an area who go to university. In particular, the majority of parliamentary constituencies in London plot above the regression line showing that they have levels of young participation which are higher than that predicted on the basis of prior levels of achievement,

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There are a range of factors, such as proximity to a large and diverse number of higher education institutions, which might explain why young people from London are more likely to go to university than those in other regions with similar levels of academic achievement. There is a strong geographical pattern, however, to higher education participation within London. The figure below shows the geographical distribution of areas across London which have higher and lower numbers of admissions than expected on the basis of their levels of GCSE achievement. The figure shows that there is a pronounced East/West divide in participation with many of the areas of London which have significantly higher than expected proportions of young people going to university in West London (e.g. Brent, Ealing and Harrow) and many of the areas with lower than expected proportions of young people going to university are in East London (e.g. Havering, Bexley and Bromley). The geographical differences in university participation correspond closely to variations in the proportion of young people in each area from ethnic minority backgrounds. Several recent studies have shown that young people from ethnic minority backgrounds are more likely to aspire to go to university than those from White backgrounds and it seems likely that the higher proportion of young people going to university in London may, in part, be related to ethnicity.

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In order to investigate this further I have recently been using survey data from the Longitudinal Study of Young People in England (LSYPE) to examine regional variations in young people’s attitudes to higher education. The work I have been doing is exploratory and has been using information provided by the cohort member at wave 1 in 2004, when they were in year 9, and at wave 7 in 2010, two years after they would normally have taken their A levels. The figure below shows differences between London and remaining regions in young people’s aspirations to go to university at wave 1, GCSE results at age 16 years and actual admissions to university at wave 7 separately for White and non-White cohort members.

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The first panel shows the variation in the proportion of respondents who stated that they were either very or fairly likely to go to university at wave 1 by ethnic group and region. The figure shows that respondents from non-White backgrounds were more likely to state that they intended to go to university than those from White backgrounds among both respondents who lived outside of London and those who lived in London. The figure also shows, however, that in both non-White and White groups, there is a regional difference of around 10 percentage points in the proportion of young people who intend to go to university with respondents who live in London more likely to intend to go to university than those in remaining regions.

The second panel shows the corresponding variation in GCSE results by ethnic group and region. The figure shows that there is little variation in GCSE results by ethnicity with non-White and White respondents who lived outside of London and non-White and White respondents who lived inside of London having similar GCSE results. There was also no difference in the GCSE results of White respondents between London and remaining regions, however, non-White respondents who lived in London achieved significantly better GCSE results than those who lived outside of London. Finally, the third panel shows the proportion of respondents who were at university at wave 7 by ethnic group and region. The figure shows that respondents from non-White backgrounds were more likely to be at university than those from White backgrounds both among respondents who lived outside of London and those who lived in London. In each ethnic group, respondents were more likely to be at university if they lived in London with the proportion of respondents at university around 10 percentage points higher in London than in remaining regions.

Overall, therefore, the results suggest that the higher aspirations of non-White and White respondents and the relatively good GCSE scores of non-White respondents in London might be able to explain the higher proportion of young people who go to university in London. This finding can be interpreted in several different ways. The simplest interpretation is that the higher aspirations of young people who live in London directly lead to the higher proportion of young people from London going to university. This type of explanation doesn’t give any reason, however, for why young people in London should have higher aspirations to go to university than in remaining regions. It is also possible to view aspirations as being a consequence of region, however. From this perspective, regional differences including opportunities to go to university and the wider economic situation help shape young people’s aspirations to go to university, while the proportion of young people going to university in turn influences both the economic competitiveness of a region and the educational aspirations of younger generations. Circular processes of this type are a common cause of geographical differences and the cumulative nature of change means that they can lead to durable differences in the characteristics of areas. The important point for policies aiming to increase the number of young people going to university in different regions is to recognise that the wider environment has an influence on young people’s aspirations so that a one-size fits all approach is unlikely to be useful.

Increasing Educational Achievement?

A recent report from the National Audit Office argued that school inspections are ineffective in increasing the achievement of failing schools in England. The assumption that policies to improve educational achievement should target schools might seem natural. Policies aimed at improving educational achievement have, however, been targeted at different levels of intervention. Area-based policies which see the broad contexts in which schools are located as influencing educational achievement have been popular with policy makers at different times (e.g. Sure Start in the early 2000’s), while currently the main emphasis is on interventions at the level of the individual child rather than the context (see, for example, the Toolkit produced by the Education Endowment Foundation).
Unfortunately, the research evidence doesn’t provide a great deal of advice for policy makers on whether to intervene at the level of area, school or individual child. Part of the reason for this is that researchers have used different types of relationships to try to understand the determinants of school achievement. Some studies have used cross-sectional data and examined the variation in school achievement across children while other studies have collected longitudinal data and based their analyses on the variation in school achievement within individual children. It is helpful to illustrate the difference between these types of studies with an example. The figure below shows the relationship between the average points score of children at Key Stage 2 (age 11 years) and deciles of neighbourhood deprivation separately for each English region (using data for 2008). The figure shows that if we compare children living in neighbourhoods characterised by different levels of deprivation we find that there is a marked negative gradient in school achievement with neighbourhood deprivation in each region. In contrast, however, those studies which have based their conclusions on the relationship between neighbourhood deprivation and school achievement on the within child relationship between changes in neighbourhood deprivation and changes in school achievement have concluded that neighbourhood deprivation has little effect on school achievement.
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In most studies the tendency has been to assume that the within-child relationship gives the more reliable estimate of the effect of neighbourhood deprivation on school achievement. The reason for this is that families in different types of neighbourhood differ in terms of both observed and unobserved family characteristics such as income, health, parenting style etc. If these effects are constant over time they can be removed from the analysis when we take differences within a child. In consequence, the within-child relationship is often considered to be a more accurate reflection of the true relationship between neighbourhood deprivation and children’s achievement than the between-child relationship.
There are some drawbacks, however, to this approach. Firstly, the extent of change in neighbourhood deprivation experienced by children over time will typically be much smaller than the variation in neighbourhood deprivation between individual children. For example, the figure below shows the relationship between the proportion of the working age population in receipt of a low-income benefit in 2002 and 2010 for areas with a population of around 1500 people for each region in England. The figure shows that the variation in the proportion of the population in receipt of a low-income benefit across areas is much higher than the change within an area. While the proportion of the population in receipt of a low-income benefit does vary from year-to-year, these changes are small in comparison to the extent of variation across areas. Studies which base their conclusions on the within child relationship discard the between area variation in neighbourhood deprivation and throwing away the majority of information in the data should be more of a concern for researchers.
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From a substantive perspective, it also seems doubtful whether changes in neighbourhood deprivation capture the structural aspect of neighbourhood deprivation in a reasonable way. In the social sciences, structural characteristics refer to factors over which individuals have limited control and which are therefore relatively durable. The concept of neighbourhood deprivation most relevant to children’s achievement should therefore refer to the long-run average conditions in a neighbourhood rather than to year-to-year changes in neighbourhood deprivation. Unless children move home, the ranking of where they live in terms of neighbourhood deprivation would appear likely to be durable throughout their childhood and it is this structural aspect of neighbourhood deprivation which influences the routines that families adopt and which in turn have the most direct influence on children’s achievement. This structural characteristic of neighbourhood deprivation is not captured in studies which measure the effect of neighbourhood deprivation on children’s attainment using changes in the level of neighbourhood deprivation experienced by individual children.
It is possible to estimate how much of the variability in children’s experience of neighbourhood deprivation is due to differences between individual children, differences due to neighbourhood change or due to residential mobility using statistical techniques. I’ve recently been working on this using nine years of data for a cohort of children who started school in 2002 using data from the National Pupil Database. The results show that more than 85 percent of the variation in children’s exposure to neighbourhood deprivation is between individual children while around 10 percent is due to residential mobility with neighbourhood change accounting for the remainder. While approaches that discard the between child component of neighbourhood deprivation and estimate the effect of neighbourhood deprivation on educational achievement from variation within children might be technically sophisticated they don’t seem to be answering a useful question.

Is Money Multiplicative?

When I was looking at data on the wealth of UK universities recently I plotted the value of institutions net assets on the y-axis using a log scale. Using a log scale means that equal differences refer to a constant multiplicative factor, rather than, as is more usually the case, a constant additive factor. For example, the distance on the y-axis from 500000 to 1000000 is the same as the distance from 1000000 to 2000000. It is standard to use a log scale when there are a significant number of observations which are more than three standard deviations above the mean. There are quite a few variables which have this type of distribution with lots of low values but only a few high values, including household wealth, city populations and the number of citations for academic papers.

Distributions which have a long tail are almost always the result of processes which are multiplicative rather than additive. Phenomenon which result from multiplicative processes can be modelled using a power law distribution which has the form:

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where c and α are constants. In the social sciences, variables that have a power law distribution are often produced by what are termed processes of cumulative advantage. These refer to processes in which patterns of cumulative causation lead to small initial differences between people or between institutions becoming magnified over time. Multiplicative phenomena may also be described, however, using the lognormal distribution. The log-normal distribution is the natural way to model phenomena, like investment funds, which grow by a small multiplicative factor each period.

The difference between the type of process that lead to power law and lognormal distributions can be illustrated with an example. If we put a given sum of money in the bank and reinvest the interest, the amount by which the sum accumulates depends on the initial investment. If the interest rate is 10 percent then a sum of £1000 grows by £100 but a £10000 sum grows by £1000. The difference in the value of the two investments grows exponentially over time from £9900 at the start to £14400 after 5 years and £23300 after 10 years. The ratio of the value of the two investments remains constant over time (at 10:1), however. If instead the interest rate depends on the initial sum (for example, 5 percent interest on £1000 but 10 percent interest on £10000) then both the difference and the ratio of the value of the two investments would grow over time.
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One way for determining whether a variable follows a power law or a lognormal distribution is to plot P[X > x] on a log-log scale. Both power law and lognormal distributions should follow a straight line but the power law distribution should have a shallower slope because of its longer tail (see Mitzenmacher 2005). For an empirical example, I decided to look at whether the size of universities assets followed either a power law or lognormal distribution which might tell us something about the kind of processes influencing inequalities in higher education. I used data from 2013 for the value of the endowment funds for US and Canadian higher education institutions (www.nacubo.org). The US institution with the largest endowment fund is Harvard ($32 billion) followed by Yale ($20 billion) and the University of Texas ($20 billion). In contrast, over 90 percent of institutions have an endowment fund with a value of less than $1 billion. The figure above shows a log-log plot of P[X > x] for the endowment funds of US institutions with fitted lines for both a power law distribution and a lognormal distribution. The figure suggests that the lognormal distribution is a better fit than the power law distribution. Although the universities with the largest endowments are wealthier than other institutions, inequalities in endowments between institutions seem to be described by differences in inherited wealth and constant proportional growth, rather than by the ability of the most wealthy institutions to benefit preferentially from their financial assets.