Social class and sex differences in absolute and relative educational attainment in England, Scotland and Wales since the middle of the twentieth century

ABSTRACT Changes over time in social-class inequality of educational attainment have been shown by previous research to depend on whether attainment is measured absolutely or relatively. The pioneering work in this respect by Bukodi and Goldthorpe found that inequality has fallen when attainment is measured absolutely (for example, as the percentage completing full secondary schooling) but has changed less when a relative measure is used (for example, reaching the top quarter of the distribution of attainment). Although absolute measures remain intrinsically interesting, insofar as they represent cognitive or cultural accomplishment, relative measures are more relevant for understanding the role of education in allocating people competitively to employment. Implicit in this previous research, as in much research on the connection between education and social mobility, is that the society over which the relative standing of qualifications is measured is the same as that in which they are used to gain social rewards, such as a job. When labour markets operate across educational borders, this assumption might be open to question. The present analysis investigates the interpretation of absolute and relative educational inequality by comparing England, Scotland and Wales, which have distinct education systems but a common labour market.


Introduction
have pointed out the importance of distinguishing between absolute and relative definitions of educational attainment in the investigation of changes over time in educational inequality, and of changes in the effect of education on social mobility.They show that inequality has declined when thresholds of attainment are measured absolutely, but not when measured relatively to the rest of a birth cohort.They conclude that, to the extent that the labour market allocates a finite number of high-status jobs on the basis of a competition in which credentials are part of the sorting mechanism, it is likely to be relative rather than absolute attainment that will be more relevant.
These ideas provide the general framework used in the present paper.However, implicit in that approach is that the society over which the relative standing of credentials is measured is the same as that in which they are used to gain social rewards.When labour markets operate across borders while educational systems remain primarily defined by national governments and traditions, this assumption might be open to question (Raffe et al. 1999, 19).The present analysis asks whether this disjunction of social referent might lead to more complex conclusions about the trajectory of inequality.
Questions of this kind matter because of the general understanding of educational expansion and its relation to social mobility which abundant research has provided.The relevant changes in Britain may be summarised as two large, interacting processes.One is the expansion of education (Breen et al. 2009;Bukodi and Goldthorpe 2016;Mandler 2020;Murphy et al. 2015;Paterson 2020).From the mid-1960s, the proportion of people who completed a full secondary education expanded very greatly, partly because of the near ending of selection into different kinds of secondary school.Higher education also then expanded, between the 1960s and the late-1970s, and even more markedly in the 1990s (ibid.).The other large process consisted of changes to the structure of employment, as manual work in predominantly manufacturing industry declined, and as professional occupations expanded (Gallie 2000).This change was partly also a change in sex differences, because women entered the new sectors of employment in larger proportions than men.
The analysis reported here attempts to draw upon as lengthy as possible a time series of data on these questions, and to do so while also adhering to a further principle, that the most valid way of investigating them is by means of cohort studies which gather data at the time of the educational and occupational experiences that they seek to understand, rather than through retrospective recall many years after these events.Our main data cover people born between the mid-1940s and the early 1990s; we examine their educational attainment and social status around age 30, between the early 1980s and the second decade of the present century.

Education, social origins and status attainment
Research on educational inequality and social mobility in England, Scotland and Wales has found that these societies share experiences that are common across the developed world (Erikson and Goldthorpe 1992;Müller and Karle 1993;Paterson and Iannelli 2007a,b).Despite the initial optimism associated with modernisation theory (Treiman 1970;Glass 1954;Lipset and Bendix 1959), the direct association of class origins with class destinations did not weaken in the second half of the twentieth century.Although the large rise in the share of the employment taken by service-class jobs did depend on a strengthening of educational credentials, the persisting inequalities in access to these credentials maintained inequality of mobility at mostly unchanging levels (Bukodi and Goldthorpe 2019, 34-51;Buscha and Sturgis 2018;Erikson and Goldthorpe 1992;Gallie 2000, 285-6;Goldthorpe 2014;Shavit and Blossfeld 1993).When inequalities of attainment at a particular educational level did fall -usually because the attainment of the most advantaged social classes had reached a high plateau -the social-class inequality merely shifted to the next education level above that (Breen 2004;Breen et al. 2009), a process which Raftery and Hout (1993) called 'maximally maintained inequality'.Most of these results have been found to apply equally to men and women (van de Werfhorst et al. 2018;Bukodi and Goldthorpe 2019, 191-202).
These general trends in the developed world are the broad context for the present analysis, showing as they do that empirical findings relating to England, Wales and Scotland are likely to be relevant to many other places.The same general importance also attaches to the key distinction between absolute and relative educational attainment that was drawn by Bukodi and Goldthorpe (2016).This is a problem when access is expanding.For example, in the data which we consider below, the proportion whose education was at mid-secondary level or higher was 33% for people born in Scotland before the second world war, but 95% for those born towards the end of the century.In that later group, 32% had completed a university degree.So do we equate the nominally similar levels defined by secondary schooling, or do we equate the levels attained by similar proportions, so that secondary schooling in the middle of the century is functionally equivalent to university education at the end (Heath and Clifford 1990)?Bukodi and Goldthorpe (2016) showed that how we answer this question can have a large effect on our conclusions about the trajectory of inequality.For Britain treated as a single society in the second half of the century, they found that with an absolute definition the association with education declined both for class origin and for class destination; but with a relative definition the association with origins declined far less, and there was no decline of the association with destination.Shavit (2011) found similar results for Israel, although Triventi et al. (2016) reported declining associations for both absolute and relative definitions in Italy.Wakeling and Laurison (2017) found that, in the UK, expansion of undergraduate higher education had shifted inequality to postgraduate levels of attainment.van de Werfhorst et al. (2018) have described the contrast of absolute and relative conclusions as showing what they call 'positionally maintained inequality'.That is, as education expands, the rank order of social advantage maps onto the rank order of educational attainment regardless of the nominal meaning of each position in that educational hierarchy.
A useful set of ideas for interpreting the distinction between absolute and relative credentials in the labour market is labour-queue theory (Goldthorpe 2014;Thurow 1976, 95-97).According to this, the role of credentials is mainly to sort people into a queue, the best jobs going to those at its head.Credential inflation would then not affect people's position in that metaphorical queue, even though their nominal attainment might be higher than someone in the same position in the queue several decades previously.We refer to these as the distinction between the job-queue and the education-queue.The jobqueue is an entry queue -people seeking positions in the labour market.The educationqueue is an exit queue -people ranked according to their credentials.(Economists might call the latter the 'labour-queue', but, because we have information here only on credentials, not on any other aspect of employability, we prefer the label 'education'.)So the rationale for a relative measure of educational attainment is this idea of a queue.The rationale for an absolute measure is that there is an intrinsic benefit of education, which economists would call a consumption good.
But what if there are several education-queues contributing to the same job-queue?Suppose that someone at, say, the 50 th percentile of one education-queue had nominal credentials that would place them at the 60 th percentile in a different education-queue, and suppose also that this latter queue was the main education-queue for the labour market.Then that person's relative education standing, so far as the labour market was concerned, would be more strongly determined by that second queue (where they were above-average) than by the one where they were merely average.In essence, enabling this switching to a different job-queue has been one of the important roles which education has played in peripheral societies, allowing people to compete for better jobs in the core economy than they could do at home and, crucially, to out-compete products of the education system in that core economy (Findlay et al. 2008).
Transfer to a different education-queue will work most smoothly when there is a common job-queue, and where credentials in the different education-queues are regarded as equivalent in a nominal sense.That is why studying England, Wales and Scotland can be illuminating here (Raffe et al. 1999).On the one hand, increasingly since the mid-twentieth century, the labour market has operated according to the same mechanisms throughout Britain, the main reasons being the growth in public-sector employment (conducted according to the same rules throughout the UK), the growth of employment by multinational companies, and the increasing regulation of the labour market by the UK state (Raffe et al. 1999;Raffe and Courtenay 1988).The regions of Britain converged in their industrial structure during the twentieth century (McCrone 1992, 70-4).The emergence of London as the strong driver of UK economic activity also imposed a greater homogeneity of recruitment practices, especially for entry to professional employment, even for labour markets outside London (Champion and Gordon 2021;Fielding 1992): London's role was as an 'escalator' region where highly qualified young people gain expertise, then promotion, before moving at a senior level to influential positions outside London.
On the other hand, the education-queues of Scotland and England have long been distinct, with historically higher rates of participation in post-compulsory schooling in Scotland (as confirmed by our data below).Welsh education, by contrast, was closely tied to that of England throughout the development of mass elementary and secondary schooling (also confirmed below), and has begun to diverge only since the devolution of some legislative autonomy to Wales from 1999.So there have been three educationqueues, but with reasons to believe that two of these (Wales and England) would behave in similar ways.
Furthermore, credentials in the different education-queues are regarded as being nominally equivalent.The boards which supervise school-leaving examinations in England and Wales have long sought common definitions of credentials (Newton 2021;Tymms and Fitz-Gibbon 1991), and that has extended to the different system of school-leaving assessment in Scotland (Philip 1992).Similarly, the process of awarding academic degrees has been regulated by the system of external examiners of UK universities, and also, when there was a distinction between universities and polytechnics before 1993, by the Council for National Academic Awards (Barnett 1987;Halsey and Trow 1971).
The reasons why these standardised credentials can nevertheless produce different education-queues include different institutional structures, different patterns of accessibility, and different quality of provision (Machin, McNally, and Wyness 2013).Relative attainment may differ also because of different incentives arising from the very phenomenon we are studying here.If education is a means by which young people from economically peripheral regions may gain access to opportunities in a metropolitan core, then the incentive for high attainment may be greatest for students far from that centre (Findlay et al. 2008).It is a matter for empirical investigation, then, whether relative attainment measured on the same basis across different but connected education systems is a more cogent way of assessing inequality of attainment or of opportunity than when attainment is measured separately within each system.
Thus, comparison of Scotland and Wales with England has the unique advantage of combining a common job-queue with distinct education-queues.These considerations lead to two research questions: (1) Has there been variation among the three nations in the socio-economic and sex differences in educational attainment, and does the answer to this question of variation depend on whether attainment is measured in absolute or relative ways?This first question is essentially a matter of comparing the demographic basis of the education-queues of the three nations.(2) Has there been any variation among the three nations in the role of education in mediating between class origins and destinations, and, as in question (1), does the answer to this question vary when attainment is measured relatively?This question thus asks whether access to the UK-wide job-queue by people from the two peripheral education systems of Scotland and Wales is influenced more strongly by positions in the UK-wide education-queue or by positions in the local education-queue of their home nation.

Data
We use data from five surveys of people born in the Britain between 1936 and 1993.The first four are prospective cohort surveys, and the last is a panel survey.The advantage of cohort studies over, for example, the retrospective construction of synthetic cohorts based on age is less reliance on respondents' memory, and less susceptibility to differential migration and mortality.The disadvantage is attrition, but analysis of the second, third and fourth cohorts here has suggested that it is not biasing (Hawkes and Plewis 2006;Kuh et al. 2011;Nathan 1999).The sample sizes available for analysis are shown in Table 2.

Scottish Mental Survey 1947 (SMS; born 1936)
This survey was confined to Scotland, and so can be used only for the purpose of tracing inequality in Scotland over time.It was conducted by the Scottish Council for Research in Education (Deary, Whalley, and Starr 2009).Almost every 11-yearold who was at school in Scotland was tested, and a detailed sociological inquiry was made into the lives of the 1,208 children who were born on the first day of the even-numbered months.These people were followed to 1963.

MRC National Survey of Health and Development (NSHD; born 1946)
This study has followed a sample of children born in Britain in a specific week in March 1946 to married parents (Kuh et al. 2011).The sample included all singleton births in that week whose father was in non-manual or agricultural employment, and a random one-in-four of those whose father was in manual employment.Weights compensate for this varying sampling fraction.

National Child Development Study (NCDS; born 1958)
This study has followed everyone born in Britain in a specific week in 1958 (NCDS website).

British Cohort Study(British Cohort Study web site)
This has followed everyone born in Britain in a specific week in 1970 (BCS website).

UK Household Longitudinal Study (UKHLS; subset born 1975-1993)
This panel study started in its present form in 2009-11, with annual follow-up; the latest wave used here was in 2017-19 (Lynn and Knies 2016).At its second wave, it subsumed the earlier British Household Panel Study (BHPS), which started in 1991 with annual follow-up to 2008.The samples were stratified and clustered, with weights available to compensate for different sampling fractions for different ethnic groups and the different nations of the UK.Only residents in Britain at the second wave are included in the analysis.
As with any secondary analysis of data sets that have been collected over a long period, compromises have had to be made to allow comparison.The aim was to record highest educational attainment and highest-status social class when respondents were aged approximately 25-35.That choice was constrained by the oldest age available from the 1936 birth cohort, though also by an intention to take the story to as close to the present as possible (by extending the range of birth-years into the 1990s).The choice is also consistent with work by other researchers on status attainment (Barone and Schizzerotto 2011;Bukodi and Goldthorpe 2016;Buscha and Sturgis 2018;Passaretta 2017).Bukodi et al. (2015) provide the closest parallel to the present work, because they used the 1946, 1958 and 1970 birth cohorts along with people born in 1980-4 in the first wave of the UKHLS.
The ages from which data were used are shown in Table 1.For the cohort surveys, they corresponded to specific sweeps, and so attainment and class were recorded as the highest reached by the later age noted for each survey.For the UKHLS, every panel member who, at any of the first nine sweeps, was within the age range 25-35 was included, and then their highest attainment and class were recorded for those sweeps of the data when they were not older than 35.Thus, the birth dates of this sub-sample ranged from 1975 to 1993 (the oldest and youngest people to be within the 25-35 range at some point within these sweeps).We explain below how we also took account of specific years of birth within that group.We used this two-decade range so as to give adequate sample sizes in Wales and Scotland.The first four surveys will be referred to by the year of the oldest age at which information was recorded (respectively, 1963, 1982, 1991, 2000), and the final survey by the median year of the oldest age at which information was recorded (2014).
Attainment in absolute terms was recorded at the seven levels shown in Table 2.In the analysis of absolute attainment, the two categories 'degree' and 'post-graduate degree' have been combined, as have the two categories 'low' and 'none'.For relative attainment, we had to devise a measure that could be sensitive to different distributions in the three nations as a means of indicating each respondent's position in the different education-queues.An ideal measure would rank every sample member, but in the absence of a finely differentiated measure of attainment we derive an approximation based on the distributions in Table 2. Consider as an example people in the category 'Mid-secondary' in the 1982 survey in England.They lie between the 54 th and the 73 rd percentile of the distribution of attainment in England in that survey, because 53% of respondents had lower attainment (in the categories 'Low' or 'None'), and the next 20 percentage points are in this category 'Mid-secondary'.Then the score which is given to all those people in this category is mid-way between 54 and 73, in other words 64.So, in this metric, a respondent's value reflects their relative standing in the distribution of attainment in a specific year in a specific nation, a higher value corresponding to higher levels of credentials.A second version of the metric used the distribution into the categories of attainment across all three nations.In this version, a respondent's value reflects their relative standing in relation to the whole of Britain.For the Scotland-only cohort of people born in 1936, the Britainwide distribution was approximated from Table 5.24 in Smith (2000).
For each of these two metrics, people with the same nominal credential have the same position in the education-queue.That position might differ between the nation-specific education queue and the common education-queue across all three nations.One disadvantage of defining the education-queues in this way is that it loses the distinctions among the categories of attainment, but in a sense this is intrinsic to the very idea of a queue.What matters is not the categories but the relative standing.The categories can still be studied through our measure of absolute attainment.
Outcome was recorded in terms of Registrar General class, the former official classification used by UK census authorities, with categories shown in Table 4.This measure is not ideal sociologically, but is all that is available for the oldest survey.For 2014, we use an approximation based on the official NS-SEC classification that superseded Registrar General class in 2000 (Office for National Statistics 2004: 24).The outcome measure on which we concentrate -entering classes I or II -is closely congruent with the 'managerial and professional' class in NS-SEC (analytic categories 1.1, 1.2 and 2): for the respondents whom we use from the UKHLS, 94% who were in class I&II were in the 'managerial and professional' category of NS-SEC, and 92% who were in that category were in classes I&II.
Constructing measures of parental socio-economic circumstances was more complicated.We have derived three -relating to mother's and father's education, and to the family social class.The age at which each parent left full-time education is available in the 1963, 1991 and 2000 data.In the 1982 data, the information is recorded as whether the parent had primary education only, secondary only, schooling along with post-school technical education, or higher education.In the 2014 data, the categories are having left school with no certificates or with some certificates, having gaining post-school certificates below higher-education level, or having a higher-education certificate.These disparate measures were put onto a common scale by converting them into Normal scores, thus giving a measure of the rank order of the parent's education, ranked separately within each survey year but on the same scale in each year.The sum of the two variables was used in the modelling.This approach also has the advantage of being analogous to the relative measure of attainment for the respondents.
In four of the surveys, the social class of upbringing was recorded as Registrar General class in the same categories as outcome class, at the ages shown in Table 1.The reason for using two ages (10 and 16) with the 2000 data is that the response rate of the survey in 1986 was relatively low.In each survey, class of upbringing was defined to be the higher of father's and mother's class where the latter was available (in 1991 and 2000), and father's class where only that was available (1963 and 1982).For the 2014 data, a more elaborate approach had to be used.It was not possible to use the approximation to Registrar General class that was used for the respondent's class because the parental class was not recorded in enough detail (only in the 8-category NS-SEC rather than the full version).However, in the part of the UKHLS which came from the former BHPS (20% of total), the Registrar General Class of parents had been recorded as well as 8-category NS-SEC.The relationship between Registrar General Class and 8-category NS-SEC in that part of the UKHLS sample then was used as the core of an imputation of Registrar Class for all parents in the rest of the UKHLS.
The technique was imputation by chained equations, in the package 'mice' in R (Lumley 2010, 193-200;van Buuren and Groothuis-Oudshoorn 2011).The predictor variables for the imputation were not only the 8-category NS-SEC of each parent, but also the relative education level of each parent (as defined above), and the age of the respondent (which provided some control for the age of the parents).Five sets of imputations were run, with satisfactory graphs of convergence in the terms recommended by van Buuren and Groothuis-Oudshoorn (2011), and with close matches of the kernel densities (which may be thought of as the probability distributions) of the original and imputed data.A further check was obtained by running the same structure of imputation for respondent's own class (instead of parents' class), again using the BHPS respondents to impute values of Registrar General Class for the non-BHPS respondents, with predictors the same as for parents' class but with respondent's education replacing parents' education.These imputed values could then be compared with the values of respondent's Registrar General class recorded in the data sets.The correlation of the two sets of values was high (0.81) for each of five imputations, which suggests that this method of estimating Registrar General class is reasonable.
The analysis reported below uses the first of the five imputations of father's and mother's class, again using the higher of the two; the distribution is shown in Table 3.A comment is made towards the end of the analysis section on variation among the five sets of imputations.

Statistical models
After the imputations of the parental class variable in the 2014 data set, the completed data set for that year was concatenated with the data from the other years.Repeating the analysis using different imputations involved constructing a new concatenation.The main analysis was done in R using the package 'survey' in order to be able to include the clustering, stratification, and weighting from the UKHLS.
The analysis as presented below defines dependent variables to be dichotomous.For the models of absolute attainment, three indicators were created (reaching or not reaching the thresholds of senior secondary education, of any higher education, and of a university degree).These indicators were then the dependent variables in binomial logistic regressions using the function 'svyglm'.The same was done for modelling entering or not entering the managerial and professional class I&II.For the relative measures of education, the scores were treated as dependent variables in a linear regression, also using 'svyglm' with the distribution set to 'gaussian'.The explanatory variables in the models of education were year, sex, parental education, father's class (grouped into I&II, III, and IV&V&unclassified), respondent's age in the 2014 data, nation of birth, and interactive effects among these.Respondent's education was added to the models for entering classes I&II, giving five different models: the three thresholds, and the two relative measures.The models are summarised by tables of chi-squared values corresponding to Type II tests (with the Anova function from the 'car' package in R), which are the results of dropping each term in turn from the model shown in the table.These tables are in the supplementary material.The purpose of presenting such tables is to show the relative size of the statistical effects of the various explanatory variables (and their interactions).For interpretation, what matters more are the substantive differences associated with the categories of the variables.These are calculated by predicted values from the models, using the function 'predict'.The predicted values are shown by graphs, and by specific values reported in the text.Parental education was set in the predictions to be the mean value in the sample within each of the social classes in each year, and age in the 2014 survey was set to be 30 (the median).Comment in the text is made only on differences that are unlikely to have occurred by chance (as assessed by measures of statistical significance), thus taking account of the differing sample sizes in each combination of survey year and nation.For that same reason, summary standard errors are given as footnotes to each graph.As well as the results corresponding to these dichotomous indicators, we also briefly summarise results from loglinear models (as in Bukodi and Goldthorpe (2019)).In order to allow the algorithm to converge, both the education and class variables had to be reduced to three categories (higher education; secondary education; lower than secondary; I&II; III; IV&V&unclassified); there were four survey years.Separate models were run for each combination of nation and sex.Tests were run on whether the interactive effects with year could be replaced by what are called 'unidiff' models, which aim to encapsulate the association of two other variables in each year by a single parameter.For example, in the table origin-by-education, a unidiff model would have just one association parameter in each survey year, instead of potentially 9 (from three origins by three categories of attainment and four years).The reasons to prefer our binomial approach are summarised when we summarise the results of these models at the end of the analysis section.

Analysis
The increase in educational attainment across the cohorts is clear in Table 2.The proportion completing a full secondary education, or better, rose between 1982 and 2014 from 27% to 69% in England, 20% to 68% in Wales, and 26% to 79% in Scotland.The increase in the proportion with a degree was proportionately even greater, from 7-8% to 28-32%.Correspondingly, there was a very large fall in the proportion with low or no formal attainment, from over one half to fewer than one in ten.The main difference among the nations is at higher education below a degree, where the percentage in Scotland reached higher levels than in England or Wales.The changing occupational structure is reflected in Table 3 (for origins) and Table 4 (for destinations at age around 30).The proportion with origins in classes I or II rose similarly in each nation from around one in ten to about one half.The proportion with destinations in these classes rose from around a quarter to around 40%.The rise in educational attainment and the changing occupational structures all confirm that these three societies are quite typical of developed societies in general, where -as noted abovethese trends are common.

Educational attainment
Figure 1 illustrates that Scotland's higher rates of attaining full secondary education or better are seen for people in all classes except men in the routine and manual class.Among women with origins in the managerial or professional class, the average percentage across the four cohorts was 14 points higher in Scotland than in England (p < 0.001), and 13 higher than in Wales (p = 0.002).For men, the differences were 7.8 with England (p = 0.001) and 8.4 with Wales (p = 0.039).Among people from the intermediate origin class, the average Scottish female differences were 13 with England (p < 0.001) and 16 with Wales (p < 0.001).For men, the differences were evident only from the second cohort onwards (respectively, 13 and 15, with p < 0.001).For women with origins in the routine and manual class, the average rate was 11 points higher in Scotland than in England, and 15 points higher than in Wales (p < 0.001).Figure 1 also shows that England and Wales mostly had similar percentages for each combination of sex and class, though with Wales behind England in the first two cohorts for people of intermediate-class origin (men: 15 points, p < 0.001; women: 9.1 points, p < 0.001).
The patterns for attaining any higher education qualification were similar to those in Figure 1, though with somewhat smaller differences among the nations.For degrees, the differences were generally much less.The only evidence of Scottish advantage was in the managerial and professional class, and any such advantage came to an end by 2014 for men, and by 1991 for women.A1.
Measuring education relatively in a common way across all three nations produces a pattern of differences that is similar to that for secondary education or better: Figure 2.For women from the managerial and professional class, Scotland had a better outcome in each cohort, whereas England and Wales are similar.(The average difference of Scotland compared to England is 5.2 points (p < 0.001).)The same was true for men except in the last cohort.(The average difference in the first three cohorts is 3.8 (p = 0.01), but in last cohort is only 0.2.)For the intermediate class, Scotland became better than England and Wales (Scotland compared to England, 1991-2014: male, 6.2 points, p < 0.001; female 5.1 points, p < 0.001).For the routine and manual class, there was little difference, though women in Scotland probably moved ahead of women in England and Wales in the final cohort (10 points; p = 0.04).A1.
However, when the scale of relative education is defined separately in each nation, the differences are generally smaller, as may be seen by comparing Figure 3 (separate scales) with Figure 2, noting that the vertical axis has the same range in each graph.How this comparison may be interpreted can be illustrated by considering the relative values in relation to medians.Consider, say, a Scottish woman who is typical of origin class managerial and professional.In Figure 3, this woman is estimated to be on average across the cohorts 16.7 points ahead of the Scottish median attainment, while a woman of the same class in England is 12.8 points ahead of the English median, a difference of 3.9.But when these two women are compared to the common British median (Figure 2), the Scottish women is 17.9  A1.
points ahead while the English woman is 12.7 points ahead, a difference of 5.2.Thus (reversing a common metaphor from school-effects research) the Scottish woman is a bigger fish in the bigger British pool than she is in the smaller Scottish pool.
One consequence is that the comparison of inequality across the three nations depends on the measure of attainment that we use.Figure 4 is based on the same numbers as Figure 1, but now focuses on comparing classes in the three nations.Scotland is more unequal than England or Wales up to 2000.For example, in the first three cohorts, the difference between the top and bottom class is, for men, 11 points greater in Scotland than in England (p = 0.01), and, for women, 9.4 points greater (p = 0.02).Figure 4 also shows that this difference is not because of any poorer performance by people from the routine and manual class, but rather because of a higher rate of completing secondary education by people from the top class.Indeed, the lowest class in Scotland mostly has a higher percentage in these graphs than the corresponding classes in England and Wales.The fall of inequality in this measure is greater in Scotland than elsewhere, as is also clear from this graph.The difference between the top and bottom class fell by 38 points (male) and 51 points (female) between the first and fourth cohorts in Scotland, but only by 17 and 18 points in England, and 24 and 26 points in Wales.Similar conclusions are reached from analysing the attainment of any higher-education qualification and of attaining degrees, though the differences and the changes are less than for secondary education.
Moreover, when we take the Scottish picture further back in time (Figure 5), the importance of the top class in producing the relatively high inequality in 1982 is reinforced.Between 1963 and 1982, the line for that classes rises more rapidly than the lines for the other two classes.Indeed, this graph is a typical instance of maximally maintained inequality: when an education level expands, the first group to benefit is the most advantaged, and only when it reaches saturation do the other classes rise too, so that inequality falls.So the high inequality in Scotland in 1982 when compared to England and Wales may be seen as a consequence of Scotland's having embarked earlier on a process that eventually led to a reduction of inequality, but only after at least a further two decades had elapsed.
Inequality is also greater in Scotland when attainment is measured according to the common relative scale, as is illustrated in Figure 6 (which re-presents the data from Figure 2 in order to show class disparities).In all three nations, the reduction of inequality using this relative measure is less than when using the criterion of attaining secondary education or better, exactly as we would expect from the work of Bukodi and Goldthorpe.Moreover, again, if the Scottish data are taken back to the first survey, as shown in Figure 7, inequality at the end of the series is little different from 1963.Nevertheless, the implications for opportunity are ambiguous, as with the absolute measure in Figure 4.In Figure 6, people from the two lower origin classes in Scotland, though temporarily further behind people from the top class in Scotland, are equal to or ahead of people from the corresponding lower classes in England or Wales.A3.
Thus, we have a potential paradox, depending on whether we consider changes in attainment over time or differences in attainment between nations.On the one hand, within each nation the reduction of inequality in relation to attaining a full secondary education is much greater than the reduction of inequality when attainment is defined relatively.In that sense, higher absolute attainment over time does not much improve the standing of the lowest class.That is as true within Scotland as it is elsewhere.On the other hand, the greater inequality in Scotland than elsewhere is not because of lower attainment in the lowest class, and -when seen in the longer time-scale available for Scotland -is transitional towards a reduction of inequality.If the lowest class in Scotland only ever competed with other Scottish classes of a similar age, then this point would be irrelevant to their opportunity, and they would face the situation described by Bukodi and Goldthorpe.But where the labour market and the social networks extend across a wider territory than Scotland, then the comparison with the same class outside Scotland potentially is of great importance.One way we can assess these questions is our next step, by investigating entry to a high-status class.

Class attainment
Figure 8 shows the rate of entry to the managerial and professional class by people who have attained full secondary education or better.The rate varies by social origin, despite this control for attainment.It also falls gently over time, which corresponds to the declining competitive advantage of education measured in this absolute way.But it does not vary very much or systematically by national origin.Any such national variation is less than the corresponding variation in this level of educational attainment (Figure 1).For example, in Figure 8, the Scottish rate for men whose origin is in the managerial and professional class is on average 6 points lower than the corresponding rate for people in England.We noted above from Figure 1 that the rate of attaining this educational level among such men was 7.8 points higher in Scotland than in England.So, for Scottish men from this class with this level of educational attainment, even the small deficit in the rate of entering the highest class does not cancel their advantage in attainment.Even where there is sustained or growing Scottish advantage in reaching this level of education in Figure 1, there is no sign of  A3.
any reduction in its capacity to enable entry to the highest class, as shown in Figure 8: this is true of intermediate-class men between 2000 and 2014 (growing educational advantage and also growing rate of entry), intermediate-class women throughout (sustained educational advantage but almost identical to England in entry), and lowest-class women between 2000 and 2014 (growing educational advantage but stable rates of entry).
In short, Scotland's higher attainment at the absolute educational level of secondary or better did not lead to a consistently lower rate of return than for the same absolute level elsewhere, even though, within each nation, the growth of secondary education led to a declining rate of return to that absolute level of education.
Similar conclusions were reached for attaining any higher-education qualification.For attaining a degree, the results are in Figure 9. Again, there are no systematic differences between the nations, especially in the last two cohorts.This might be thought to be uninteresting because there was little such difference in attaining a degree, as noted above.But this combination of results acts as a kind of control for the conclusions relating to secondary education or better.In essence, we can say that degrees are similarly distributed and similarly rewarded in each nation, suggesting that educational credentials are of similar value in the Britain-wide labour market.So that  A2.
reinforces the interpretation of the combination of Figures 1 and 8 that credentials are similarly rewarded despite variation among the nations in the distribution of secondary education.
Next, consider what happens to these conclusions about variation among the nations when education is measured relatively.Figure 10 shows the rate of entry to the managerial and professional class of people with high relative attainment (at the 75th percentile) in the scale measured in common across the nations.Recall from Figure 2 that Scottish people mostly had higher predicted values on this scale than similar people from elsewhere.In Figure 10, men from the managerial and professional class do have lower rates of entry to the highest class than similar men from England.But for all the other combinations of sex and class, the advantages in Scotland in relative attainment in Figure 2 are not systematically rewarded any less in Figure 10 than people of the same class and sex elsewhere.
All the analysis was re-run using the other four imputed data sets for the measurement of parental social class in 2014.In all cases, the results were very close to those reported above, using as a criterion the correlation of the predicted values as in the graphs here.For the full analysis involving all three nations, these correlations were 0.95 or higher.For  A2.
the analysis of Scotland alone, the correlations were also at least 0.95, except with the modelling of entry to class I&II in terms of the relative measures of education, in which the mimimum correlation was 0.87.So we may conclude that the choice of imputation did not affect our interpretation.
The analysis of educational inequality (using the absolute definitions) was also re-run using loglinear models, one for each combination of sex and nation.There was clear evidence of a three-way interaction in the case of all except males in Scotland: that is, there was evidence that the association of origin class with education changed over time.This in effect replicates our findings but with fewer explanatory variables.The unidiff model did not capture this interaction, and so is an inadequate approximation to it.Nevertheless, it did confirm one point in our main analysis: the steeper decline of inequality in Scotland than elsewhere.In the final cohort, the unidiff parameter in Scotland had fallen to 0.4 for both men and women (from the reference value of 1 in the oldest cohort), whereas in England and in Wales for men it was over 0.6, and for women was over 0.5.There are several advantages of using the binomial modelling that we have concentrated on.Many more explanatory variables can be included, including continuous variables, with more  A2.
complex interactions among them.Unidiff only works for three-way tables, and so needs multiple separate analysis to be done, and even then, as we have noted in the Methods section, the algorithm is unstable when many cells of the cross-classified table are small.The full loglinear model for the classification origin-by-education-by-cohort is equivalent to the series of nested binomial models that we have used, and any interpretation of the education margin of the full model becomes, in practice, a consideration of these nested thresholds, such as the contrast of holding or not holding a higher-education credential.

Conclusions
The strength of this analysis of educational and social-class attainment at ages around 30 is the length of time which it covers and the capacity to consider distinct education systems serving a labour market that generally has operated in a common way.By using a cohort born in 1946 we have been able to start the series with people who attended school before the ending of selection for secondary school, and well before the expansion of higher education.By using the large UK Household Longitudinal Study to construct a cohort born in the last quarter of the twentieth century, we have taken the series forward to the second decade of the new century, while retaining a large enough sub-sample of people born in Scotland and Wales to allow comparison of both of these with England.For Scotland, we were able to take the starting point back to people who entered the stable selective system in the immediately post-war period.
The weaknesses of the analysis are consequences of using surveys covering a very long period, with the resulting differences of definitions and detail.The most sociologically serious issue that then arises is that we had to use Registrar General social class to measure both origins and destinations.However, we noted that, for entry to the professional and managerial class I&II, this is likely to give us similar conclusions to those that would have arisen if we had been able to use the class scheme which replaced the Registrar General measure.Being able to use the Registrar General scheme for origin class in the latest survey required estimating it by means of statistical imputation, but there is evidence (reported in the Methods section) that this was probably quite a valid model of estimation, and (from the Analysis section) that using statistical imputation was a reliable technique for doing so.
On this basis, we have been able to offer tentative answers to the research questions, both of which resulted from applying the ideas of relative educational attainment -as developed by Bukodi and Goldthorpe (2016) -to a situation where the social context for the relative measures might differ from the context for measuring the relative status of social-class outcomes.For attaining at least a full secondary education, Scotland had higher attainment than in England or Wales, except among men in the lowest class.The same was true of attaining a higher-education qualification.When education was measured relatively to a common British norm, these Scottish advantages persisted, but not when the norm was specific to each nation.Inequality was consistently greater in Scotland than elsewhere except when all classes were close to saturation, which was only for secondary education in the later time points.But not only was the Scottish inequality not due to any poorer performance of the lowest Scottish class.Taking the Scottish data back to the 1936 cohort showed that it was also a temporary phenomenon associated with the initial period of expansion.
Then the crucial test was whether these differences in educational attainment were associated with different returns in the rate of entry to the managerial and professional class.Our data confirmed, within each nation, the findings of Bukodi and Goldthorpe that over time, at each level of absolute attainment, its declining relative standing led to declining rewards in social-class outcomes.But that pattern mostly did not apply over space.There was no evidence that the higher relative share of, say, secondary school attainment in Scotland led to poorer class outcomes than the same absolute measure in England or Wales.
In all these respects, moreover, Wales was similar to England.So the greater distinctiveness of Scottish educational policy over many decades may have enabled its students to take advantage of education in the classic way that peripheral societies have been able to do.Wales, also peripheral, was not able to provide this advantage historically, being too tightly tied to the dominant educational model of England.In terms of Thurow's queuing theory for employment, the education-queue produced by Scotland between the 1930s and the early years of the present century enabled people to join the pan-Britain job-queue at a higher point than people emerging in the education-queue in England or Wales.
These comments remain speculative, and testing them would require the analysis of specific occupational careers using much larger data sets for students from Wales and Scotland.The speculations may also be tested further in practice in the coming decades as education policy in Wales -as well as in Scotland -diverges further from that in England because of legislative devolution in 1999.We might also draw a tentative policy conclusion from the theoretical conclusions about education-queues and job-queues.It continues to make sense for policy in peripheral societies, such as Scotland and Wales, to invest in expanding access to secondary and higher education not only for consumption reasons but also to confer a competitive advantage, despite the conclusions that general expansion merely shifts inequality to higher levels of the system: expansion of this kind can be of competitive value to young people leaving the education system of peripheral societies if they then gain an advantage in a job-queue that extends across a wider territory.This advantage is contingent, because it depends on there being less expansion in the educationqueue of the core society, in this case England.Any advantage is also likely to be temporary, as the core society catches up.But what we can say in conclusion is that the fundamental insight of Bukodi and Goldthorpe in forcing attention to relative definitions of educational attainment when seeking to understand change over time is also of great value in understanding variation in space.More education may not be a competitive advantage when the distribution of attainment shifts upwards, but our analysis suggests that it may be an advantage when distinct education systems feed into a common occupational structure.

Figure 2 .
Figure 2. Education score (common metric), by sex, class, year and nation.'Common metric' means that the score is measured in the same way in all three nations: see text.Average standard error: England, 1.1; Scotland, 2.8; Wales, 3.6.Source: predicted values from Model 4 in TableA1.

Figure 3 .
Figure 3. Education score (nationally specific metrics), by sex, class, year and nation.'Nationally specific metrics' means that the score is measured differently in each nation: see text.Average standard error: England, 1.1; Scotland, 2.8; Wales, 3.7.Source predicted values from Model 5 in TableA1.

Figure 4 .
Figure 4. Attainment of full secondary education or better, by sex, nation, year and class.Same data as Figure 1.

Figure 5 .
Figure 5. Attainment of full secondary education or better, by sex, year and class: Scotland only.Average standard error: 4.8.Source: predicted values from Model 3 in TableA3.

Figure 6 .
Figure 6.Education score (common metric), by sex, nation, year and class.Same data as Figure 2.

Figure 7 .
Figure 7. Education score (common metric), by sex, year and class: Scotland only.'Common metric' means that the score is measured in the same way in all three nations: see text.Average standard error: 2.6.Source: predicted values from Model 4 in TableA3.

Figure 8 .
Figure 8. Entry to managerial and professional class, by sex, class, year and nation:people who attained full secondary education or better.Average standard error: England, 2.8; Scotland, 5.8; Wales, 7.8.Source: predicted values from Model 3 in TableA2.

Figure 9 .
Figure 9. Entry to managerial and professional class, by sex, class, year and nation:people who attained university degree.Average standard error: England, 4.0; Scotland, 7.0; Wales, 9.0.Source: predicted values from Model 1 in TableA2.

Figure 10 .
Figure 10.Entry to managerial and professional class, by sex, class, year and nation:people at upper quartile of common metric of relative attainment.'Common metric' means that the score is measured in the same way in all three nations: see text.Average standard error: England, 2.5; Scotland, 5.7; Wales, 7.5.Source: predicted values from Model 4 in TableA2.

Table 2 .
Highest educational attainment at age c.30, by survey and nation.

Table 1 .
Sources of data.

Table 3 .
Social class of upbringing, by survey and nation.Percentages in rows.For sample sizes, see Table 2. 1982 and 2014 percentages are weighted.Father's class for 1963 and 1982 surveys; higher of father's and mother's class for 1991, 2000 and 2014 surveys.2014 percentages include imputed data: see text.

Table 4 .
Social class of destination at age c.30, by survey and nation.Percentages in rows.For sample sizes, see Table 2. 1982 and 2014 percentages are weighted.