Brendan Halpin (1999) 'Is Class Changing? A Work-Life History Perspective on the Salariat'
Sociological Research Online, vol. 4, no. 3, <http://www.socresonline.org.uk/4/3/halpin.html>

To cite articles published in Sociological Research Online, please reference the above information and include paragraph numbers if necessary

Received: 26/2/1999 Accepted: 27/9/1999 Published: 30/9/1999

Abstract

Has the massive transformation of the class structure over the twentieth century changed the consequences of class? In particular, does the fact that the salariat has taken over from the manual working classes as the largest category mean that the implications of membership of the salariat for one's life chances is no longer the same? This paper takes retrospective life-history data from the British Household Panel Study and models patterns of change in the structure of work-life mobility between the ages of 25 and 35 for individuals born between 1900 and 1959. The purpose is to seek evidence of broad changes in the consequences of class, through the middle and late 20th century, using an extremely valuable data resource. The evidence suggests that there is cross-cohort change in the patterns of work-life mobility, both in terms of traditional class categories and in terms of the relationship between class and more general employment status categories, but more strongly in the latter case. In general, the pattern is one of declining immobility, including declining salariat retentiveness. The paper concludes with a consideration of what the data mean, and what this particular bounded analysis has to say about the question of change in the consequences of class.

Keywords:

Class Analysis; Cohort; Employment; Loglinear; Longitudinal; Social Mobility

Introduction

1.1

Is the structure of social class changing? With the huge growth in white-collar and administrative work in western societies throughout the second half of the twentieth century, can we continue to use concepts of class developed in a time when the mass class was manual? Further, given changes in recent years in the nature of white-collar employment that many commentators see as a radical end to the security hitherto enjoyed, do we need to make a fundamental change to the way we see the position of the 'middle classes'?

1.2

These are grand questions, outside the scope of, but motivating, this paper: by exploiting work-life history data to examine the longitudinal consequences of class, we can begin to address these issues. In particular, can we find evidence of fundamental change in the patterns of longitudinal security of different class locations? Comparing successive cohorts' careers, can we find systematic change in the prospective 'life chances' that class location at a particular time confers?

1.3

This paper reports an analysis of class location and its consequences, in particular the professional-managerial class or 'salariat', at different points in the life cycle, seeking evidence of change in the pattern of association across cohort (and therefore through historical time), using British Household Panel Study retrospective work-life history data.

Class as a Contested Concept

2.1

As a sociological concept class has a long pedigree, playing an important role in some traditions, vigorously rejected by others. This is as true now as ever, with a resurgence of intellectual and popular debate about the applicability of the concept to late twentieth century society. Opponents of class analysis have claimed variously that it carries a lot of Marxist and historicist baggage, or is otherwise demonstrably irrelevant to the analysis of contemporary societies (e.g., Hindess 1987; Turner 1989; Pahl 1989, 1993; Sørenson 1991; Pakulski and Waters 1996). Other factors, such as gender, race, housing tenure and consumption (Saunders; 1990), lifestyle or preferences (Hakim; 1998) are claimed to supersede, rather than supplement it. Proponents of class analysis either reject these claims outright, or assert that certain of the targets attacked are peripheral to the core concept of class (especially Goldthorpe and Marshall 1992; see also Breen and Rottman 1995; Scott 1994, 1996; Marshall 1997).

2.2

An important element of the debate has concerned recent changes in employment conditions of professional-managerial workers, altering or even destroying some of their characteristic advantages; this perception is also widespread in journalism and management literature (e.g., Handy; 1994). To a significant extent these claims are prompted by perceptions of change in the way large organisations treat their white collar employees: practices such as the 'de-layering' and 'downsizing' of the late 1980s and early 1990s are adduced as evidence that the security and predictability of the traditional bureaucratic career no longer apply, as organisations are becoming capable of, and the market is demanding, closer and more exploitative control of higher white-collar workers. One could say that the inexorable progress of the 'iron cage of bureaucracy' has come to degrade the position of the bureaucrats themselves.

2.3

Some of this corporate re-structuring is likely, of course, to have been driven by the business cycle or other entirely market-based processes, but there is a clear tension in the employment situation of members of the salariat. That is, the impossibility of close control of their day-to-day work gives them an advantage which their employing organisations have a substantial incentive to overturn, where it becomes possible. Thus it is reasonable that, over time, certain occupations will move from a service relationship to a more constrained one. However, it is far less plausible that the service relationship as a whole could somehow be overturned by organisational and technological changes: the service relationship is a solution to a quite general problem of control (see Goldthorpe; 2000).

2.4

The growth in size in the salariat is impressive: in the data reported below we see a rise in salariat membership at age 35 from less than 15 percent for men in the oldest cohort (born before 1920) to 37 percent for men in the youngest cohort (born in the 1950s). For women the rise is of similar magnitude from a lower base, 12 to 27 percent. Between the 1950s and the 1990s the salariat has thus more than doubled in size. Growth of this magnitude suggests certain consequences. First, the incentive for employing organisations to redefine the service relationship has become more significant simply because it is more widespread. Second - and this may be naïve sociology - as the group becomes larger one suspects it must lose some if its élite status; at any rate the suspicion arises that in some respect this growth of advantage is more apparent than real and that the nature of service-class occupations is deteriorating in some measure as they become more common. More formally, it is plausible that the means of the expansion of the salariat, which is largely the growth of large-scale organisations, is also the means of enforcing less advantageous conditions on it. Therefore it becomes important to look for evidence of historical change in the characteristics of the salariat, ideally with a source of information that is consistent over time.

2.5

There is another relevant thread in the literature on class, and in particular on the salariat: among writers who broadly endorse class analysis, the concept of the salariat as a homogeneous group has been criticised, and the argument made that professional and managerial occupations constitute two separate clusters of class locations (Halford and Savage; 1995; Mills; 1995; Savage et al.; 1992). It is clear that the work-life trajectories of professional and managerial workers are relatively distinct (despite evidence of increasing movement between these categories), though intergenerationally they are more homogeneous. Theoretically the argument starts from the idea that classes can be distinguished according to the different sorts of assets they possess (drawing in particular on the work of Erik Olin Wright (1985)), and the specialised, credentialled, skill assets professionals hold are argued to have different consequences from the organisational assets of managers (Butler and Savage; 1995a). While this is not the place to debate the merits of assets versus employment relations as the underpinning of class (and differences between professionals and other white-collar workers are not directly dealt with in the analysis below), the fact that there are distinguishable subgroups within the salariat and that their proportions are changing, is an important potential dynamic of change that has to be taken into account. As will be seen below, the disproportionate growth of non-professional salariat occupations (and indeed, of professionals with the employment status of employees) is one of the likely sources of change in the 'average' characteristics of the class.

2.6

Thus we see that the applicability of class to late twentieth-century society is widely contested, with particular focus on the changing conditions of the salariat. Even among class analysts, the status of the salariat as a homogeneous category has been contested. So what has been the experience of the salariat?

Class as a Longitudinal Concept

3.1

In much existing sociological work, class as a measure is an attempt to use cross-sectional data to pick up important aspects of likely longitudinal experience. This is clear even in Weber's development of the concept of life chances (Weber; 1968): positions vary in their likely consequences throughout the life course (the concept is partly probabilistic, but also very clearly longitudinal). This is also more or less explicit in writers like Goldthorpe (e.g., Erikson and Goldthorpe; 1992; Goldthorpe; 1987) or Scott (1996), though of course, for all these writers there is much more substance to the concept of class than longitudinal predictive power.

3.2

The main tool of quantitative sociology is the cross-sectional survey, something that has both strengths and weaknesses. Among the weaknesses of this perspective are the difficulty in causal reasoning based on a snapshot, the potential transience of the observed conditions, and the fact that time and the processes of the lifecourse tend to be obscured. The use of social class in empirical research (be it the Registrar-General's Social Class or a theoretically based scheme such as Goldthorpe's or the new ONS Socio-Economic Classification (the NS-SEC, see Rose and O'Reilly; 1998)) is often oriented to getting around the second of these, transience, by identifying current characteristics associated with longer-term outcomes - for instance, class can be a better predictor of life-time income than current income is.

3.3

Longitudinal data, on the other hand, allow us to avoid some of these problems. Data about conditions at more than one time point allow us the luxury of committing the 'post hoc ergo propter hoc' error: if B follows A in time, to claim that A causes B. Cross-sectional data that show association between A and B do not allow us to choose between 'A causes B' and 'B causes A' but with longitudinal data if we can show that B happens before A, we can at least exclude the claim that A causes B. Also with longitudinal data, transience (or durability) becomes something we observe, rather than a weakness in the data. For instance, we can see how people move in and out of poverty over time rather than report a simple poverty rate (Jenkins and Jarvis; 1998). A further important advantage of longitudinal data from a sociological perspective is the re-inclusion of time, as calendar, cohort and lifecourse. The re-inclusion of lifecourse is perhaps the most valuable contribution of longitudinal data. The cross-sectional measurement of class, for instance, is a pretty thin thing, compared with the richer picture of the life-long trajectory we can derive from longitudinal data.

3.4

The recent increase in availability of longitudinal data¹ makes it necessary to look again at class as a longitudinal concept. In particular it provides the opportunity to examine the association of class with longitudinal outcomes, to validate it or replace it with lower-level concepts where appropriate, and to better understand the mechanisms by which it bears on longitudinal experience. That is, having longitudinal information means it is no longer necessary to use class as a proxy for its longitudinal consequences, but also that we can examine these very longitudinal consequences.

3.5

This paper seeks to examine the situation of the salariat in British society in the mid- to late-twentieth century, using longitudinal data to look for evidence of change in its consequences across the decades. If the critics of class analysis are right (in particular those who argue that class has become irrelevant) we should see a waning of its association with later states. It may be too early to test the claims of those who see very recent change as fundamental (i.e., if the 'job for life' has recently disappeared, we will have to wait some portion of a lifetime to see the consequences) but if the changes in employment conditions are profound it is likely that some evidence of the process should be visible. But even if we accept the fundamentals of class analysis, we have to ask to what extent the extraordinary growth in white-collar occupations has had on the nature of the salariat, both in absolute terms and in terms of the changing mix between professional and managerial occupations.

Class versus 'General Status'

4.1

Social mobility research conventionally analyses square tables relating class position at two time points. However, because of the present interest in the stability and meaning of the measure of class it makes sense to displace the conventional method with an analysis that relates the class measure, in particular the salariat, with phenomena to which it is understood to be causally linked. That is, it is interesting to relate the salariat to states the likelihood of entry to which is part of the 'life-chances' its membership is taken to affect.

4.2

Therefore the main analysis reported is of what may be called 'general status', comprising a set of states including being in a salariat occupation, being unemployed and so on (see below for fuller detail). A parallel analysis using conventional class categories is also carried out, in order to make clear the effect of using the non-conventional categories. Since conventional class analyses tend to show little change in the pattern of association over time, it is important to identify the extent to which change evident in the new analysis is due to the different categories used, and how much is due to change in the data which will also show up in a conventional analysis.

Data and Method

5.1

The data set used to address this issue is the British Household Panel Study, and in particular, its work-life history components. The BHPS is primarily a panel study, and as such collects detailed labour market status histories during the period of the panel (September 1991 to the present, and continuing), but it also collected two retrospective labour-market histories: in its second year it collected a comprehensive employment-status history, covering all spells since first leaving full-time education, and in its third year it collected information on all jobs held. By combining the two (see Halpin; 1998) into a single history, and then integrating that with panel-derived data, a data set can be constructed with enough information to look at class position in the context of labour market status, and to examine, for instance, the subsequent pattern of unemployment conditioned on class at a given time. There are many possible ways of conducting such an analysis, but because of problems of recall bias (see next section) this paper examines the pattern of association between the status at two time points, separated by a 10-year span (analysis in terms of durations or transitions will be more severely affected by recall bias than that in terms of status at particular moments). If class is a good predictor of future states, we should find a strong relationship, even over a ten-year period.

**Figure 1:** Cohort, age and historical time
$\includegraphics{lexisminus.eps}$

Bias

6.1

Measurement error is an ever-present problem in survey data, and in longitudinal and especially retrospective data it is particularly significant, in the form of recall bias. While there may not be a simple relationship between length of the recall period and the amount of error, there is certainly an association. As Figure 1 shows, the present data set may involve recall periods up to 70 years, for the very oldest members of the earliest cohort remembering their state at age 25 (though for most respondents the period is much less). What is damaging from the analyst's point of view is that the length of recall is directly associated with cohort, and thus apparent cross-cohort change may simply be due to measurement error. However, given the sorts of biases that can be expected to operate, this problem will be more acute for certain forms of analysis than others. Paull (1996) makes a number of hypotheses about how recall error might bear on retrospective data:

Recall error may depend on the length of the recall period
Short spells are more likely to be forgotten
Spell durations will be exaggerated
Transitions will be under-reported
Unemployment will be under-reported.

6.2

Elias (1997) has corroborated the latter point in detail, for the BHPS and for other retrospective data sets. He finds the recall of unemployment to be particularly poor, and to tail off sharply as the recall period extends. Apart from the poor recollection of unemployment, the other effects suggested will be particularly damaging for analyses of duration, such as hazard models, or models that focus on transitions. Thus a model that shows the hazard of leaving a job to be higher for younger cohorts cannot be trusted: it is as likely that younger cohorts simply remember more job changes.

6.3

However, if instead of spells, durations and transitions, we use the retrospective data to obtain estimates of respondents' states at given times, we avoid some of the most important problems. There will still be measurement error, and it will still be associated with cohort: older cohorts will show less unemployment, and more of their reports will be wrong in general. But we will not be depending on the absence of error over the entire spell, as we would when using hazard models (i.e., if a spell covers an omitted period in another state, its duration will be much greater than it should be). Therefore the following approach is used in this paper: for each respondent the states at age 25 and at age 35 are extracted and the relationship between them modelled. With a ten-year separation, the point estimates of state can be assumed to be reasonably independent. That is, if the age-25 state is erroneous it is not likely that the age-35 state will be wrongly reported for the same reason. However, it is not impossible, nor is it impossible that the state correctly reported for one age is also reported for the other. Nevertheless, this approach is less vulnerable to the sorts of data-quality problems anticipated.

The Method

7.1

The methodological paradigm this paper uses is one of association models of state at age 25 and age 35 (and in some cases age 25 and age 40, lengthening the span at the expense of losing approximately half of the youngest cohort), specifically, loglinear models of square turnover tables, with mobility over a ten-year span. In particular, the focus is on how the association changes across cohort.

7.2

Because of the interest in class, it would seem logical to model mobility between class categories, and this is indeed done in parallel with the main analysis. But there are several reasons why this is not enough. Primarily, we are interested in issues relating to change in the nature of class, and to model only in terms of the categories of interest makes it hard to see how they may be changing. Secondly, the way respondents are assigned to class categories tends to obscure information relevant to this analysis. For instance, conventionally respondents are assigned to the category appropriate for their current or last occupation and employment status. This has the consequence that unemployment and non-employment disappear which, while appropriate in many contexts, is a drawback for analysis that might consider entry to these states as interesting outcomes.

7.3

Therefore the primary analysis is in terms of the following set of categories:

In a salariat occupation (i.e., professional/managerial)
In a non-salariat occupation
Unemployed
Not in the labour force.

In practice these categories are supplemented by respondents in employment but without occupational information, and therefore not assignable to a class category.² It is important to include this category as such recall discrepancies may be associated with cohort, and its exclusion may bias the results.

7.4

A secondary advantage in using this more general set of categories is that the sample is slightly larger, as there are respondents for whom the class variable is missing at one or other age (due, for instance, to never having been in the labour force).

7.5

Given that the concern with the changing nature of class focuses to a large extent on the changing nature of the service class (or salariat), either due to its enormous historical increase, or due to changes in the organisational context of white-collar work, class enters this scheme as a division between the salariat and all other classes.

Table 1: The general status variable

Category	Description
1	In a salariat occupation
2	In a non-salariat occupation
3	Employed, occupation not known
4	Unemployed
5	Not in the labour force

Table 2: The reduced version of the EGP class scheme

Class	Description
I-II	The 'salariat': professional and managerial employees
III	Routine non-manual employees
IV	Self-employed and small employers, and farmers
V-VI	Supervisory and skilled manual employees
VII	Semi- and unskilled manual employees, industrial and agricultural

Note: This is based on the seven category EGP version of the Goldthorpe class schema, described in Erikson and Goldthorpe (1992), pp. 35ff, especially figure 2.1.

7.6

Tables 1 and 2 summarise the categories of the two variables. The class categories in Table 2 are based on the Goldthorpe class schema (see inter alia Erikson and Goldthorpe; 1992) but rather than use his seven-category version, we have collapsed the two agricultural classes (farmers and agricultural labourers) into their non-agricultural analogues (classes IV and VII, respectively), since agriculture is numerically unimportant in Britain.

Table 3: Cohort by sex

Cohort	General status			Class
	Men	Women	Total	Men	Women	Total
1900-19	298	507	805	231	347	578
1920-29	486	600	1086	401	499	900
1930-39	524	597	1121	480	498	978
1940-49	745	872	1617	694	768	1462
1950-59	803	890	1693	761	775	1536
Total	2856	3466	6322	2567	2887	5454

Note: The numbers in each analysis differ, primarily because of missing class information.

Descriptives

8.1

Though the BHPS nominally has of the order of 10,000 respondents, the sample used in this analysis is somewhat smaller. This is primarily because we restrict ourselves to the 7,000 or so for whom we have retrospective life-history data. Missing values reduce this sample further to c.6,300 for the general status analysis and c.5,450 for the class analysis. These respondents are distributed across the five cohort groups (those born before 1920, and thereafter on a decennial basis until 1959) as shown in Table 3: women's greater longevity is evident in their over-representation in the earlier cohorts.

Table 4: Status at 25 by status at 35, men and women

Status at 25	Status at 35
	Salariat	Non-salariat	Employed (job not known)	Unemployed	Non-employed	Total
Men
Salariat	507	32	2	9	9	559
Non-salariat	129	1573	10	56	39	1807
Employed (unknown)	12	15	179	13	5	224
Unemployed	2	17	3	16	5	43
Non-employed	61	109	24	2	27	223
Total	711	1746	218	96	85	2856
Women
Salariat	242	26	2	3	120	393
Non-salariat	59	743	6	8	466	1282
Employed (unknown)	15	17	76	0	104	212
Unemployed	4	6	1	14	3	28
Non-employed	95	545	59	6	846	1551
Total	415	1337	144	31	1539	3466

8.2

Table 4 shows the relationship between general status at age 25 and age 35, by sex, for the whole sample. Looking at the marginals (i.e., the row and column totals) it is clear that for men the most important state is non-salariat employment - at each age, and indeed the largest single cell in the table is that indicating presence in this state at both ages. For women the largest category at each age is non-employment, closely followed by non-salariat employment, with the corresponding diagonal cells being the largest. Whereas for men the concentration in one category means that more than half the sample are 'immobile'³ in non-salariat employment, much more of the cases in the women's table are off-diagonal, particularly in cells representing movement between the two largest categories. This is not to say that there is not a lot more going on: e.g., for both sexes movement from non-salariat to salariat employment is relatively common (but the movement is not symmetrical: either because of life-cycle effect - an upgrading of occupational status between age 25 and age 35 - or the retentiveness of salariat occupations, movement from salariat to non-salariat occupations is less common).

Figure 2: Cross-tabulation of cohort by sex by general status, age 25 and age 35.

Men
Women

This is a cross-tabulation with numbers replaced by boxes whose area is proportional to the cell percentage within each 5 x 5 subtable. In each subtable the area of the boxes sums to the same quantity. Empty cells are indicated by circles.

Table 5: Class at 25 by class at 35, men and women

Class at 25	Class at 35
	I-II	III	IV	V-VI	VII	Total
Men
I-II	549	11	16	4	6	586
III	63	177	14	9	17	280
IV	3	3	209	8	8	231
V-VI	68	12	45	591	74	790
VII	33	13	58	65	511	680
Total	716	216	342	677	616	2567
Women
I-II	434	30	8	5	10	487
III	99	1085	41	23	120	1368
IV	2	5	48	0	2	57
V-VI	8	23	11	173	43	258
VII	15	95	15	31	561	717
Total	558	1238	123	232	736	2887

8.3

Table 5 shows the analogous table for the five-category class variable (described in Table 2). For men and women, and at both ages, this is a much more even distribution, mostly because the 'non-salariat' is spread over four classes. Nonetheless we see a good deal of immobility, with well over half the men represented in the I-II, V-VI and VII diagonal cells, and over 1,000 of the c.2,900 women immobile in III, routine non-manual work. Again, we can see some evidence of upward mobility, in the greater incidence of moves into the salariat than out.

Figure 3: Cross-tabulation of cohort by sex by class, age 25 and age 35.

Men
Women

This is a cross-tabulation with numbers replaced by boxes whose area is proportional to the cell percentage within each 5 x 5 subtable. In each subtable the area of the boxes sums to the same quantity. Empty cells are indicated by circles.

8.4

However, simple inspection is not adequate to perceive structure that is not simply a reflection of the overall distribution at each age: for this we need to explicitly model the association. Moreover, when we add the dimension of cohort to each table (raising the number of cells in each from 25 to 125) even inspection becomes difficult, and it is infeasible to detect changing patterns in the relationship between early and late states. Nonetheless, inspection of data is always to be recommended, and to this end Figures 2 and 3 present the tables in a graphical form, designed to highlight the pattern of association between early and late states in each cohort in such a way that broad cross-cohort (and male-female) differences are relatively easy to see. Each

panel of the figures represents a particular cohort and sex, in the same format as Table 4. In each panel, the area of the boxes is proportional to the percentage in each cell, and thus the total area of the boxes in each panel is the same (empty cells are indicated by circles). This facilitates comparison across panels, as the effect of cohort size is eliminated.⁴

8.5

Looking first at Figure 2, at the column for men, we can see that the diagonality apparent in Table 4 is repeated within each cohort. What is interesting is to glance down the column and see how this pattern changes: the amount of off-diagonal ink does not change much, with one exception: cohorts 1 and 2 have substantial numbers not in the labour force at age 25 who move into the labour force by age 35. The bulk of these individuals were in the armed forces: a clear period effect. The distribution of ink on the diagonal shifts too: in earlier cohorts category 3 is sizeable, but it declines to very small numbers by cohort 5. This is the incomplete-data category, where we do not know the occupation, and it does, as expected, increase with length of recall period. Otherwise, non-salariat occupations are much more common than salariat occupations, but this declines sharply across cohort: by cohort 5 the ratio is closer to 2:1 than the 8:1 seen earlier. Overall these are very highly patterned tables, with the vast majority of cases residing in two or three diagonal cells (this causes certain problems with estimation: see appendix D below).

8.6

When we look at the column for women, we see far less diagonality in all five cohorts. Women move in and out of the labour force for a variety of reasons, so the row and column indicating non-employment are as well-populated as the diagonal. Tracking down along the cohorts we can see a certain but not dramatic growth in salariat employment, and a decline in the indeterminate employment category. The most dramatic change is probably the decline in immobility in non-employment: there is far more movement into employment from this category in later cohorts.

8.7

Turning our attention to Figure 3 we can see how different the class tables are. The first thing to note is how now both sexes exhibit substantial diagonality. In the case of women, this is because of excluding the effect of non-employment. For all the diagonality, however, the incidence of zero cells is less than in Figure 2. Looking at men, the cross-cohort change is a move from a predominance of manual work (classes V-VI and VII) to one of salariat employment. For women, there is a steady decline in unskilled work, class VII, which probably reflects the decline in domestic service. In all cohorts, females outside this class are largely in routine-non manual work (class III), and to a lesser extent in the salariat. Another visible feature is the apparent increase in outflow from routine non-manual, in particular to the salariat.

8.8

However, while this exercise provides an overview of the structure of the data, it is next to impossible to see change in the relationship between status at 25 and at 35 that is not driven by the substantial changes in distributions of these states. This requires formal modelling of the tables.

Models

9.1

The same set of models is fitted to both data sets, in an attempt to test for cross-cohort change in the pattern of association. The models are chosen so that the contrasts between them will pick up different possible forms of change. All models are fitted separately for men and women. Results are presented below for general status, and class, for the age spans 25-35 and 25-40 (see Tables 6 and 7, discussed below).

9.2

More formal descriptions of the models and their relations are available in an appendix (in appendix A; hyperlinks to this appendix are present in all references to the models in the main text).

9.3

Eight distinct models are considered. (For a more formal presentation of the models see appendix B.) Model 1 is that consisting of all two-way interactions (and, implicitly, their first-order components). This can be considered a base model against which more interesting models can be compared. It takes account of the fact that early status is associated with late status, and both are associated with cohort (that is, it controls for the fact that, for instance, the distribution of status at age 25 is different across the different cohorts). However, it does not allow the relationship between early and late status to change across cohort: insofar as the model fits well it asserts that though the distribution of states (at both ages) may change substantially, the underlying association between them - the pattern of odds ratios in each cohort-specific subtable - stays the same. In social mobility terms (Erikson and Goldthorpe; 1992, pp. 55ff) the pattern of relative mobility rates is constant.

9.4

Having fitted all the two-way interactions, the next logical step appears to be to fit the three-way interaction between status at 25, at 35 and cohort. However, this yields the saturated model, which fits the data exactly, with no degrees of freedom and no explanatory power. Instead the next seven models considered fit constrained versions, or subsets, of the full three way interaction in order to test for different aspects of change in the pattern of association across cohorts. The remaining models are in pairs, both allowing cross-cohort change in a subset of the status-at-25/status-at-35 subtable, but one constrained so that the difference between each successive cohort is proportionately constant (and thus linear in the logs), the other allowing unconstrained change. The former, 'trend', model is more parsimonious.

9.5

The first pair of models focuses on the salariat, by including a special term for the cells indicating retention therein, and allowing this to change across cohort. We thus allow the predicted numbers of cases in the salariat to change across cohort, over and above the change we would expect from the 2-way model, model 1. The 'trend' variant is model 2, which allows this extra change to be proportional, and the 'free' variant is model 3, which allows non-monotonic change.

9.6

An equally simple form the change could take is that of an overall change in immobility: not just the salariat, but all states might be changing in the same way and to the same degree in their propensity to hold people at both ages. Models 4 and 5 allow this sort of change, respectively in trend and non-monotonic form. These can be referred to as 'diagonal' models as they allow change in the number of cases in the diagonal cells.

9.7

One step less restrictive than these models are models 6 and 7. These allow cross-cohort change in immobility, but allow it to be different for each state. Thus we could find that, for instance, the salariat is becoming less likely to hold people at both ages while unemployment becomes more likely to. These models are generalisations of both the 'salariat' models, 2 and 3, (they allow the salariat and other diagonal cells to vary) and of the 'diagonal' models, 4 and 5.

9.8

Finally we come to the full trend model, model 8. Here we allow the full status-at-25/at-35 pattern of association to vary across cohort, in a trending or log-linear manner. That is, each cell in the status-at-25/at-35 subtable is allowed to vary in this trending manner. This allows certain forms of mobility (e.g., from the salariat to non-employment) to become more or less common across cohort, as well as permitting change in immobility as models 4 to 7 do. The 'free' equivalent of this model is the saturated model, model 9, which simply reproduces the data with no explanatory power. 'Trend' models of this form are described in Payne et al. (1994).

9.9

To recapitulate, we fit a baseline model of no change, and then four sorts of cross-cohort change in association:

1.: change in salariat immobility
2.: overall change in immobility ('diagonal' models)
3.: state-specific change in immobility and
4.: trending change in immobility and mobility.

9.10

For further detail on the models see the appendix, which contains

a graph mapping the relationships between the models (section A)
a slightly more formal presentation of the models (section B)
a discussion on how to choose between them statistically (section C), and
a discussion of the problem of sparsity, that is, the relatively large number of empty cells (section D).

Results: General status to age 35

10.1

Table 6 presents results for the models of general status. For each model, the significance of its improvement in fit is given, relative to the immediately simpler model (this is for model 2 over model 1, model 3 over model 2, model 4 over model 1, model 5 over model 4, model 6 over model 4, model 7 over model 6, and model 8 over model 6; see appendices A and B to clarify the logic of this set of comparisons).

Table 6: Fitting the general status tables

		Significance of improvement in fit over next simpler model
		25-35		25-40
New	Simpler
Model	Model	Men	Women	Men	Women
2: Salariat (trend)	1	0.001	0.000	0.002	0.002
3: Salariat (non-monotonic)	2	0.339	0.059	0.059	0.059
4: General immobility (t)	1	0.827	0.000	0.004	0.000
5: General immobility (n-m)	4	0.000	0.065	0.000	0.511
6: State-specific immob. (t)	4	0.000	0.020	0.000	0.002
7: State-specific immob. (n-m)	6	0.002	0.074	0.019	0.027
8: Full trend	6	0.000	0.048	0.002	0.300

Note: The models are described in the text. The p-values are the significance of the improvement in fit over the next simpler model. Counts are adjusted so that zero values are incremented by 0.01. Results with raw counts are given in Table A.1.

10.2

Looking first at the figures for men, we see that model 2 improves the fit significantly: allowing salariat immobility to vary in a trending fashion fits better than the 2-way model (of no cross-cohort change). A trending effect is sufficient: non-monotonic model 3 fits no better than model 2. A single trending effect for the main diagonal (model 4) is not supported, but a 'free' effect is (model 5). Allowing separate trending effects for each diagonal cell (model 6) fits much better than the single trend; model 7, where the change is allowed to be non-linear, fits better again. Model 8, the overall trend model, also improves on model 6, showing that the off-diagonal part of the status-at-25/at-35 association is changing too. Were model 7 nested within model 8 the trend model would be preferred.

10.3

Thus for men to age 35 we see substantial evidence of change, including a trending change in salariat immobility, differential and non-linear change in immobility outside the salariat, and change also in the off-diagonal association.

10.4

When we look at the results for women we see a broadly similar picture. The main difference is that model 4 improves over model 1, even more than model 2 does: change in immobility in general is not largely accounted for by change in salariat immobility, though there is some evidence of a trending salariat effect. The 'free' single diagonal effect of model 5 is only marginally better than the trend, but the multiple diagonal trend (model 6) fits better, and again the 'free' variant (model 7) is weak. The full trend model is a very marginal improvement over model 6. Thus for women the picture is dominated by a trending change in general immobility.

Table 7: Fitting the class tables

		Significance of improvement in fit over next simpler model
		25-35		25-40
New	Simpler
Model	Model	Men	Women	Men	Women
2: Salariat (trend)	1	0.305	0.000	0.126	0.000
3: Salariat (non-monotonic)	2	0.059	0.797	0.081	0.296
4: General immobility (t)	1	0.006	0.000	0.006	0.000
5: General immobility (n-m)	4	0.069	0.420	0.006	0.042
6: State-specific immob. (t)	4	0.063	0.201	0.039	0.307
7: State-specific immob. (n-m)	6	0.334	0.084	0.312	0.052
8: Full trend	6	0.858	0.416	0.493	0.115

Class to age 35

11.1

Table 7 presents the results for the same analysis for the five-category class scheme described in Table 2. For men the first model to improve on the base model is model 4, the single diagonal trend. A free single diagonal effect is hardly any better fitting. Neither of the multiple diagonal models (6 and 7) improve over models 4 and 5. The trend model fits quite poorly. Thus we are drawn to a model which identifies cross-cohort change with a single trending immobility parameter.

11.2

For women we see that allowing salariat immobility (2) to vary improves fit, but allowing immobility in general to vary (4) fits much better. Neither of the 'free' variants of these models improves. Allowing independent variation in immobility fits no better in trend form (6) or in free form (7), and the full trend model (8) is not much better. If we compare its fit with other models than model 6 (these comparisons are not shown) it improves over the base model and model 2 but not over model 4, which can be considered the preferred model here.

11.3

Thus for women we come down to the same model as for men, but with the additional knowledge that there is something happening in salariat immobility.

Mobility to age 40

12.1

Cutting off career information at age 35 can be justified on several grounds, but it restricts mobility to a relatively short span, ten years. It is interesting to extend the span by 50 per cent, at the cost of losing about half the youngest cohort. For a start, we can expect somewhat less diagonality, in that we have given the respondents more time to change category. Inspection of the data (Figures A.2 and A.3 and Tables A.4 and A.6, in the appendix) show relatively little difference from the age-35 data, but there is a little less diagonality and there are some subtle differences. Modelling these tables confirms the difference.

12.2

The right-hand panel of Table 6 presents modelling results for general status to age 40. For men, fit is improved at nearly every step of the sequence. That is, model 3 now improves somewhat over model 2, as does model 5 over model 4: there is evidence of non-linearity in immobility, both in the salariat and as a general effect. The less parsimonious models are still favoured, making it a choice between the non-monotonic state-specific immobility model (7) and the full-trend model (8).

12.3

For women, the general pattern of significance is repeated, with the exception that the free single diagonal model (5) loses all power, as does the trend model (8).

12.4

Looking at the models of the class tables (in the right-hand of Table 7), we find less difference than for the general-status tables. For men, the general pattern of significance is repeated. For women, apart from a strengthening of model 5 the picture is largely as for 25-35.

Reviewing the results: the direction and magnitude of change

13.1

For both men and women, for class and general status, the analysis shows that there is change in the pattern of association between early and late state: that is, the patterns of work-life mobility show evidence of change across cohort that is not driven by the changing distribution of states. The questions are to what extent this change relates to the salariat (rather than to, say, mobility in general) and what form the change takes.

13.2

Reversing the usual order, consider class first: here for both men and women the model suggesting a simple one-parameter diagonal trend effect performs well (for men there is some evidence (p=0.06) that the diagonal effect differs by class). There is no evidence, that is, that the change can be adequately described by allowing change in salariat immobility alone, nor that there may be non-linear change, and only weak evidence (for men) that changes in immobility vary by state. Nor is there need to allow trending change in the whole table. Looking at the male parameter estimates for the diagonal trend effect we see a diagonal effect of 4.01 -0.13k, where k indexes cohort. That is, diagonal cell counts are raised by a factor of about 48 in cohort 1, falling to about 29 in cohort 5. For women the estimate is 4.92 -0.33k, leading to a factor of about 98 in cohort 1 and 26 in cohort 5. These are very dramatic numbers, both in absolute level and in the cross-cohort decline, but inspection of the data as in Figure 3 will confirm that the tables are very strongly characterised by diagonality. It is less easy to see how this may be changing across cohort, which is the justification for the modelling.

Table 8: Trend residuals, men, 25-35, General Status

	State at 35
State at 25	1	2	3	4	5
1: Salariat	0.96	1.47	2.02	1.47	1.26
2: Non-salariat	1.14	0.99	5.53	1.01	0.57
3: Employed (unknown)	0.98	2.44	0.80	0.84	0.47
4: Unemployed	1.41	1.05	0.66	0.84	1.39
5: Non-employed	0.99	0.18	0.15	1.45	2.52

Note: The figures are the ratio between the fitted value under the trend model and that under the 2-way model, for cohort 5. A figure below 1.0 indicates a declining trend, and vice versa. Cells with fifteen or fewer cases in the table as a whole are italicised.

13.3

Turning to the general status tables, we find that the analysis leads us to a more complex model. For men, we favour the full trend model, which allows each cell in the status-at-25/at-35 subtable to trend across the five cohorts. There are rather too many parameters to present in this model, so instead we look at fitted values, and in particular how the fitted values for cohort 5 differ under the trend model from those under the 2-way model. Table 8 presents the ratio between the trend fitted value and the 2-way fitted value, for cohort 5. A figure below 1.0 indicates that the trend model predicts a lower value, and therefore a downward trend across cohort. Looking at the diagonal we first notice that salariat immobility is indeed reducing, but that immobility in non-salariat occupations is fairly close to flat (though reference to Figure 2 will show that this is a very large cell, and therefore that a small change may refer to relatively many individuals). Retention in the indeterminate employment and the unemployment states also falls, more dramatically than for the salariat. Given that these two states are affected by recall problems, it is hard to say exactly what is going on. The biggest figure in the diagonal is 2.52 for non-employment, which may be entirely driven by the high incidence of this state in cohorts 1 and 2 (due to war-time military service). Exits from the salariat seem to go disproportionately to the indeterminate employment state, but this combination has very small numbers (as does the salariat to unemployment combination) in the table as a whole. Slightly more weight can be given to the increases registered in transitions to non-salariat occupations. Exits from non-salariat occupations show a more interesting pattern: while the biggest ratio refers to the relatively rare category of indeterminate employment, we also see a notable increase in entry to the salariat, and a drop in entry to non-employment. Another interesting element is the growth in moves from indeterminate employment to non-salariat work (but this may say more about the nature of the recall process than real change).

13.4

The most significant elements of the table, however, relate to categories 1 and 2: along with the direct consequences of growth in salariat employment, we see falling immobility, and disproportionately higher moves in both directions between these two types of occupation.

13.5

For women, the analysis is simpler, as the preferred model is a trending change in general immobility: this single effect for all diagonal cells varies from 6.05 in cohort 1 to 3.28 in cohort 5. The average level is much less dramatic than in the class tables, largely because women have always tended to move in and out of the labour market, but the decline is still big: women are moving in and out at a greater rate, even after controlling for the greater numbers of women in the labour market.

Discussion

14.1

This analysis has been motivated by an interest in change in the longitudinal consequences of class, that is, its effect on life-chances, especially that of the salariat. The particular analyses carried out utilise a valuable retrospective data resource in a narrow but powerful way, and the results suggest that there is change in the way status at age 25 is associated with status at age 35, across cohorts throughout the mid/late twentieth century. But what does this finding mean, that association patterns are changing? What might be happening in the data, and what about the 'grand question' of what is happening to class?

14.2

The finding of changed association, and in particular the increased mobility out of the salariat, can be interpreted in a number of ways:

1.: Recall bias;
2.: Changed occupational life-cycle patterns;
3.: Changed composition of the salariat;
4.: Fundamental change to the nature of the salariat.

14.3

Recall bias, though ever-present, is more severe in long-term retrospective data. Moreover, it is possible to think of mechanisms by which recall bias would produce patterns like those observed. If older people are more likely to erroneously report the same status at both ages, then we may see a pattern of decreasing immobility in younger cohorts. It is impossible to discount this mechanism entirely, but certain features suggest that it is not the whole story. First, the mechanism should lead to increased mobility in general (such as is seen in the class analysis) but cannot be expected, a priori, to 'explain' the increased salariat mobility in the general-status analysis, nor the overall pattern of trending change for men (similarly the strong increase in women cycling in and out of the labour force has nothing to do with recall). Secondly, extending the age-span to 25-40 results in a rather more complex pattern of change, suggesting that the analysis is sensitive to the increased time the life-course mobility processes operate (if the change was entirely driven by recall bias it should not differ much from the 25-35 analysis). Thirdly, experimenting with dropping the oldest cohort from the analysis does not significantly alter the results: to the extent that recall bias is a problem this cohort will be by far the worst affected. Fourthly, this analysis is designed to minimise the effect of recall bias, by comparing paired time-points rather than durations or patterns of transitions, each of which will be much more severely affected. In sum, while recall bias can never be discounted it cannot be taken as driving the results.

14.4

The remaining three interpretations, in contrast, stand as sociologically meaningful observations about changing class processes, though in increasing order of theoretical interest. First, the patterns we see may be driven by the changing occupational life-cycle. That is, though nominally like is compared with like by analysing the same age span, the rise in average school-leaving age may mean that the significance of status at age 25 is not static. In older cohorts, 25 year-olds will have had a longer time to get established in work, whereas younger cohorts will be more likely to be still settling in. To the extent this is true, a pattern of decreasing immobility should be apparent, perhaps especially for the salariat, whose members will in general have more education.

14.5

This in itself would be a sociologically interesting change, and one with substantive consequences for the operation and experience of class through the lifecourse. If we spend longer preparing to enter the labour force, and therefore experience the instability of the early years of labour force participation at later ages, then clearly the effect of class in at least part of the lifecourse has changed. Moreover, it is possible that the growing postponement of entry with the consequent later experience of instability could weaken the overall effect of class throughout the lifecourse. However, it is theoretically equally plausible that the other side of this coin - the fact that the postponement is the result of spending longer in education - will enhance the longitudinal consequences of one's class position once in the labour force (for instance, it may be that the more credentials become the sine qua non of entry to favoured positions, the more secure the tenure of credentialled individuals becomes).

14.6

This interpretation suggests further research utilising this retrospective data set, looking directly at longitudinal patterns of the early career, or repeating an analysis such as the present but shifting the age-span according to changing school-leaving patterns. But insofar as this was the main or only process underlying change in the apparent patterns of long-term mobility into the salariat, there would be, clearly, no substantial implication for class analysis as an intellectual activity: though an interesting change, it calls for an adjustment of parameters, not paradigms.

14.7

The second sociologically meaningful interpretation is that the change in salariat mobility may be driven by its changing composition. The increase in managerial occupations is greater than that in professional occupations, so the growth in the salariat has been accompanied by a change in its composition. It is well known that managerial and professional occupations differ in their characteristics, in particular in terms of work-life mobility (e.g., Mills; 1995; Savage et al.; 1992), with those in managerial occupations more likely to experience mobility to other categories. This difference has given rise to claims that the salariat should be sub-divided along this line in Goldthorpe's class scheme, a claim which has some pragmatic appeal but violates the conceptual basis of that scheme (Mills; 1995). Butler and Savage (1995a), however, propose an alternative way of building up a class scheme, based on different sorts of assets, such that professionals hold skill assets and managers organisational assets. There is nothing in the present exercise that provides any purchase on the question of the relative merits of assets and employment relations as conceptual bases for a class scheme, but it is necessary to come to grips with the problem at a practical level if

1.: sub-groups within the salariat have significantly different characteristics, and
2.: the relative share of these subgroups changes over time.

14.8

Insofar as these conditions seem to apply (and condition 1 seems to apply in the context of work-life mobility, in that to a large, though lessening extent, professional and managerial careers tend to be distinct, though intergenerational mobility between these categories is high), there is a case for introducing this distinction into the analysis. This raises interesting issues about phenomena such as the growing tendency for persons with traditional liberal professional occupations (e.g., lawyers) to be employees rather than self-employed (i.e., partners).

14.9

But there is more to compositional change than the changing relative shares of these two categories: we also have to be open to the question of the rise of entirely new occupations in areas such as information technology (broadly conceived). Are such occupations likely to have such radically different employment relations (or to carry such distinctly different skill assets) as not to fit existing class schemes at all? Or will they match well with existing occupations? More technologically-determinist views would tend towards the former option but the truth is likely to be somewhere in between the two poles.

14.10

To the extent that this issue raises a challenge to conventional class analysis, and particularly the Goldthorpe scheme, it arises not from the empirical exercise but in the theoretical domain. That is, the raw findings test no formal hypothesis to differentiate between, for example, the Goldthorpe and the Butler and Savage approaches, but they do stimulate speculation about the processes. When we speculate about changes arising from changing composition, be this a changing professional-managerial ratio, or the growth of novel categories within the salariat, we have to take seriously the possibility that the salariat may better be thought of as a grouping of sub-categories with different characteristics and theoretically distinct bases. However, such speculation does not require abandoning a unitary defining principle for the salariat (i.e., the service relationship): a priori the changes may be as likely homogenising (professionals becoming employees) as polarising.

14.11

Though the debate, by its nature, resides at a conceptual level, empirical analyses arising from the present one are likely to throw light on the theory: in particular, more analysis focusing on the longitudinal and intergenerational characteristics of subgroups within the salariat, is called for. It is important that, in doing so, special attention is paid to the characteristics of 'new' salariat occupations, as well as to the professional-managerial divide. It is also necessary that this empirical research works both at the level of society-wide sample surveys, ideally longitudinal in nature, and more narrowly focused in-depth studies of particular milieux, particularly where we have reason to expect novel circumstances.

14.12

The third of these interpretations represents the strongest assertion: that the essential nature of the salariat is changing, that its effect on life chances is not the same across cohort. This is the strongest claim because it bears on the characteristics of salariat positions themselves, and what they confer on the occupant's lifecourse, rather than the relative proportions of subgroups we already know about, or the relevance of the timing of observations. Matters of timing can be accommodated quite easily, insofar as the consequences are limited to particular parts of the lifecourse. Matters of changing composition, insofar as it affects the average outcome, indicate a need to take account of the subgroups where this is empirically warranted. To the extent that changing composition is brought about by the emergence of new categories with new characteristics, there is a need for new research oriented to locating these new occupations, though it is unlikely that the employment relations attaching to these categories could be so novel as to overturn existing conceptualisations of class.

14.13

Thus the most consequential interpretation, and perhaps the hardest to demonstrate, is that the nature of the individual class locations that make up the salariat is changing. The present analysis raises this possibility by showing that there is change in the association between status at ages 25 and 35, but cannot in itself separate the competing explanations of changing life-cycle or compositional effects. To do that is outside the scope of the paper (which is intended as a starting point for further research), but what the paper does determine is that there is evidence of change in the longitudinal effect of certain class categories, to be observed in retrospective BHPS work-life history data.

14.14

This interpretation, were it to be supported by further empirical analyses designed to test it, might pose the greatest challenge, if not to class analysis as such, at least to those forms of it which claim that the consequences of class positions are effectively unchanging. Now, while Erikson and Goldthorpe (1992) go to great lengths to set up and explore the 'common social fluidity model', which suggests that the underlying patterns of social mobility are largely constant across time and (developed) societies, they treat it as an important empirical regularity and not as a theoretical requirement. Moreover, they find some systematic departures from the 'common' pattern, usually attributable to country-specific historical conditions. Certainly, departures from the pattern are not theoretically ruled out, and especially not when using more extensive data, as, for instance, Vallet (1999) has recently done for France with repeated cross-sectional data. More extensive data, such as Vallet's long series of contemporaneously collected mobility tables, or long retrospective individual histories as in the present case, have a lot more power to elucidate both change over time, and the processes underlying the structure. Erikson and Goldthorpe explicitly recognise that an 'empirical regularity' can only be a starting point for more investigation. This exercise begins one such investigation, exploiting a particularly rich form of data, life histories, and raises a number of other questions that can be directly addressed by further research in a longitudinal perspective.

14.15

Is class changing? In the narrow terms of this analysis, it may be. Certainly aspects of the class life-course over the 25-35 age-span show evidence of change, due to changing life-course patterns, changing salariat composition, or more fundamental change in the characteristics of class locations. Starting from this observation, we need to continue the debate at the conceptual level, dealing with issues such as the assets versus employment-relations argument, or other arguments about changes in the nature of the organisation of occupations such that the employment relations of the salariat are changing in their character. Whatever way the theoretical debate goes, it is necessary that it is couched in terms that allow empirical tests of its claims and counter-claims. It is also necessary that, in designing empirical tests of the theory, researchers take account of time: insofar as class has consequences, they operate temporally and we now have data and techniques that allow us to deal with the longitudinal. One of the main advantages of the present analysis is the data used to address the issue: work-life histories for respondents whose experience covers a wide historical time-span. If we are to address questions of change in the nature of class we need doubly longitudinal data: longitudinal from the respondent's point of view in order to observe long-term outcomes, and longitudinal in a calendar sense, in order to observe the processes in different periods. In practice such data can only be had by retrospective means⁵ and it is incumbent on those interested in historical change in social processes to exploit such data to the full.

Notes

¹ There are several different types of longitudinal dataset, including panel studies which interview the same random sample of people at regular intervals, cohort studies which interview a sample of people born in a particular period, retrospective studies where respondent's recall their life histories, and linked administrative records where different official databases are linked to create longitudinal records. Among panel studies are the US Panel Study on Income (PSID), an influential early example, the British Household Panel Study (BHPS), the German Socio-economic Panel (GSOEP), the Panel Study of Belgian Households (PSBH), and the European Community Household Panel (ECHP), coordinated by Eurostat. There are two well-known UK cohort studies, the National Child Development Study of persons born in 1958 (NCDS) and the British Cohort Study of persons born in 1970 (BCS70). Retrospective studies include the UK Family and Working Lives Survey from 1994 (FWLS) and the influential German Life History Studies (GLHS). Linked administrative studies are less common, but several Scandinavian countries link tax and social welfare records for research, and in the UK the Census Longitudinal Study (ONS-LS) links information from three censuses with vital registration records to create anonymised longitudinal data for about 1 percent of the population over a 20-year period.

² These cases arise because the data used are drawn from a combined data set (ljemp) based on the two long-term retrospective work-life histories in the BHPS, BLIFEMST, which records employment status and CLIFEJOB, which records occupational information. In certain cases, these records do not match, and we end up with employment status information but not occupational, or vice versa. See Halpin (1998) for details.

³ We will speak of the diagonal in these tables as indicating immobility. This is inexact: someone who is genuinely immobile will be represented on the diagonal, but someone who moves out of his/her status and then back will also be on the diagonal.

⁴ For those who prefer arithmetic to geometry, the raw figures are presented in Tables A.3 and A.5 in the appendix.

⁵ Very long panels will give better data (with less recall bias) over a shorter historical period.

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Appendix

How the models relate to one another

Figure A.1: How the models relate to one another

$\includegraphics{nest50.eps}$

The models are arrayed in order of their parsimony, from the 2-way model at one extreme to the saturated model at the other. The links between models indicate nesting, with more parsimonious models being nested within less parsimonious. Vertical links connect trend/free pairs of models. Nesting is transitive but not all less parsimonious models are nested within more parsimonious ones: for instance, model 8 is not nested within model 7, nor 4 within 3.

Trend/free pairs of models allow cross-cohort variation in the same component of the state-at-25/state-at-35 association, but differ in that the 'trend' model imposes the constraint that change is linear (in the logs) while the 'free' model allows the component to vary independently in each cohort.

Model specifications

Model 1: The 2-way interaction model.

This model implies that the cohort specific patterns of association do not significantly differ from the overall pattern of association. It thus serves as a baseline model and is nested within all the other models discussed.

$\framebox{\ensuremath{F_{ijk} = \lambda_0 \lambda_i^A \lambda_j^B \lambda_k^C\lambda_{ij}^{AB}\lambda_{ik}^{AC}\lambda_{jk}^{BC}} }$

This model takes account of an overall status-at-25/at-35 association, the changing distribution of status at 25 across cohort and the changing distribution of status at 35 across cohort.

See model graph A.1

Model 2: The salariat-trend model.

This model implies that there is cross-cohort change in the patterns of association, which can be summarised as a trending increase or decrease in immobility in the salariat.

$\framebox{\ensuremath{ F_{ijk} = \lambda_0 \lambda_i^A \lambda_j^B \lambda_k^C\lambda_{ij}^{AB}\lambda_{ik}^{AC}\lambda_{jk}^{BC}\sigma^{k}} }$

where $\sigma$ is equal to 1 unless status at 25 and status at 35 are both salariat and is otherwise to be estimated, with $\sigma$ being raised to the power of k, the index of cohort.

See model graph A.1

Model 3: The salariat-free model.

This model implies allows for cross-cohort change in the patterns of association, that can be attributed to changing immobility in the salariat. It differs from model 2 in that the change can be non-monotonic rather than trending.

$\framebox{\ensuremath{ F_{ijk} = \lambda_0 \lambda_i^A \lambda_j^B \lambda_k^C\lambda_{ij}^{AB}\lambda_{ik}^{AC}\lambda_{jk}^{BC}\sigma_{k}^{C}} }$

where $\sigma_k^C$ is equal to 1 unless status at 25 and status at 35 are both salariat and is otherwise to be estimated, with $\sigma_k^C$ having independent values for each cohort.

See model graph A.1

Model 4: The diagonal model.

This model implies that cross-cohort change takes the form of a trending increase (or decrease) in the overall tendency to immobility: the diagonal cells in general become more (or less) populated over cohort.

$\framebox{\ensuremath{ F_{ijk} = \lambda_0 \lambda_i^A \lambda_j^B \lambda_k^C\lambda_{ij}^{AB}\lambda_{ik}^{AC}\lambda_{jk}^{BC}\delta^{k}, } }$

where $\delta$ is equal to 1 unless i = j, in which case it is to be estimated.

See model graph A.1

Model 5: The diagonal-free model.

This model implies that cross-cohort change takes the form of a non-monotonic pattern of change in the overall tendency to immobility: the diagonal cells in general are differently populated in each cohort. It differs from model 4 in that the change can be non-monotonic rather than trending.

$\framebox{\ensuremath{ F_{ijk} = \lambda_0 \lambda_i^A \lambda_j^B \lambda_k^C\lambda_{ij}^{AB}\lambda_{ik}^{AC}\lambda_{jk}^{BC}\delta_{k}^{C}, } }$

where $\delta_k^{C}$ is equal to 1 unless i = j, in which case it is to be estimated.

See model graph A.1

Model 6: The free-diagonal model.

This model extends model 4 by allowing trending change in immobility that is allowed to be different for each category. It is also an extension of model 2 which allows immobility for one category only to change.

$\framebox{\ensuremath{ F_{ijk} = \lambda_0 \lambda_i^A \lambda_j^B \lambda_k^C\lambda_{ij}^{AB}\lambda_{ik}^{AC}\lambda_{jk}^{BC}\delta_{i}^{k}} }$

where $\delta_i$ is equal to 1 unless i = j, and is otherwise to be estimated. ( $\delta_i$ is equivalent to $\delta_j$ given this condition; the choice of subscript is arbitrary.) $\delta_i$ is raised to the power of k, the index of cohort.

See model graph A.1

Model 7: The free free-diagonal model.

This model is the non-monotonic version of model 6 and allows immobility to vary across cohort differently for each category in a non-monotonic manner. It is thus also an extension of models 5 and 3.

$\framebox{\ensuremath{ F_{ijk} = \lambda_0 \lambda_i^A \lambda_j^B \lambda_k^C\lambda_{ij}^{AB}\lambda_{ik}^{AC}\lambda_{jk}^{BC}\delta_{ik}^{C}} }$

where $\delta_{ik}^{C}$ is equal to 1 unless i = j, and is otherwise to be estimated. ( $\delta_i$ is equivalent to $\delta_j$ given this condition; the choice of subscript is arbitrary.)

See model graph A.1

Model 8: The full-trend model.

This model implies that cross-cohort change in the association is not restricted to the diagonal, that is, to cells representing immobility, but that there is also change in the off-diagonal cells which represent mobility. This change is a trending change. If we relax this linearity constraint we arrive at model 9, the saturated model.

$\framebox{\ensuremath{ F_{ijk} = \lambda_0 \lambda_i^A \lambda_j^B \lambda_k^C \lambda_{ij}^{AB} \lambda_{ik}^{AC} \lambda_{jk}^{BC} (\beta_{ij}^{AB})^{k}} }$

where $\beta_{ij}^{AB}$ is a term for each element of the status at 25/at 35 association, raised to the power of k.

See model graph A.1

Model 9: The saturated model.

This model implies the association is different in each cohort, and that this difference is unsystematic. The model exactly reproduces the data and has no explanatory power. It can be regarded as the 'free' version of model 8, bearing the same relation to it as model 5 does to model 4 or model 3 to 2.

$\framebox{\ensuremath{F_{ijk} = \lambda_0 \lambda_i^A \lambda_j^B \lambda_k^C\lambda_{ij}^{AB}\lambda_{ik}^{AC}\lambda_{jk}^{BC}\lambda_{ijk}^{ABC}} }$

This differs from model 1 in the three-way interaction term, $\lambda_{ijk}^{ABC}$ , and has no degrees of freedom.

See model graph A.1

Evaluating models

Figure A.1 illustrates the relationship between the models, showing both their relative parsimony - with the saturated model (not fitted) entirely non-parsimonious, and model 1 the most parsimonious - and the hierarchical connections between them (shown by the links). All the models are 'nested' within the saturated model: that is, they are equivalent to the saturated model with certain of its terms constrained to 1. Similarly, model 1 is nested within all the other models, as they are elaborations of it. Nesting is transitive, that is, if M_a is nested within M_b and M_b within M_c, then M_a is nested within M_c. Trend/free pairs of models are shown vertically one above the other.

Nesting is important because it can be shown mathematically that when one model is nested within another (say, M_a within M_b), the significance of the improvement in fit in moving from M_a to M_b is given by the significance of the difference in deviance, or G², in conjunction with the difference in degrees of freedom, asymptotically distributed as $\chi^2$ (see, e.g., Bishop et al. 1975, pp. 524ff). Where models are not nested, as, for instance, models 7 and 8, this relationship does not hold, and insofar as we examine their difference in fit in these terms it can only be illustrative. Model 8 is both more general than model 7, in that it allows change in the off-diagonal association, and less, in that it restricts the change in diagonal association to be log-linear (i.e., proportional). It is, however, slightly more parsimonious.

Zero cells

As examination of Figures 2 and 3 will show, there is a relatively high incidence of zero cells in the tables, more so in the status table than in the class table, and more so in earlier cohorts than in late. This is partly due to the very poor long-term recollection of unemployment in the BHPS, a common feature of retrospective data of this sort. Zero cells present a problem for loglinear modelling, in particular for models with many interactions. Part of the problem is that zero cells can cause numerical instability, with the estimation failing to converge, and part is that models may report more degrees of freedom than is strictly correct. That is, where zero cells contribute no information to the model, they should not contribute degrees of freedom either. Lindsey (1989) proposes a method, named DFCT, for correcting the degrees of freedom, by fitting each model a second time, eliminating those zero cells whose initial fitted value is very close to zero. Because it reduces the number of cells in the data, it reduces the available degrees of freedom. Because this is more likely to occur in complex models the technique can be regarded as having a conservative effect (though he revises his interpretation of the method in Lindsey (1995), its conservative effect holds).

Another technique that is widely used, primarily to solve convergence problems, is to add a small constant to all zero cells (for instance, 0.1). While it is easy and effective, it is not based on statistical theory (see Hagenaars; 1990, pp. 87ff), and constitutes an alteration, albeit minor, to the data. An addition of 0.01 is used in the present exercise.

In the modelling, both of these techniques are applied, and Tables A.1 to A.2 report results in quadruplicate, without and with the Lindsey correction, for raw and altered counts. In general the first are to be preferred (uncorrected raw counts) but in the analysis adjusted counts are used throughout, because of estimation problems with the raw counts.

As can be seen from the tables, to use DFCT would somewhat increase the likelihood of rejecting the more complex models.

**Table A.1:** Fitting the general status tables
	Significance of improvement in fit
	Age span: 25-35				Age span: 25-40
	Raw counts		Adj. counts		Raw counts		Adj. counts
Model	Plain	DFCT	Plain	DFCT	Plain	DFCT	Plain	DFCT
Men
2: Salariat:	0.001	0.001	0.001	0.004	0.002	0.002	0.002	0.007
3: Salariat-f:	0.345	0.345	0.339	0.190	0.060	0.060	0.059	0.025
4: Diagonal:	0.824	0.824	0.827	0.827	0.004	0.004	0.004	0.004
5: Diagonal-f:	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
6: Diag-2:	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
7: Diag-2-f:	0.002	0.001	0.002	0.001	0.018	0.039	0.019	0.008
8: Trend:	--	--	0.000	0.000	0.001	0.048	0.002	0.061
Women
2: Salariat:	0.000	0.000	0.000	0.000	0.002	0.002	0.002	0.002
3: Salariat-f:	--	--	0.059	0.059	0.059	0.059	0.059	0.059
4: Diagonal:	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
5: Diagonal-f:	0.065	0.065	0.065	0.065	0.511	0.511	0.511	0.511
6: Diag-2:	0.019	0.019	0.020	0.020	0.002	0.005	0.002	0.006
7: Diag-2-f:	--	--	0.074	0.074	0.026	0.053	0.027	0.019
8: Trend:	0.040	0.059	0.048	0.097	0.256	0.403	0.300	0.353
Note: The models are described in the text. The p-values are the significance of the improvement in fit over a simpler model, in the following pattern: 2 : 1; 3 : 2; 4 : 1; 5 : 4; 6 : 4; 7 : 6; 8 : 6. The symbol '--' indicates a model for which there were estimation problems arising from zero cells. Adjusted counts have zero values incremented by 0.01. The DFCT correction weights out zero cells which have low fitted values, and re-fits the model, reporting a more conservative fit estimate.

Table A.2: Fitting the class tables

	Significance of improvement in fit
	Age span: 25-35				Age span: 25-40
	Raw counts		Adj. counts		Raw counts		Adj. counts
Model	Plain	DFCT	Plain	DFCT	Plain	DFCT	Plain	DFCT
Men
2: Salariat:	0.298	0.298	0.305	0.305	0.123	0.123	0.126	0.126
3: Salariat-f:	0.059	0.059	0.059	0.059	0.082	0.082	0.081	0.081
4: Diagonal:	0.006	0.006	0.006	0.006	0.006	0.006	0.006	0.006
5: Diagonal-f:	0.070	0.070	0.069	0.069	0.006	0.006	0.006	0.006
6: Diag-2:	0.058	0.058	0.063	0.063	0.037	0.037	0.039	0.039
7: Diag-2-f:	0.322	0.527	0.334	0.334	0.300	0.502	0.312	0.312
8: Trend:	0.850	0.850	0.858	0.858	0.474	0.474	0.493	0.493
Women
2: Salariat:	--	--	0.000	0.000	0.000	0.000	0.000	0.000
3: Salariat-f:	--	--	0.797	0.797	0.295	0.295	0.296	0.296
4: Diagonal:	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
5: Diagonal-f:	0.416	0.416	0.420	0.420	0.042	0.042	0.042	0.042
6: Diag-2:	--	--	0.201	0.201	0.302	0.302	0.307	0.307
7: Diag-2-f:	--	--	0.084	0.112	0.052	0.052	0.052	0.052
8: Trend:	--	0.395	0.416	0.416	0.088	0.219	0.115	0.246
Note: The models are described in the text. The p-values are the significance of the improvement in fit over a simpler model, in the following pattern: 2 : 1; 3 : 2; 4 : 1; 5 : 4; 6 : 4; 7 : 6; 8 : 6. The symbol '--' indicates a model for which there were estimation problems arising from zero cells. Adjusted counts have zero values incremented by 0.01. The DFCT correction weights out zero cells which have low fitted values, and re-fits the model, reporting a more conservative fit estimate.

Figure A.2: Cross-tabulation of cohort by sex by general status, age 25 and age 40.

Men
Women

This is a cross-tabulation with numbers replaced by boxes whose area is proportional to the cell percentage within each 5 x 5 subtable. In each subtable the area of the boxes sums to the same quantity. Empty cells are indicated by circles.

Figure A.3: Cross-tabulation of cohort by sex by class (25-40)

Men
Women

This is a cross-tabulation with numbers replaced by boxes whose area is proportional to the cell percentage within each 5 x 5 subtable. In each subtable the area of the boxes sums to the same quantity. Empty cells are indicated by circles.

**Table A.3:** General status, age 25 by age 35, by cohort and sex
State	State at 35
at 25	Men						Women
	1	2	3	4	5	Total	1	2	3	4	5	Total
Cohort 1
1	15	2	0	0	0	17	14	2	0	0	18	34
2	6	128	1	0	15	150	3	83	1	1	89	177
3	1	0	42	0	2	45	0	0	23	0	35	58
4	0	2	1	0	0	3	0	0	0	2	2	4
5	14	53	14	0	2	83	1	30	9	0	194	234
Total	36	185	58	0	19	298	18	115	33	3	338	507
Cohort 2
1	41	2	0	0	0	43	24	0	1	0	20	45
2	14	285	0	1	3	303	3	132	0	2	98	235
3	1	0	58	0	1	60	0	2	27	0	14	43
4	0	1	1	1	0	3	0	0	0	4	0	4
5	20	43	8	0	6	77	9	70	14	0	180	273
Total	76	331	67	2	10	486	36	204	42	6	312	600
Cohort 3
1	91	5	1	0	1	98	34	4	1	0	24	63
2	15	346	1	1	3	366	7	109	2	2	82	202
3	2	1	34	0	0	37	4	3	12	0	20	39
4	0	1	0	0	0	1	0	0	0	1	0	1
5	8	7	2	0	5	22	22	103	13	0	154	292
Total	116	360	38	1	9	524	67	219	28	3	280	597
Cohort 4
1	176	8	1	0	4	189	78	5	0	1	24	108
2	33	434	3	13	4	487	14	204	0	3	101	322
3	2	4	33	6	0	45	4	5	6	0	15	30
4	0	4	1	3	0	8	2	2	1	5	0	10
5	8	1	0	0	7	16	27	187	15	2	171	402
Total	219	451	38	22	15	745	125	403	22	11	311	872
Cohort 5
1	184	15	0	9	4	212	92	15	0	2	34	143
2	61	380	5	41	14	501	32	215	3	0	96	346
3	6	10	12	7	2	37	7	7	8	0	20	42
4	2	9	0	12	5	28	2	4	0	2	1	9
5	11	5	0	2	7	25	36	155	8	4	147	350
Total	264	419	17	71	32	803	169	396	19	8	298	890
Grand total	711	1,746	218	96	85	2,856	415	1,337	144	31	1,539	3,466

**Table A.4:** General status, age 25 by age 40, by cohort and sex
State	State at 40
at 25	Men						Women
	1	2	3	4	5	Total	1	2	3	4	5	Total
Cohort 1
1	14	2	0	0	1	17	17	4	0	0	13	34
2	8	138	2	0	2	150	4	90	2	0	81	177
3	1	0	42	0	2	45	0	2	25	0	31	58
4	0	2	1	0	0	3	0	1	0	1	2	4
5	14	54	14	0	1	83	2	36	17	0	179	234
Total	37	196	59	0	6	298	23	133	44	1	306	507
Cohort 2
1	39	4	0	0	0	43	20	2	1	0	22	45
2	17	282	1	0	3	303	5	145	2	1	82	235
3	1	1	57	0	1	60	0	1	27	0	15	43
4	0	1	1	1	0	3	0	1	0	3	0	4
5	20	43	8	0	6	77	12	96	16	0	149	273
Total	77	331	67	1	10	486	37	245	46	4	268	600
Cohort 3
1	92	5	0	0	1	98	39	7	2	0	15	63
2	22	329	3	5	7	366	14	137	2	1	48	202
3	2	1	31	0	3	37	6	7	11	1	14	39
4	0	1	0	0	0	1	0	1	0	0	0	1
5	9	7	2	0	4	22	34	143	12	2	101	292
Total	125	343	36	5	15	524	93	295	27	4	178	597
Cohort 4
1	175	10	2	1	1	189	79	9	1	0	19	108
2	48	409	5	15	10	487	26	217	4	6	69	322
3	4	9	22	6	4	45	4	6	3	1	16	30
4	0	5	1	2	0	8	1	1	1	6	1	10
5	8	1	0	0	7	16	42	218	16	3	123	402
Total	235	434	30	24	22	745	152	451	25	16	228	872
Cohort 5
1	102	12	0	5	2	121	47	8	0	1	11	67
2	50	191	3	23	11	278	35	111	2	7	50	205
3	2	5	1	4	2	14	9	7	1	0	5	22
4	1	2	0	2	2	7	0	1	0	0	2	3
5	5	3	0	1	2	11	24	102	5	5	58	194
Total	160	213	4	35	19	431	115	229	8	13	126	491
Grand total	634	1517	196	65	72	2484	420	1353	150	38	1106	3067

**Table A.5:** Class, age 25 by age 35, by cohort and sex
State	State at 35
at 25	Men						Women
	1	2	3	4	5	Total	1	2	3	4	5	Total
Cohort 1
1	20	2	2	0	0	24	36	3	1	0	0	40
2	6	22	2	0	0	30	1	107	0	0	2	110
3	0	0	13	0	0	13	0	1	11	0	0	12
4	4	2	2	70	9	87	2	3	1	41	3	50
5	3	2	3	11	58	77	1	8	0	5	121	135
Total	33	28	22	81	67	231	40	122	13	46	126	347
Cohort 2
1	44	0	0	1	1	46	56	2	0	1	0	59
2	7	41	2	3	6	59	9	210	1	2	15	237
3	0	0	30	1	0	31	0	0	7	0	0	7
4	7	2	5	94	8	116	0	3	0	36	12	51
5	8	2	7	12	120	149	3	19	1	3	119	145
Total	66	45	44	111	135	401	68	234	9	42	146	499
Cohort 3
1	96	1	4	1	0	102	79	5	1	0	0	85
2	8	25	2	0	3	38	10	195	7	6	18	236
3	0	0	46	1	1	48	0	1	5	0	0	6
4	9	3	6	124	21	163	3	6	4	27	7	47
5	3	2	13	6	105	129	3	14	1	6	100	124
Total	116	31	71	132	130	480	95	221	18	39	125	498
Cohort 4
1	182	3	4	0	2	191	122	10	1	1	4	138
2	11	51	3	1	4	70	27	294	14	8	47	390
3	1	2	61	2	3	69	1	1	20	0	1	23
4	21	1	13	140	17	192	2	7	2	42	12	65
5	8	2	19	20	123	172	4	24	6	5	113	152
Total	223	59	100	163	149	694	156	336	43	56	177	768
Cohort 5
1	207	5	6	2	3	223	141	10	5	3	6	165
2	31	38	5	5	4	83	52	279	19	7	38	395
3	2	1	59	4	4	70	1	2	5	0	1	9
4	27	4	19	163	19	232	1	4	4	27	9	45
5	11	5	16	16	105	153	4	30	7	12	108	161
Total	278	53	105	190	135	761	199	325	40	49	162	775
Grand total	716	216	342	677	616	2567	558	1238	123	232	736	2887

**Table A.6:** Class, age 25 by age 40, by cohort and sex
State	State at 40
at 25	Men						Women
	1	2	3	4	5	Total	1	2	3	4	5	Total
Cohort 1
1	20	2	2	0	0	24	34	4	2	0	0	40
2	6	22	2	0	0	30	2	103	0	1	4	110
3	0	0	13	0	0	13	0	1	11	0	0	12
4	5	2	3	65	12	87	4	4	1	35	6	50
5	4	4	5	14	50	77	1	10	1	4	119	135
Total	35	30	25	79	62	231	41	122	15	40	129	347
Cohort 2
1	42	1	1	2	0	46	55	2	0	0	2	59
2	10	36	3	3	7	59	11	194	5	6	21	237
3	0	1	29	1	0	31	0	1	5	0	1	7
4	7	4	4	91	10	116	0	4	2	28	17	51
5	8	3	7	11	120	149	4	23	1	7	110	145
Total	67	45	44	108	137	401	70	224	13	41	151	499
Cohort 3
1	97	1	2	2	0	102	72	9	2	0	2	85
2	9	23	3	0	3	38	23	176	7	6	24	236
3	0	0	46	1	1	48	0	1	5	0	0	6
4	16	3	8	116	20	163	3	7	4	23	10	47
5	4	2	13	11	99	129	7	21	2	9	85	124
Total	126	29	72	130	123	480	105	214	20	38	121	498
Cohort 4
1	178	7	3	1	2	191	116	11	4	1	6	138
2	18	43	2	2	5	70	48	261	14	12	55	390
3	3	2	59	3	2	69	1	1	19	0	2	23
4	23	0	18	134	17	192	3	8	2	38	14	65
5	11	3	18	23	117	172	5	28	7	7	105	152
Total	233	55	100	163	143	694	173	309	46	58	182	768
Cohort 5
1	113	1	4	4	2	124	65	6	3	0	4	78
2	22	12	5	5	1	45	48	142	10	15	30	245
3	1	1	29	4	1	36	1	0	2	1	2	6
4	26	3	11	78	11	129	0	4	2	17	4	27
5	12	3	11	11	45	82	7	15	6	7	50	85
Total	174	20	60	102	60	416	121	167	23	40	90	441
Grand Total	635	179	301	582	525	2222	510	1036	117	217	673	2553