Bringing Intergenerational Social Mobility Research into

the 21st Century: Why Mothers Matter*

Emily Beller

Abstract.

In measuring family class background with respect to the father’s class characteristics only, conventional social mobility research practice relies on an outmoded picture of families in which in which mothers’ economic participation is uncommon or unimportant. This article demonstrates that this conventional practice is theoretically and empirically untenable. Models which incorporate both mothers’ and fathers’ characteristics into class origin measures fit observed mobility patterns better than conventional models do, for men as well as for women. Furthermore, in contrast to the current consensus that the conventional practice does not alter substantive research conclusions, this article presents the example of analyzing cohort changes in social mobility to illustrate the distortions that typical practice can produce in stratification research findings. By failing to measure the impact of mothers’ class, researchers would miss a recent upturn in the importance of family background for class outcomes among men. The conventional approach suggests no change between cohorts, but updated analyses reveal that inequality of opportunity increased for men born since the mid-1960s compared to men born earlier in the century.

*Address correspondence to: ebeller@berkeley.edu. I thank Michael Hout, Caroline Hanley, Claude Fischer, Sam Lucas, Robert Mare, and Jane Zavisca for helpful comments.

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In order to understand current inequality, social mobility researchers must bridge a

longstanding gap between theory and practice which increasingly distorts social mobility and

stratification research findings. A gap exists because, in theory, class background (i.e. childhood

class position) is a family-level variable, but the conventional mobility research practice is to

equate class background with fathers’ class position. This practice assumes that mothers’

economic participation is uncommon or unimportant to class background and that father-headed

families are the norm. Yet, families have become increasingly complex since intergenerational

class mobility models were first developed—rates of labor force participation among mothers

have steadily increased, and so has the diversity of family forms (e.g. single or step-parent

families). Figure 1 illustrates these trends. There are practical incentives to continue the

conventional practice, including that data on mothers’ occupation is limited. For example, until

1994 the General Social Survey (GSS) did not ask respondents about their mothers’ occupations.

The research consequences of measuring class background without accounting for the

class characteristics of mothers are increasingly important but not widely recognized or

understood. Given practical considerations such as limited data on mothers’ occupations, it is

important to note that the payoff to adequately defining and measuring class background to bring

it in line with theory is not simply methodological (e.g. improving “model fit” in and of itself).

Rather, the payoff is that the resulting measures adequately capture the concepts that analysts

intend them to capture; if they do not, substantive research conclusions could be distorted.

Scholarly debate over the conceptualization and measurement of family-level class has waned

since the early1990s, with a general consensus that the conventional approach remains adequate.

In contrast, in this article I demonstrate not only that updated class background measures fit

observed mobility patterns much better than conventional measures do, for both men and

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women, but also that conventional and updated class origins measures can generate different

research conclusions. To illustrate the latter point, I examine change in social class fluidity for

recent birth cohorts and show that the conventional practice distorts substantive conclusions

about the cohort comparison. For example, without updating intergenerational mobility models

to incorporate mothers’ class, researchers would miss a recent upturn in the importance of class

background for men’s class destinations—the conventional approach suggests that there was no

change in social fluidity between cohorts, but updated analyses reveal that social fluidity

increased for men born since the mid-1960s compared to men born earlier in the century.

BACKGROUND

Structural Mobility and Social Fluidity

Intergenerational mobility research analyzes the strength of the association between an

individual’s class background or childhood class position (“class origin”) and his or her current

individual or family-level class position (“class destination”), as well as patterns of movement

or immobility between particular origins and destinations. Intergenerational class mobility has

two components. The first is the extent of equality of opportunity, or the extent to which class

background is associated with barriers or advantages, which is called social fluidity (sometimes

also referred to as exchange mobility). The second component, called structural mobility,

captures shifts which affect everyone’s mobility regardless of class origins, such as an upgrading

of the economy toward better jobs. The analyses presented in this article will hold structural

mobility constant in order to focus on social fluidity.

When structural mobility is factored out, the upward mobility of one individual must be

balanced by the downward mobility of another individual. Greater social fluidity increases the

odds of better outcomes for people from disadvantaged origins, but it also increases the odds of

worse outcomes for people from advantaged origins. When one group experiences higher social

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fluidity rates than another, for example blacks versus whites (Featherman and Hauser 1978: 325-

239), or children raised in single-parent versus two-parent families (Biblarz, Raftery and Bucur

1997), the discrepancy may indicate a relative inability of one set of parents to pass on

advantages compared to other parents; high mobility can in fact perpetuate between-group

inequality. Perfect social fluidity—the absence of association between origins and

destinations—is neither plausible nor, arguably, desirable, if some of the processes leading to an

intergenerational persistence in class position seem legitimate. For example, cognitive abilities

are inherited to some degree through both genetics and environment. Perfect mobility would

therefore imply no link between ability and outcome (Harding et al. 2005; Roemer 2004).

Because there is no external benchmark such as perfect mobility to aid in interpretation,

estimates of the extent of social fluidity mean little in and of themselves but become instructive

in comparative context. For example, researchers compare the social fluidity levels of different

periods or cohorts to assess whether opportunity is increasing or decreasing over time.

Researchers also often compare social fluidity levels between countries in an effort to understand

which societies are the most or least fluid. The comparative nature of social mobility research is

an important reason that moving the measurement of class background more closely in line with

theory is of more than simply technical or methodological interest. When measurement is

biased, the extent to which it is biased can vary between the cohorts, countries, or other groups

being compared. As a result, researchers could mistake differences in measurement error

between groups as substantive differences, of lack thereof, in social fluidity. In this article I use

the example of change in social fluidity between successive birth cohorts, about which little is

known for recent cohorts, to illustrate this concern.

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Comparing Social Fluidity Rates over Time

Research on change over time in social fluidity may utilize either a period or a cohort

approach. In the period approach, researchers compare social fluidity levels between different

survey years (i.e. periods). Unless researchers hold respondents’ year of birth (cohort) and/or

age constant, comparisons of social fluidity levels between periods tend to include unmeasured

cohort and/or age effects. In the cohort approach, survey data collected in different years or

periods is pooled, but respondent birth cohort is held constant. Unless period and/or age at the

time of the survey are also held constant, differences between cohorts could contain unmeasured

period and/or age effects.

Period-related shifts in mobility apply to individuals across the board at a given point in

time, independently of their birth cohort. Cohort-related shifts in mobility trends arise from the

different experiences of individuals born in specific cohorts. For example, because the

association between class origins and destinations is comparatively low among individuals with a

college degree (Hout 1988), the mid-century expansion of higher education resulted in higher

overall mobility among individuals young enough take advantage of it early in their lives. On the

other hand, it did not greatly affect class mobility for those who had already completed their

education. Breen and Jonsson (2007) argue convincingly that changes over time in social

fluidity are more likely to be cohort-driven than period-driven.

Research on change over time between either periods or cohorts has demonstrated that

social class fluidity, or openness, increased over the course of the century in the United States

until about the mid-1980s1 (DiPrete and Grusky 1990; Featherman and Hauser 1978; Hout

1988). Trends in social class fluidity after that time are unclear, in part because changes to the

1 Because the models separate social fluidity from structural mobility, this increased openness is measured after

holding constant the periods of economic growth and decline which also characterized the century.

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census coding of occupations in the 1980s made it impossible to directly compare new survey

data to the old (Vines and Priebe 1988). Some research suggested possible slowing, or “speed

bumps,” in the trend of increasing social fluidity after the mid-1980s (Hout 1996); others

predicted a continued trend of increasing fluidity due to a growing proportion of individuals

raised in non-intact families, who appear more mobile than their peers raised in intact families

(Biblarz and Raftery 1999). This article addresses the gap in knowledge by examining changes

in social fluidity between recent successive birth cohorts.

Defining Social Classes

The analyses in this article employ the Erikson and Goldthorpe class schema (1992; 35-47;

see also Erikson, Goldthorpe and Portocarero 1979), which is widely used in social mobility

research. The schema defines classes in terms of the employment relationships that characterize

them. It makes a basic distinction between employment that is regulated by labor contracts in

return for piece wages and employment in a bureaucratic context, which entails employment

security, pensions, salary increments, and the like. There are two main classes within each of

these broad categories which are further hierarchically distinguished into higher and lower

classes of each type. Two intermediate classes include occupations for which the distinction

between the labor contract versus bureaucratic employment relationship is blurred—one such

class includes the routine non-manual jobs which support professional bureaucracies, while the

other covers manual supervisory and technical positions. There is also a self-employed class.2

Despite the focus on employment relationships in defining the class schema, its authors

argue against a strongly work-centered view of class and maintain that the family rather than the

individual worker is the unit of class “fate” (Erikson and Goldthorpe 1992; 233). While class

2 The schema also includes various agricultural classes which I exclude because of data limitations.

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experiences follow from involvement in different types of employment relations, they are not

limited to the workplace, such that if members of a family live together they experience similar

material life conditions and similar future life chances. These experiences may involve, for

example, “experiences of affluence or hardship, of economic security or insecurity, of prospects

of continuing material advance, or of unyielding material constraints” (Erikson and Goldthorpe

1992; 236) which members of a family share in common. In addition, family members engage in

joint economic decision making (e.g. about consumption). For these reasons, the authors argue

that family members share one class position even if their individual jobs fall in differing classes.

Goldthorpe (1983; 1984) initially argued that the shared family-level class position is

determined by the husband. Therefore, married women’s class positions are determined by their

husbands’ occupations rather than their own even if they are employed. This position sparked a

debate in which some argued that a better conceptualization of family-level class would be a

“joint” one in which the position of employed women contributes to family class composition

(Davis and Robinson 1998; 1988; Heath and Britten 1984), or that family-level treatment of class

should be abandoned altogether (Acker 1973). Proponents of the conventional view revised it to

specify that the spouse with the “dominant,” or higher, class position—could determine family

class position (Erikson 1984; Erikson and Goldthorpe 1992),3 and maintained that the joint

perspective blurs class boundaries and creates too many possible class positions (1992; 238).

CONCEPTUALIZING FAMILY-LEVEL CLASS

The debate over how to define family-level class had important limitations—it focused

the class position of adults as opposed to children, and on families in which adults were

employed in different classes (“mixed-class” families) over class-consistent families or families

3 See Breen and Rottman 1995 and Sorensen 1994 for more detailed reviews of this debate.

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with only one spouse in the labor market (single-earner families). Key questions of the debate

included how to measure the proportion of mixed-class families in order to determine the

significance of the problem they might pose to researchers, and in what way mixed-class families

might “matter” to substantive research results given findings that the subjective class

identification, class related behavior such as voting, or life chances of married women can be

better predicted by their husbands’ than by their own occupations4 (Baxter 1994; Erikson and

Goldthorpe 1992; Goldthorpe 1983; 1984; Heath and Britten 1984; Stanworth 1984). Research

findings from the debate provided mixed support for both the conventional and joint viewpoints,

leading to a conclusion that the conventional treatment of class may not strongly distort research

results (Sorensen 1994). In the following discussion, I argue that the conventional practice has

more potential to distort social mobility research conclusions than has been previously believed.

Reframing the Debate to Consider Class-Consistent Families and Children’s Life Chances

The debate over family-level class focused on mixed-class, dual-earner families. Families

with only one employed spouse or with both spouses employed in the same class were not

considered problematic. Further, the class positions of these two types of families were

considered to be the same—the position in which one or both spouses work. Sorensen (1994, p.

43) characterizes this assumption as surprising, noting that a major reason for developing new

measures of the class location of families is the hypothesis that women’s employment makes a

difference for the family’s lifestyle, interests, and the like. That is, if the joint perspective is

correct, it should logically apply not only to mixed-class but also to class-consistent families. For

example, if individual spouse class characteristics jointly contribute to family class, dual-earner

families where both adults are employed in the professional class might be expected to have a 4 For example, employed married women’s subjective class identification is better predicted by their husband’s

occupational class than their own (Baxter 1994; Yamaguchi and Wang 2002).

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more advantaged class position than families with one spouse employed in the professional class

and another spouse who is either not in the labor market or employed in a less advantaged class.

An equally important limitation of the prior debate is that it centered on the treatment of

adult, especially women’s, class position rather than on children’s class (i.e. on class destinations

rather than origins) despite that intergenerational class mobility research is centrally concerned

with the influence of family-level class origins on children’s future class positions. For example,

as Erikson and Goldthorpe (1992: 250) note, researchers critiquing the conventional view of

class destinations nonetheless relied upon conventional measures of class origins. Given a focus

on how class affects future life chances, the adequacy of different views of family class must be

evaluated from children’s perspectives as well as from adults’ perspectives. With respect to

family class origins in particular, the underlying idea of the joint perspective is that individual

spouses’ class characteristics have a cumulative, though not necessarily equal, impact on the

family-level class. If this is the case in mixed-class families, it is just as likely the case in class-

consistent families. Conversely, the conventional view is consistent with the idea that the class

characteristics of individual adults in a family are redundant in the sense that, once the key class

position is measured, a second spouses’ position does not affect the family-level class whether it

is the same or different. The question of whether the conventional measurement strategy

remains adequate for class origins can therefore be approached by examining whether effects of

parent class characteristics on children’s outcomes are redundant or cumulative.

Evidence of Cumulative Impact of Parent Class Characteristics on Children’s Life Chances

Theorized mechanisms of the intergenerational class transmission process are consistent

with the joint view of family class with respect to class origins, in that key mechanisms suggest

that individual parent class characteristics could cumulatively shape children’s outcomes. For

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example, Breen and Jonsson (2007) propose a theoretical model of social mobility in which

arrival at a particular class destination depends on class-related parental assets that can be either

directly transmitted (e.g. genetics; property) or indirectly transmitted between generations. The

role of indirect transmission of assets in this process reflects that parent class position and

consequent assets influence the extent to which the next generation is able to accumulate assets

such as education which then generate particular returns (class destinations). Differential

economic resources that may be adequately captured by conventional views of class play a key

role in indirect transmission of assets (Conley 2001; Duncan, Yeung, Brooks Gunn and Smith

1998; Hill and Duncan 1987) but economic resources are only part of the story (Mayer 1997).

Differential cultural resources theoretically play a key role in indirect transmission, and

unlike their money, the extent to which parents’ cultural resources help children accumulate

class-related assets is substantially (though certainly not entirely) dependent upon parent-child

involvement and interaction. For example, middle and upper class parents intentionally cultivate

children’s social skills such as addressing and negotiating with authority figures (Lareau 2003).

Parent cultural class resources shape home cognitive environments (Gottfried 1984; Guo and

Harris 2000), knowledge of educational bureaucracies (Deil-Amen and Rosembaum 2003;

Lareau 1989; Lucas 1999), how parents spend disposable income (Mayer 1997), aspirations for

children (Hauser, Tsai and Sewell 1983; Sewell, Haller and Portes 1969), and the like.

Interactions with advantaged parents help provide children with advantageous cultural class

resources (Bourdieu and Passerson 1977; Lareau 2003). If both parents spend time with children,

the role of parent-child interaction in the indirect transmission of assets could plausibly be

cumulative, highlighting the salience of the joint perspective for conceptualizing and measuring

family class origins.

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In keeping with theories suggesting that the indirect transmissibility of parental assets

could be a cumulative process, prior research provides empirical evidence that parent class

characteristics have independent, cumulative effects on children’s class-related assets and on

class destinations. Among employed parents, both parents’ occupations independently affect

children’s educational outcomes (Kalmijn 1994b; Korupp, Ganzeboom and Van Der Lippe

2002), just as both parents’ education levels do (Mare 1981). Models of occupational mobility

for respondents whose mother had an occupation are significantly improved for women

(Rosenfeld 1978) and for both sexes (Khazzoom 1997) when mothers’ occupation is added to the

model. Yet, the importance of mothers’ occupation for children’s outcomes is difficult to

pinpoint because not all mothers have one. When all respondents are included in research

regardless of mothers’ employment status, via a category of homemakers, mothers’ occupation

does not independently affect children’s occupational attainment (Marini 1980).

However, grouping together all homemaker mothers in one class category could bias

estimates of the impact of mothers’ occupation toward zero. Although many mothers do not

have occupations outside the home, the theorized role of parent-child interaction in the

intergenerational transmission process raises the issue of whether the joint perspective on family

class origins even may apply to single-earner families—that is, homemaker mothers may affect

children’s class origins despite not having an individual employment-based class position. As

opposed to static views of class (e.g. Erikson and Goldthorpe 1992; Wright 1997), dynamic

views of class (Marshall, Roberts and Burgoyne 1996; Pultzer and Zipp 2001) posit that the non-

employed are, regardless, “class actors”— a series of experiences such as childhood class

background, education, and previous employment or unemployment spells contribute to one’s

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class position (and associated cultural resources that shape children’s class outcomes).5 In either

case, after considering the theorized role of cultural class resources in the class mobility process,

in examining the joint perspective it is reasonable to test whether non-employed parents may

contribute to the transmission of class-related assets, rather than assume they do not.

Implications for Mobility Research

The theoretical and empirical evidence described above suggests that individual parent

class characteristics may cumulatively affect children’s life chances—involvement with each

parent likely adds up, although not necessarily equally. Therefore, it is important to consider the

individual class positions of each parent, even if these positions are the same. With this in mind,

rather than conceiving of classes as necessarily bounded positions that individuals or families

occupy, in the social mobility research context it may be helpful to conceive of family-level

classes as sets of economic and cultural resources which shape mobility chances, and which are

consequences of the employment relationships and other class-related experiences of adults in

the family. In addition to resolving the conceptual problem of “too many” class positions noted

by Erikson and Goldthorpe (1992; 238), the concept of family class resources helps illuminate

some research implications of joint versus conventional measurement strategies.

Because the prior debate over the joint versus conventional measurement strategies for

family class did not problematize class-consistent families, assortative marriage patterns (which

result in a high prevalence of class-consistent families) have, on a practical level, appeared to

justify conventional measurement. However, in the case of class origins, this justification relies

on the assumption that parent class characteristics make redundant contributions to family class

5 Currently mothers with children under age eighteen have high rates of labor force participation (Hayghe 2001),

presenting the need to revisit class origin measurement regardless of whether or not one adopts a dynamic view of class.

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resources. If parent class characteristics instead cumulatively shape family class resources, the

conventional practice would actually be less problematic if marriage were random with respect

to class. A systematic relationship between measured and unmeasured independent variables

such as that caused by marital sorting is one condition for omitted variable bias. A second

condition is that the omitted variable, here mothers’ class, significantly affects the outcome

(class destination) net of other independent variables. In other words, the second condition is

that parent class characteristics cumulatively affect children’s class destinations. If these two

conditions hold, conventional research practice could generate misleading research results

because class-based assortative marriage patterns6 mean that measurement error is non-random,

and the degree of non-randomness is unlikely constant over time or between groups.

Table 1 shows a simplified schema of how well the conventional and joint perspectives

would categorize family class, depending on whether parent class characteristics are redundant

or cumulative in defining class origins. The first row of Table 1 illustrates that if effects of

parent class characteristics on children’s outcomes are redundant, conventional origin measures

will be equally accurate whether or not parents’ class characteristics are the same (as long as the

key class position is captured). Conversely, the second row shows that, if effects of parent class

characteristics are cumulative, the conventional strategy will credit the effects of both parents’

class positions to those of the parent whose position is measured. Under conventional

measurement, class resources within the same measured family class category could therefore

6 Occupational similarity between spouses in two-earner families is prevalent (Hout 1982), with cultural/educational

similarity stronger than economic similarity (though the importance of the latter is increasing (Kalmijn 1994a)). Furthermore, if all adults affect family-level class resources regardless of employment, class-based marital sorting doesn’t depend on both spouses being employed. Erikson and Goldthorpe (1992: 253-264) report a strong association between husbands’ class and wives’ fathers’ class (see also Tyree and Treas 1974), and marital sorting by education is strong (Kalmijn 1998) and increasing (Mare 1991).

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differ between class-consistent and mixed-class families because the unmeasured characteristics

of the second parent differ between the two.7

If parent class characteristics are indeed cumulative in their effects on children’s

outcomes, conventional estimates of the strength of father - child association in class position

will include the correlated but unmeasured effects of mothers’ class on the process. However,

because the correlation between mothers’ and fathers’ class is not perfect, the total association

between origins and destinations could be underestimated. Furthermore, if marital sorting by

class differs between comparison groups such as nations, cohorts, or racial/ethnic groups, the use

of conventional origins measures could lead analysts to misinterpret changes in the degree of

measurement error as substantive differences between groups in social fluidity levels.

ANALYSIS

In this article I evaluate whether conventional or joint measures of family-level class

background (origins) best fit the observed mobility patterns, and demonstrate that conventional

origins measures are inadequate for both men and women. Models that employ conventional

origins measures do not fit the mobility table well compared to models which utilize joint origins

measures; they also overestimate social fluidity. I restrict the initial analysis to respondents who

reported a mother’s occupation, but approximately one-third of respondents’ reported that their

mothers worked in the home rather than in the paid labor force. In the second section I expand

the analysis to include all respondents and test various methods of incorporating homemaker

mothers into joint-parent class origin measures. The results are similar whether or not

respondents with homemaker mothers are included in the analyses. Finally, I evaluate the effects

of different class origin measures on substantive conclusions about social fluidity. I use a cohort 7 Measuring family-level class origins with respect to the two original parents alone leaves out many other

potentially important family members, including grandparents, older siblings, and step-parents. I am unable to incorporate additional family members into the analyses presented in this article due to data considerations.

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perspective to analyze change over time, and find that, among men in particular, recent changes

in social fluidity levels emerge when I employ joint-parent measures of class origins, but are

masked when I employ conventional measures of class origins.8 Among women, neither type of

origins measure provides evidence of significant change in social fluidity between cohorts, but

conventional measures overestimate fluidity levels.

Data and Methods

The data set is a compilation of the years of the General Social Survey (GSS) which

collected mothers’ occupational data—1994, 1996, 1998, 2000, 2002, 2004, and 2006 (Davis,

Smith and Marsden, 2007). I conduct separate analyses for men and women, and restrict

analyses to respondents who were ages 25 to 64 and in the labor force at the time of the survey. I

also restrict the analyses to respondents with valid data for their own and for two parents’ (or

parental figures) occupations.9 The GSS, like most surveys,10 does not collect information on

non-custodial parent occupation; therefore, respondents raised by single parents unfortunately

cannot be included.

I adopt a five-class version of the internationally used EGP class schema (Erikson and

Goldthorpe 1992; Erikson, Goldthorpe, and Portocarero 1979) to define occupational classes.

The class categories are:11

8 At the same time, as explained further in the discussion, I do not examine joint, family-level measures of class

destinations and instead rely on an individual-level measure of adult class—current occupational class position—for both men and women. Individual class resources are the building blocks of family-level class resources. In using a joint measure of class origins and an individual measure of class destinations I ask a different but equally important research question—how family-level class resources shape children’s individual occupational class outcomes, which in turn will contribute to adult family-level class composition. Determining the best measure of class destinations is an important next step in this line of research, but is beyond the scope of the article.

9 I conducted the same analyses on a more restricted sample of respondents raised in intact families only, with similar results.

10 E.g., Occupational Changes in a Generation; National Survey of Families and Households; National Educational Longitudinal Survey; High School and Beyond; the National Longitudinal Survey of Youth.

11 Agricultural classes are excluded due to limited data.

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PI & II Professionals, higher and lower level

IIIab Routine non-manual and service workers

IVab Self-employed, with or without employees.

V/VI Technical specialists and supervisors of blue-collar workers; skilled manual workers

VIIa Semi-skilled and unskilled manual workers.

Separately for men and women, I organize these data into a 3-way intergenerational class

mobility table by cross-classifying the mother’s class category variable by the father’s class

category variable by the respondent’s class category variable. Again separately for men and

women, I further cross-classify these tables by respondents’ birth cohort in the final section of

the analysis (generating 4-way tables).12 To incorporate the GSS case weight variable without

distorting model fit statistics, the counts in the mobility tables are the unweighted frequencies,

but all models include a weight vector containing average cell weights (Clogg and Eliason 1987).

I use Goodman’s (1979) log-multiplicative RC association model (also called the RC-II

model) to analyze the mobility tables described above. To illustrate the RC model, consider a

simpler two-way contingency table such as the conventional intergenerational mobility table of

father’s class (i) by class destination (j), where Fij, is the expected frequency the model predicts

for cell i,j of the table. The RC model simultaneously estimates row scores (µi) to rank class

origin categories and column scores (νj) to rank class destination categories, along with an

intrinsic association parameter (Φ). The association parameter conveys the overall strength of

the relationship between the ranked class origin and destination categories, and is interpreted

similarly to a regression coefficient in that zero means there is no association (Hout 1983). For

such a two-way table, an example of notation for the RC model is:

12 The problem of non-comparability in census coding does not apply because, as noted above, my analyses are

restricted to recent survey years and all occupational data in these survey years are recorded in 1980 basis census codes. It is possible to use these newer survey data alone to compare social fluidity between cohorts because the respondents vary widely in age.

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Log Fij = λ0 + λiF + λj

D + Φuiνj,

where λ0 is the mean of the logarithms of the expected frequencies, λiF controls for the

distribution of fathers’ class position (class origins), λjD controls for the distribution of class

destinations, and Φuiνj measures the degree of association between ranked origin scores and

destination scores. For identification, Σλ0 = ΣλiF = Σλj

D= Σiui = Σjνj = 0, and Σiui2

= Σjνj2

= 1. If the

model is accurate the expected frequencies resemble observed frequencies in the mobility table.

I utilize RC log-multiplicative association models rather than log-linear models because

of the greater parsimony of the former and because the association parameter Φ of the RC model

is readily interpretable as a descriptor of the overall strength of association between class origins

and destinations. This feature of the RC model simplifies the illustration and discussion of the

consequences of various origins measures. However, one limitation of the RC model is that, in

describing origin and destination categories in terms of ranked scores, it analyzes only one

hierarchical dimension of origin-destination association.13 I replicated the analyses presented in

this article using both log-linear models, which do not impose a unitary hierarchical dimension

of association, and Erikson and Goldthorpe’s (1992) core social fluidity model, which includes

multiple non-hierarchical and hierarchical log-linear parameters to describe origin-destination

association, with substantively similar results; see Appendix tables A1 and A2 for these analyses.

The mobility tables I analyze are somewhat sparse (due primarily to clustering of mothers

and female respondents in certain classes), so I assess overall model fit using the Pearson chi-

squared goodness of fit statistic (X2) rather than the likelihood-ratio goodness of fit statistic (L2,

also known as G2); X2 performs better than L2 given sparse data (Agresti and Yang 1987). To

adjudicate among models, I use the BIC criterion (Raftery 1995) and I compare nested models 13 Multi-dimensional RC(m) models (see Becker and Clogg 1989; Clogg and Shihadeh 1994: 84) are possible, but

are not as easily interpretable. Allowing for multiple dimensions of association does not change the substantive conclusions of this research.

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using the likelihood-ratio test (which is unaffected by sparse data; see Agresti and Yang 1987).

Likelihood-ratio tests assess whether a reduction in L2 is statistically significant given the

difference in degrees of freedom between two nested models. The BIC criterion emphasizes

model parsimony more than the likelihood-ratio test does; the rationale is that, with large sample

sizes, substantively unimportant improvements in L2 can be statistically significant. However, I

evaluate relative model fit in terms of both likelihood-ratio tests and BIC (Powers and Xie 2000,

145-146; Xie 1999). Given the sample sizes, marginal differences in BIC (of fewer than

approximately ten points) can be considered equivalent (Wong 1994). I use the LEM program to

estimate all models (Vermunt 1997).

The Impact of Mothers’ and Fathers’ Class Positions on Class Destinations

The first question I address is whether models which utilize conventional class origins

measures adequately fit the mobility table, as well as whether models which utilize joint

measures provide significant improvements to model fit compared to models utilizing

conventional measures. To do so, I use the RC model described above to fit the partial

association between class destinations and various measures of class origins. The partial

association is the association net of the distributions of mothers’ class position (M), fathers’ class

position (F), mothers’ and fathers’ class positions (MF), and class destination (D), and net of

dummy variables for “diagonal” inheritance effects. The diagonal inheritance parameters

capture the tendency of respondents to remain immobile (i.e. to cluster along the diagonal cells

of the mobility table, where origin = destination) over and above what RC models would

otherwise predict. The inclusion of diagonal parameters is standard when RC models are used to

analyze mobility tables (Goodman and Clogg 1992; Gerber and Hout 2004), but their inclusion

affects the interpretation of the association parameters, which no longer index the total origin-

18

destination association. I estimated all models without diagonal parameters with the same results

in regard to relative model fit (see Appendix Table A3); however, the X2 statistics show that

none of the models which lack controls for father-son diagonal inheritance effects fit the overall

mobility table well among men. Diagonal inheritance parameters are of less import for women,

but I include them in models for both sexes for consistency.

I adjudicate between several different measures of class origins:

A) I fit four models with origins measures which specify that effects of parent class

position are redundant in that only one parent’s class position defines class origins. These are the

conventional father-only model, a mother-only model, a higher class dominance model (Erikson

1984) in which the higher class position solely defines the family class (regardless of parent

gender), and a lower class dominance model, in which the lower class position solely defines the

family class (regardless of parent gender). The conventional father-only model is:

Log Fhij = λ0 + λhM + λi

F + λhiMF + λj

D + δDij + Φuiνj , [1]

where ΣhλhM = Σiλi

F = ΣhΣiλhiMF = Σjλj

D = Σiui = Σjνj = 0, Σiui2

= Σjνj2

= 1, and δDij = 1 if i = j (i.e.

δDij = 1 if the class destination is the same as the father’s class, and = 0 otherwise).

The mother-only model replaces Φuiνj with Φuhνj, and replaces δDij with δDhj. The

higher and lower class dominance models specify u so that the origin scores can be based on

either parent’s class position depending on who holds the higher or lower position. Φuiνj from

equation 1 is replaced with Φuhiνj, creating potentially 5 x 5 possible separate origin scores for

each combination of mothers’ and fathers’ class categories, but these 5 x 5 scores are constrained

such that the scores are solely determined by the parent with the higher or lower class position.

The design matrices for the constraints are shown in Table 2. The higher and lower class

dominance models also replace δDij or δDhj with δDhij, a diagonal parameter based on the higher

19

(lower) class position rather than on fathers’ or mothers’ class positions, where δDhij = 1 if the

higher (lower) of h or i = j.

B) I fit four models with joint origins measures which specify that effects of parent class

position are cumulative in that they define class origins with respect to both parents’ positions.

The first two such models are a mother + father model and a lower + higher class model. The

latter differentiates parents by relative class position rather than by gender (Korupp et. al 2002).

These models combine the mother-only and father-only models and the higher class and lower

class dominance models described above. For example, the mother + father model is:

Log Fhij = λ0 + λhM + λi

F + λhiMF + λj

D + δ1Dij + δ2Dhj + Φuiνj + Φuhνj , [2]

where ΣhλhM = Σiλi

F = ΣhΣiλhiMF = Σjλj

D = Σiui = Σhuh = Σjνj = 0, Σiui2

= Σhuh2 = Σjνj

2 = 1, δ1Dij = 1

if i = j and δ2Dhj = 1 if h = j. The destination scores νj are held equal between Φuiνj and Φuhνj.

The second two joint-parent origins models are averaged versions of the mother + father and

higher + lower class models, which replace Φuiνj + Φuhνj with Φuhiνj, and δ1Dij + δ2Dhj with

δ3Dhij, and which add the constraint that ui = uh = mean ui, uh, and δ3Dhij = mean δ1Dij, δ2Dhj.

C) I fit two additional models with joint-parent origins measures that also include

interaction effects between parent gender and/or parent class positions. The first is a full

interaction model which allows each combination of parent class and gender to result in a unique

class origin category. For example, under this model the class origin of a family with a

professional mother and a skilled/technical father may differ from that of a family with a

professional father and a skilled/technical mother. The second of these two models is the class

interaction model which is a constrained version of the full interaction model—it includes

interaction effects between pairs of parent class positions, but not between parent class position

and parent gender. In other words, in the class interaction model the family class origin score for

20

a family with a professional mother and a self-employed father is held equal to the score for a

family with a professional father and a self-employed mother. By contrast, in the full interaction

model the scores for these two combinations of parent class positions are free to differ.

The full interaction model is:

Log Fhij = λ0 + λhM + λi

F + λhiMF + λj

D + δ1Dij + δ2Dhj + Φuhiνj , [3]

where ΣhλhM = Σiλi

F = ΣhΣiλhiMF = Σjλj

D = Σiui = Σhuh = Σjνj = 0, Σiui2

= Σhuh2 = Σjνj

2 = 1, δ1Dij = 1

if i = j, and δ2Dhj = 1 if h = j. The full interaction model retains all 5 x 5 separate scores, which

correspond to unique combinations of mothers’ and fathers’ class positions. The class interaction

model sets equality constraints on the 5 x 5 origin scores as described above (see Table 2).

Table 3 shows the results of these ten models, in comparison to an independence model

which posits no origin-destination association. I report X2 tests in order to assess overall model fit

(if model p is significant (<0.05), the estimated frequencies differ significantly from the observed

frequencies of the saturated model). I report likelihood-ratio (L2) tests comparing each model to

a) the full interaction model (i.e. the saturated version of the RC association model), and b) the

father-only model. The L2 comparisons between joint-parent models and the father-only model

assess whether any improvement in model fit is significant compared to the more parsimonious

conventional model. I also report the index of dissimilarity (D). I prefer models that show

equivalent fit compared to the saturated and full interaction models, and that have a lower BIC

by at least ten points.

The key overall result, for both men and women, is that the various model fit statistics

agree that the joint-parent class origins measures significantly outperform the one-parent class

origins measures. None of the models utilizing one-parent measures adequately fit the mobility

table compared to the saturated model, while all of the models utilizing joint-parent measures do

21

achieve adequate overall fit. Similarly, likelihood-ratio tests show that most of the models which

employ joint-parent measures fit well compared to the full interaction model, while all of the

models employing one-parent measures show significant loss of information compared to the full

interaction model. All of the joint-parent models significantly improve L2 compared to the

conventional father-only model. The BIC criterion demonstrates that the most parsimonious

(averaged) joint-parent models are preferred to the father-only model. The moderately

parsimonious joint-parent models are equivalent to the father-only model with respect to BIC,

and the least parsimonious joint-parent models (full and class interaction) are rejected by BIC

compared to the father-only model.14

Among the one-parent measures, the higher-class dominance model, which has been

suggested as an improvement over the conventional father-only model, has a poorer overall fit

than the father-only model among men and, notably, a poorer fit than the lower-class dominance

model among both men and women. The father-only model is strongly preferred over the

mother-only model for men, but the two are equivalent for women. Among the joint-parent

measures, Models 1 and 2 (full and class interaction) fit well overall but are much less

parsimonious than the other two-parent models, and the remaining joint-parent models do not

show a significant loss of information in comparison. Models 3 and 4 (the mother + father and

higher + lower class models) are more parsimonious than the models with parent class

interaction effects, are equivalent in terms of BIC but significantly improve L2 compared to the

father-only model, and fit the mobility table well overall. Models 5 and 6, which specify that

effects of parents’ class positions are averaged, are the most parsimonious of the joint-parent

models and are preferred over all other models in terms of BIC. As a final note, the higher + 14 I tested whether these findings are robust to different modeling strategies and the results were consistent (see

Appendix Tables A1 and A2). I also fit these models without diagonal parameters, again with similar results (see Appendix Table A3).

22

lower class measures and mother’s + father’s class origin measures have similar fit statistics; I

prefer the mother + father conceptualization as it is more conceptually straightforward.

A remaining question is whether the choice of origin measure affects the estimated

degree of social fluidity as indexed by the association parameters (reported in Table 4).15 The

origin and destination scores in all models are scaled using uniform weights so that the

association parameters will be standardized across models with different numbers of origin

categories (Becker and Clogg 1989; Clogg and Shihadeh 1994, 51).16 Comparisons of the

estimated family-level association in Table 4 show that the that the father-only model

underestimates the overall family-level class origin-destination association—and therefore

overestimates total social fluidity—compared to most of the joint-parent models of family class

origins, with some exceptions for women. The extent to which the association is underestimated

may appear modest, but later in the article I show that the father-only model approximates the

joint-parent class origin-destination association among older cohorts, but provides an

increasingly inaccurate picture of association among more recent cohorts. The association

parameters in Table 4 are estimated from data combining varying birth cohorts, and the

distortion produced by conventional measures is not as acute is the case for recent cohorts.

Can Homemaker Mothers be Incorporated in Joint-Parent Measures of Class Origins?

For simplicity, the previous analysis excluded respondents who reported that their mother

worked in the home rather than in the labor force, or 33 percent of otherwise eligible

respondents. However, if joint-parent class origins measures are to be useful, they must be

applicable to a more comprehensive population of respondents that includes those with

15 The LEM software program does not generate standard errors for association parameter estimates. However, the

poor fit of the baseline model of independence (model 11 in Table 3) indicates that the origin-destination association is significantly different from zero.

16 Use of uniform weights does not alter model fit statistics, but affects estimated scores and association parameters.

23

homemaker mothers. This portion of the analysis includes all respondents of the appropriate age

range and labor force status who were raised in two-parent families, including those with

homemaker mothers. I evaluate whether the same measures for class origins that were preferred

for respondents raised in dual-earner families are again preferred over the conventional measures

when respondents raised in single-earner families (i.e. with homemaker mothers) are included.

I focus on the preferred joint-parent models and the preferred one-parent model from the

previous analysis (mother + father, averaged mother + father, and father-only);17 I also report

model fit statistics for the full interaction and class interaction models for comparison. I evaluate

three alternative ways of incorporating homemaker mothers: first by treating the homemaker

category as a class category, second, by specifying that while employed mothers’ class positions

influence class origins, the homemaker category does not (i.e. by constraining the homemaker

origin score to zero), and third, by differentiating the homemaker category by husbands’ class.18

The first series of models (A, in Table 5) include a single class category for homemaker

mothers, while the second series of models (B, in Table 5) provide a comparison in which the

homemaker category is ignored. It is not possible to estimate the class interaction or full

interaction models while simultaneously ignoring the homemaker mother category, so these

models are omitted in the B series. Table 5 shows that the A and B series of models have similar

fit statistics. One interpretation of these results is that joint conceptions of family class may apply

only to dual-earner families, while another possible interpretation is that, if homemaker mothers

contribute varying class resources drawn from their upbringing, prior employment, education,

and/or husbands’ class, the measurement error inherent in the single broad category of 17 I also estimated all other models from Table 3 with similar results to the previous analysis regarding relative

model fit among various origins measures, and with similar results to the current analysis regarding relative model fit between different methods of including homemaker mothers (results not shown but available from the author).

18 Diagonal parameters for mother’s class=respondent’s class are omitted from these models because they do not significantly improve model fit in these or in the prior analyses.

24

homemakers with diverse class resources could depress the observable effects of such resources

toward zero.

To further investigate, in an additional series of models I differentiate the homemaker

category by husbands’ class position, as a proxy for homemaker mothers’ class resources (given

assortative marriage).19 These models are shown in the C series in Table 5. The class interaction

and full interaction models would be the same as in the A series above, so are omitted in the C

series. Indicating that homemaker mothers’ class resources may in fact shape class origins, the C

series models significantly improve L2 compared to equivalent models in the A or B series. For

men the BIC statistics show that the improvement in model fit achieved by differentiating

homemaker mothers in this fashion is not enough to support the reduced parsimony of the

models. But among women the BIC statistics are equivalent between the A or B and C series of

models, meaning that the reduction in parsimony is not rejected by BIC, and that the

improvement in model fit with respect to L2 may be substantively important. The results for the

A, B, and C series of models each confirm that the substantive findings of the previous analysis

continue to apply when respondents with homemaker mothers are included in mobility tables—

joint-parent models are preferred over the conventional model.

Cohort Change in Social Fluidity

The previous analyses demonstrated that class origin measures which jointly capture the

class positions of both parents provide the most accurate picture of intergenerational mobility.

Furthermore, defining class origins with reference to the father’s position or the higher class

position alone can inflate social fluidity estimates. This finding indicates that conventional class

19 Note that this differentiation does not mean that homemaker mothers married to professionals, for example, will

be placed in the same category as professionally employed mothers; the models instead include 5 distinct scores for homemaker mothers in addition to the scores for the 5 categories of employed mothers.

25

origins measures could produce misleading comparisons of social fluidity levels between groups.

In this section of the analysis I evaluate the research consequences of class origin measurement

choices for detecting whether social fluidity levels have increased, decreased, or stayed constant

across birth cohorts. The results demonstrate that different measures of class background can

indeed affect conclusions about cohort change or trends in social fluidity.

By necessity, I exclude respondents from GSS survey years prior to 1994, the year when

the GSS began to collect data on mothers’ occupation. This restriction limits the cohort sample

sizes and the ability to include respondents born during the first half of the 20th century. I define

cohorts broadly in order to include an adequate number of respondents in each cohort—for men

and women separately, I initially compare the social fluidity levels for respondents born between

1950 and 1964 to social fluidity levels for respondents born between 1965 and 1979. While a

central goal of this analysis is to illustrate how outdated class origins measures might distort

substantive research conclusions, another goal is to provide new information on the mobility

experiences of recent cohorts. To that end, I also provide a descriptive picture of trends in social

fluidity for a broader range of cohorts by comparing social fluidity levels among overlapping or

“rolling” cohorts, namely respondents born in 1945-1959, 1950-1964, 1955-1969, 1960-1974,

and 1965-1979 (model fit statistics not shown due to the overlapping data). I focus the analysis

on preferred models for joint-parent and one-parent origins measures (mother + father, averaged

mother + father, and father-only) and include the class interaction model as well for comparison.

I estimate RC association models as described earlier in the article, but in this portion of

the analysis the mobility tables are further differentiated by cohort. As in the previous analyses, I

estimate separate models for men and women. For each gender, the father-only model is:

Log Ffhij = λ0 + λfC + λh

M + λiF + λj

D + λfhCM + λfi

CF + λhiMF + λfhi

CMF + λfjCD

+ δDij + Φcuiνj, [4]

26

where C= cohort, M= mother’s class position, F= father’s class position, D= respondent’s class

destination, with the identifying restrictions ΣfλfC = Σhλh

M = ΣiλiF = Σjλj

D = ΣfΣhλfhCM = ΣfΣiλfi

CF =

ΣhΣiλhiMF = ΣfΣhΣiλfhi

CMF = ΣfΣjλfjCD = Σiui = Σjνj = 0, Σiui

2 = Σjνj

2 = 1. δDij is a diagonal

inheritance parameter that is equal to 1 if i=j, ui and νj are the scores for origin and destination

categories, respectively, and Φc is the association parameter along with a log-multiplicative

layer-effect of cohort, which indexes the degree to which Φ increases or decreases in strength

between cohorts (Xie 1992).

While Φc differs between cohorts, ui and νj remain equal between cohorts, so that it is

only the strength and not the pattern of association that is permitted to vary between cohorts.

This specification provides a parsimonious test for differences between cohorts in the overall

strength of origin-destination association. Equation 4 controls for the interaction between C and

D, as well as for all interactions between the independent variables C, M and F, and therefore the

association between origin and destination is estimated net of cohort differences in the

distribution of class origins and destinations (cohort change in structural mobility). The diagonal

parameters are not cohort specific, as there is no evidence that the degree of diagonal inheritance

changed significantly between cohorts for either men or women (analyses not shown; available

from the author). In baseline models of no cohort change in social fluidity, Φc1 is held equal to

Φc2. The mother + father model adds Φuhνj to equation 4, where the νj scores are held equal

between Φuiνj and Φuhνj. Finally, the averaged mother + father model replaces the Φuhνj and

Φuiνj of the father + mother model with Φuhiνj, with the constraint that uhi = uh = ui = mean uh, ui.

Model fit statistics are shown in Table 6, and cohort-specific association parameter

estimates are shown in Figure 2. Among men, the conventional father-only model indicates no

significant change in social fluidity levels between cohorts. Compared to a baseline model of no

27

cohort change, the father-only model permitting cohort change does not significantly reduce L2,

and the baseline model of no change is also BIC preferred. In contrast, the models employing

joint-parent origins measures provide evidence of a significant decline in fluidity in the younger

compared to the older cohort. The models permitting cohort change in association significantly

reduce L2 (BIC statistics are equivalent), compared to baseline models of no cohort change, for

all of the joint-parent origins measures considered for men. As Figure 2 shows, the conventional

father-only class origins measure overestimates social fluidity (e.g. underestimates the origin-

destination association) for the younger male cohort, masking a reduction in fluidity between

cohorts that is revealed by joint-parent class origins measures. Among women, there is no

evidence of cohort change in social fluidity regardless of the type of origin measure used, but the

father-only model overestimates social fluidity, and particularly so in the younger cohort.

To illustrate cohort trends in association over a broader period of time and to provide a

better understanding of why the different origins measures produce conflicting conclusions

regarding cohort change among men, I analyzed cohort trends in association among respondents

in successive rolling birth cohorts (1945-1959, 1950-1964, 1955-1969, 1960-1974, and 1965-

1979). Figure 3 shows the evolving association parameters across overlapping male cohorts.20

The figure displays the trend estimated by the father-only model and the trend produced by the

mother + father model, alongside trends in the net, individual parent-respondent association

parameters (e.g. net mother-respondent and net father-respondent association).21 The father-only

model indicates relatively constant association in the first four cohorts followed by a modest

increase in association (decline in social fluidity) in the youngest cohort. However, the trend

produced by the mother + father model suggests that the association between family-level origins 20 Results for women are consistent with the previous finding of no cohort change in association (see Figure 3). 21 The net mother and net father association parameters should not be interpreted as additive components of the

joint-parent, mother + father association parameter, because the underlying origin scores differ.

28

and destinations has steadily increased among men born since 1950. The trend-line for mother-

son association over this period, net of father-son association, explains this finding. The overall

growth in origin-destination association is masked by leaving mothers’ class positions, which

were increasingly associated with sons’ class destinations, unmeasured.

DISCUSSION

The theoretical argument and empirical analyses presented in this article demonstrate the

substantive importance of an adequate conceptualization of, and measurement strategy for,

children’s class background. As theorized mechanisms of intergenerational persistence in class

would suggest, there is strong evidence that the impact of parents’ class on family-level class

resources, and thereby children’s class destinations, is cumulative. Joint-parent measures of

class origins capture the observed mobility patterns significantly better than do conventional

measures of class origins, which are based on the fathers’ or higher class position. Further,

because both parents’ class positions shape children’s outcomes and because marriage is not

random with respect to class, conventional research practice distorts the estimated the strength of

overall association between class origins and destinations. For example, in addition to

underestimating the strength of origin-destination association for men and women in each cohort,

conventional intergenerational mobility models do not reveal a significant decline in social class

fluidity among men born between 1965 and 1979 compared to men born between 1950 and 1964

(a result of growing association between mothers’ class and sons’ class destinations).

Neither conventional nor joint class origins measures produce evidence of cohort change

in social fluidity among women, raising the question of why men and women’s social fluidity

29

might be dissimilar,22 especially among the youngest cohort of men and women whom we might

expect to have experienced the least gender inequality. Part of the answer is likely that the social

fluidity estimates are not directly comparable between female cohorts because of shifts in the

degree and type of selectivity of women’s labor force participation. Stable as opposed to rising

origin-destination association between female cohorts could be due to proportionally more

women entering the labor force in the younger cohort, and doing so less selectively.23

The analyses presented in this article illustrate that the conventional measurement of

family class origins can distort research conclusions when social fluidity is compared between

cohorts, but the implications of these findings for intergenerational mobility and stratification

research extend well beyond the particular example of cohort change, and apply to comparative

mobility research more generally. For example, if mothers’ class remains unmeasured and

marital sorting by class differs cross-nationally, the greater measurement error with respect to

class origins in countries with comparatively weak assortative marriage patterns could be

misinterpreted as substantive differences between countries in social fluidity levels. On the flip

side, substantive cross-national differences in social fluidity could equally be masked.

This article provides initial steps toward modernizing family stratification research, but

important challenges and avenues for further research remain. First and foremost, I have not

measured class destinations at the family-level, and the current line of inquiry will be logically

incomplete until the same scrutiny here applied to class origins can also be extended to class

destinations. Yet individual class destinations are important in their own right in addition to

22 Prior research did not find evidence of differences between men and women in social fluidity trends over time, but

it was based codes for occupations that are not comparable to the occupational codes used in this analysis, and it employed a period approach rather than distinguishing between cohorts (Hout 1988).

23 Women who participate in the labor force are a more selected group than men who participate in the labor force, and the degree of selectivity has declined across cohorts. The type of selectivity has also differed between cohorts—the likelihood of women’s labor force participation is related to class origins, but this relationship has weakened between cohorts (analysis not shown; available from the author).

30

constituting the building blocks of adult, family-level class outcomes. Given space limitations, it

is appropriate to approach the evaluation of conventional versus joint perspectives of family-

level class origins and family-level class destinations in conceptually distinct steps. But it will

be of compelling interest as a next step for research, as well as logically consistent with the

current line of inquiry, to evaluate how the inequalities of family class origins may or may not be

compounded given family-level as opposed to individual measurement of class destinations.

A second challenge is that, although this article illustrates the importance of measuring

the class resources of both parents to adequately define class origins, the growing prevalence of

single parent families presents problems for doing so because most surveys do not collect

information on non-custodial parent attributes such as occupation. In conventional mobility

research practice, mothers’ and/or stepfathers’ occupation may arguably be substituted for that of

non-custodial fathers if such data is available, but the solution is not so simple for joint-parent

measures of class origins, because information on both parents is required. Therefore the

analyses presented in this article exclude a sizeable and growing proportion of the population—

individuals raised in single parent families.

For future research, there are at least three options for incorporating single parents in

joint-parent class origins measures if non-custodial parent class data is unavailable. One

common practice for handling missing data is to assign average attributes (i.e. an average origin

score) to non-custodial parents on the assumption that the conditional distribution of the missing

information (here, class position) is the same for custodial and non-custodial parents. However,

this option is problematic given the theoretical mechanisms of intergenerational transmission of

cultural resources described above, in which parent-child interaction plays a key role, coupled

with evidence that non-custodial parents have reduced interaction with children on average

31

(Seltzer 1994). It would also possible for a model to specify that non-custodial parent class has

no effect on children’s class outcomes, but although the impact of non-custodial parents class on

children’s outcomes may be lower than that of custodial parents, it does not follow that such

impact should be expected to be non-existent. Third, a middle ground option would be to allow

the RC association model to independently calculate a score to describe the average position of

non-custodial mothers and fathers in comparison to custodial parents, whose class positions are

known. This strategy would allows origin scores to reflect that non-custodial parents may, on

average, contribute different class resources than custodial parents do (e.g. due to lower class

position on average, or due to children’s reduced access to non-custodial parent class resources).

As illustrated by the absence of questions about non-custodial parent attributes in most

surveys and by the only recent addition in 1994 of the question of mothers’ occupation in the

GSS (and the continued absence of questions regarding mothers’ occupation from many other

surveys), limited data is a substantial constraint to updating the practice of intergenerational

social mobility research, as well as stratification research more generally. Surveys must begin

collecting class-related information on all adults in the respondents’ family, including mothers

and non-custodial parents, in order for family stratification researchers to adequately measure

respondents’ class origins. For the time being, stratification and mobility research should, of

course, proceed despite data limitations. This article has demonstrated that the best practice is to

measure children’s class background with respect to the class characteristics of both parents, but

this will often not be possible with current data sources. Researchers can move forward despite

limited data by, on the one hand, measuring children’s class origins as comprehensively as

possible, when possible, and on the other hand, by carefully considering in the interpretation of

32

research findings the potential for omitted variable bias to affect research results, given that

important aspects of children’s class backgrounds may remain unmeasured.

33

REFERENCES Acker, Joan. 1973. “Women and Social Stratification: A Case of Intellectual Sexism.” American

Journal of Sociology 78: 936-945. Agresti, Alan and Ming-Chung Yang. 1987. “An Empirical Investigation of Some Effects of

Sparseness in Contingency Tables.” Computational Statistics and Data Analysis 5: 9-21. Baxter, Janeen. 1994. “Is Husband’s Class Enough? Class Locations and Class Identity in the

United States, Sweden, Norway and Australia.” American Sociological Review 59: 220-235. Becker, Mark P. and Clifford C. Clogg. 1989. “Analysis of Sets of Two-Way Contingency Tables

Using Association Models.” Journal of the American Statistical Association 84: 142-151. Biblarz, Timothy J., Adrian Raftery and Alexander Bucur. 1997. “Family Structure and Social

Mobility.” Social Forces 75: 1319-1341. Biblarz, Timothy J. and Adrian Raftery. 1999. “Family Structure, Educational Attainment, and

Socio-economic Success: Rethinking the Pathology of Matriarchy.” American Journal of Sociology 105: 321-365.

Bourdieu, Pierre and Jean-Claude Passerson. 1977. Reproduction in Education, Society and Culture. London: Sage Publications.

Breen, Richard and Jan O. Jonsson. 2007. “Explaining Change in Social Fluidity: Educational Equalization and Educational Expansion in Twentieth-Century Sweden.” American Journal of Sociology 112: 1775-1810.

Breen, Richard and David B. Rottman. 1995. Class Stratification: A Comparative Perspective. Hertfordshire: Harvester Wheatsheaf.

Coleman, James S. 1964. An Introduction to Mathematical Sociology. New York: Free Press Glencoe. Clogg, Clifford C. and Scott R. Eliason. 1987. “Some Common Problems in Log-Linear Analysis.”

Sociological Methods and Research 16: 8-44. Clogg, Clifford C. and Edward S. Shihadeh. 1994. Statistical Models for Ordinal Variables.

Thousand Oaks: Sage Publications. Conley, Dalton. 2001. Capital for College: Parental Assets and Postsecondary Schooling.

Sociology of Education 74: 59-72. Davis, James A., Tom W. Smith, and Peter V. Marsden. GENERAL SOCIAL SURVEYS, 1972-

2006 [CUMULATIVE FILE] [Computer file]. ICPSR04697-v1. Chicago, IL: National Opinion Research Center [producer], 2007. Storrs, CT: Roper Center for Public Opinion Research, University of Connecticut/Ann Arbor, MI: Inter-university Consortium for Political and Social Research [distributors], 2007-05-31.

Davis, Nancy J. and Robert V. Robinson. 1998. “Do Wives Matter? Class Identities of Wives and Husbands in the United States, 1974-1994.” Social Forces 76: 1063-1086.

Davis, Nancy J. and Robert V. Robinson. 1988. “Class Identification of Men and Women in the 1970s and 1980s.” American Sociological Review 53: 103-112.

Deil-Amen, Regina and James E. Rosenbaum. 2003. “The Social Prerequisites of Success: Can College Structure Reduce the Need for Social Know-How?” The Annals of the American Academy of Political and Social Science 586: 120-143.

DiPrete, Thomas A. and David Grusky. 1990. “Structure and Trend in the Process of Stratification for American Men and Women,” The American Journal of Sociology 96: 107-143.

Duncan, Greg I., W. Jean Yeung, Jeanne Brooks Gunn, and Judith R. Smith. 1998. “How Much Does Childhood Poverty Affect the Life Chances of Children.” American Sociological Review 63: 406-23.

34

Erikson, Robert. 1984. “Social Class of Men, Women and Families.” Sociology 18: 500-514. Erikson, Robert, John H.Goldthorpe and Lucienne Portocarerro. 1979. “Intergenerational Class

Mobility in Three Western Societies: England, France, and Sweden.” The British Journal of Sociology 30: 415-441.

Erikson, Robert and John H. Goldthorpe. 1992. The Constant Flux. Oxford: Clarendon Press. Featherman, David L. and Robert M. Hauser. 1978. Opportunity and Change. New York:

Academic Press. Gerber, Theodore P. and Michael Hout. 2004. “Tightening Up: Class Mobility During Russia’s

Market Transition.” American Sociological Review 69: 677-703. Goodman, Leo. 1979. “Multiplicative Models of the Analysis of Mobility Tables and Other

Kinds of Mixed-classification Tables.” American Journal of Sociology 84: 804-819. Goodman, Leo A. and Clifford C. Clogg. 1992. “Review: New Methods for the Analysis of

Occupational Mobility Tables and Other Kinds of Cross-Classifications.” Contemporary Sociology 21: 609-622.

Goldthorpe, John H. 1983. “Women and Class Analysis: In Defense of the Conventional View.” Sociology 17: 465-488.

Goldthorpe, John H. 1984. “Women and Class Analysis: A Reply to the Replies.” Sociology 18: 491-99. Gottfried, Allen W. 1984. Home Environment and Early Cognitive Development: Longitudinal

Research. Orlando, FL: Academic Press. Guo, Guang and Kathleen Mullan Harris. 2000. “The Mechanisms Mediating the Effects of

Poverty on Children's Intellectual Development.” Demography 37: 431-447. Harding, David J., Christopher Jencks, Leonard M. Lopoo, and Susan E. Mayer. 2005. “The

Changing Effects of Family Background on the Incomes of American Adults,” in Unequal Chances: Family Background and Economic Success, ed. Bowles, Gintis, and Groves. New York: Russell Sage Foundation; Princeton, N.J: Princeton University Press.

Hauser, Robert M., Shu-Ling Tsai and William H. Sewell. 1983. “A Model of Stratification with Response Error in Social and Psychological Variables.” Sociology of Education 56: 20-46.

Hayghe, Howard V. 1990. “Family Members in the Work Force.” Monthly Labor Review, March: 14-19.

Heath, Anthony and Nicky Britten. 1984. “Women’s Jobs Do Make a Difference: A Reply to Goldthorpe.” Sociology 18: 475-490.

Hill, Martha, and Greg Duncan. 1987. “Parental Family Income and the Socioeconomic Attainment of Children.” Social Science Research 16:39-73.

Hout, Michael. 1982. “The Association Between Husbands’ and Wives’ Occupations in Two Earner Families.” American Journal of Sociology 88: 397-409.

Hout, Michael. 1983. Mobility Tables. Series: Quantitative Applications in the Social Sciences. Newbury Park: Sage.

Hout, Michael. 1988. “More Universalism, Less Structural Mobility: The American Occupational Structure in the 1980s.” American Journal of Sociology 93: 1358-1400.

Hout, Michael, Clem Brooks and Jeff Manza. 1995. “The Democratic Class Struggle in the United States, 1948-1992.” American Sociological Review 60: 805-828.

Hout, Michael. 1996. “Speed Bumps on the Road to Meritocracy: The American Occupational Structure in the 1980s.” Working Paper, Survey Research Center, Berkeley: CA.

Ishii-Kuntz, Masako. 1994. Ordinal Log-Linear Models. Series: Quantitative Applications in the Social Sciences. Newbury Park: Sage.

Kalmijin, Matthijs. 1994a. “Assortative Mating by Cultural and Economic Occupational Status.”

35

American Journal of Sociology 100: 422-452. Kalmijn, Matthijs. 1994b. “Mother’s Occupational Status and Children’s Schooling.” American

Sociological Review 59: 257-275. Kalmijn, Matthijs. 1998. “Intermarriage and Homogamy: Causes, Patterns, Trends.” Annual

Review of Sociology 24: 395-421. Khazzoom, Aziza. 1997. “The Impact of Mothers’ Occupations on Children’s Occupational

Destinations.” Research in Social Stratification and Mobility 15: 57-90. Kohn, Melvin L., Kazimierz M Slomczynski, and Carrie Schoenbach. 1986. “Social Stratification

and the Transmission of Values in the Family.” Sociological Forum 1: 73-102. Korupp, Sylvia E., Harry B. G. Ganzeboom and Tanja Van Der Lippe. 2002. “Do Mothers Matter? A

Comparison of Models of the Influence of Mothers’ and Fathers’ Educational and Occupational Status on Children’s Educational Attainment.” Quality and Quantity 36: 17-42.

Lareau, Annette. 2003. Unequal Childhoods: Class, Race and Family Life. Berkeley: UC Press. Lareau, Annette. 1989. Home Advantage: Social Class and Parental Intervention in Elementary

Education. New York: Falmer Press. Lucas, Samuel R. 1999. Tracking Inequality: Stratification and Inequality in American High

Schools. New York: Teachers College Press. Mare, Robert D. 1981. “Change and Stability in Educational Stratification.” American

Sociological Review 46: 72-97. Mare, Robert D. 1991. “Five Decades of Educational Assortative Mating.” American

Sociological Review 56: 15-32. Marini, Margaret. 1980. “Sex Difference in the Process of Occupational Attainment: A Closer

Look.” Social Science Research 9: 307-361. Marshall, Gordon, Stephen Roberts and Carole Burgoyne. 1996. “Social Class and Underclass in

Britain and the United States.” The British Journal of Sociology 47: 22-44. Mayer, Susan E. 1997. What Money Can’t Buy: Family Income and Children’s Life Chances.

Cambridge: Harvard University Press. Powers, Daniel A. and Yu Xie. 2000. Statistical Methods for Categorical Data Analysis. San

Diego: Academic Press. Plutzer, Eric and John F. Zipp. 2001. “Class, Gender and the Family Unit: A Dynamic Model of

Stratification and Class Politics.” Social Science Research 30: 426-448. Raftery, Adrian E. 1995. “Bayesian Model Selection in Social Research.” Sociological

Methodology 25: 111-163. Roemer, John E. 2004. “Equal Opportunity and Intergenerational Mobility: Going Beyond

Intergenerational Income Transition Matrices,” in Generational Income Mobility in North America and Europe, ed. Corak. Cambridge: Cambridge University Press.

Rosenfeld, Rachel. 1978. “Women’s Intergenerational Occupational Mobility.” American Sociological Review 43: 36-47.

Seltzer, Judith. 1994. “Consequences of Marital Dissolution for Children.” Annual Review of Sociology 20: 235-266.

Sewell, William H., Archibald O. Haller, and Alejandro Portes. 1969. “The Educational and Early Occupational Attainment Process.” American Sociological Review 34: 83-92.

Sorensen, Annemette. 1994. “Women, Family and Class.” Annual Review of Sociology 20: 27-47. Stanworth, Michelle. 1984. “Women and Class Analysis: A Reply to John Goldthorpe.”

Sociology 18: 159-170. Tyree, Andrea and Judith Treas. 1974. “The Occupational and Marital Mobility of Women.”

36

American Sociological Review 39: 293-302. Vermunt, Jeroen K. 1997. “LEM: A General Program for the Analysis of Categorical Data.

User’s Manual.” Tilburg University, The Netherlands. Vines, P., and Priebe, J.A. 1988. “The Relationship between the 1970 and 1980 Industry and

Occupation Classification Systems.” Washington, DC: U.S. Government Printing Office. Winkler, Anne. 1998. “Earnings of Husbands and Wives in Dual-earner Families.” Monthly

Labor Review 121: 42-48. Wong, Raymond Sin-Kwok. 1994. “Model Selection Strategies and the Use of Association

Models to Detect Group Differences.” Sociological Methods and Research 22: 460-491. Wright, Erik Olin. 1997. Class Counts: Comparative Studies in Class Analysis. New York:

Cambridge University Press. Xie, Yu. 1992. “The Log-Multiplicative Layer Effect Model for Comparing Mobility Tables.”

American Sociological Review 57: 380-39. Xie, Yu. 1999. “The Tension between Generality and Accuracy.” Sociological Methods and

Research 27: 428-435. Yamaguchi, Kazuo and Yantao Wang. 2002. “The Class Identification of Employed Married Women and Men in

America.” American Journal of Sociology 108: 440-475.

37

TABLE 1 Family Level Class Resources in a Two Parent Family Class Position of Parents Effects of Parent Class Resources Homogenous Heterogeneous

Redundant A+A= A A+B= A Cumulative A+A= AA A+B=AB

38

TABLE 2 Design Matrices for Class Origins Measures Full Interaction Father's Class Position (F) Mother's Class Position(M) PI&II IIIab IVab V/VI VIIa PI&II 1 2 3 4 5 IIIab 6 7 8 9 10 IVab 11 12 13 14 15 V/VI 16 17 18 19 20 VIIa 21 22 23 24 25 Class Interaction Father's Class Position (F) Mother's Class Position(M) PI&II IIIab IVab V/VI VIIa PI&II 1 6 7 8 9 IIIab 6 2 10 11 12 IVab 7 10 3 13 14 V/VI 8 11 13 4 15 VIIa 9 12 14 15 5 Higher Class Dominance Father's Class Position (F) Mother's Class Position (M) PI&II IIIab IVab V/VI VIIa PI&II 1 1 1 1 1 IIIab 1 2 3 2 2 IVab 1 3 3 3 3 V/VI 1 2 3 4 4 VIIa 1 2 3 4 5 Lower Class Dominance Father's Class Position (F) Mother's Class Position (M) PI&II IIIab IVab V/VI VIIa PI&II 1 2 3 4 5 IIIab 2 2 2 4 5 IVab 3 2 3 4 5 V/VI 4 4 4 4 5 VIIa 5 5 5 5 5 PI& II: Professional, Higher and Lower IIIab: Routine Non-Manual & Service IVab: Self Employed V/VI: Technical & Skilled Manual Labor VIIa: Unskilled Manual Labor

39

TABLE 3 Fit Statistics for RC Association Models: Comparing Various One-Parent and Joint-Parent Class Origins Measures

Men

Model Description X 2 L2 df BIC D p vs. 1 p vs. 9 Model p1 Full Interaction 52.25 54.18 67 -474.58 0.04 0.00 0.91 2 Class Interaction 64.35 65.66 77 -542.03 0.04 0.32 0.00 0.85 3 Father + Mother 69.53 71.71 83 -583.33 0.05 0.35 0.00 0.85 4 Higher Class + Lower Class 83.84 83.60 83 -571.45 0.05 0.02 0.00 0.45 5 Average Father + Mother 91.27 88.69 88 -605.81 0.05 0.03 0.38 6 Average Higher + Lower Class 90.10 89.75 88 -604.75 0.06 0.02 0.42 7 Higher Class Dominance 177.39 167.28 88 -527.22 0.09 0.00 0.00 8 Lower Class Dominance 133.83 128.44 88 -566.06 0.07 0.00 0.00 9 Father-Only 115.54 116.86 88 -577.64 0.07 0.00 0.03 10 Mother-Only 257.83 239.00 88 -455.50 0.12 0.00 0.00 11 Quasi-Independence [FD] 140.34 143.95 91 -574.23 0.08 0.00 0.00 12 Independence 384.05 367.31 96 -390.33 0.15 0.00 0.00

Women

Model Description X 2 L2 df BIC D p vs. 1 p vs. 9 Model p1 Full Interaction 80.24 85.91 67 -446.47 0.04 0.00 0.13 2 Class Interaction 83.65 89.77 77 -522.07 0.05 0.95 0.00 0.28 3 Father + Mother 105.59 111.64 83 -547.87 0.05 0.06 0.00 0.05 4 Higher Class + Lower Class 101.20 105.53 83 -553.98 0.05 0.24 0.00 0.09 5 Average Father + Mother 110.13 116.91 88 -582.33 0.05 0.07 0.06 6 Average Higher + Lower Class 108.18 116.68 88 -582.56 0.05 0.08 0.07 7 Higher Class Dominance 140.91 145.31 88 -553.93 0.07 0.00 0.00 8 Lower Class Dominance 127.25 130.47 88 -568.77 0.06 0.00 0.00 9 Father-Only 146.63 150.94 88 -548.30 0.07 0.00 0.00 10 Mother-Only 147.09 150.04 88 -549.20 0.08 0.00 0.00 11 Quasi-Independence [FD] 163.09 170.49 91 -552.59 0.08 0.00 0.00 12 Independence 236.38 237.40 96 -525.40 0.10 0.00 0.00 Note: [F][M][FM][D] are fitted in all models. N= 2,676 (men); N = 2,824 (women).

40

TABLE 4 Association Parameter Estimates for RC Association Models With and Without Diagonal Parameters: Comparing Various One-Parent and Joint-Parent Class Origins Measures Men Women Mena Womena Model Description Φ Φ (Φ) (Φ) 1 Full Interaction 0.22 0.29 (0.25) (0.29) 2 Class Interaction 0.16 0.25 (0.22) (0.25) 3 Father + Mother 0.16 0.20 (0.22) (0.20) 4 Higher Class + Lower Class 0.16 0.22 (0.22) (0.22) 5 Average Father + Mother 0.14 0.18 (0.21) (0.17) 6 Average Higher + Lower Class 0.13 0.19 (0.21) (0.16) 7 Higher Class Dominance 0.17 0.18 (0.21) (0.17) 8 Lower Class Dominance 0.16 0.18 (0.21) (0.20) 9 Father-Only 0.14 0.18 (0.21) (0.17) 10 Mother-Only 0.18 0.19 (0.19) (0.20)

a The estimates in parentheses are from models which omit diagonal parameters (see Appendix Table A3).

41

TABLE 5 Fit Statistics: Methods for Including Homemaker Mothers in Joint-Parent Class Origins Measures

Men

A: Adding a class category for homemaker mothers

Model Description X 2 L2 df BIC D p vs. A1

p vs. A5

Model p

A1 Full Interaction 82.70 85.74 83 -604.03 0.04 0.00 0.49 A2 Class Interaction 90.40 92.73 93 -680.14 0.04 0.73 0.00 0.56 A3 Father + Mother 104.76 107.88 103 -748.10 0.05 0.33 0.00 0.43 A4 Average Father + Mother 112.07 114.60 107 -774.61 0.06 0.23 0.00 0.35 A5 Father-Only 143.15 144.73 108 -752.79 0.06 0.00 0.01 B: Setting the homemaker class category equal to zero

Model Description X 2 L2 df BIC D p vs. A (3, 4)

p vs. A5

Model p

B3 Father + Mother 104.89 108.00 104 -756.28 0.05 0.37 0.00 0.46 B4 Average Father + Mother 112.64 115.10 108 -782.43 0.06 0.30 0.36 C: Differentiating the homemaker mother class category by husband's class

Model Description X 2 L2 df BIC D p vs. A (3, 4)

p vs. A5

Model p

C3 Father + Mother 95.49 98.04 99 -724.69 0.04 0.04 0.00 0.58 C4 Average Father + Mother 104.37 106.70 103 -749.27 0.05 0.10 0.00 0.44

Women A: Adding a class category for homemaker mothers

Model Description X 2 L2 df BIC D p vs. A1

p vs. A5

Model p

A1 Full Interaction 103.38 109.36 83 -581.56 0.04 0.00 0.06 A2 Class Interaction 110.81 117.50 93 -656.66 0.04 0.00 0.00 0.10 A3 Father + Mother 156.82 163.46 103 -693.94 0.06 0.00 0.00 0.00 A4 Average Father + Mother 159.30 166.02 107 -724.68 0.06 0.00 0.00 0.00 A5 Father-Only 196.56 202.68 108 -696.35 0.07 0.00 0.00 B: Setting the homemaker class category equal to zero

Model Description X 2 L2 df BIC D p vs. A (3, 4)

p vs. A5

Model p

B3 Father + Mother 161.08 167.75 104 -697.99 0.06 0.04 0.00 0.00 B5 Average Father + Mother 163.20 170.12 108 -728.91 0.06 0.04 0.00 C: Differentiating the homemaker mother class category by husband's class

Model Description X 2 L2 df BIC D p vs. A (3, 4)

p vs. A5

Model p

C3 Father + Mother 125.71 132.60 99 -691.51 0.05 0.00 0.00 0.05 C5 Average Father + Mother 132.05 139.65 103 -717.76 0.05 0.00 0.00 0.04 Note: [F][M][FM][D] are fitted in all models. N= 4066 (men); N = 4123 (women).

42

TABLE 6 Fit Statistics: Testing for Cohort Change in Origin-Destination Association

Men

Model Description X 2 L2 df BIC D p vs. no change

Model p

1 Class Interaction 211.62 234.54 209 -1447.12 0.08 0.44 1a 1 + Association varies by cohort 204.77 226.26 208 -1447.35 0.07 0.00 0.55 2 Father + Mother 223.20 250.81 219 -1511.31 0.08 0.41 2a 2 + Association varies by cohort 217.24 243.21 217 -1502.83 0.08 0.02 0.48 3 Average Father + Mother 229.25 257.92 224 -1544.44 0.08 0.39 3a 3 + Association varies by cohort 224.13 251.84 223 -1542.47 0.09 0.01 0.47 4 Father-Only 257.99 281.59 224 -1520.77 0.09 0.06 4a 4 + Association varies by cohort 258.36 280.44 223 -1513.87 0.09 0.28 0.05

Women

Model Description X 2 L2 df BIC D p vs. no change

Model p

1 Class Interaction 239.22 252.16 215 -1477.37 0.07 0.12 1a 1 + Association varies by cohort 239.16 252.03 213 -1461.40 0.07 0.94 0.11 2 Father + Mother 245.31 257.48 215 -1472.05 0.07 0.08 2a 2 + Association varies by cohort 245.32 257.48 214 -1464.00 0.07 0.97 0.07 3 Average Father + Mother 223.64 240.59 209 -1440.67 0.07 0.23 3a 3 + Association varies by cohort 223.63 240.57 207 -1432.64 0.07 0.99 0.20 4 Father-Only 299.33 309.44 224 -1492.49 0.09 0.00 4a 4 + Association varies by cohort 299.01 308.82 223 -1485.06 0.09 0.43 0.00 Note: [C][F][M][CF][CM][FM][CFM][CD][D] are fitted in all models. N= 3,122 (men); N=3,116 (women).

43

FIGURE 1 Percent of Respondents with a Mother Who Worked Outside the Home or Who Were Raised in a Non-Intact Family, by Year of Birtha

010203040

5060708090

1920-24 1925-29 1930-34 1935-39 1940-44 1945-49 1950-54 1955-59 1960-64 1965-69 1970-74 1975-79 1980-84

Perc

ent

Employed Mother Non-Intact Family at Age 16

a Source: General Social Surveys 1972-2004.

44

FIGURE 2 Association Parameter Estimates by Cohort, Respondents Born 1950-1964 Compared to Respondents Born 1965-1979 Men

0

0.05

0.1

0.15

0.2

0.25

Father-Only Mother + Father Average Mother+ Father

ClassInteraction

Ass

ocia

tion

Para

met

er

Born 1950-64

Born 1965-79

Women

0

0.05

0.1

0.15

0.2

0.25

Father Only Mother + Father Average Mother+ Father

ClassInteraction

Ass

ocia

tion

Para

met

er

Born 1950-64

Born 1965-79

45

FIGURE 3 Cohort Trends in Social Fluidity

Men

0.0

0.1

0.2

0.3

1945-1959 1950-1964 1955-1969 1960-1974 1964-1979Year of Birth

Ass

ocia

tion

Para

met

er

Mother + Father Net Father

Net Mother Father Only

Women

0.0

0.1

0.2

0.3

1945-1959 1950-1964 1955-1969 1960-1974 1964-1979Year of Birth

Ass

ocia

tion

Par

amet

er

Mother + Father Net Father

Net Mother Father Only

46

APPENDIX TABLE A1 Fit Statistics for Log-Linear Models: Comparing Various One-Parent and Joint-Parent Class Origins Measures

Men

Model Description X 2 L2 df BIC D p vs. 9 Model p 1 Full Interaction (=saturated model) 2 Class Interaction 53.73 46.33 40 -269.36 0.03 0.01 0.07 3 Father + Mother 47.09 47.68 64 -457.41 0.04 0.00 0.94 4 Higher Class + Lower Class 68.15 61.20 64 -443.89 0.04 0.00 0.34 5 Average Father + Mother 80.56 75.09 80 -556.28 0.05 0.46 6 Average Higher + Lower Class 79.71 75.00 80 -556.37 0.05 0.49 7 Higher Class Dominance 170.54 153.59 80 -477.78 0.08 0.00 8 Lower Class Dominance 118.63 114.44 80 -516.92 0.07 0.00 9 Father-Only 108.42 108.67 80 -522.69 0.07 0.02 10 Mother-Only 246.86 227.31 80 -404.05 0.11 0.00 11 Independence 384.05 367.31 96 -390.33 0.15 0.00

Women

Model Description X 2 L2 df BIC D p vs. 9 Model p 1 Full Interaction (=saturated model) 2 Class Interaction 49.70 55.85 40 -261.99 0.02 0.00 0.14 3 Father + Mother 81.88 87.21 64 -421.33 0.04 0.00 0.07 4 Higher Class + Lower Class 79.62 83.29 64 -425.25 0.04 0.00 0.09 5 Average Father + Mother 93.55 102.60 80 -533.07 0.05 0.14 6 Average Higher + Lower Class 95.78 105.01 80 -530.66 0.05 0.11 7 Higher Class Dominance 129.97 134.51 80 -501.16 0.06 0.00 8 Lower Class Dominance 108.02 114.89 80 -520.78 0.06 0.02 9 Father-Only 141.27 144.71 80 -490.96 0.07 0.00 10 Mother-Only 130.72 137.67 80 -498.00 0.07 0.00 11 Independence 236.38 237.40 96 -525.40 0.10 0.00

47

TABLE A2 Fit Statistics for Core Model of Social Fluidity: Comparing Various One-Parent and Joint-Parent Class Origins Measures

Men Model Description X 2 L2 df BIC D p vs. 1 p vs. 9 Model p1 Full Interaction 44.20 47.93 46 -315.10 0.03 0.01 0.55 2 Class Interaction 76.63 72.21 71 -488.12 0.04 0.50 0.00 0.30 3 Father + Mother 76.85 76.50 86 -602.22 0.05 0.91 0.00 0.75 4 Higher Class + Lower Class 91.45 88.30 86 -590.42 0.05 0.45 0.00 0.32 5 Average Father + Mother 99.33 93.94 91 -624.24 0.06 0.43 0.26 6 Average Higher + Lower Class 99.21 93.87 91 -624.31 0.06 0.43 0.26 7 Higher Class Dominance 189.35 176.29 91 -541.89 0.09 0.00 0.00 8 Lower Class Dominance 137.38 131.75 91 -586.43 0.07 0.00 0.00 9 Father-Only 119.33 119.86 91 -598.32 0.07 0.01 0.02 10 Mother-Only 270.77 247.29 91 -470.89 0.12 0.00 0.00 11 Independence 384.05 367.31 96 -390.33 0.15 0.00 0.00

Women Model Description X 2 L2 df BIC D p vs. 1 p vs. 9 Model p1 Full Interaction 77.04 77.97 46 -287.55 0.03 0.00 0.00 2 Class Interaction 104.86 115.03 71 -449.13 0.05 0.06 0.00 0.01 3 Father + Mother 118.25 128.36 86 -554.99 0.06 0.13 0.00 0.01 4 Higher Class + Lower Class 125.84 133.23 86 -550.11 0.06 0.05 0.00 0.01 5 Average Father + Mother 128.42 136.87 91 -586.20 0.06 0.08 0.00 6 Average Higher + Lower Class 131.14 137.48 91 -585.60 0.06 0.07 0.00 7 Higher Class Dominance 154.12 158.60 91 -564.48 0.07 0.00 0.00 8 Lower Class Dominance 143.32 150.11 91 -572.97 0.06 0.01 0.00 9 Father-Only 169.15 175.39 91 -547.69 0.08 0.00 0.00 10 Mother-Only 144.94 153.74 91 -569.34 0.08 0.00 0.00 11 Independence 236.38 237.40 96 -525.40 0.10 0.00 0.00

48

TABLE A3 Fit Statistics for RC Association Models without Diagonal Parameters: Comparing Various One-Parent and Joint-Parent Class Origins Measures

Men

Model Description X 2 L2 df BIC D p vs. 1 p vs. 9 Model p1 Full Interaction 112.62 104.47 69 -440.09 0.06 0.00 0.00 2 Class Interaction 120.02 111.65 79 -511.82 0.06 0.71 0.00 0.00 3 Father + Mother 125.64 116.65 85 -554.18 0.06 0.73 0.00 0.00 4 Higher Class + Lower Class 124.78 116.08 85 -554.74 0.06 0.77 0.00 0.00 5 Average Father + Mother 127.18 118.52 89 -583.87 0.06 0.83 0.00 6 Average Higher + Lower Class 131.79 122.38 89 -580.01 0.06 0.59 0.00 7 Higher Class Dominance 196.61 181.52 89 -520.88 0.09 0.00 0.00 8 Lower Class Dominance 163.01 151.65 89 -550.74 0.08 0.00 0.00 9 Father-Only 167.23 156.99 89 -545.41 0.08 0.00 0.00 10 Mother-Only 258.67 241.08 89 -461.32 0.12 0.00 0.00 11 Independence 384.05 367.31 96 -390.33 0.15 0.00 0.00

Women

Model Description X 2 L2 df BIC D p vs. 1 p vs. 9 Model p1 Full Interaction 85.79 90.61 69 -457.66 0.05 0.00 0.08 2 Class Interaction 89.18 94.56 79 -533.16 0.05 0.95 0.00 0.20 3 Father + Mother 110.99 114.68 85 -560.72 0.05 0.09 0.00 0.03 4 Higher Class + Lower Class 107.55 110.00 85 -565.40 0.05 0.25 0.00 0.05 5 Average Father + Mother 115.82 119.03 89 -588.16 0.05 0.10 0.03 6 Average Higher + Lower Class 117.33 119.77 89 -587.41 0.05 0.08 0.02 7 Higher Class Dominance 142.82 145.87 89 -561.32 0.07 0.00 0.00 8 Lower Class Dominance 130.45 132.37 88 -574.82 0.06 0.00 0.00 9 Father-Only 156.06 157.14 89 -550.05 0.07 0.00 0.00 10 Mother-Only 146.05 150.51 89 -556.67 0.08 0.00 0.00 11 Independence 236.38 237.40 96 -525.40 0.10 0.00 0.00