bringing intergenerational social mobility research into · 2014. 8. 4. · bringing...
TRANSCRIPT
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: [email protected]. 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
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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