Effectively Maintained Inequality: Education Transitions, Track Mobility, and Social
Background Effects
Author(s): Samuel R. Lucas
Source: The American Journal of Sociology, Vol. 106, No. 6 (May 2001), pp. 1642-1690
Published by: The University of Chicago Press
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1642 AJS Volume 106 Number 6 (May 2001): 1642–90
᭧ 2001 by The University of Chicago. All rights reserved.
0002-9602/2001/10606-0004$02.50
Effectively Maintained Inequality: Education
Transitions, Track Mobility, and Social
Background Effects1
Samuel R. Lucas
University of California, Berkeley
This article proposes a general explanation for social backgroundrelated
inequality. Educational attainment research indicates that
the later an education transition, the lower the social background
effect. While some suggest life course changes in the parent-child
relationship or between-family competition explain this pattern, others
contend the result is a statistical artifact, and that the analytic
strategy presupposes agents are irrationally myopic. This article addresses
these criticisms by framing educational transitions in terms
of students’ movement through the stratified curriculum. Students
select their stratum, one of which is dropping out. To make these
choices, they consider their most recent salient performance. Using
time-varying performance measures to predict students’ track placement/school
continuation sustains the validity of the educational
transitions approach and suggests substantively important social
background effects even for nearly universal transitions. Results are
consistent with the general perspective termed effectively maintained
inequality.
Two distinct literatures have developed to examine students’ movement
through secondary school. One strain of research uses ethnography and
statistical analysis to focus on students’ placement in the stratified curriculum
or, in other words, students’ track location. This literature treats
track location both as a determinant of important factors such as achieve-
1
I thank Adam Gamoran for comments on an earlier draft, and Aime´e Dechter and
three anonymous reviewers for additional helpful comments. All analyses were conducted
at the Survey Research Center of the University of California-Berkeley using
LIMDEP 7.0 running on a Sun Sparc (for all model estimation) and SPSSx version
4.0 running on an IBM RS6000 (for all data manipulation). An earlier version of this
article was presented at the American Sociological Association Annual Meeting in San
Francisco, August 1998, under the title “Bringing the Tracks (All the Way) Back In:
Inequality
1643
ment (e.g., Gamoran and Mare 1989), college entry (e.g., Rosenbaum 1980),
and political efficacy (e.g., Paulsen 1991), and as an outcome in its own
right (e.g., Rehberg and Rosenthal 1978; Hallinan 1992).
A second line of inquiry has viewed educational attainment as a process
of completing a sequence of transitions. In this line of research, henceforth
termed the educational transitions tradition, students in any given grade
either continue on to the next grade or level of schooling or end their
formal education. Thus, educational attainment is analyzed as the cumulation
of a sequence of yes/no decisions (e.g., Mare 1980; Shavit and
Blossfeld 1993). By treating educational attainment in this manner, analysts
have sought to discern the transition points where social background
effects are largest, and they have apparently shown a nearly universal
pattern, whereby effects of social background appear lower for later educational
transitions than for earlier ones. However, as analysts have
attempted to explain this common pattern, the entire enterprise of educational
transitions analysis has come to be questioned; indeed, some
researchers now call for the abandonment of educational transitions research
(e.g., Cameron and Heckman 1998).
This division between the tracking literature, on the one hand, and the
educational transitions literature, on the other, is unfortunate for at least
four reasons. First, tracking research provides important findings that can
justify continuing to study educational attainment as a sequence of transitions.
Recent research suggests that educational transitions analyses are
based on untenable behavioral assumptions, but findings from research
on tracking imply at least some of those assumptions are actually
appropriate.
Second, a problem in the treatment of dropouts in the tracking literature
is resolved by adopting an educational transitions perspective. The tracking
literature sees each grade as composed of a set of stratified positions,
and students’ location in the stratification system in a given year has
potentially important implications for social and psychological development.
For this reason, tracking researchers are interested in the determinants
of track location and track mobility. When studying these processes,
track researchers have usually deleted dropouts from the analysis
(e.g., Rosenbaum 1976; Hallinan 1996). When viewed through the lens of
the education transitions tradition, however, deleting dropouts from the
analysis is problematic. Instead, given the logic of educational transitions,
research on track mobility can treat dropout as an important absorbing
state or destination in the track structure.
Third, an inconsistency in the educational transitions literature’s treatment
of the stratified curriculum can be resolved by elaborating the destinations
students may reach. The educational transitions literature focuses
on the accumulation of an additional year of formal education;
American Journal of Sociology
1644
educational attainment is of interest because of its well-documented implications
for social, political, and economic behavior. While the educational
transitions literature has often considered students as existing in a
stratified curriculum prior to making a transition, and thus has not ignored
the insights of tracking research, it has not seen the destination as also
composed of stratified curricular positions. Thus, the treatment of origins
and destinations in the educational transitions literature is often not consistent
(e.g., Lucas 1996). This inconsistency is consequential, because
treating origins and destinations consistently will facilitate investigation
of two important explanations for the commonly found pattern of waning
social background effects across transitions: the life course perspective
(LCP) and maximally maintained inequality (MMI).
Fourth, when we consider educational transitions through a stratified
curriculum, it becomes feasible to estimate the effects of social background
both on making a transition and on reaching particular locations in the
stratified curriculum. Obtaining both estimates will make it possible to
investigate whether results support a comprehensive explanation for both
school continuation and in-school processes of tracking. As school continuation
and track placement are two parts of the same process—accumulating
resources to enter the world of adults—a comprehensive
explanation may be appropriate.
These two literatures separately have provided important insights into
the workings of schools and society. However, each literature has been
pursued largely in isolation from the other. This article seeks to bring the
two together. With respect to educational transitions, the article treats
both in-school origins and in-school destinations as stratified, the better
to estimate direct effects of social background and thus allow comparative
assessment of LCP and MMI. With respect to track mobility, this article
makes dropping out a part of the process of allocating students to positions
in school, the better to estimate the effects of factors of interest. And with
respect to their convergence, the article seeks to address rising doubt as
to the value of educational transitions analyses and to offer a comprehensive
explanation of both facets of educational attainment, an explanation
I term effectively maintained inequality.
To pursue these aims, I first describe the logic and results of educational
transitions research. I then relate two theories devised to explain the
common pattern of results educational transitions analysts have found. I
then shift attention to tracking research, detailing changes in tracking
that encourage the convergence of these research traditions. This convergence
facilitates development of a comprehensive explanation for social
background effects on school continuation and track placement. I propose
effectively maintained inequality as one such comprehensive explanation.
After outlining this explanation, I return to educational transitions re-
Inequality
1645
Fig. 1.—Perspective of traditional education transitions analyses
search, presenting several existing criticisms of educational transitions
research and suggesting responses to them. Afterward, the particular
methods used in this analysis are described, and the results and conclusions
of the research are presented. Thus, to begin this effort, it is important
to relate the logic and results of educational transitions research.
EDUCATIONAL TRANSITIONS RESEARCH: LOGIC AND RESULTS
The educational transitions literature flows from the long-held interest in
whether the effect of social background on educational attainment differs
over time or across societies. One way to investigate educational attainment
is to regress years of school completed on a set of explanatory
variables. However, ordinary least squares (OLS) coefficients reflect not
only the level of association but also the variance of educational attainment.
Because the variance of educational attainment has changed over
time given the expansion of educational systems, comparisons of OLS
coefficients across different cohorts or countries will not reveal whether
the structural parameters governing the process of educational attainment
differ.
To obtain estimates that can be compared across cohorts, Mare (1980),
following on the work of Fienberg and Mason (1978), proposed that analysts
treat education as a series of transitions or school continuation
decisions. Mare reasoned that total years of school completed is the result
of a series of decisions to stop or continue schooling. If each year students
have the option of continuing or ending their formal education, each
decision to stop or continue is a binary variable, scored one for students
who continue on and zero for students who elect to stop. Figure 1 details
American Journal of Sociology
1646
the process of educational attainment as seen through the lens of the
educational transitions tradition.
Using Mare’s approach, analysts have investigated whether logit coefficients
for social background change across transitions, and within a
given transition whether the coefficients change across cohorts, in at least
18 countries (e.g., Garnier and Raffalovich 1984; Kerckhoff and Trott
1993; Treiman and Yamaguchi 1993; Shavit 1993; Szele´nyi and Aschaffenburg
1993; Raftery and Hout 1993). In nearly every cohort in country
after country, researchers have found logit coefficients to decline across
transitions.
EXISTING EXPLANATIONS OF THE WANING COEFFICIENTS
PATTERN
The vast majority of educational transitions analyses have found logit
coefficients for social background to decline across transitions (e.g., Mare
1980; Shavit and Blossfeld 1993). Two major explanations of this finding
have been constructed.2
Life Course Changes
Mu¨ller and Karle (1993) speculate that a life course perspective (LCP)
could explain the waning coefficients pattern. They suggest that changes
in the relationship between children and their parents may be at the root
of the pattern. Allegedly, parental characteristics decline in value because
students, who are older at each transition, are also less dependent economically
and socially on their parents with each transition. If students
are less dependent on their parents for later transitions, then social background
should be less important for determining who receives additional
schooling.
Maximally Maintained Inequality
Raftery and Hout offer a second explanation (Raftery and Hout 1993;
Hout, Raftery, and Bell 1993). These authors argue that the pattern of
background effects across cohorts can be explained by a theory of maximally
maintained inequality (MMI), which has four tenets.
First, ceteris paribus, expansion of secondary and higher education will
reflect increased demand generated by two typically glacial forces: (1)
2
Mare (1980) originally proposed that selective attrition might explain the waning
coefficients pattern, but recent research has led analysts to doubt this explanation is
sufficient (e.g., Mare 1993; Shavit and Blossfeld 1993; Lucas 1996).
Inequality
1647
population increase and (2) social origins upgrading. Second, if enrollment
rises faster than demand (where demand is the amount of schooling expected
on the basis of population level and social class background composition),
then lower-class persons obtain more schooling. Even so, the
social class effect remains the same. Third, if completion of a given level
of education becomes universal for upper-class persons, then the effect of
social background on that transition declines over time, but only if educational
expansion cannot be maintained otherwise (hence the name of
the theory). And fourth, falling effects of social background can reverse
to become rising effects of social background. If public support for education
is reduced, social class effects will increase (Hout et al. 1993).
MMI was devised to explain cross-cohort variation in social background
effects. Yet, MMI is potentially relevant to understanding the pattern of
background effects across transitions. Most important in this context is
the fourth precept of MMI, which states that when public support for a
particular level of education changes, the impact of social background on
completion of that transition will also change. Notably, if support for
making a particular transition declines, then social background will become
more important for making that transition. Given sufficient change
in the support for a particular transition, MMI suggests that social background
may actually become more important for later transitions than it
is for earlier ones. This is the key difference between MMI and LCP;
LCP emphasizes that as children age they become more and more independent
of parents, whereas MMI implies that adolescents’ independence
itself depends on the sociopolitical context and the resulting social
support for particular levels of education.
Educational transitions research has furthered our understanding of
educational stratification. However, research on tracking has also been
concerned with stratification issues and thus is potentially relevant for
educational transitions research. Therefore, consideration of tracking research
is in order.
TRACKING RESEARCH AND IMPLICATIONS FOR EDUCATIONAL
TRANSITIONS
MMI and LCP were devised to explain the results of educational transitions
analyses. Educational transitions research highlights the cumulative
nature of the process of educational attainment. Although researchers
have at times referenced qualitative differences in schooling to make sense
of educational transitions results, the qualitative differences these interpretations
highlight are collinear with the level of schooling. This is the
result of the strategy of educational transitions analyses, which, as figure
American Journal of Sociology
1648
1 suggests, suppresses within-level differences in schooling.3
Thus, in educational
transitions research, it is impossible to assess the role of social
background on qualitative dimensions of schooling that are not collinear
with the level of schooling.
This is a limitation of educational transitions analysis, because qualitative
differences in schooling are an important feature of educational
systems in their own right, and many of those qualitative differences are
not collinear with the level of study. One such qualitative feature is curricular
tracks. Educational systems are often composed of explicit or implicit
curricular strata or tracks. Such tracks are not collinear with the
level of schooling. The strategy of educational transitions analysis, therefore,
may systematically miss or greatly deemphasize processes of in-school
stratification. If qualitative differences in students’ experience are an important
pathway through which social background affects educational
transitions, de-emphasizing processes of in-school stratification may lead
one to mischaracterize the pattern of social background effects on educational
attainment.
Change and Stability in Tracking in the United States
In order for the treatment of tracking to matter for educational transitions
research, two conditions must be met. First, track location must be an
important part of the process of educational transitions, and second, social
background must be a determinant of track location.
With respect to the first condition, it is important to distinguish more
recent cohorts from earlier ones. At the inception of the educational transition
tradition, it may have been sufficient to ignore track location in
analyzing the cumulation of years of schooling for American cohorts.
However, considering the way tracking has come to work in the United
States raises questions as to whether suppressing the complexities of tracking
is still warranted. These questions arise because the in-school stratification
system—the track system—is more complex than formerly believed.
Indeed, as I have noted elsewhere, the simple view of how schools
work implicit in many theories of the school-economy relation is based
3
Buchmann and Charles’s (1993) analysis of educational transitions in Switzerland is
an exception. Notably, they included qualitative dimensions in their analysis and failed
to replicate the waning logit coefficients pattern. Yet, the sample sizes are small (approximately
500 for each sex/cohort studied, and each sex/cohort combination is analyzed
separately), the response rate of the study is low (45%), and the data were
collected long after the modal person would complete high school, allowing dropouts
to possibly obtain enough later schooling to endanger accurate estimation of the effect
of parental status characteristics. For these reasons, the implications of the results
remain unclear.
Inequality
1649
on an outdated understanding of how schools track students in the United
States (Lucas 1999). The difference between the old understanding and
the new reality is best reflected in research on track mobility.
Historically tracking researchers found low levels of track mobility and
a greater incidence of downward mobility than upward mobility. This
finding was explained by a theory of tournament track mobility. Tournament
track mobility (Rosenbaum 1976) explained students’ extremely
low mobility chances by highlighting the ideational and institutional supports
for tracking. Ideationally, mobility might call into question the legitimacy
of earlier placements and thus was subtly discouraged. Institutionally,
school personnel appeared to hold overwhelming power to
assign students to tracks, and evidence suggests they wielded this power
on a regular basis (e.g., Cicourel and Kitsuse 1963). In such a world, it
would be sufficient to treat track location as an independent variable in
educational transitions analyses and ignore the track destinations of students,
because mobility was so rare that one could regard students in
disparate tracks as following unalterably separate paths.
Recent analyses, however, have been unable to replicate earlier findings
concerning track mobility. Indeed, more recent research finds a high incidence
of mobility, and none find upward mobility to be rare (e.g., Wilson
and Rossman 1993; Hallinan 1996; Lucas 1999; Lucas and Good 2001).
As analysts have looked closer, they have come to explain this new set
of findings by pointing to an unremarked revolution in how schools track
students (Lucas 1999). Evidence suggests that schools no longer formally
assign students to overarching tracks that determine their course-taking
(e.g., Carey, Farris, and Carpenter 1994; Hayes 1990). Now tracking is
activated in many separate, yearly, subject-specific decisions rather than
in one global assignment to a track at one pivotal point in a career (e.g.,
Moore and Davenport 1988).
The above suggests that tracking has become a possibly important part
of the process of educational transitions. Students are not allocated to one
track that governs their schooling for multiple years. Instead, students
encounter many separate decision points that implicitly allocate them to
different curricula. In order for changes in tracking to matter for educational
transitions research, however, social background must matter for
students’ track placement. Are these decisions made under conditions that
might allow social background to matter for placement? Evidence suggests
that students make enrollment decisions with comparatively less
counselor input than previously, as counselors have retreated from the
proactive role they formerly played (e.g., Rosenbaum, Miller, and Krei
1996). The retreat of the counselors ushers in an environment of ostensible
student choice; in this environment, researchers continue to find social
American Journal of Sociology
1650
background to matter in track placement (e.g., Garet and DeLany 1988;
Hallinan 1992).
Sociologists have identified two ways that social background appears
to matter. Middle-class parents appear to be proactive both as individuals
and as a class, maintaining tracking in general and securing for their
children the best positions within the track structure of the school (e.g.,
Useem 1992; Wells and Serna 1996). Class conflict around schools’ decisions
to track or not track is well-documented, as socioeconomically
advantaged parents often work to maintain tracking in the schools (e.g.,
Wells and Oakes 1996; Wells and Serna 1996).
Social background also affects individual placements. Socioeconomically
advantaged parents can secure advantaged places for their child,
not only because they may use a wide array of resources in a given
instance, but perhaps more important, they have personal experiences
that make it more likely they will be able to recognize the pivotal “given
instance” to which they may want to bring those resources to bear. They
know which decision points involve high stakes and which can be ignored
safely. Having been to college themselves, they can help their children
navigate the high school curricular structure in ways that make subsequent
college entry a real possibility.
Socioeconomically disadvantaged parents may certainly cheer their
children on in their efforts to reach college. But socioeconomically advantaged
parents may not only cheer, but also coach, their children in
their efforts to reach college. The difference between cheering and coaching
is information as to what matters for college. Given the retreat of the
former school gatekeepers, as evidenced by existing research, and the
episodic nature of track decisions, students whose parents lack such
knowledge are on their own. This environment, with many more decision
points, unclear signs for the uninitiated, and continued effects of social
background, has two important implications for how we may study educational
attainment.
Implications of Tracking Research for Educational Transitions
Research
The first implication of tracking research is that we need to change our
focus from the yes/no decision of educational transitions research to decisions
about a more varied set of options. Students make decisions yearly
as to which structural path they will follow—drop out; stay in school in
college preparatory courses in academic subjects such as math, English,
foreign language, science, and social studies; stay in school in noncollege
preparatory courses in academic subjects; or stay in school but avoid
academic subjects. Thus, this new state of affairs means both that the
Inequality
1651
Fig. 2.—Education transitions with stratified destinations
vision of educational transitions evident in figure 1 is no longer sufficient
and that educational attainment is produced through a sequence of transitions.
This suggests it is potentially useful for the tracking and educational
transitions literatures to converge. When these literatures converge,
the vision of the process of educational transitions is as illustrated in figure
2. In figure 2, dropping out becomes one of a small subset of potential
locations to which students may move, and students who decide to continue
also decide within which curriculum they will continue. Seen in this
way, the distinction between the educational transitions literature, on the
one hand, which treats school as a sequence of transitions, and the track
mobility literature, on the other hand, which sees students as moving
through a stratified curriculum, dissolves.
Second, the unremarked revolution heightened the potential importance
of student performance for students’ placement in the stratified curriculum.
The consistent finding from the recent research is that there is far
more mobility in the recent period than previously observed. Students
routinely obtain updated information as to their performance in school
in the form of grades; these grades are obtained in particular curricular
positions. Students and others can use this updated information—this
time-varying covariate—to aid in placements for the following academic
year. This is possible because placements for the following year are not
completely determined by prior placement, as seemed to be the case prior
to the change in school practice. Thus, time-varying covariates are a
routinized and potentially consequential feature of the educational career.
Analysts, therefore, may use such information to aid their study of the
determinants of educational transitions.
American Journal of Sociology
1652
EFFECTIVELY MAINTAINED INEQUALITY
The joint study of educational transitions and track mobility raises the
possibility of providing a comprehensive explanation of the role of social
background in educational attainment. I propose that a theory of effectively
maintained inequality (EMI) may illuminate both processes of
school continuation and track mobility.
Effectively maintained inequality posits that socioeconomically advantaged
actors secure for themselves and their children some degree of advantage
wherever advantages are commonly possible. On the one hand,
if quantitative differences are common, the socioeconomically advantaged
will obtain quantitative advantage; on the other hand, if qualitative differences
are common the socioeconomically advantaged will obtain qualitative
advantage.
EMI
For educational attainment, the above claims could be true in one of at
least two ways. It may be that as long as a particular level of schooling
is not universal (e.g., high school completion throughout the first half of
the 20th century in the United States), the socioeconomically advantaged
use their advantages to secure that level of schooling. Once that level of
schooling becomes nearly universal, however, the socioeconomically advantaged
seek out whatever qualitative differences there are at that level
and use their advantages to secure quantitatively similar but qualitatively
better education.
The above suggests that the focus of activity may change over time as
qualitative differences supplant quantitative differences in importance.
Alternatively, it is possible that even when quantitative differences are
common, qualitative differences are also important; if so, I posit that the
socioeconomically advantaged will use their socioeconomic advantages to
secure both quantitatively and qualitatively better outcomes.
Unfortunately, it is not possible to adjudicate between these two possibilities
in the current analysis, because we lack detailed data on the
track placements of earlier cohorts. However, it is possible to determine
whether in one cohort studied we find consequential effects of social background
on qualitative placements, even where quantitative differences
are virtually nil. Finding such a pattern of effects will provide evidence
consistent with effectively maintained inequality; the central implication
of EMI for educational attainment is that for nearly universal levels of
schooling, background will affect differences in kind.
Inequality
1653
EMI, MMI, and LCP
EMI and LCP are not mutually exclusive, but they do highlight different
processes. LCP emphasizes the relationship between children and their
parents, and how that relationship changes over time as children mature.
Owing to changes in the parent-child relationship, parental status characteristics
are expected to wane in importance over time. EMI is agnostic
with respect to whether this causal story explains the waning logit coefficient
pattern. The pace at which persons’ own status characteristics
replace their parents’ status characteristics is both an empirical question
whose answer may depend on the outcome under study and an issue in
need of theoretical reflection beyond the scope of this analysis. However,
EMI implies that for as long as parents’ status characteristics are students’
status characteristics, the children of the socioeconomically advantaged
will be allocated to quantitatively and qualitatively advantaged positions
on that basis. Further, EMI implies that once parents’ status characteristics
are truly replaced by children’s own status characteristics, the adult
children’s own status characteristics will serve the same purpose parents’
status characteristics served in the past.
EMI and MMI are somewhat more divergent. Both highlight class
competition between families, but MMI suggests competition will be nil
for any level of education that is universal. In contrast, EMI implies that
for levels of education that are universal, competition will occur around
the type of education attained. Thus, for some levels, MMI implies the
maximum amount of background-related inequality is virtually zero,
whereas EMI implies that for those very same levels inequality will not
only be nonzero but also nontrivial, that is, the background-related inequality
will be consequential. However, MMI and EMI do not disagree
about every aspect of schooling, for both perspectives would predict social
background effects to be nontrivial at levels of education that are not
universal.
EVALUATING EDUCATIONAL TRANSITIONS RESEARCH:
CRITIQUES AND RESPONSE
MMI and LCP were crafted to make sense of the waning coefficients
pattern educational transitions researchers have found. I have suggested
that bringing tracking and educational transitions research together is
appropriate, given changes in tracking, and useful, given the possibility
of developing a comprehensive explanation of school continuation and
track mobility.
However, several analysts have suggested that the waning coefficients
pattern of educational transitions research may be a statistical artifact.
American Journal of Sociology
1654
The arguments concerning this issue have raised doubt as to whether
researchers should continue to study educational attainment in this manner.
Thus, in order to continue to conduct educational transitions research,
even educational transitions research informed by research on tracking,
a response to the critiques is required.
Improper Functional Form and Untenable Behavioral Assumptions
Cameron and Heckman’s (1998) criticisms of educational transitions research
culminate in their declaring that the near universal finding of
declining logit coefficients should be ignored. They argue that the finding
is an artifact of ad hoc decisions regarding the functional form of the
model. They reach this conclusion by contending that the functional form
for the model makes it possible to obtain estimates, but absent timevarying
covariates, it is impossible to assess whether effects of social
background vary across transitions. They show that the logistic regression
model with transition-specific coefficients can be identified when the values
of at least one covariate vary across transitions, but they maintain
that time-varying covariates are not usually available.
The lack of time-varying covariates is important because if covariates
do not vary across transitions, then one must assume a distribution for
the error term in order to identify the model with transition-specific parameters.
Further, if there are no time-varying covariates, the only factor
inducing differences on the dependent variable across transitions is the
error term. Cameron and Heckman argue that under these conditions the
sequential decision-making process underlying the educational transitions
logit model implies students assume that their current school experience
perfectly predicts their future school experience, and thus students act
only on contemporaneous conditions. Cameron and Heckman regard this
as an untenable assumption of student myopia.4
In response, they offer
what they regard as a rational choice perspective in which persons know
their endowments, know the costs of investments (including foregone earnings),
and know the payoffs that attend certain levels of education. Using
4
Cameron and Heckman argue that under the sequential model with time-invariant
covariates, the error term ( ) is the only person-specific factor varying over transitions.␧
The person-specific, across transition distribution of is a martingale; the most im-␧
portant implication of this is that , i.e., if is a martingale, then personsE(␧ ) p ␧ ␧t tϪ1
use their most immediate experience to decide on their next move, ignoring experiences
earlier than . Because the sequential decision-making model with time-invariantt Ϫ 1
regressors implies that persons make decisions sequentially, and the only factor inducing
variation is a martingale in this situation, Cameron and Heckman contend that
the model implies myopic agents.
Inequality
1655
this information, persons obtain just enough schooling to maximize net
benefits.5
Cameron and Heckman propose a statistical model that reflects their
preferred behavioral assumptions, an ordered discrete choice model with
multiplicative heteroskedasticity. The dependent variable for their analysis
appears to be years of school completed, but the discrete choice model
relaxes the assumption of equal intervals between years. Were one to
assume that the error was normally distributed and homoskedastic, their
model would become the ordered probit model, with years of schooling
as the dependent variable. Thus, essentially Cameron and Heckman are
calling for a return to years of school completed as the focus of analysis
and suggesting that a different functional form will resolve the problems
that attend using OLS regression. They allow for heteroskedastic errors
to allow for differences they do not observe; they assert that a major
portion of the unobserved heterogeneity reflects differences in ability.
On the basis of estimates derived from their preferred model, Cameron
and Heckman argue against expanding financial support for college. They
contend that such support entices students from the bottom of the distribution
of their unobserved variable to continue schooling. Given their
assertion that the unobserved variable is ability, they suggest that though
those induced to continue schooling with increases in financial aid are
more productive than they would otherwise be, the productivity gains to
their continued education fall short of the productivity gains typically
observed for college entrants. Thus, they contend, financial aid for college
should not be expanded.
In sum, Cameron and Heckman reject the educational transitions literature.
They essentially argue that without time-varying covariates one
cannot identify the education transitions model with transition-specific
parameters independent of the assumption for the distribution of the error
term. But solving the identification dilemma by assuming a distribution
for the error term leaves the error term to induce all over-time variation
in the dependent variable. This implies that as soon as the error term
pushes a person below the school continuation threshold, the person falls
5
I have attempted to use the term Cameron and Heckman use—rational
choice—without joining the debate about the meaning of the term. Suffice it to say,
their reasons for assuming that students use a particular kind of information in a
particular way are clear, but I see no analytic justification for labeling use of that
information in that particular way as rational. The assumption is what it is, regardless
of whether one judges behavior that matches the assumption as rational or not. And,
as an unsubstantiated assumption, it is as subject to Manski’s (1993) cogent criticism
of social scientific presumptions about how students form expectations, as are any of
the analyses Cameron and Heckman critique. Thus, in this article, I will attempt to
defend the behavioral assumption that underlies the model used but will offer no
judgment as to the rationality of the behavior.
American Journal of Sociology
1656
out of school, even if a later error term would have been such that they
would have accrued substantial gains upon continuing. Cameron and
Heckman argue that this is a restatement of myopia, and thus the behavioral
theory behind the sequential decision-making model requires
myopic agents. Thus, they reject the sequential decision-making model
and the educational transitions literature. (See appendix B for a more
technical explication of their position as well as my response).
However, although Cameron and Heckman argue that the sequential
decision-making model creates the assumption of myopia, in actuality, the
sequential decision-making model in concert with the lack of time-varying
covariates creates the assumption of myopia; the presence of both features
is necessary in order to force the error term to take the decisive role in
creating over-time variation in a student’s decision of whether to stop or
continue schooling. Cameron and Heckman decide to retain the idea that
observed characteristics are stable over time and change the functional
form of the model to jettison the implication of myopia. But their response
seems arbitrary in the face of research on tracking showing that students’
structural locations change, implying that their performance—a key piece
of information—can also in principle change over time.
Cameron and Heckman call for researchers to use statistical models
that reflect defensible behavioral models and processes. A response consistent
with their counsel would be to retain the sequential decision-making
behavioral model and add theoretically defensible time-varying covariates
to the statistical model. That is the approach taken here, because
evidence shows that the process of educational attainment in the United
States occurs in a stratified curriculum that requires sequential decision
making. Once time-varying covariates are allowed, the educational transitions
model with transition-specific parameters is identified without recourse
to an assumption for the distribution of the errors. Once it is
identified, person-specific variance in the dependent variable over time
is not driven only by the error term. Once the error term does not drive
the variance in Y, the claim of myopia is not sustained.
The observations above are sufficient to support the work that follows.
However, several other important observations concerning the existing
critiques of the educational transitions approach need to be made for at
least two reasons. First, these observations will suggest further dangers
analysts must avoid should they seek to conduct educational transitions
research specifically. Second, some of the critiques actually violate generally
good research practice and thus may have created much confusion.
Inequality
1657
Myopia
Despite the discomfort of some with the prospect of myopic decision
making, all students pursue options as the sequence of opportunities unfolds.
All students select from among immediately visible options whose
long-term implications they cannot accurately estimate and perhaps would
not know how to begin to evaluate (Manski 1993). The extent to which
decisions are myopic is likely dependent on the resources a student has
to gather pertinent information. All students have records of their performance
in courses by which to judge the appropriateness of continued
study at different levels. However, socioeconomically advantaged students
have college-experienced parents, and students in college track courses
have teachers pointing them to college with time-tested strategies of success.
Other students lack these resources. Access to knowledgeable parents
and teachers makes savvy and strategic forward-looking behavior more
likely, while lack of access to these resources diminishes its likelihood.
Thus tracking research, and a line of reasoning consistent with it, suggests
that students—even socioeconomically advantaged students—make
decisions both sequentially, as Mare contends, and potentially myopically,
as Cameron and Heckman deny (Powell, Farrar, and Cohen 1985). However,
myopia is likely to be a differentially allocated feature of students’
educational decision making. If one considers the process of schooling,
one may adopt modeling strategies that make it unnecessary to assume
myopia in the modeling process. However, myopia may be present even
if it is not assumed; indeed, known and commonly measured social factors
such as parents’ education and students’ track location are associated
with the extent to which students are exposed to persons who can dispel
the myopic elements of their decision making. Thus the social background
coefficients from a sequential decision model may reflect in part the element
of myopia. Similarly, the social background coefficients from an
ordered probit model of years of school completed with heteroskedastic
errors may reflect in part the element of myopia.
Appropriate Parameters to Estimate
One criticism of educational transitions analysis is that the waning logit
coefficients pattern is the result of a particular parameterization of the
relationship between social background and educational attainment. The
case for the logit coefficient as an appropriate index of the relationship
between social background and attainment is based on the claim that
logit coefficients are not contaminated in the same way as OLS coefficients
are. However, De Graaf and Ganzeboom (1993) note that although OLS
coefficients are an amalgam of different processes, including socioeco-
American Journal of Sociology
1658
nomic upgrading of parents’ characteristics and expansions in educational
systems, they remain descriptively accurate for the entire cohort, whereas
logit coefficients for later transitions do not. Mare (1993) agrees but maintains
that logit coefficients are more structural than OLS coefficients,
because logit coefficients reflect the way that educational attainment actually
occurs, namely, through an unfolding sequence of decisions.
Clearly, different summaries of nonlinear relationships can lead to different
substantive conclusions (e.g., Long 1997). However, as Long suggests,
the fundamental focus of many analyses is the probability of a
discrete outcome. Advances in computing have facilitated determining
how changes in independent variables are associated with changes in the
probabilities of an outcome. As probabilities are the fundamental focus
of many analyses, analysts may want to make probabilities the fundamental
focus of presentation. Indeed, in order to assess EMI, it will be
necessary to focus on how probalities differ for students with different
social background characteristics, rather than on coefficients from the
model.
Appropriate Dependent Variables to Study
When Cameron and Heckman resurrect years of schooling as the dependent
variable of interest for investigation of educational attainment, they
alter the functional form of the model to avoid estimating OLS coefficients;
they also inadvertently suppress potentially important qualitative differences
in schooling even more than education transitions analyses do. Although
they allow the scaling distances between years of schooling to
differ, this forces all qualitative differences to be translated into the unidimensional
scale of years of school completed. This translation may
obscure more than it reveals, because persons who obtain the same number
of years of schooling, but do so in different types of programs, will
be assigned the same value on the dependent variable. This may lead
some persons to be misclassified, in that a proper translation of their
educational attainment into years of schooling would put them higher or
lower on the scale than their nominal years in school actually does. Because
of these difficulties, even with the altered functional form, Cameron
and Heckman lose the ability to investigate whether social background
matters, not only for how much education a person receives, but also
what kind of education a person receives. As the research discussed above
suggests, however, this is an important question that is directly related
to the concerns, if not the common analysis, of educational transitions
researchers.
The existence of the stratified curriculum certainly suggests that a return
to years of school completed may mask important pathways through
Inequality
1659
which social background has its effects. Yet, adding qualitative dimensions
to educational transitions analyses may complicate cross-national
comparison. A central motivation for the development of the educational
transitions tradition was the desire to conduct cross-national comparative
analysis, and thus this limitation is an important one. Many qualitative
characteristics may be country-specific, and even for those that are common
across nations (e.g., the existence of stratified curricula), the actual
categories and the meaning of the categories may differ markedly from
country to country. Balancing the desire to make cross-national comparisons,
on the one hand, with the aim of accurately capturing important
country-specific features, on the other, is of course a challenge. Most likely,
approaches that de-emphasize qualitative dimensions can aid in estimating
the total effect of social background on the amount of educational
attainment; these analyses may be most directly comparable across
nations. This seems to be the strategy followed to great effect by Shavit,
Blossfeld, and colleagues. However, to discern the mechanisms producing
the pattern of social background effects, it is likely we will need to attend
to the nuances of particular educational systems.6
Unobserved Heterogeneity
An additional criticism of educational transitions research contends that
unobserved heterogeneity may make the waning coefficients pattern an
incorrect representation of students’ experience (e.g., Mare 1993). In some
analyses, omitted variables must be correlated with independent variables
included in the model in order to bias results, but in other analyses,
including education transitions research, biases arise even if the omitted
variable is not correlated with the included independent variables (Vaupel
and Yashin 1985).
Analysts have long been concerned with unobserved heterogeneity. A
big improvement is to use data that would allow one to directly measure
the factors that are typically unobserved, if measurement is possible. Using
good data is a helpful response because unobserved heterogeneity is an
omitted variable problem. However, any finite set of regressors leaves a
vast untapped reservoir of additional variables with the potential to create
bias by their omission. Hence, although this strategy may be useful, it
cannot dismiss the possibility that findings are driven by unobserved
heterogeneity.
Thus, even when good data are available, some unobserved heterogeneity
may remain, in which case one may adopt one of the many prom-
6
I am thankful to an anonymous reviewer for drawing my attention to these
implications.
American Journal of Sociology
1660
ising statistical tools analysts have devised to account for unobserved
heterogeneity when indicators for the potentially biasing variables are
lacking. Such methods include the use of sibling models (e.g., Mare 1993;
Mare and Chang 1998), parametric mixture distributions (e.g., Manton,
Stallard, and Vaupel 1981), nonparametric mixture distributions (e.g.,
Heckman and Singer 1982), and a general nonparametric latent variable
approach (Vermunt 1997). Each of these approaches is promising, but
each has limitations as well. Limitations for the different approaches
include variously the possibility that one may overcorrect for unobserved
heterogeneity and thus produce results biased in the opposite direction,
the necessity of assuming that unobserved heterogeneity is independent
of included covariates, and sensitivity to the functional form assumed for
the time-dependence or mixture distribution (e.g., Griliches 1977, 1979;
Yamaguchi 1991).
However, taken together, these methods have an important use, for
with these methods, it would be possible and advisable to calculate bounds
on the parameters of interest, as Manski (1995) proposes. The calculation
of bounds and detailed investigation of the sensitivity of results to different
assumptions about unobserved heterogeneity is an effort worth conducting,
but the purpose of this article is different. Here I seek to complete
an essential precursor to such a project, for before assessing the sensitivity
of results to a variety of different assumptions concerning unobserved
heterogeneity, it is important to determine whether the framework under
investigation has promise sufficient to justify deeper investigation.
The strategy I adopt in this article, therefore, is to include a lengthy,
theoretically defensible set of covariates (e.g., Gamoran and Mare 1989).
As I later describe, I will attempt to use a healthy set of time-varying
and time-invariant covariates, given the possibilities and limitations of
the data, the data collection strategy, and sociological theory. I admit this
approach cannot remove the possibility of unobserved heterogeneity, but
because it is grounded in the current state of sociological knowledge, as
we learn more over time, the specification can be adjusted explicitly.
Further, should the findings prove sociologically interesting, the baseline
established by this investigation can and should be probed with detailed
analysis, using a variety of specifications for unobserved heterogeneity, to
determine the sensitivity of results to different assumptions.
Still, it should be noted that statistical developments may soon ease the
treatment of unobserved heterogeneity. As these advances cumulate, it is
extremely important that analysts refrain from making inferences beyond
what such techniques allow. It is important to remember that the unobserved
heterogeneity claim is an arguably admirable admission of ignorance.
It means we do not know what induces the observed variance.
Despite this obvious point, analysts often strain to attribute some positive
Inequality
1661
content to the unobserved component. A case in point is the Cameron
and Heckman (1998) analysis. The analysis asserts that unobserved (by
the analyst) heterogeneity is largely ability, and policy prescriptions are
then based on this assertion. By definition, however, unobserved heterogeneity
could be any of a number of factors, and the relative weight of
those factors cannot be established and remain unobserved heterogeneity.
Under these conditions, analysts should refrain from making policy prescriptions
that depend on identifying the content behind unobserved
heterogeneity.
Data Selection and Handling
Although the discussion of unobserved heterogeneity touched on the selection
of data, additional issues make data selection an important concern
for educational transitions research. The elegance and, consequentially,
apparent simplicity of educational transitions analysis belies the high data
requirements for effective research. Both Cameron and Heckman (1998),
implicitly, and Mare (1993), explicitly, call for analysts to attend closely
to the data requirements of such modeling, which depend in part on the
theories one seeks to assess. If the data requirements for a theory are not
met, the theory cannot be evaluated. For example, in order to assess the
key claim of LCP, one must use data that does not allow persons decades
to complete their schooling. Otherwise, the LCP explanation is true but
trivial; educational and other life pursuits of older persons are virtually
always made in the context of weakened power of parental status characteristics
relative to the power of those characteristics when the child
was not yet an adult. But the life-course explanation of Mu¨ller and Karle
is not trivial; it has sociological punch owing to its potential to explain
why disadvantaged youngsters continue their schooling in such numbers
that the logit coefficients for social background decline across transitions.
In order to assess this claim, analysts either need to restrict their analysis
to relatively young potential students, or use information on the timing
of educational transitions in their analysis. Unfortunately, many educational
transitions analyses have used samples of the general adult population
that lack information on the timing of educational transitions.
Thus, they do not meet the data requirements for assessing LCP and can
provide no evidence with respect to the validity of the LCP claim.
Again, Cameron and Heckman illustrate how problems ensue when
data are not matched to the research question. Cameron and Heckman
conclude that widening financial aid availability is unwise because it
induces low-ability students to continue schooling. Setting aside the earlier
observation that assertions concerning the content of unobserved heter-
American Journal of Sociology
1662
ogeneity are by definition problematic, Cameron and Heckman cannot
speak to policy generally because of several other errors in data analysis.
First, they restrict their analysis to white males, thus preventing their
analysis from reflecting parameters of the process generally considered.
This should reduce one’s faith in the general applicability of the policy
prescription they offer, although on the basis of their analysis, one might
infer that one should restrict the financial aid available to white males.
However, Cameron and Heckman also delete all cases missing on any
variable, a tactic that necessitated removal of approximately one-third of
the white males. This approach to missing data substantially lowers the
likelihood that their analysis can generalize even to the population of
white males.7
An additional data problem is that the bulk of their analysis is based
on Occupational Changes in a Generation (OCG) data. Thus, Cameron
and Heckman study educational transitions for persons who may have
completed their education at any time within a window spanning several
decades. Given that OCG respondents’ reports may summarize educational
experiences that occurred decades after leaving their parents’ household,
the Cameron and Heckman analysis is insufficiently precise to address
the policy issue of the role of financial liquidity in constraining
college entrance. That is not to say that the finding would not be replicated
with better data, but it is to say that the Cameron and Heckman analysis
fails to address the question.8
The Cameron and Heckman analysis is unable to address their research
question; this is unfortunate because they raise an intriguing possibility.
In general, then, analysts need attend to the theoretical and substantive
claims they seek to address and assure that the methods and data are
sufficient to address them.
7
For analogous analyses led astray in part by problematic treatment of missing data,
see Herrnstein and Murray 1994; for a correction, see Fischer et al. 1996, and for a
discussion of strategies for handling missing data and the implications of failures to
effectively treat missing data, see Little and Rubin 1987.
8
However, if we ignore both the deletion of nonwhites and women and the mistreatment
of missing data, the data may be appropriate to assess their explanation. This
is so because it is likely that, all else equal, a person who has several decades of
adulthood in which to make further investments in education will make those decisions
based on more reflection and knowledge than will a youth who has little experience
with the world of work. A 45-year-old person considering their own educational investments
will probably more closely approximate the nonmyopic agent than will the
17-year-old student of the American high school. The implication of this observation,
however, is that the Cameron and Heckman analysis cannot comparatively assess their
theory and others, because they inadvertently used data that is biased in favor of their
explanation.
Inequality
1663
Evaluating Educational Transitions Research: Brief Summary of Key
Responses
The foregoing discussion has offered several observations on the conduct
of education transitions research. Analysts have raised many questions
about education transitions analyses, but three are most prominent: (1)
how can one account for unobserved heterogeneity, (2) how can one identify
transition-specific effects without making an ad hoc assumption, and
(3) how can one select appropriate parameters to index social relations?
Unobserved heterogeneity is an escapable possibility in every analysis.
In the education transitions approach, it is certainly more difficult to
protect against because an omitted variable may bias results even when
that variable is not associated with included independent variables. In
this situation, there are four possible responses. One response is to stop
conducting education transitions research. However, our knowledge of
tracking suggests that sequential decision making produces educational
attainment. Were we to halt education transitions research, our statistical
model, rather than our knowledge of social processes, would be driving
our investigatory strategy. Our knowledge of social processes suggests that
the educational transitions framework, or something very much like it,
is needed, and thus efforts to address the unobserved heterogeneity problem
seem worthwhile.
In that vein, a second response is to attempt to account for unobserved
heterogeneity using one of the methods developed for missing data analysis.
A third approach is to attempt to account for unobserved heterogeneity
by including a lengthy, theoretically defensible set of covariates.
Neither approach offers certainty that one has successfully removed unobserved
heterogeneity, for both may miss important heterogeneity.
A fourth approach is to use a variety of methods, either separately or
together, to establish bounds on parameters and to investigate the sensitivity
of findings to assumptions concerning unobserved heterogeneity.
In the present case, drawing on existing theories and within the limits of
the available data, I use the third approach. Should the findings prove
of sociological interest, detailed investigation of unobserved heterogeneity
using a variety of specifications would be in order.
To avoid ad hoc identifying assumptions, findings from tracking research
should be considered. These findings not only affirm that students
follow a sequential decision-making process as they navigate schools, but
also reveal a higher incidence of track mobility than previously existed.
This suggests the potential importance of the time-varying covariate of
performance. Because time-varying covariates identify the education transitions
model with transition-specific parameters, one need only invoke
American Journal of Sociology
1664
the substantively defensible assumption that grades matter, and use measures
consistent with this assumption, to identify the model.
Different summaries of nonlinear relations may lead to different conclusions.
Given this observation, one response is to highlight the fundamental
unit of measure underlying the analysis, which for education transitions
analysis is the probability of obtaining particular categorical
outcomes.
These three questions have been raised, and responses to them have
been offered. Although the first and third questions and responses are
important, the foundational basis of the analysis concerns the second, the
fusing of educational transitions and tracking research. It is that fusion
that highlights the time-varying covariate of performance, facilitates the
comparative assessment of existing explanations of school continuation
(see below), and allows investigation of a comprehensive explanation for
both school continuation and track location. The following pages describe
the methods used to address the questions this fusion brings to the fore,
relate the results of the analysis, and close with concluding remarks.
ANALYSIS PLAN
The prime aim of the analysis is to assess effectively maintained inequality.
Before doing so, however, it is possible and useful to evaluate LCP and
MMI comparatively, for several reasons. First, MMI and LCP are existing
explanations for this subject area. Thus, I would be remiss to ignore them
at this juncture. Second, MMI and LCP have not been studied in an
analysis that fuses tracking and educational transitions. Yet, as I will note
below, it is just this kind of analysis that is needed to comparatively assess
MMI and LCP. Third, the same model that produces the information
needed to evaluate EMI also produces the information needed to comparatively
assess MMI and LCP. Thus, it will not be necessary to estimate
multiple models to consider the different explanations. Yet, because assessing
the different explanations entails perusing different types of parameters
(from the same model), it will be most effective to proceed by
first comparing MMI and LCP and then turning to consideration of EMI.
For these reasons, therefore, I will spend some time investigating MMI
and LCP, even as the bulk of the analysis is focused on considering the
evidence for and against effectively maintained inequality.
Conditions for Comparing MMI and LCP
LCP and MMI do not have mutually exclusive implications for the total
effect of social background under all circumstances. However, they do
Inequality
1665
imply potentially different patterns of direct effects under certain conditions.
LCP implies that the direct effect of social background declines
across transitions, for it is the direct effect that captures parents’ contemporaneous
role in students’ successful completion of a particular transition.
Whatever that role, LCP implies it is lower for later transitions than
for earlier ones. In contrast, MMI implies that direct effects will be responsive
to shocks to the system, rising or falling depending upon the
changing structure of social support for different stages of education. If
so, it is possible for direct effects on later transitions to exceed the direct
effects for earlier ones, if the shock to the relevant transition(s) is strong
enough.
Still, under general conditions, it is not necessarily possible to differentiate
between LCP and MMI explanations. However, Reagan-era policy
change increased the financial costs of attending college for early 1980s
cohorts (e.g., Evangelauf 1987). Of course, the Reagan-era policy change
may not have been sufficient to raise the effect of social background on
college entry above the effect of background on high school graduation.
But many elements made up the Reagan-era reforms. The 1981–82 academic
year marked the start of a period of sharply rising tuitions. In
addition, that year saw the introduction of decreases in the availability
of grants, increases in the interest rate for Guaranteed Student Loans
(GSLs; from 7% to 9%), and the inception of a 10% surcharge on GSLs
(points). The magnitude of these changes certainly suggest that the era
provides a chance to discern a greater effect of social background on
college entry than on earlier transitions. Thus, although the analysis cannot
provide the proverbial “crucial experiment” that will adjudicate forever
between MMI and LCP, the conditions of the Reagan era do seem
to provide an opportunity to assess them comparatively.
However, in order to estimate the direct effect of social background, it
is important to account for the role of social background in allocating
students to different locations in the stratified curriculum in earlier years.
Otherwise, indirect effects of social background that work through prior
placement will be inadvertently included in estimates of the direct effect
of social background. In order to compare LCP and MMI, therefore, it
is necessary to study school continuation and students’ track mobility
simultaneously, for doing so facilitates proper estimation of the direct
effects of social background.
The Sample
The investigation uses the 1980 sophomores from High School and Beyond
(HS&B). Analyzing these data is particularly advantageous for pursuing
our concerns, for these data include the variables necessary to es-
American Journal of Sociology
1666
timate direct effects of social background and, owing to the period of data
collection, these data allow one to consider the transition to college for a
cohort that encountered both higher tuitions and a public policy environment
that had just become decidedly less generous with financial aid
(e.g., Evangelauf 1987). Note that the legislative changes mentioned above
were all passed after January 1981 and took effect for the 1981–82 academic
year. Thus, one advantage of using this sample is that not only did
support decline, but also the decline was decidedly abrupt. Moreover, by
using only the 1980, 1982, and 1986 waves, this analysis is constructed
so that it is plausible to regard social background effects as indexing the
relevance of parental characteristics for youths’ educational attainment.
Further, these data include information on the curricular tracks students
followed, as well as the grades they obtained. Taken together, these features
are essential for comparing LCP and MMI.
HS&B used a complex sample design. Thus, standard errors are adjusted
using a design effect of 2.4, which reflects a slight upward adjustment
from the design effect of 2.19 estimated by Sebring et al. (1987).
Moreover, weights were constructed to account for nonresponse; I use
weights in the analysis.
Methods
Appendix A describes the measurement of social background, measured
achievement, and performance, and table 1 provides descriptive statistics
for these variables. It is necessary to use at least one time-varying covariate
in this analysis. The measures of performance—grades—are time-varying
covariates obtained from students’ transcripts. HS&B also contains several
other time-varying measures, including standardized measures of
achievement in the form of tenth and twelfth grade tests, measures of
student behavior such as cutting class, and measures of student experience
with the disciplinary authorities of the school such as suspension. Each
of these indicators, however, has some problems. First, students did not
have access to their HS&B test scores, and thus neither their scores nor
changes in the scores could have informed their decision making. Moreover,
some argue that achievement tests actually measure stable ability.
To give this position the benefit of the doubt, I use only the tenth grade
test scores and thus treat standardized measured achievement as constant
over time.
The indicators of class cutting, suspensions, and other involvement with
disciplinary authorities are only partially time varying, because they were
recorded during the two survey years (grades 10 and 12) but not in grade
11. Thus, to include these variables as time-varying covariates is to specify
different lag structures for different academic years, which might differ-
TABLE 1
Descriptive Statistics
Variable and Value
Proportions/Means in Each Sample
Grade 11 Grade 12 College
Fathers education:
! High school graduate .......... .218 .207 .202
High school graduate ............ .289 .291 .291
Some college ...................... .204 .209 .212
College graduate or more ....... .203 .209 .214
Missing ............................ .087 .084 .081
Mother’s education:
! High school graduate .......... .182 .171 .162
High school graduate ............ .409 .414 .419
Some college ...................... .220 .223 .226
College graduate or more ....... .135 .139 .141
Missing ............................ .055 .054 .052
Father’s occupation:
Mean .............................. 38.968 39.317 39.518
SD ................................. 17.703 17.764 17.807
Proportion missing ............... .084 .083 .079
Family earnings:
Mean .............................. 25,697.376 25,957.542 26,157.868
SD ................................. 21,262.278 21,655.499 21,961.580
Proportion missing ............... .081 .061 .047
Farm background:
Yes ................................. .046 .047 .047
Missing ............................ .084 .083 .079
Siblings:
Mean .............................. 2.889 2.852 2.822
SD ................................. 1.631 1.610 1.596
Proportion missing ............... .127 .131 .135
“Broken” family:
Yes ................................. .385 .372 .360
Missing ............................ .132 .099 .074
Male .................................. .485 .483 .482
Black ................................. .097 .095 .095
Latino/a .............................. .117 .114 .112
Math 1:
Mean .............................. 15.105 15.267 15.406
SD ................................. 5.269 5.286 5.292
Proportion missing ............... .162 .148 .140
Math 2:
Mean .............................. 4.519 4.560 4.597
SD ................................. 1.901 1.925 1.937
Proportion missing ............... .166 .153 .144
Science:
Mean .............................. 11.335 11.415 11.486
SD ................................. 3.289 3.297 3.294
Proportion missing ............... .167 .153 .145
American Journal of Sociology
1668
TABLE 1 (Continued)
Variable and Value
Proportions/Means in Each Sample
Grade 11 Grade 12 College
Writing:
Mean .............................. 10.819 10.910 10.998
SD ................................. 3.465 3.460 3.437
Proportion missing ............... .175 .161 .153
Civics:
Mean .............................. 6.031 6.066 6.099
SD ................................. 1.833 1.843 1.846
Proportion missing ............... .181 .167 .158
Reading:
Mean .............................. 9.457 9.538 9.619
SD ................................. 3.543 1.925 3.581
Proportion missing ............... .160 .146 .139
Vocabulary:
Mean .............................. 11.333 11.420 11.509
SD ................................. 3.888 3.896 3.899
Proportion missing ............... .161 .147 .139
No course last year .............. .145 .310 .470
College prep last year ........... .529 .385 .270
Last math grade:
Mean .............................. 2.110 2.142 2.209
SD ................................. 1.139 1.030 1.112
Proportion missing ............... .007 .006 .005
Incomplete previous time ....... .001 .003 .003
Audited course previous time ... .001 .000 .001
Sample size ....................... 10,292.000 9,709.000 9,268.000
Note.—Proportions of mutually exclusive categories (e.g., father’s education) may not sum to 1 due
to rounding.
entially bias coefficients for the different transitions. Further, analysts
have yet to settle whether cutting class, involvement with disciplinary
school authorities, and other correlates of delinquency are causes or consequences
of track placement (e.g., Wiatrowski et al. 1982; Berends 1994).
Indeterminance about causal direction problematizes the inclusion of these
variables in this analysis.
Students’ destinations are the dependent variable for the analysis. Because
changes have made tracking a subject-specific phenomenon, it is
necessary to select a subject for study. The ideal subject to study would
be central to the curriculum, on the one hand, but would allow students
some freedom to be allocated to any of the logically possible categories
(including not taking a course in the subject), on the other. Mathematics
and English are the two central subjects in American high schools. However,
in comparison to English, math allows more freedom of placement,
because it is not required every year in most schools. For the HS&B
Inequality
1669
cohort, the modal requirement for English was four years, while the modal
requirement for math was two. Thus, mathematics is the subject of study
in this analysis. For this reason also, I use mathematics grades, because
these grades are probably most salient for math course-taking. As test
scores in other subjects are controlled, ability in other domains is allowed
to influence mathematics course-taking.
I have analyzed students’ movement from grade 10 to grade 11, from
grade 11 to grade 12, and from grade 12 to college. In moving to grade
11 and grade 12, students have the possibility of moving to any one of
four destinations. In each transition, a student may drop out (coded 0),
in which case the student is not considered for later transitions (which is
the common treatment of dropouts in educational transitions analyses).9
Or they may remain in school and take a college preparatory mathematics
course (coded 3), remain in school and take a noncollege preparatory math
course (coded 2), or remain in school and take no math course (coded 1).
Thus, the destination variable is an ordered categorical variable with four
categories—drop out, no math, noncollege math, or college preparatory
math.
The ordered probit model:
P(y p 0) p F(m Ϫ b X),i 1
P(y p 1) p F(m Ϫ b X) Ϫ F(m Ϫ b X),i 2 1
P(y p 2) p F(m Ϫ b X) Ϫ F(m Ϫ b X),i 3 2
P(y p 3) p 1 Ϫ F(m Ϫ b X),i 3
where signifies the normal cumulative distribution function (CDF), ’sF m
represent thresholds, represents a matrix of explanatory variables, andX
represents a vector of estimated parameters linking variables to theb
outcome, is appropriate for analyzing just such an ordered categorical
variable. Essentially, the model posits that an interval-level latent variable
with a standard normal distribution underlies the observed categorical
variable. The thresholds carve the latent variable into the appropriate
number of categories.
The high school destinations have four categories, but the last destination,
college entry, has only two categories—either the student did not
enter college (coded “0”) or the student did enter college (coded “1”). In
9
This is not the same as deleting dropouts from the overall analysis. Former tenth
graders who drop out in eleventh grade are deleted from the analysis of movement to
twelfth grade; similar treatment occurs for later dropouts and transitions. This approach
provides estimates of the correlates of dropping out. Were dropouts deleted
from the analysis completely this would not be possible.
American Journal of Sociology
1670
reality, colleges are stratified. Yet there is no consensus as to how one
should measure the stratification of collegiate institutions. Thus, college
entry is coded as a dichotomous variable.
The ordered probit model in this analysis is estimated as
P(y p 0) p F(m Ϫ b X ),it 1 t it
P(y p 1) p F(m Ϫ b X ) Ϫ F(m Ϫ b X ),it 2 t it 1 t it
P(y p 2) p F(m Ϫ b X ) Ϫ F(m Ϫ b X ),it 3 t it 2 t it
P(y p 3) p 1 Ϫ F(m Ϫ b X ),it 3 t it
for i individuals across t transitions. Note that this means that the thresholds
for all transitions are the same, but the effects of characteristics as
well as some of the characteristics themselves are allowed to vary over
time. Note that parameters for each outcome, including college entry, are
estimated simultaneously, even though college entry has but two possibilities.
This is addressed, however, by treating the college entry outcome
as right-censored. College entry is censored because I know whether or
not a student entered college, but if a student did enter college, I do not
know where their institution falls in the distribution of collegiate institutions.
Thus, all that can be done for college entry is to distinguish
between those who enter college and those who do not.
Also note that each year students who continue in school reach a destination
in the stratified curriculum. This destination is a particular track
location and serves as the track origin for the students’ next transition.
Thus, for each year, I constructed two dichotomous variables to capture
the effects of track location on students’ likelihood of making the next
transition—one variable scored 1 for students who did not take math and
zero for others, and one variable scored 1 for students who enrolled in
college preparatory math and zero for others. Thus, the omitted category
is students who took noncollege prep math (because dropouts are not at
risk of entering a grade above the grade they never entered). Note that
this implies two types of time-varying covariates are included: (1) students’
performance and (2) students’ track location the previous year.
Parameters
Above, I described the debate concerning which parameters one should
use to assess the relation between social background and school continuation.
Because the fundamental dependent variable in the analysis is
students’ probability of reaching particular destinations in the stratified
educational system, I focus on how the predicted probability is associated
with differences in social background.
Inequality
1671
Indeed, predicted probabilities, not regression-type coefficients, are required
in order to assess EMI, because effectively maintained inequality
contends that the advantages that accrue to the socioeconomically wellplaced
are sufficient to secure for them desired outcomes. The dependent
variable of this analysis is composed of a small set of discrete ordered
locations; a student experiences a particular outcome if the student exceeds
the threshold dividing that outcome from the one just below it. Given
this image, social background becomes effective if it can move people
over thresholds.
Regression-type coefficients by themselves cannot reveal whether social
background moves people over thresholds. Thus, a good question to ask
is, What kind of evidence would allow us to assess whether empirical
findings are consistent with a process of effectively maintained inequality?
One kind of evidence would be whether the effect of social background
is such that we would predict a different outcome for a person at the low
end of the social background continuum than one at the high end. A
common decision rule for predicting discrete outcomes is to predict the
outcome that has the largest predicted probability. Thus, in order to evaluate
whether the effect of social background works to effectively maintain
inequality, we need see whether its effect on the predicted probability is
such that our best prediction will change simply on the basis of differences
in social background. Surely, it would be possible to find some values of
covariates for which this is true, but some protection from a search for
such values is to use theoretically interesting values and investigate
whether the prediction would change for such focal students. Thus, predicted
probabilities are the focus of the analysis.
However, because MMI and LCP were devised with respect to logit
coefficients (which differ from probit coefficients by a fairly constant multiple),
it will be useful to briefly consider the findings one would reach
on the basis of ordered probit coefficients. By comparing the results obtained
by the focus on coefficients to those obtained by considering differences
in probabilities, it will be possible to determine whether the
preference for one or the other explanation is consistent given two different
ways of indexing effects of social background on school continuation.
RESULTS
MMI, LCP, and the Ordered Probit Coefficients
Table 2 contains the ordered probit (OP) coefficients for a model predicting
students’ educational transitions. The coefficient for broken family rises
in absolute value then falls, while the coefficient for farm background
rises in absolute value across the three transitions. Further, the coefficient
TABLE 2
Ordered Probit Coefficients and t-values for Models Predicting School
Continuation and Track Location
Grade 11 Grade 12 College
Constant ......................... .264 .424 Ϫ3.042
(5.356) (8.256) (Ϫ32.942)
Father’s education .............. .092 .059 .160
(11.857) (5.581) (10.278)
Mother’s education ............. .063 .037 .164
(7.934) (3.717) (9.938)
Father’s occupation ............ .004 .002 .003
(8.624) (3.516) (2.812)
Family earnings in $10,000s ... .021 .005 .043
(6.016) (1.762) (8.104)
Farm background .............. Ϫ.015 Ϫ.070 .076
(Ϫ.359) (Ϫ1.566) (1.019)
Number of siblings ............. Ϫ.037 Ϫ.015 Ϫ.041
(Ϫ9.955) (Ϫ3.196) (Ϫ4.814)
“Broken” family ................. Ϫ.121 Ϫ.149 Ϫ.099
(Ϫ6.873) (Ϫ7.395) (Ϫ3.677)
Male ............................. .091 .131 .055
(6.694) (7.514) (1.810)
Black ............................. .324 .402 .290
(15.313) (9.391) (4.350)
Latino/a .......................... .097 .141 .064
(4.766) (4.659) (1.318)
Math 1 ........................... .022 .013 .026
(8.773) (4.159) (5.937)
Math 2 ........................... .027 .025 .022
(4.131) (3.602) (2.024)
Science ........................... Ϫ.007 Ϫ.002 .003
(Ϫ1.571) (Ϫ.377) (.434)
Writing .......................... .011 .006 .017
(2.727) (1.477) (2.507)
Civics ............................ .008 .014 .056
(1.415) (2.140) (6.127)
Reading .......................... .011 .015 .012
(2.825) (3.539) (1.855)
Vocabulary ...................... .002 Ϫ.002 .031
(.645) (Ϫ.456) (5.162)
No course last year ............. Ϫ.065 Ϫ.232 Ϫ.115
(Ϫ3.427) (Ϫ10.620) (Ϫ3.390)
College prep last year .......... .643 .604 .543
(42.083) (30.716) (15.626)
Last performance grade ........ .217 .185 .138
(40.866) (25.047) (10.061)
Audit previous time ............ .225 Ϫ1.738 .000
(.607) (Ϫ.017) (.000)
Incomplete previous time ...... Ϫ.316 Ϫ.680 .111
(Ϫ1.112) (Ϫ4.315) (.338)
Inequality
1673
for father’s occupation declines from grade 11 to grade 12 and rises thereafter,
but the coefficient on college entry does not exceed the coefficient
for grade 11. These complexities occur, however, amid a more general
story. OP coefficients for parents’ education, family earnings, and siblings
are higher for college entry than for the other transitions. Indeed, OP
coefficients for these four indicators of social background decline between
grade 11 and grade 12, and rise for college. These last four indicators of
social background suggest that an equalization is reversed; such a reversal
provides more support for MMI than for LCP.
MMI, LCP, and School Continuation Probabilities
To broaden the assessment of the effects of social background on students’
school continuation, I graph the predicted probabilities of school continuation
by earnings holding all remaining interval-level factors except previous
mathematics grade constant at their means; I hold previous mathematics
grade constant at a B to signify a capable but not outstanding
performance. Ordinal- and nominal-level indicators are held constant such
that the graph represents white females from intact nonfarm families who
were taking noncollege prep mathematics the previous year. For such
middling white female students of middling family backgrounds, the effects
of earnings are nearly linear throughout so that one may compare
the effects of earnings on different outcomes by comparing the difference
between the predicted probability for students from extremely poor families
and the predicted probability for students from wealthy families (see
fig. 3). Owing to the near certain probability of school continuation for
such eleventh and twelfth graders, the effects of earnings appear trivial,
approximately one percentage point difference for eleventh grade, and
smaller for twelfth grade.
However, the difference between poverty and wealth is associated with
a difference of approximately 20 percentage points in the likelihood of
entering college, certainly a substantively nontrivial difference. This finding
suggests that the effects of earnings are higher for college entry than
for high school continuation, which is the same inference we drew above
on the basis of the OP coefficients. And, as above, the evidence favors
MMI over LCP.
Table 3 presents differences between the predicted probability of reaching
a particular outcome for the most disadvantaged and most advantaged
students for each of five social background variables, holding all other
variables constant as above. Because the underlying dependent variable
in this analysis is the probability of reaching a particular track destination
in a given year, the numbers that appear in the “diff” columns, which
reflect the difference between the probability for the most advantaged
American Journal of Sociology
1674
Fig. 3.—Selected destinations and earnings
and most disadvantaged students, can reveal the effects of social background
for particular parts of the educational transitions process. When
one peruses the table, a common pattern is evident—the effect of social
background is far larger for college entry than for high school
continuation.
For example, the difference in the probability of college entry for those
with fathers who did not complete high school and those with fathers
who completed college or more is 0.185 points. In contrast, the same social
locations differ by only 0.013 points in the probability of continuing in
school to grade 11 or grade 12.
Thus, when we consider the pattern of effects of social background on
school continuation probabilities, we find that social background matters
more for college entry than for high school completion. This finding is
consistent with MMI.
One caveat, however, is that I have not determined whether the pattern
of social background effects on the probabilities of college entry were
different for older cohorts, and thus cannot say whether Reagan-era policy
change lies behind my results. But it is apparent that the pattern of effects
on school continuation probabilities are more consistent with MMI than
with LCP, because LCP implies that social background effects on college
entry will be lower than social background effects on high school graduation.
I do not find this to be true when I consider probabilities of school
TABLE 3
Predicted Probabilities for Selected Variables for Disadvantaged (Low) and Advantaged (High) Students
School Continuation College Prep Enrollment
Grade 11 Grade 12 College Entry Grade 11 Grade 12
Low High Diff Low High Diff Low High Diff Low High Diff Low High Diff
Broken family ......... .974 .981 .007 .953 .966 .013 .371 .409 .038 .274 .315 .041 .192 .235 .043
Father’s education .... .973 .986 .013 .959 .972 .013 .322 .507 .185 .269 .368 .099 .210 .264 .054
Mother’s education ... .976 .985 .009 .962 .970 .008 .326 .516 .190 .286 .353 .067 .220 .254 .034
Father’s occupation ... .977 .987 .010 .963 .972 .009 .384 .459 .075 .288 .372 .084 .223 .261 .038
Number siblings ....... .975 .985 .010 .962 .969 .007 .360 .455 .095 .276 .353 .077 .220 .248 .028
Note.—In this table, disadvantaged students (low) are females having, variously, nonintact families, a mother/father who did not graduate from high
school, a father at the lowest value in the SEI scale, or with six or more siblings. In contrast, advantaged students (high) are females having, variously, intact
families, a mother/father who completed college or more education, a father at the highest value in the SEI scale, or no siblings.
American Journal of Sociology
1676
continuation, which mirrors the conclusion reached after perusal of the
OP coefficients. Thus, the preference for MMI over LCP does not depend
on whether OP coefficients or probabilities are considered.
Effectively Maintained Inequality
The key question to ask to assess effectively maintained inequality is
whether one’s prediction of a student’s destination will change on the
basis of social background. Consider figure 3 again, which illustrates how
the probability of college entry differs as family income differs for middling
female students who are in the noncollege track, from an intact
nonfarm family, and with mean values on other social background factors.
The results in figure 3 show that the difference in the predicted probability
of college entry is enough to move us from predicting that our focal student
would not enter college to predicting that the student would enter college,
because the predicted probability of college entry for the poor student is
below 50%, while the analogous estimate for the wealthy student is above
50%.
Of course, estimating the probability of a given outcome by itself will
not help in other cases, a fact well-illustrated by the bottom of figure 3.
Figure 3 also shows predicted probabilities for college track location,
conditional on prior track location and all other variables in the model,
for grades 11 and 12. The difference between poverty and wealth is associated
with a difference of nine points in the probability of enrolling in
college prep math in eleventh grade. This effect is less than half as large
as the effect of earnings on college entry but substantially larger than the
effect of earnings on school continuation. Similarly, results in table 3 show
that the effects of social background on college prep entry approach and
may sometimes even surpass those for college entry (e.g., the effect of
broken family status on college prep entry exceeds the effect of broken
family status on entering college itself). These results allow us to assess
whether social background effects are higher for college prep assignment
or college entry, but they do not provide the kind of evidence needed to
evaluate effectively maintained inequality, primarily because in order to
assess EMI, one must calculate probabilities for all discrete outcomes.
When there are more than two discrete possibilities, one must determine
which outcome has the largest predicted probability. Although none of
these probabilities may exceed 50%, the largest still identifies our best
categorical guess.
Table 4 lists estimated probabilities of experiencing each of the four
outcomes in grade 11 for our focal students when they have extreme values
Inequality
1677
TABLE 4
Predicted Probabilities for Eleventh Grade Destinations for Disadvantaged
and Advantaged Students
Dropout No Course Non–College Prep College Prep
Family earnings:
Disadvantageda
... .022 .343 .336 .299
Advantaged ....... .012 .264 .334 .391
Father’s education:
Disadvantageda
... .027 .371 .333 .269
Advantaged ....... .014 .283 .336 .368
Mother’s education:
Disadvantageda
... .024 .355 .335 .286
Advantaged ....... .015 .295 .337 .353
Father’s occupation:
Disadvantageda
... .023 .353 .335 .288
Advantaged ....... .013 .279 .336 .372
Broken family:
Disadvantageda
... .026 .367 .333 .274
Advantaged ....... .019 .328 .337 .315
Number of siblings:
Disadvantageda
... .025 .365 .334 .276
Advantaged ....... .015 .294 .337 .353
Socioeconomically:
Disadvantagedb
... .064 .496 .287 .153
Advantaged ....... .012 .272 .335 .381
a
Disadvantaged students are females having, variously, nonintact families, a mother/father who did
not graduate from high school, a father at the lowest value in the SEl scale, or with six or more siblings.
In contrast, advantaged students (high) are females having, variously, intact families, a mother/father
who completed college or more education, a father at the highest value in the SEI scale, or no siblings.
b
Disadvantaged students are females from families with both parents and six children, a mother and
father who did not graduate from high school, a father whose occupation is approximately that of a
forging machine operator, and whose family income is approximately $14,936 (in 1980 dollars). Advantaged
students are females from intact families with two children, parents who have some college, a
father whose occupation is approximately that of a general public administrator, and whose family income
is approximately $36,267 (in 1980 dollars).
on each separate indicator of socioeconomic background taken in turn.10
Note that this means that a prediction of college prep track entry is also
a prediction of upward mobility, while a prediction of noncollege prep
course-taking is a prediction of stability. If one would predict the student
does not take a course in the subject, one predicts downward track
mobility.
In every case, altering the students’ socioeconomic status would change
the prediction for their destination. In most cases, the prediction change
is so large that social background appears to send students in opposite
10
When comparisons concern parents education, family background, earnings, or number
of siblings, they refer to persons from intact nonfarm families.
American Journal of Sociology
1678
directions. For example, if a student’s father did not complete high school,
then we would predict that the student would not take math in grade 11
and thus would be downwardly mobile. In contrast, if a student’s father
completed college, then we would predict that the student would take
college prep math in grade 11, and thus would be upwardly mobile. This
“diverging trajectories” pattern holds for all of the social background
factors considered and is extreme for five of the six indicators.
Note, however, that the predictions above assume that social background
factors are statistically independent of each other. The last two
lines of table 4 relax this assumption, presenting predicted probabilities
for focal students from intact families who are one standard deviation
below (and above) the mean in father’s education, mother’s education,
father’s occupation, and number of siblings, and one-half standard deviation
below (and above) mean family income.11
This comparison, which
reflects some degree of association between these indicators of social background,
show that we would predict the disadvantaged student would
take no course. Indeed, the predicted probability for the “no course” category
for the disadvantaged student approaches 50%. Yet, our prediction
for the socioeconomically advantaged student is again very different; we
would expect this student to rise from noncollege prep math to enter the
college preparatory track.
The stark contrast between socioeconomically disadvantaged and advantaged
students is consistent with effectively maintained inequality and
is a far cry from the suggestion that social background effects decline to
zero when a level of education becomes universal. Instead, it suggests
that when a level of education is universal, social background may matter
for qualitative dimensions of education that are relevant at that level of
education and that have implications for students’ chances of making
later transitions.
CONCLUDING REMARKS
When students move from grade to grade, they also move from one stratified
curriculum to another. The factors that determine whether they continue
schooling also determine where in the stratified curriculum that
schooling will occur. Students’ location in the stratified curriculum has
11
Given the values on the variables we can flesh out the illustration. The disadvantaged
student is a female from an intact family of six children, whose parents dropped out
of high school, whose father’s occupation is a forging machine operator, with a family
income of $14,936 (in 1980 dollars). The advantaged student has one sibling, parents
who have some college, a father who is a general public administrator, and whose
family income is $36,267 (in 1980 dollars).
Inequality
1679
implications for their likelihood of making additional transitions, and thus
their location in the stratified curriculum is an integral part of the process
of educational attainment. The observations above serve to connect two
distinct literatures—research on educational transitions and analyses of
track mobility. Their convergence addresses issues raised in a provocative
critique of the educational transitions tradition by supporting the sequential
decision-making model, highlighting the theoretical importance
of the time-varying covariates of track location and performance, and
invalidating the suggestion that the sequential model of educational attainment
requires a behavioral assumption of myopia. Thus, the foregoing
analysis has investigated students’ movements through the stratified curriculum.
Although I present and discuss ordered probit coefficients to
connect the findings to previous work, the argument that findings may
be sensitive to the functional form of the model led me to assess existing
theories using the effects of social background on the probabilities of
school continuation as well. Finally, I evaluated whether the role of social
background on the probability of reaching particular destinations was
consistent with effectively maintained inequality. Because the analysis
produced evidence consistent with this alternate explanation, it appears
that the convergence of the tracking and education transitions treatments
is not only statistically useful but also sociologically intriguing.
When we consider the life course explanation and the theory of maximally
maintained inequality, we find that the pattern of background
effects is most consistent with the maximally maintained inequality explanation.
Key social background factors rise in importance as students
attempt to enter college in comparison to their effects on previous transitions,
just as MMI should predict for Reagan-era cohorts. Although few
would deny that as children mature their dependence declines, and thus
the life course perspective remains useful, the evidence suggests that declining
dependence on parents does not explain the pattern of social background
effects on educational transitions.
However, owing to the simultaneous treatment of school continuation
and track placement, I found important social background effects operating
even before the college entry transition, and thus the findings contradict
a key implicit tenet of MMI. While MMI suggests that backgroundrelated
inequality will go to zero when a level of education is nearly
universal, EMI states that at that very level social background will allocate
students to different types of education that have different implications
for educational attainment. The evidence presented here is most
consistent with the EMI claim.
The idea of effectively maintained inequality is not only that advantaged
social background is associated with increased chances of better
placements, but also that the increases are consequential for theoretically
American Journal of Sociology
1680
focal students. Given that school strata are discrete locations, effectively
maintained inequality suggests that social background works efficaciously
if we would alter our prediction of students’ destinations simply on the
basis of differences in social background. In other words, if social background
can move an otherwise “average” student over a threshold, then
social background effectively maintains inequality. When we considered
the predictions we would make on the basis of the model results, we found
that social background advantages consistently serve to “move” children
(or our predictions for them) from disadvantageous discrete locations to
advantageous ones. Thus, even though the increment for social background
effects may be small, we observed it to be effective.
These findings have important implications for how to understand the
provision of educational opportunity and the process of educational attainment.
The findings lend credence to the postulation that even though
high school completion is nearly universal, high school remains an important
site of competition in which social background matters. Maximally
maintained inequality implied that when a level of education is universal,
socioeconomically related contestation (i.e., class conflict) would center on
higher levels of education. Other research contradicts this vision, pointing
to intense class conflict around the maintenance of tracking (e.g., Wells
and Serna 1996). The findings here might help us understand this class
conflict.
We find that in high school social background appears to matter for
the kind of education received rather than for high school completion.
Clearly, however, social background cannot allocate persons to qualitatively
better or worse positions if all positions are equal. Thus, class
conflict may occur at the high school level as different actors attempt not
only to obtain advantageous positions for their children, but also to secure
or dismantle the stratified curriculum.
Indeed, contrary to the MMI implication, universality of access may
be largely irrelevant to the intensity of class conflict, as the focus of conflict
may simply change once access is universal. Further, the results of this
analysis, which show that social background continues to matter even in
the presence of universal access, gives reason to speculate that the simple
extension of universal access to institutions is unlikely to undo the effective
power of social resources indexed by common indicators of social background,
at least in the United States. This speculation, if true, would
greatly complicate efforts to ameliorate the inheritance of social disadvantage,
although it of course has no implications either way for the
desirability of such efforts.
One may speculate further as to whether the idea of effectively maintained
inequality has applicability to other educational situations or to
even broader arenas. It is easy to suggest at least one other place one
Inequality
1681
might search for the operation of effectively maintained inequality. As
one example, consider that the proportion of a cohort that enters preschool
is increasing. It would be illuminating to ascertain whether the effect of
social background on whether the child enters preschool declines as the
proportion of the cohort entering preschool increases, while the effect of
social background on the features of the child’s preschool was maintained,
increased, or became consequential for otherwise average children. If so,
this would be consistent with effectively maintained inequality.
That said, there is ample additional research to do even on students’
high school experiences and educational attainment. Will we find similar
patterns if additional subjects are studied? Would similar patterns be
observed for additional cohorts? Would other qualitative dimensions of
education in the United States, and studies of other nation’s systems of
education, reveal similar patterns of effects? Would models with more
regressors, or different treatments for unmeasured heterogeneity, reveal
similar patterns of effects? Thus, although the research presented here
provides support for effectively maintained inequality, more work is
needed to assess the robustness and generalizability of this claim even in
the realm of social stratification and education.
Even as we acknowledge the importance of the questions above and
more, we can also imagine the mechanisms behind effectively maintained
inequality working in many different arenas, areas as important as health
care (e.g., the role of social background shifting from allocating scarce
organs to persons to allocating leading surgeons to perform the surgery),
as well as the relatively trivial (e.g., the role of social background shifting
from allocating personal transportation to allocating the type of vehicle
for personal transportation). However, at this juncture, it should suffice
to say that when we investigate both school continuation and track mobility,
we find consequential effects of social background in each year
studied. This suggests that the effects of social background occur in at
least two ways: (1) they determine who completes a level of education if
completion of that level is not nearly universal, and (2) they determine
the kind of education persons will receive within levels of education that
are nearly universal. Either way, social background advantages seem to
work to effectively and continuously secure for the children of advantage
advantaged locations of their own.
APPENDIX A
Independent Variables
All variables are recoded to the midpoint for missing cases, and a control
American Journal of Sociology
1682
for missing on each category of variable is used (owing to high collinearity
on the missing indicators within each category)
Social Background
Father’s occupation.—Students’ responses to a 17 category question
were recoded to the 1980 SEI score of the mean of the illustrative occupations
in the questionnaire using Stevens and Cho’s (1985) updated
occupational scores for the total labor force. Students’ 1980 responses
were taken unless the responses were missing, in which case, the 1982
response was taken. Homemakers and military were coded as missing
given that there is no SEI code for those pursuits.
Mother’s education and father’s education.—Students’ responses to a
10-category question were recoded into the following ordered levels: l p
less than high school graduate; 2 p high school graduate; 3 p some
college only; and 4 p college degree or more.
Farm background.—Mother or father was a farmer (1) or not (0).
Male.—Students’ self-report of sex was used.
Family income.—Students were asked twice in the base year and twice
in the follow-up to report family income. Base-year data are used unless
missing; follow-up data are used if the base year is missing. Responses
are coded to the midpoint of categories; the unbounded upper category
is coded using the Pareto transformation for an unbounded category.
Number of siblings.—Students were asked to report on the number of
siblings in 1980; as herein used, the codes are 0 p none, 1 p 1 sibling,
and so on, up to 6 p 6 or more siblings.
“Broken” family.—Students’ report of whether in 1980 or 1982 the
student lived with both mother and father (0) or not (1).
Race/Ethnicity
The omitted category for two dichotomous race/ethnicity indicators is nonblack,
non-Latino/a (approximately 95% of the omitted category are
white). Black indicates students’ self-report of black or not. Latino/a indicates
students’ self-report of Latin ancestry.
Measured Achievement
Tenth grade tests in vocabulary (range 0–21), reading (0–19), math 1
(0–28), math 2 (0–10), science (0–20), writing (0–17), and civics (0–10)
capture measured achievement.
Inequality
1683
Academic Performance
Last performance grade.—Grade in last math class taken, ranges from
0.0 (F) to 4.3 (Aϩ).
Audit.—Student audited last math course taken.
Incomplete.—Student given an incomplete in the last math course
taken.
APPENDIX B
Each year students encounter an opportunity to either continue their
schooling or elect to stop. Thus, educational attainment is the cumulation
of a sequence of decisions. For an individual student, then:
T
Y p Y ,͸is it
tp1
where i refers to the individual student, t refers to transitions, and s refers
to the sum of the transitions. Educational transitions analyses do not
model but, instead, typically model several ’s using logistic regressionY Yis it
techniques. The full set of transitions is implied below:
(X b )1
e
( )Prob y p 1 p ϩ e ,1 1(X b )1
(1 ϩ e )
(X b )2
e
( )Prob y p 1 d y p 1 p ϩ e ,2 1 2(X b )2
(1 ϩ e )
(X b )3
e
( )Prob y p 1 d y p 1 p ϩ e3 2 3,(X b )3
(1 ϩ e )
. . . .
. . . .
. . . .
(X b )15
e
( )Prob y p 1 d y p 1 p ϩ e ,15 14 15(X b )15
(1 ϩ e )
(X b )16
e
( )Prob y p 1 d y p 1 p ϩ e ,16 15 16(X b )16
(1 ϩ e )
American Journal of Sociology
1684
(X b )17
e
( )Prob y p 1 d y p 1 p ϩ e .17 16 17(X b )17
(1 ϩ e )
The key portion of the Cameron and Heckman critique can be demonstrated
as follows; consider the logistic regression equations below:
K
pi1 2
( )log p b X ϩ e e ∼ L 0,p /3 , (B1)͸e 1k ik i1 1( )1 Ϫ p 1i1
K
pi2 2
( )log p b X ϩ e e ∼ L 0,p /3 , (B2)͸e 2k ik i2 2( )1 Ϫ p 1i2
K
pi3 2
( )log p b X ϩ e e ∼ L 0,p /3 , (B3)͸e 3k ik i3 3( )1 Ϫ p 1i3
or, in general:
K
pit 2
( )log p b X ϩ e e ∼ L 0,p /3 ,͸e tk ik it t( )1 Ϫ p kp1it
where refers to the probability of person i making transition t, isp bit tk
the association between variable and the probability of making tran-Xk
sition t, and is a person-specific, transition-specific error term.eit
Consider equations B1 through B3 from the point of view of a single
student; suppress until further notice the assumption for the distribution
of the error term. Assume, for illustration purposes, that the student completes
the first two transitions but not the third. Thus, for this student,
there is clearly variation in the dependent variable.12
The question Cameron and Heckman ask is what, according to equations
B1–B3, induces the variation? The ’s and ’s are unknowns esti-b e
mated from the data, and for any given student, the value of does notXk
vary across transitions. In this situation, an infinite number of estimates
for the ’s satisfy the constraints imposed by the data. Therefore, theb
equations are not identified.
To obtain identification, researchers assume a distribution for the error
term. This identifies the logit model. However, recall the single student.
The assumption for the error term essentially implies a value for the error
term for this student for each transition. This error term can, in principle,
vary across transitions for the individual student. What this implies, how-
12
Of course, the probability of making transitions varies for any student across transitions,
because the (un)conditional population proportion making transitions may vary,
and the best estimate of a student’s probability of completing a transition is the
(un)conditional population proportion making the transition. However, this illustration
may be facilitated, and certainly is not hindered, by assuming variation in the student’s
decisions across transitions.
Inequality
1685
ever, is that the only right-hand side element that varies independently
across equations is the error term. Thus, when the do not vary for aXk
person across transitions, the assumption for identifies all estimatede
differences between the ’s. Cameron and Heckman correctly note thatb
changing the assumption for the error term may change the findings.
This problem has an obvious solution: introduce a time-varying covariate.
The foregoing analysis followed just this strategy. Requirements
that the time-varying covariate must meet are not stringent. Consider
equations B4–B6:
K
pi1 2
( )log p b X ϩ g Z ϩ e e ∼ L 0,p /3 , (B4)͸e 1k ik 1 i1 i1 1( )1 Ϫ p 1i1
K
pi2 2
( )log p b X ϩ g Z ϩ e e ∼ L 0,p /3 , (B5)͸e 2k ik 2 i2 i2 2( )1 Ϫ p 1i2
K
pi3 2
( )log p b X ϩ g Z ϩ e e ∼ L 0,p /3 , (B6)͸e 3k ik 3 i3 i3 3( )1 Ϫ p 1i3
where , , and are time-specific realizations of Z. To simplify theZ Z Z1 2 3
presentation, assume they are centered on their means. Because the Z
variables vary across transitions, two factors potentially create variation
in a student’s decisions across transitions: Z and . Now, assume, thee
following relationships:
Z p l Z ϩ d ,i2 1 i1 1
Z p l Z ϩ d ,i3 2 i2 2
where and are errors from regression equations with the standardd d1 2
assumptions of regression. and imply that the regression equationd d1 2
does not perfectly predict the dependent variable. The relationships above
transform equations B4–B6 as follows:
K
pi1 2
( )log p b X ϩ g Z ϩ e e ∼ L 0,p /3 ,͸e 1k ik 1 i1 i1 1( )1 Ϫ p 1i1
K
pi2 2
( )log p b X ϩ g (l Z ϩ d ) ϩ e e ∼ L 0,p /3 ,͸e 2k ik 2 1 i1 1 i2 2( )1 Ϫ p 1i2
K
pi3 2
( )log p b X ϩ g (l l Z ϩ d ϩ l d ) ϩ e e ∼ L 0,p /3 .͸e 3k ik 3 2 1 i1 2 2 1 i3 3( )1 Ϫ p 1i3
Rearranging terms produces the following three equations:
American Journal of Sociology
1686
K
pi1 2
( )log p b X ϩ g Z ϩ e e ∼ L 0,p /3 , (B7)͸e 1k ik 1 i1 i1 1( )1 Ϫ p 1i1
K
pi2
log p b X ϩ g l Z ϩ g d ϩ e͸e 2k ik 2 1 i1 2 1 i2( )1 Ϫ p 1i2
2
( )e ∼ L 0,p /3 , (B8)2
K
pi3
log p b X ϩ g l l Z ϩ g (d ϩ l d ) ϩ e͸e 3k ik 3 2 1 i1 3 2 2 1 i3( )1 Ϫ p 1i3
2
( )e ∼ L 0,p /3 , (B9)3
Note that for identifying the ’s in the sequence of logistic regressionb
equations (equations B7–B9), what we require is a variable that varies
across transitions independently. Even if there is a relationship between
the time-varying covariate over time, the s—the portion of that isd Zt
independent of (where u is a positive integer)—satisfy that require-ZtϪu
ment. This implies that as long as one can find a single time-varying
covariate whose cross-time correlation is not perfect, one can identify
differences between the ’s by including that variable as a time-varyingb
covariate.
Nothing is changed by assuming that some of the variables in X also
determine , for unless the X variables in concert with the lagged valuesZt
of Z perfectly determine , there is still some independent variation inZt
. It is that independent variation—not to say measurement error inZt
—that provides the leverage needed to identify the differences in theZt
s across transitions.b
Once the differences in the s are identified in this manner, Cameronb
and Heckman’s claim that the education transitions model assumes myopia
no longer holds. This claim depends upon the error term being the
only right-hand side determinant that varies independently across transitions.
However, because time-varying covariates also vary at least somewhat
independently across transitions, introducing time-varying covariates
makes the claim about myopia inaccurate.
The nonidentification of the differences in the s, and the descriptionb
of why this is so, is the major contribution of the Cameron and Heckman
article. However, introducing time-varying covariates solves that problem.
In the foregoing analysis, two types of time-varying variables were used:
(1) measures of student performance and (2) previous track location. Evidence
certainly supports the contention that track location is not perfectly
correlated over time (e.g., Lucas 1999). For theoretical reasons, the foregoing
analysis highlighted the role of tracking, but surely there are likely
other time-varying covariates that can serve to identify the standard lo-
Inequality
1687
gistic regression education transitions model. This still leaves the issue of
unobserved heterogeneity, about which many analysts have written. Analysts
may continue to work on this problem, because the identification
issues Cameron and Heckman raise can be resolved by making theoretically
defensible assumptions concerning time-varying covariates. Hence,
given appropriate data, it is still too early to reject the education transitions
logistic regression approach.
REFERENCES
Berends, Mark. 1994. “Educational Stratification and Students’ Social Bonding to
School.” British Journal of Sociology of Education 16:327–51.
Buchmann, Marlis, and Maria Charles, with Stefan Sacchi. 1993. “The Lifelong
Shadow: Social Origins and Educational Opportunity in Switzerland.” Pp. 177–92
in Persistent Inequality: Changing Educational Attainment in Thirteen Countries,
edited by Yossi Shavit and Hans-Peter Blossfeld. Boulder, Colo.: Westview Press.
Cameron, Stephen V., and James J. Heckman. 1998. “Life Cycle Schooling and
Dynamic Selection Bias: Models and Evidence for Five Cohorts of American Males.”
Journal of Political Economy 106:262–333.
Carey, Nancy, Elizabeth Farris, and Judi Carpenter. 1994. Curricular Differentiation
in Public High Schools: Fast Response Survey System E.D. Tabs. Rockville, Md.:
Westat.
Cicourel, Aaron V., and J. I. Kitsuse. 1963. The Educational Decision-Makers: An
Advanced Study in Sociology. Indianapolis: Bobbs-Merrill.
De Graaf, Paul M., and Harry B. G. Ganzeboom. 1993. “Family Background and
Educational Attainment in the Netherlands for the 1891–1960 Birth Cohorts.” Pp.
75–99 in Persistent Inequality: Changing Educational Attainment in Thirteen
Countries, edited by Yossi Shavit and Hans-Peter Blossfeld. Boulder, Colo.:
Westview Press.
Evangelauf, Jean. 1987. “Costs of Attending College Appear Likely to Rise Faster
than Inflation for the 8th Year in a Row.” Chronicle of Higher Education 34 (25):
A29–30.
Fienberg, Stephen E., and William M. Mason. 1978. “Identification and Estimation of
Age-Period-Cohort Models in the Analysis of Discrete Archival Data.” Sociological
Methodology 10:1–67.
Fischer, Claude, Michael Hout, Martı´n Sa´nchez Jankowski, Samuel R. Lucas, Ann
Swidler, and Kim Voss. 1996. Inequality by Design: Cracking the Bell Curve Myth.
Princeton, N.J.: Princeton University Press.
Gamoran, Adam, and Robert D. Mare. 1989. “Secondary School Tracking and
Educational Equality: Compensation, Reinforcement, or Neutrality?” American
Journal of Sociology 94:1146–83.
Garet, Michael S., and Brian DeLaney. 1988. “Students, Courses, and Stratification.”
Sociology of Education 61:61–77.
Garnier, Maurice A., and Lawrence E. Raffalovich. 1984. “The Evolution of
Educational Opportunities in France.” Sociology of Education 57:1–10.
Griliches, Zvi. 1977. “Estimating the Returns to Schooling: Some Econometric
Problems.” Econometrica 45:1–22.
———. 1979. “Sibling Models and Data in Economics: Beginnings of a Survey.” Journal
of Political Economy 87: S37–S64.
Hallinan, Maureen T. 1992. “The Organization of Students for Instruction in Middle
School.” Sociology of Education 65:114–27.
———. 1996. “Track Mobility in Secondary School.” Social Forces 74:983–1002.
American Journal of Sociology
1688
Hayes, III, Floyd W. 1990. “Race, Urban Politics, and Educational Policy-Making in
Washington, D.C.: A Community’s Struggle for Quality Education.” Urban
Education 25:237–57.
Heckman, James J., and Burton S. Singer. 1982. “The Identification Problem in
Econometric Models for Duration Data.” Pp. 39–77 in Advances in Econometrics,
edited by Werner Hildebrand. Cambridge: Cambridge University Press.
Herrnstein, Richard J., and Charles Murray. 1994. The Bell Curve: Intelligence and
Class Structure in American Life. New York: Free Press.
Hout, Michael, Adrian E. Raftery, and Eleanor O. Bell. 1993. “Making the Grade:
Educational Stratification in the United States, 1925–1989.” Pp. 25–49 in Persistent
Inequality: Changing Educational Attainment in Thirteen Countries, edited by Yossi
Shavit and Hans-Peter Blossfeld. Boulder, Colo.: Westview Press.
Kerckhoff, Alan C., and Jerry M. Trott. 1993. “Educational Attainment in a Changing
Educational System: The Case of England and Wales.” Pp. 133–53 in Persistent
Inequality: Changing Educational Attainment in Thirteen Countries, edited by Yossi
Shavit and Hans-Peter Blossfeld. Boulder, Colo.: Westview Press.
Little, R. J. A., and Donald B. Rubin. 1987. Statistical Analysis with Missing Data.
New York: John Wiley.
Long, J. Scott. 1997. Regression Models for Categorical and Limited Dependent
Variables. Thousand Oaks, Calif.: Sage Publications.
Lucas, Samuel R. 1996. “Selective Attrition in a Newly Hostile Regime: The Case of
1980 Sophomores.” Social Forces 75:511–33.
———. 1999. Tracking Inequality: Stratification and Mobility in American High
Schools. New York: Teachers’ College Press.
Lucas, Samuel R., and Aaron D. Good. 2001. “Race, Class, and Tournament Track
Mobility.” Sociology of Education 74:139–56.
Manski, Charles F. 1993. “Adolescent Econometricians: How Do Youth Infer the
Returns to Schooling?” Pp. 43–60 in Studies of Supply and Demand in Higher
Education, edited by Charles T. Clotfelter and Michael Rothschild. Chicago:
University of Chicago Press.
———. 1995. Identification Problems in the Social Sciences. Cambridge, Mass.:
Harvard University Press.
Manton, Kenneth G., Eric Stallard, and James W. Vaupel. 1981. “Methods for
Comparing the Mortality Experience of Heterogenous Populations.” Demography
18:389–410.
Mare, Robert D. 1980. “Social Background and School Continuation Decisions.”
Journal of the American Statistical Association 75:295–305.
———. 1993. “Educational Stratification on Observed and Unobserved Components
of Family Background.” Pp. 351–76 in Persistent Inequality: Changing Educational
Attainment in Thirteen Countries, edited by Yossi Shavit and Hans-Peter Blossfeld.
Boulder, Colo.: Westview Press.
Mare, Robert D., and Huey-Chi Chang. 1998. “Family Attainment Norms and
Educational Attainment: New Models for School Transitions.” Paper presented at
the International Sociological Association Research Committee 28 Meetings in
Montreal, August.
Moore, Donald R., and Suzanne Davenport. 1988. The New Improved Sorting Machine.
Madison: National Center on Effective Secondary Schools, School of Education,
University of Wisconsin.
Mu¨ller, Walter, and Wolfgang Karle. 1993. “Social Selection in Educational Systems
in Europe.” European Sociological Review 9:1–23.
Paulsen, Ronnelle. 1991. “Education, Social Class, and Participation in Collective
Action.” Sociology of Education 64:96–110.
Powell, Arthur G., Eleanor Farrar, and David K. Cohen. 1985. The Shopping Mall
Inequality
1689
High School: Winners and Losers in the Educational Marketplace. Boston, Mass.:
Houghton Mifflin Company.
Raftery, Adrian E., and Michael Hout. 1993. “Maximally Maintained Inequality:
Expansion, Reform, and Opportunity in Irish Education, 1921–75.” Sociology of
Education 66:41–62.
Rehberg, Richard A., and Evelyn R. Rosenthal. 1978. Class and Merit in the American
High School: An Assessment of the Revisionist and Meritocratic Arguments. New
York: Longman.
Rosenbaum, James E. 1976. Making Inequality. New York: Wiley.
———. 1980. “Track Misperceptions and Frustrated College Plans: An Analysis of the
Effects of Tracks and Track Perceptions in the National Longitudinal Survey.”
Sociology of Education 53:74–88.
Rosenbaum, James E., Shazia Rafiullah Miller, and Melinda Scott Krei. 1996.
“Gatekeeping in an Era of More Open Gates: High School Counselors’ Views of
Their Influence on Students’ College Plans.” American Journal of Education 104:
257–79.
Sebring, Penny, Barbara Campbell, Martin Glusberg, Bruce Spencer, and Melody
Singleton. 1987. High School 1980 Sophomore Cohort Third Follow-Up (1986) Data
File User’s Manual. Washington, D.C.: Center for Education Statistics.
Shavit, Yossi. 1993. “From Peasantry to Proletariat: Changes in the Educational
Stratification of Arabs in Israel.” Pp. 337–49 in Persistent Inequality: Changing
Educational Attainment in Thirteen Countries, edited by Yossi Shavit and HansPeter
Blossfeld. Boulder, Colo.: Westview Press.
Shavit, Yossi, and Hans-Peter Blossfeld. 1993. Persistent Inequality: Changing
Educational Attainment in Thirteen Countries. Boulder, Colo.: Westview Press.
Stevens, Gillian, and Joo Hyun Cho. 1985. “Socioeconomic Indexes and the New 1980
Census Occupational Classification Scheme.” Social Science Research 14:142–68.
Szele´nyi, Szonja, and Karen Aschaffenburg. 1993. “Inequalities in Educational
Opportunity in Hungary.” Pp. 273–302 in Persistent Inequality: Changing
Educational Attainment in Thirteen Countries, edited by Yossi Shavit and HansPeter
Blossfeld. Boulder, Colo.: Westview Press.
Treiman, Donald J., and Kazuo Yamaguchi. 1993. “Trends in Educational Attainment
in Japan.” Pp. 229–49 in Persistent Inequality: Changing Educational Attainment
in Thirteen Countries, edited by Yossi Shavit and Hans-Peter Blossfeld. Boulder,
Colo.: Westview Press.
Useem, Elizabeth. 1992. “Middle Schools and Math Groups: Parents’ Involvement in
Childrens’ Placement.” Sociology of Education 65:263–79.
Vaupel, James W., and Anatoli I. Yashin. 1985. “Heterogeneity’s Ruses: Some
Surprising Effects of Selection on Population Dynamics.” American Statistician 39:
176–85.
Vermunt, Jeroen K. 1997. Log-Linear Models for Event Histories. Thousand Oaks,
Calif.: Sage Publications.
Wells, Amy Stuart, and Jeannie Oakes. 1996. “Potential Pitfalls of Systemic Reform:
Early Lessons from Detracking Research.” Sociology of Education 69:E135–E143.
Wells, Amy Stuart, and Irene Serna. 1996. “The Politics of Culture: Understanding
Local Political Resistance to Detracking in Racially Mixed Schools.” Harvard
Educational Review 66:93–118.
Wiatrowski, Michael D., Stephen Hansell, Charles R. Massey, and David L. Wilson.
1982. “Curriculum Tracking and Delinquency.” American Sociological Review 47:
151–60.
Wilson, Bruce L., and Gretchen B. Rossman. 1993. Mandating Academic Excellence:
American Journal of Sociology
1690
High School Responses to State Curriculum Reform. New York: Teachers College
Press.
Yamaguchi, Kazuo. 1991. Event History Analysis. Newbury Park, Calif.: Sage
Publications.