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A Dynamic Model of Cultural Reproduction1
Mads Meier JægerUniversity of Copenhagen
Richard BreenYale University
The authors draw on Pierre Bourdieu’s theory of cultural reproduc-tion to develop a formal model of the pathways through which cul-tural capital acts to enhance children’s educational and socioeconomicsuccess. The authors’ approach brings conceptual and empirical clarityto an important area of study. Their model describes how parents trans-mit cultural capital to their children and how children convert culturalcapital into educational success. It also provides a behavioral frameworkfor interpreting parental investments in cultural capital. The authorsreview results from existing empirical research on the role of culturalcapital in education to demonstrate the usefulness of their model for in-terpretative purposes, and they use National Longitudinal Survey ofYouth 1979—Children and Young Adults survey data to test some ofits implications.
INTRODUCTION
Pierre Bourdieu’s theory of cultural capital and cultural reproduction is oneof the most influential explanations in social stratification research of whyinequalities in educational and socioeconomic outcomes persist over gen-erations. The theory outlines a complex system in which parents transmit cul-tural capital to children, children exploit their acquired cultural capital in the
AJS Volume 121 Number 4 (January 2016): 1079–1115 1079
1Earlier versions of this article were presented at the RC28 Meeting at the University ofVirginia, August 2012, and at research seminars at the University of Oxford, the Univer-sity of Turku, and the University of Copenhagen. We thank the AJS reviewers and DavidGrusky, Jan O. Jonsson, Paul Kingston, Karl-Ulrich Meyer, Wout Ultee, Tak Wing Chan,Michael Biggs, Juho Härkonen, and Martin Hällsten for constructive comments. The re-
© 2016 by The University of Chicago. All rights reserved.0002-9602/2016/12104-0003$10.00
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educational system, and, as a consequence, families who possess cultural cap-ital have an advantage that helps them reproduce their privileged socioeco-nomic position ðBourdieu 1977a, 1984; Bourdieu and Passeron 1990Þ.Despite the enormous popularity of the theory of cultural reproduction,
we know surprisingly little about how cultural capital gets transferred fromparents to children and whether it facilitates educational and socioeconomicsuccess. The reasons for these limitations are twofold: a lack of clarity inBourdieu’s theory of cultural reproduction and, partly as a consequence ofthis, a large body of empirical research that provides inconclusive results.There is agreement among interpreters of Bourdieu that core concepts andmechanisms are ill defined in his writings on cultural reproduction ðLamontand Lareau 1988; Kingston 2001; van de Werfhorst 2010Þ. For example,Bourdieu provides no consistent explanation of what cultural capital is,how parents transmit it to children, and how it leads to educational success.The lack of theoretical clarity has had a detrimental impact on empirical re-search, which is characterized by highly diverse approaches to measuringcultural capital, piecemeal tests of the theory of cultural reproduction, andlittle attention to identifying the causal pathways through which culturalcapital might lead to educational success ðKingston 2001; Sullivan 2002;Lareau andWeininger 2004; Goldthorpe 2007; Jæger 2011; Xu andHampden-Thompson 2012Þ.This article begins from the observation that the combination of a lack of
clarity in the theory, together with limitations in empirical research that hassought to test it, warrants a new approach to analyzing cultural reproduction.We argue that if the theory of cultural reproduction is to remain a relevantexplanation of intergenerational inequalities in educational and socioeco-nomic outcomes, it needs to provide a clear theoretical account of core con-cepts and mechanisms that can be tested empirically. Debates on the exactmeaning of Bourdieu’s writings on cultural reproduction have been ongoingfor decades ðDiMaggio 1982; Lamont and Lareau 1988; Mohr and DiMaggio1995; Swartz 1997; Kingston 2001; van de Werfhorst 2010Þ with no sign ofconsensus, suggesting that effort might better be spent rethinking the coreideas of cultural reproduction rather than attempting to clarify Bourdieu’soriginal thoughts.In this article we present a formal model, expressed verbally, mathemat-
ically, and diagrammatically, describing the process of cultural reproduction.Compared to previous research, the main benefit of our model is that it ex-
search leading to the results presented in this article has received funding from the Euro-pean Research Council under the European Union’s Seventh Framework Programmeð½FP/2007-2013�/ERC grant 312906Þ. Direct all correspondence toMadsMeier Jæger, Uni-versity of Copenhagen, Øster Farimagsgade 5, 1353 Copenhagen K, Denmark. E-mail:[email protected]
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plicates and formalizes the different mechanisms through which cultural cap-ital leads to educational and socioeconomic success. In doing so, it presentsan encompassing model of cultural reproduction that has been absent fromthe literature, that helps to organize and interpret results from existing re-search, and that may act as a starting point for future research that seeksto test cultural reproduction theory. Borrowing terminology from econom-ics, the model we present is structural: it attempts to describe all the relevantrelationships and presents the behavioral assumptions needed to interpret itsparameters. In our model, parents possess a stock of cultural capital thatthey transmit to children through active investments and through children’sexposure to cultural capital in the home. Children convert their acquiredcultural capital into educational performance within the educational system,which leads to higher educational attainment and later socioeconomic suc-cess, thereby completing the process of social reproduction.In addition to presenting a formal model of cultural reproduction, our
structural model provides a behavioral framework for interpreting the pa-rameters in this model. We do this to address Bourdieu’s lack of clarity aboutwhat motivates parents’ behavior. How do parents decide on how much oftheir cultural capital to invest in a child? How strong are parents’ beliefs thatcultural capital will yield a return in the future? In order to provide answersto these questions, we build on the assumption that parents invest in chil-dren’s cultural capital in the hope that these investments will promote chil-dren’s educational and socioeconomic success. It is not clear from Bourdieuwhether parents make cost-benefit calculations when attempting to trans-mit cultural capital to children or whether this process happens more or lessunconsciously. We take the position that the best point of departure for ana-lyzing cultural reproduction is to assume that parents have beliefs and goals,and, given their limitations on time, money, and information, they act toachieve these goals. We are explicit about behavioral assumptions becausethese are crucial for interpreting not only our model but also the results ofprevious empirical research. Most research documents positive correlationsbetween empirical indicators of cultural capital, such as how often parentstake children to cultural events and children’s educational success. However,assumptions about what drives parental behavior are needed to interpretthese correlations, and the lack of a clear behavioral framework in Bourdieumeans that there is little agreement on how to do this ðe.g., Do these corre-lations arise from deliberate investments or from parents’ unconsciously re-peating behavior learned through socialization?Þ. Our structural model pro-vides a framework for analyzing how differences in resources and beliefs ðe.g.,differences by race and socioeconomic group, which we discuss in detailÞ leadto different investments in cultural capital and to differences in educationaloutcomes. Thus, our model not only helps to organize results from previousresearch but also provides a framework for interpreting them.
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As a final contribution, our model also addresses two black boxes in thetheory of cultural reproduction. Although Bourdieu argued that parents trans-mit cultural capital to children throughout childhood, he does not explainhow the transmission takes place. Similarly, the way in which children con-vert cultural capital into educational achievements is underspecified.We pro-vide a dynamic account of both mechanisms. We draw on recent dynamicmodels of intergenerational transmissions ðTodd and Wolpin 2007; Cunhaand Heckman 2008; Bisin and Verdier 2011Þ and treat childhood as a se-quence of time periods during which parents invest in transmitting culturalcapital to children. In our model, parents may change their investments overtime.Thismay be because of limitations on resources ðdue to events such as un-employment or illnessÞ, outcomes of past investments in cultural capital ðwhichmay or may not have yielded a returnÞ, or investments in other child skillsðe.g., cognitive or social skillsÞ. We also provide a dynamic account of howchildren convert cultural capital into educational performance. In each timeperiod the child converts his or her cultural capital into educational perfor-mance by affecting teachers’ perceptions of his or her academic ability, whichleads to greater teacher inputs ðe.g., of attention and helpÞ and better perfor-mance. Thus, in addition to describing the outcome of cultural reproduction,we provide an account of the process of cultural reproduction.To demonstrate the usefulness of our model, we provide illustrative em-
pirical evidence on the dynamic nature of cultural capital investments. We uselongitudinal data from the National Longitudinal Survey of Youth 1979—Children and Young Adults ðNLSY-CYAÞ and estimate dynamic panel datamodels describing, first, how parents invest over time in transmitting theircultural capital to children and, second, how cultural capital affects educationalperformance. Our findings suggest that children accumulate cultural capitalfrom parents and, furthermore, that cultural capital has a positive effect oneducational performance. And althoughwe lack direct data on teacher inputsin children, the empirical results are consistent with our model. We also findthat parents adjust their investments in cultural capital on the basis of whatthey believe to be the educational payoffs of past investments; a finding thatis also consistent with our model.In summary, while we seek to provide a new conceptual framework for
analyzing cultural reproduction, we do not claim to have captured everyaspect of Bourdieu’s thoughts: our model builds on our interpretation of thetheory of cultural reproduction. However, the model we propose is flexible,in the sense that it can be extended to cover more complex situations, keyparameters can be modified in light of new theoretical or empirical insights,and the behavioral assumptions underlying our interpretation of mecha-nisms and parameters are open to modification. We hope, therefore, that itwill stimulate research on the potentially complex ways in which culturalcapital may facilitate educational and socioeconomic success. Furthermore,
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because our model is expressed in mathematical terms, it is highly transpar-ent, so its empirical implications can readily be derived and tested.In the next section of the article we review the basic elements of Bourdieu’s
theory. Then follows the development of our theory, first in static then in dy-namic form. Next we provide a review and reinterpretation of results fromprevious research to illustrate the usefulness of our approach, followed byempirical analyses that involve direct testing of the dynamic aspects of ourmodel using the NLSY-CYA data. In the article’s conclusion we summarizeour arguments and results and consider some of the ways in which our modelcould be extended.
CULTURAL REPRODUCTION THEORY
The theory of cultural reproduction provides an explanation of the inter-generational reproduction of socioeconomic position. Bourdieu argued thatindividuals and families possess resources in the form of different types ofcapital—economic, social, and cultural—that can be invested to generate moreresources or converted from one type of capital into another ðBourdieu 1977a,1986; Bourdieu and Passeron 1990Þ. Economic capital refers to all forms ofeconomic resources ðincome, wealth, property, etc.Þ, while social capital re-fers to gainful social networks ðBourdieu 1986Þ.Although Bourdieu’s definition of cultural capital is far from clear ðLamont
and Lareau 1988; Kingston 2001; van de Werfhorst 2010Þ, at the most gen-eral level it refers to familiarity with the dominant culture in a society. Lamontand Lareau ð1988, p. 156Þ proposed an influential definition of cultural capitalas “widely shared, high-status cultural signals ðattitudes, preferences, formalknowledge, behaviors, goods and credentialsÞ used for social and cultural ex-clusion.”We follow this definition in the current article. As with economic andsocial capital, cultural capital is a resource that can be invested in order topromote one’s relative position within a social hierarchy populated by in-dividuals with different compositions and amounts of capital. Cultural capi-tal exists in three states—embodied ðlinguistic competence, mannerisms, cul-tural knowledge, etc.Þ, objectified ðcultural goods, paintings, books, etc.Þ, andinstitutionalized ðeducational credentials; Bourdieu 1977a, 1986; Bourdieuand Passeron 1990Þ—and it can contribute to social reproduction in all threestates.According to Bourdieu, cultural reproduction is an important mecha-
nism through which social reproduction takes place. Society is composedof different fields, that is, subsystems in which the different types of capitalcarry different weight ðBourdieu 1986Þ. Education is a major subfield, andone in which cultural capital is particularly important. Bourdieu argues thatthe educational system is biased toward valorizing cultural capital, ascribingpositive qualities to individuals and families that possess it. This bias arises
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from cultural capital being associated with high culture and social status,and it means that the embodied cultural capital that students put “on display”in school conveys an impression of academic brilliance that leads to favorabletreatment by teachers and to educational success. Thus, cultural capital createsa false impression of academic brilliance that yields a real return in the formof educational success. Since families in advantaged socioeconomic positionstend to possess more cultural capital than those in less advantaged positions,and because children tend to inherit capital from parents, cultural capital con-tributes to social reproduction by increasing the likelihood of educational suc-cess ðinstitutionalized cultural capitalÞ and subsequent socioeconomic successðbecause socioeconomic position in adulthood is heavily dependent on edu-cational credentialsÞ.
Intergenerational Transmission of Cultural Capital
We begin the presentation of our formal model with a simple version de-scribing the intergenerational transmission of cultural capital. We let C de-note the child’s cultural capital and subscripts c and P, respectively, the childand parents. For now we assume that there is only one child in the family.Cultural reproduction theory argues that parents possess a stock of culturalcapital and furthermore that they transmit some of this to their child. Trans-mission of cultural capital takes place through two channels: parents activelyinvesting in transmitting their cultural capital to their child ðe.g., by taking thechild to the theater and by reading to the childÞ and the child passively acquir-ing cultural capital via exposure to objectified cultural capital in the homeðe.g., works of artÞ. The child’s acquisition of cultural capital also dependson family resources other than cultural capital ðe.g., parents’ socioeconomic re-sourcesÞ and on the child’s academic ability. We let S denote parents’ totalstock of cultural capital and v the amount that they actively invest in the child.We thenwrite
Cc 5 b1vp 1 b2Sp 1 b3Xp 1 b4Ac 1 Lc; ð1Þwhich states that the child’s cultural capital depends on parents’ active in-vestments in transmitting their cultural capital to the child ðb1vpÞ and on thechild’s passive exposure to cultural capital in the home ðb2SpÞ. The returnðin terms of the child’s cultural capitalÞ to parental investments in the child’scultural capital is b1, and b2 is the “passive” rate of transfer of cultural capi-tal from parents to the child. The child’s cultural capital also depends on par-ents’ socioeconomic resources Xp, the child’s academic ability Ac ðwhich weassume to be constant over timeÞ, and luck L. The relative sizes of b1 and b2
are not clear from Bourdieu’s writings, but both are assumed to be greaterthan zero. Below, we review research that provides empirical estimates ofb1 and b2.
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Cultural Capital, Educational Success, and Social Reproduction
In addition to accounting for parental transmission of cultural capital tochildren, cultural reproduction theory argues that children convert theirðembodiedÞ cultural capital into educational success ðinstitutionalized cul-tural capitalÞ, which in turn promotes socioeconomic success. Consequently,cultural capital is a means to an end. Bourdieu ð1986, p. 247Þ writes thatcultural capital is “a symbolically and materially active, effective capitalinsofar as it is appropriated by agents and implemented.” He furthermorewrites that “academic success is directly dependent upon cultural capitaland on the inclination to invest in the academic market” ðBourdieu 1977a,p. 504Þ.2It is not entirely clear from Bourdieu how children convert their embod-
ied cultural capital into educational success. He argues that the educationalsystem is intrinsically biased toward misconceiving cultural capital as aca-demic brilliance, and, as a consequence, children who possess cultural capi-tal use it to present an impression of brilliance that is rewarded by teachersðBourdieu and Passeron 1990; Moore 2004Þ. The reason teachers miscon-ceive cultural capital as academic brilliance is that it signals familiarity withhigh culture and social status, and, as a consequence, teachers implicitlyassociate cultural capital with other desirable qualities ðGanzeboom 1982;Crook 1997Þ. Bourdieu uses the concept of the habitus to capture the waysin which children’s cultural capital, acquired from parents and manifestedin values, tastes, and behaviors, helps to create such an impression ðBourdieu1977bÞ. And although the impression of academic brilliance associated withcultural capital is false ðin the sense that, unlike economic capital, culturalcapital has no intrinsic value other than that ascribed to itÞ, its consequencesare real. Children who possess cultural capital are perceived as more aca-demically gifted than children who do not ðthus leading to better subjectiveevaluations by teachers and better gradesÞ. Moreover, they are treated in amore favorable way by teachers, which may lead to a better learning envi-ronment and so to better educational performance.3 Thus, it follows that themain channel through which embodied cultural capital is converted into in-stitutionalized cultural capital ðeducational credentialsÞ is through educa-tional performance. We now incorporate this idea into our model. Specifi-
2 In their influential paper, Lamont and Lareau ð1988, p. 154Þ interpret Bourdieu’s writ-ings as follows: “Indeed, they ½Bourdieu and Passeron� argued that individuals’ socialposition and family background provide them with social and cultural resources whichneed to be actively ‘invested’ to yield social profits.”3Bourdieu’s idea that teachers are inclined toward valorizing cultural capital has someempirical merit. For example, DiMaggio ð1982Þ cites research showing that althoughteachers are often recruited from the lower middle class, they are overrepresented amongconsumers of highbrow culture. In her qualitative study, Lareau ð2003, pp. 14–32Þ findsthat teachers place high value on pupils’ cultural activities and actively promote such ac-tivities among their own children.
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cally, letting Ec denote final educational attainment, Pc educational perfor-mance, and U and J luck, we write
Ec 5 h1Pc 1 h2Xp 1 h3Ac 1Uc;
Pc 5 j1Cc 1 j2Ac 1 Jc:ð2Þ
Equation ð2Þ states that final educational attainment depends on educa-tional performance, but furthermore that educational performance dependson the child’s cultural capital and on academic ability. Consequently, the pa-rameter j1 captures the “bonus” to educational performance from the im-pression of academic brilliance generated by cultural capital ðnet of the effectof actual ability AÞ. Cultural reproduction theory tells us that j1 > 0. Fur-thermore, the parameter h1 captures the effect of educational performanceon final educational attainment ðagain, net of actual academic abilityÞ, andwe assume h1 > 0. Note that the reason we use different letters across equa-tions to capture the luck component is that the factors that go into this com-ponent need not be the same across the different outcomes that the equationsdescribe.The final stage in cultural reproduction theory is the link between edu-
cational attainment ðinstitutionalized cultural capitalÞ and socioeconomic suc-cess. Letting Yc denote the child’s socioeconomic position in adulthood andQ luck, we write
Yc 5 r1Ec 1 r2Xp 1 r3Ac 1 Qc: ð3ÞIn this model cultural capital has no direct effect on socioeconomic successbut nevertheless contributes to it by improving educational performance,which in turn facilitates educational success, which directly affects socio-economic position ðso we assume r1 > 0Þ.
A DYNAMIC MODEL OF CULTURAL REPRODUCTION
The model presented above summarizes the main features of cultural repro-duction theory. Equation ð1Þ describes how parents transmit their culturalcapital to the child, equation ð2Þ describes how cultural capital is convertedinto educational success, and equation ð3Þ describes how educational successis converted into socioeconomic success. These are the basic building blocksin the theory of cultural reproduction. Our model, however, and Bourdieu’swritings on cultural reproduction, does not describe the actual mechanismsthat lead to the outcomes summarized in equations ð1Þ–ð3Þ. Building on re-cent models of intergenerational transmissions in economics ðTodd andWolpin 2007; Cunha andHeckman 2008; Bisin and Verdier 2011Þ, we nowextend our model to address two important black boxes in Bourdieu’s writ-ings: ð1Þ the mechanism through which parents invest in transmitting cultural
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capital to the child and ð2Þ the mechanism through which the child convertscultural capital into educational success.A necessary condition for the theory of cultural reproduction to be con-
sistent is that children acquire cultural capital from parents. In our model,we explicate this condition by assuming that b1 > 0 and b2 > 0. Bourdieuð1986, p. 249Þ writes that “the initial accumulation of cultural capital, theprecondition for the fast, easy accumulation of every kind of useful cul-tural capital, starts at the outset, without delay, without wasted time. . . .The accumulation period covers the whole period of socialization.” We takethis formulation to suggest that children accumulate cultural capital through-out childhood and, furthermore, that parents actively seek to transmit theircultural capital to their child. We now extend our model to accommodate thisidea.After the child’s birth, parents have a finite time horizon in which they
can invest in her cultural capital ðand in other endowments that facilitateeducational success, such as human capitalÞ. We assume that parents seekto transmit as much as possible of their cultural capital to the child, and theybegin investing when the child is young ðbelow, we discuss parents’ invest-ment strategies in detailÞ. For the purposes of our model, we represent child-hood as divided into T time periods ðt 5 1, . . . , TÞ, beginning at birthand ending at the time the child leaves compulsory education ðaround age16 in most countriesÞ.4 As described in equation ð2Þ, returns to cultural cap-ital are manifest in educational performance, in the form of grades, testscores, or placement in a prestigious educational track. This occurs becausecultural capital conveys an impression of academic brilliance, leading to fa-vorable evaluations, more attention, and ultimately better performance ðcap-tured by the parameter j1 in eq. ½2�Þ. However, equation ð2Þ is silent as to themechanism through which cultural capital is converted into educational per-formance, and we now address that issue. We write
Pct 5 a1Tt 1 a2Ac 1 a3Xpt 1Wct;
Tt 5 J1Pct21 1 J2Cct 1 Vct;ð4Þ
where Pct is educational performance at time t, Tt is teacher inputs ðeval-uations, attention, etc.Þ, Cct is the child’s cultural capital, A is academic ability,and Xpt is parental resources. Variables W and V capture the influence ofluck and other unmeasured factors that affect performance and teacher in-puts, respectively. Equation ð4Þ states that cultural capital affects educational
4Parents may still transmit cultural capital to the child after age 16. However, we in-terpret Bourdieu as suggesting that the main thrust of parental investments in culturalcapital takes place when the child is comparatively young. Also, it may be difficult forparents to transmit cultural capitalwhen the child has left the home, for example, to attendhigher education. Instead, parents may rely on their economic or social capital.
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performance by improving teachers’ evaluations of the child ðvia J2Þ that, inturn, determine the inputs teachers provide to the child ðvia a1Þ. We expectJ2 > 0 ðmore cultural capital leads to higher teacher inputsÞ and a1 > 0 ðhigherteacher inputs lead to better educational performanceÞ. Our model also statesthat teachers’ inputs in period t depend on the child’s educational per-formance in the previous period: teachers are not myopic, and they adjusttheir inputs in the child on the basis of her past educational performanceðso, we expect J1 > 0Þ. Equation ð4Þ thus describes the mechanism throughwhich embodied cultural capital is converted into educational performance.High educational performance during compulsory school leads to high edu-cational attainment ðeq. ½2�Þ, which in turn leads to high socioeconomic sta-tus ðeq. ½3�Þ, thus completing the process of social reproduction.Moving back in the causal chain, we now describe the mechanism through
which parents invest in transmitting cultural capital to their child. Parentspossess a stock of cultural capital, S. In each time period they actively in-vest amount v in their child. In addition, the child acquires cultural capitalvia passive exposure to cultural capital in the home. Finally, given the cu-mulative nature of cultural capital formation, the child’s stock of culturalcapital at time t also depends on how much cultural capital she had in theprevious period. Putting these components together, we write the processthrough which the child acquires cultural capital:
Cct 5 g1Cct21 1 g2vpt 1 g3Sp 1 g4Xpt 1 g5Ac 1 Lct: ð5Þ
Equation ð5Þ states that the child’s stock of cultural capital in period tdepends on her stock in the previous period, her parents’ active invest-ments in the present period, her passive exposure to cultural capital in thehome, and other factors. On the basis of cultural reproduction theory, weexpect g1 > 0, g2 > 0, and g3 > 0; that is, we expect the child to have morecultural capital in the present period if she had more cultural capital in theprevious period and if parents invest more in cultural capital. Note that vtcan be larger than S since parents may try to inculcate cultural capital intheir child that they do not themselves possess, for example, by organizingsuitable out-of-school activities.
WHAT MOTIVATES PARENTS’ INVESTMENTS?
In his writings, Bourdieu devotes little attention to describing what parentsactually do to transmit their cultural capital to children. In relation to ourmodel, this means that it is not clear from cultural reproduction theory howparents decide how much of their cultural capital to invest in each time pe-riod, and, consequently, the preferences and behaviors that generate theparameters a1, g1, g2, and g3 are unspecified.
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We combine the two mechanisms described in equations ð4Þ and ð5Þand propose a behavioral framework for interpreting the parameters inthese equations. We assume that parents are utility maximizers who seekto transmit as much as possible of their cultural capital to the child, but theymay differ in their beliefs about the returns to investments in cultural capital.We realize that this approach departs from a conventional interpretation ofBourdieu, but we find it more analytically meaningful than simply assumingthat parents more or less unconsciously reproduce behaviors learned throughsocialization. Moreover, our approach is motivated by an influential body ofempirical research that documents that, at least in the U.S. context, middle-class parents deliberately and strategically organize children’s time and lei-sure activities with the intent of cultivating their cognitive and social skillsðLareau 1989, 2003; Calarco 2014Þ.5We begin by specifying a model for the different factors that determine
the child’s educational performance. Putting together equations ð4Þ andð5Þ yields the following expression for the child’s performance in time pe-riod t:
Pct 5 a1½J1Pct21 1 J2Cct 1 Vt�1 a2Ac 1 a3Xpt 1Wct
5 a1J1Pct21 1 a1J2½g1Ct21 1 g2vpt 1 g3Sp 1 g4Xpt 1 g5Ac 1 Lt�
1 a2Ac 1 a3Xpt 1 a1Vct 1Wct
5 a1J1Pct21 1 a1J2g1Ct21 1 a1J2g2vpt 1 a1J2g3Sp 1 ða1J2g5 1 a2ÞAc
1 ða1J2g4 1 a3ÞXpt 1 a1J2Lct 1 a1Vct 1Wct
5m0Pct21 1m1Ct21 1m2vpt 1m3Sp 1m4Ac 1m5Xpt 1 εct:
ð6ÞIn this model, the child’s educational performance in time t depends on herperformance in the previous period, her cultural capital, parents’ active invest-ments in cultural capital, passive exposure to cultural capital, academic
5Lareau ð2003, p. 238Þ summarizes some of her key findings as follows: “In these ½mid-dle class� families, parents actively fostered and assessed their children’s talents, opinions,and skills. They scheduled their children for activities. They reasoned with them. Theyhovered over them and outside the home they did not hesitate to intervene on the chil-dren’s behalf. They made a sustained and deliberate effort to stimulate children’s devel-opment and to cultivate their cognitive and social skills.” Lareau also argues that the pro-pensity to invest in children, and beliefs about returns to investments, varies by social classbackground. Below, we discuss how our model accommodates this idea.
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ability, and parental resources, as well as a term capturing luck, εct.6 Theweight of each component is captured by the parameter m ðm 5 0, . . . , 5Þ.No one knows the true values of the parametersm ði.e., the values that max-imize the child’s educational performanceÞ, but parents have beliefs aboutall of them originating in past experiences and socialization ðHaller 1982;Kerckhoff 1989Þ. Our model thus states that parents differ in the extent towhich they believe that the child’s past performance, her cultural capital,parents’ own investments in cultural capital, and other factors affect theirchild’s educational performance. We believe these assumptions are in linewith cultural reproduction theory. Given the available information and theirbeliefs about m, parents must choose how much of their stock of culturalcapital ðSÞ they wish to invest ðvÞ in each time period. We assume that par-ents seek to maximize utility; that is, they wish to make the optimal in-vestment in each period given their beliefs and resources. We write theobjective function that parents want to maximize in each time period:
mPct 2 cðvptÞ: ð7ÞThe objective function has two components that reflect the benefits andcosts of investing cultural capital in the child’s educational performance.The parameter m captures altruism ðalthough all parents care about theirchild’s educational performance, some care more than othersÞ and parents’beliefs about the importance of educational performance relative to otherfactors that might affect their child’s socioeconomic outcomes.7 The termcðvptÞ is a cost function: it captures the costs associated with investing in thechild’s cultural capital. Costs principally include time and resources thatcould have been used for other purposes ðe.g., investments in other types ofskillsÞ.How do parents decide howmuch of their cultural capital to invest in each
time period? Bourdieu provides no answer to this question, and we need tomake several assumptions in order to provide one. Our first assumption isthat, given their beliefs about the values of m, parents choose the optimuminvestment, v*pt, by finding the value of vpt that maximizes the objective func-tion described in equation ð7Þ. In other words, we assume that parents choosewhatever amount of investment they think will yield the highest return for agiven cost. Our second assumption is that yccðvpÞ=yvp is greater than zero.This means that parents incur greater costs, the greater their active invest-ment in the child’s cultural capital, or, put differently, high investments are
6The error term in eq. ð6Þ is given by εct 5 a1J2Lt 1 a1Vt 1 Wt.7Some families may use means other than education to promote social reproductionðe.g., social connections or moneyÞ. Families may also invest in other types of skills, e.g.,social skills, or simply in making their child happy. Our model focuses on parents’ in-vestments in cultural capital, and investments in other types of skills enter our modelthrough the cost function that is described next.
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more costly than low investments. Our third assumption is that parents’ rel-ative cost of investing in cultural capital decreases with the size of theiroverall stock of cultural capital, S. This means that it is less costly for parentswho have a lot of cultural capital to invest in their child’s cultural capitalcompared with parents who have little cultural capital. Combining theseassumptions, and letting the term hv capture our third assumption that therelative cost of investing in cultural capital decreases when the stock of cul-tural capital S increases ðand where h is smaller, the larger is the stock ofparental cultural capitalÞ, the optimum investment at time t is
v*pt 5mm̂2t
h: ð8Þ
Here, m̂2t is parents’ belief at time t in the return ðin terms of the child’seducational performanceÞ to active investment in the child’s cultural cap-ital. Equation ð8Þ shows that the optimum investment at time t is given bythe combination of parents’ beliefs about the returns to investing in culturalcapital m̂2t and their altruism m weighted by the cost of making the invest-ment, which, as noted, is smaller for parents with a greater stock of culturalcapital. In other words, the optimum investment is the one that reconcilesparents’ expectations about which investment will generate the highest re-turn, how much they care about their child’s educational performance, andhow costly it is for them to make the investment. It also follows from ourmodel that
yv*ptySp
> 0;yv*ptym
> 0;yv*ptym̂2
> 0;
that is, parents invest more when they have a greater stock of culturalcapital, when they care more about their child’s educational performance,and when they believe that investing in their child’s cultural capital has abigger payoff in terms of educational performance. We believe these as-sumptions are consistent with Bourdieu’s idea that cultural capital is prin-cipally a means for those who possess cultural capital to promote socialreproduction.Finally, we need to consider how parents’ beliefs about the returns to
cultural capital, m̂2, evolve over time. Bourdieu does not provide any in-sights into how parents might change their beliefs about the usefulness ofinvestments in cultural capital. Instead, we draw on research that suggeststhat parents use information on the outcomes of past investments to de-cide on current investments ðBehrman 1997; Ayalew 2005; Todd andWolpin2007Þ. This research emphasizes that a feedback mechanism exists from thechild’s behavior to parents’ beliefs and investments. Building on this re-search, we propose in our model that parents use new information about thechild’s educational performance from grades and test scores to inform their
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belief about the returns to investing in cultural capital. We implement thisidea by assuming that parents update their belief according to the follow-ing rule:
m̂2t 5 m̂2t21 11 pPct21 2 Pct22
vt21 2 vt22
� �� �: ð9Þ
Equation ð9Þ captures the idea that if increases ðdecreasesÞ in culturalcapital investments, v, between one period and the next are associated withincreases ðdecreasesÞ in educational performance ði.e., the sign of vt21 2 vt22
is the same as the sign of Pct21 2 Pct22Þ, then parents increase their beliefabout the size of m2, whereas, if they have opposite signs, their belief de-clines. In other words, if investing in cultural capital seems to pay off, par-ents strengthen their belief in the value of such investments; otherwise,their belief diminishes. The degree to which their belief increases or de-creases for a given change in performance, relative to a change in invest-ment, is captured by the adjustment parameter, p. Below, we provide il-lustrative empirical evidence that parents adjust their investments in culturalcapital in light of the outcomes of past investments.Figure 1 provides a summary of the main parts of our dynamic model.
For ease of presentation, we do not show either the “luck” ðor errorÞ terms ofour equations or the effects of the X variables, and we show the underlyingrelationships at only two points in time. The notation in the figure is thesame as in the equations. The underlying logic of the model is very straight-
FIG. 1.—Dynamic model of cultural reproduction
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forward. Parents’ investment in their child’s cultural capital helps to de-termine the child’s cultural capital. This influences teachers’ perceptionsof ðand inputs inÞ the child, which, in turn, affects the child’s educationalperformance. The child’s educational performance leads parents to updatetheir investment, and this new investment, together with existing culturalcapital, shapes the child’s later cultural capital, which affects teacher per-ceptions, and so on. This process continues throughout the period of com-pulsory schooling, eventually leading to final educational attainment, whichaffects socioeconomic success.
IMPLEMENTING OUR MODEL
In the remainder of the article, we illustrate the usefulness of our model forpast and future research on cultural reproduction. First, we argue that ourmodel helps to organize results from previous research that has sought to testcultural reproduction theory. Second, we argue that our model can be used toimprove interpretations of results from a wide range of research that usescultural reproduction theory to explain persisting socioeconomic differencesin educational success ðe.g., differences by race and social classÞ. Third, weuse data from the NLSY-CYA to provide an illustrative test of the assump-tion in our model that the processes through which children accumulatecultural capital from parents and convert this capital into educational per-formance are dynamic.
Organizing Previous Research
We begin by using our theoretical model to organize previous empirical re-search on cultural capital and educational success. Table 1 summarizes theoperational measures of cultural capital used in each study in our reviewðdistinguishing indicators of highbrow culture, reading climate, educationalresources, cultural communication, and extracurricular activitiesÞ, the mainfinding, and the country in which the study was conducted. The table showsthat previous empirical research can be classified into three groups focusingon, respectively, ðaÞ the link between parents’ and children’s cultural capital,ðbÞ the direct effect of cultural capital on educational success, and ðcÞ the waysin which cultural capital is converted into educational success.From the perspective of our model, research that addresses the transmis-
sion of cultural capital from parents to children seeks to identify the param-eters b1 and b2 in equation ð1Þ. This research includes indicators of parents’active investments in cultural capital ðcultural activities, cultural communi-cation, etc.Þ and their passive cultural capital ðcultural objects, books, etc.Þand relates these measures to children’s cultural capital. Most studies findthat there is a positive correlation between parents’ cultural capital ðboth
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TABLE
1SummaryofResultsfrom
PreviousResearch
Study
Dim
ension
ofCulturalCap
ital
MainResult
Cou
ntry
Transm
ission
ofculturalcapital
from
parents
tochild
ren:
Kraaykam
pð2003Þ
...........................
RPositiveeffect
Netherlan
ds
Georg
ð2004Þ
................................
H/R/C
Positiveeffect
German
yKraaykam
pan
dvan
Eijck
ð2010Þ
................
HPositiveeffect
Netherlan
ds
Yaish
andKatz-Gerro
ð2012Þ
...................
HPositiveeffect
Israel
Culturalcapital
andeducation
alsuccess:
Outcom
e—acad
emic
achievem
ent:*
DiM
aggioð1982Þ
...........................
HPositiveeffect
United
States
DeGraaf
ð1988Þ
...........................
RPositiveeffect
German
yKatsillisan
dRub
insonð1990Þ
.................
HNoeffect
Greece
Dow
ney
ð1995Þ
............................
H/E
Positiveeffect
United
States
Sullivan
ð2001Þ
............................
HPositiveeffect
United
Kingd
omDumaisð2002Þ
.............................
HPositiveeffect
United
States
Eitle
andEitle
ð2002Þ
.......................
H/E
Mainly
positiveeffect
United
States
Cheungan
dAndersenð2003Þ
.................
RPositiveeffect
United
Kingd
omBaron
eð2006Þ
.............................
H/C
Positiveeffect
25coun
tries
Lee
andBow
enð2006Þ
......................
CPositiveeffect
United
States
Van
deWerfhorst
andHofstedeð2007Þ
..........
HPositiveeffect
Netherlan
ds
Bod
ovskian
dFarkas
ð2008Þ
..................
H/R/X
Positiveeffect
United
States
Cheadle
ð2008Þ
............................
H/C
Positiveeffect
United
States
Jægerð2009Þ
..............................
H/E/C
Positiveeffect
Denmark
Wild
hagen
ð2009Þ
..........................
HPositiveeffect
United
States
Cov
ayan
dCarbon
aroð2010Þ
.................
XPositiveeffect
United
States
Flere
etal.ð2010Þ
..........................
HPositiveeffect
Slovenia
Tramon
tean
dWillmsð2010Þ
.................
H/C
Positiveeffect
28coun
tries
Jægerð2011Þ
..............................
H/R/X
Positiveeffect
United
States
Byu
n,Schofer,an
dKim
ð2012Þ
................
HPositiveeffect
Sou
thKorea
Xuan
dHam
pden-T
hompsonð2012Þ
............
H/C/E
Positiveeffect
22coun
tries
Gad
disð2013Þ
.............................
H/R
Positiveeffect
United
States
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Study
Dim
ension
ofCulturalCap
ital
MainResult
Outcom
e—education
alattainment:y
DiM
aggioan
dMoh
rð1985Þ
...................
HPositiveeffect
Denmark
DeGraaf
ð1986Þ
...........................
H/R
Mainly
positiveeffect
Netherlan
ds
Teachman
ð1987Þ
..........................
EPositiveeffect
United
States
Graetzð1988Þ
.............................
HPositiveeffect
Australia
Kalmijnan
dKraaykam
pð1996Þ
...............
HPositiveeffect
United
States
Ascha
ffenbu
rgan
dMaasð1997Þ
...............
HPositiveeffect
United
States
Roscign
oan
dAinsw
orth-D
arnellð1999Þ
.........
H/E
Positiveeffect
United
States
DeGraaf,deGraaf,an
dKraaykam
pð2000Þ
......
H/R
Positiveeffect
Netherlan
ds
Georg
ð2004Þ
..............................
H/R
Positiveeffect
German
yKau
fman
andGab
lerð2004Þ
..................
XPositiveeffect
United
States
Jægeran
dHolm
ð2007Þ
......................
H/R
Positiveeffect
Denmark
Evan
set
al.ð2010Þ
.........................
RPositiveeffect
27coun
tries
Yam
amotoan
dBrintonð2010Þ
...............
H/R
Positiveeffect
Japan
Effectof
cultural
capitalon
teachers’
perception
s:z
Farkas
etal.ð1990Þ
...........................
Appearan
ce,ab
senteeism
,disruptiveness,workhab
its
Positiveeffect
ofstudentSESon
teacher
rating
ofclassroom
skills
United
States
Tak
ei,Johnson,an
dClark
ð1998Þ
................
XNoeffect
ofculturalcapital
onteacher
rating
ofstudent’sclassroom
skills
United
States
Roscign
oan
dAinsw
orth-D
arnellð1999Þ
...........
H/E
Teacher
perception
sof
student’saca-
dem
icskillsmediatessomeof
theef-
fect
ofculturalcapital
onacad
emic
achievem
ent
United
States
Dumaisð2006Þ
..............................
HPositiveeffect
ofculturalcapitalon
teacher
ratings
ofstudent’slangu
age
andmathskills;how
ever,effect
for
low-SESchild
renon
ly
United
States
Bod
ovskian
dFarkas
ð2008Þ
....................
H/R/X
Noeffect
ofindex
of“con
certed
culti-
vation”on
teacher
rating
ofstudent’s
acad
emic
skills
United
States
Wild
hagen
ð2009Þ
............................
HNoeffect
ofculturalcapital
onteacher
rating
ofstudent’sclassroom
skills
United
States
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TABLE
1(Con
tinued)
Study
Dim
ension
ofCulturalCap
ital
MainResult
Cou
ntry
Dumais,Kessinger,an
dGhoshð2012Þ
.............
Parentalinvolvem
ent
ðvolunteeringÞ
Effectof
parentalinvolvem
enton
teacherratingof
child
ren’s
acad
emic
skillsvariesbyparentalSES
United
States
Lareauð1987,
1989,2003Þ;Lareauan
dHorvat
ð1999Þ
...........................
Xð1ÞP
arents
use
extracurricularactivities
tofoster
culturalcapitalin
child
renan
dð2Þp
arents
use
cultural
capital
topro-
motechild
ren’s
successin
school;ð3Þv
ari-
ationsin
effectsbySESan
drace
United
States
NOTE.—
Typ
eof
culturalcapitalmeasure:H
5highbrow
culture,E
5education
alresources/objects,C
5cultural
communication/in
teraction/in
volvem
ent;
X5
extracurricularactivities;R
5read
ingbehav
ior/clim
ate.
*GPA,test
scores,etc.
yYears
ofscho
oling,
college
completion
,etc.
zTeachers’
perception
sof
child
ren’s
acad
emic
ability.
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active investments and passive cultural capitalÞ and children’s cultural cap-ital, thereby establishing that, as we argue in our model, cultural capital ispassed on from parents to children ðb1 > 0, b2 > 0Þ.Research that addresses the direct effect of cultural capital on educational
success ðwhich makes up the majority of existing empirical researchÞ ana-lyzes the effect of cultural capital on different measures of educational achieve-ment. In the terminology of our model, this research can be conceptualizedas directly identifying j1 in equation ð2Þ ðthe positive effect of cultural cap-ital on educational performanceÞ or, if the outcome variable is final educa-tional attainment, indirectly identifying this effect through h1 ðthe effect ofeducational performance on final educational attainment that is attributableto cultural capitalÞ. Table 1 shows that most studies report a positive corre-lation between cultural capital and educational success, thereby suggestingthat embodied cultural capital is converted into educational performance andattainment.Finally, research that addresses the effect of cultural capital on teachers’
perceptions of children deals with the mechanisms that lead to the expectedpositive sign of j1 in equation ð2Þ. After controlling for observable academicability, some studies find that indicators of children’s cultural capital arepositively correlated with teachers’ perceptions of children’s academic andsocial skills. This research corroborates the assumption in cultural repro-duction theory and in our model that the reason j1 is positive—even aftertaking children’s actual academic ability into account—is due to systematicmisrecognition of cultural capital as academic ability.Our review of previous research on cultural capital and educational suc-
cess from the perspective of our model shows that this research has ad-dressed, and found empirical support for, some of the core hypotheses incultural reproduction theory. However, our review also highlights that thestudies summarized in table 1 test parts of Bourdieu’s theory rather than thewhole. To our knowledge, no research has attempted to analyze the theoryof cultural reproduction in its structural form, that is, specifying and testingall the causal pathways through which cultural capital leads to educationaland socioeconomic success. Again borrowing terminology from economics,all of the studies listed in table 1 are “reduced form” in the sense that theytest only a subset of empirical implications of the theory of cultural repro-duction, in particular the implication that cultural capital has a direct posi-tive effect on educational success. And although this research has yieldedimportant insights into the link between cultural capital and educational suc-cess, at present we have no empirical evidence on whether parental invest-ments in cultural capital in childhood actually lead to socioeconomic successin adulthood ði.e., to social reproductionÞ. An advantage of our structuralmodel is that it could be used as a starting point for analyzing the entire
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causal chain through which investments in cultural capital lead to socialreproduction.
Better Interpretations of Past Research
In addition to organizing results from previous research, our model pro-vides a new framework for interpreting results from research that has usedcultural reproduction theory to explain persisting socioeconomic differencesin educational outcomes. In what follows, we use our model to reinterpretfindings from three influential lines of research that have analyzed ðaÞ black-white differences in educational outcomes, ðbÞ social class differences in edu-cational outcomes, and ðcÞ institutional differences in returns to culturalcapital. The objective of this section is to demonstrate that our model ac-commodates a wide range of proposed explanations of why cultural capitalmight account for socioeconomic differences in educational outcomes.Black-white differences.—Drawing on Bourdieu, several studies argue
that black-white differences in educational attainment in the United Statesare partly mediated by cultural capital ðFarkas et al. 1990; Farkas 1996;Kalmijn and Kraaykamp 1996; Lareau and Horvat 1999; Roscigno andAinsworth-Darnell 1999Þ. Explanations of why cultural capital mediatesthese differences build on empirical observations that blacks are ð1Þ lesslikely to participate in highbrow cultural activities than whites ðDiMaggioand Ostrower 1990; Kalmijn and Kraaykamp 1996Þ, ð2Þ less likely to orga-nize cultural trips or extracurricular activities for their children ðRoscignoand Ainsworth-Darnell 1999; Charles, Roscigno, and Torres 2007Þ, ð3Þmoremistrustful toward schooling ðLareau and Horvat 1999Þ, and ð4Þ less likelyto convert cultural capital ðif possessedÞ into educational performance ðRos-cigno and Ainsworth-Darnell 1999Þ. Our model accommodates all of theseexplanations since black-white differences in educational attainment mayarise if ð1Þ blacks possess less cultural capital than whites ði.e., they have dif-ferent values of S in eq. ½1�Þ, ð2Þ they are less likely to invest this cultural cap-ital ði.e., even for a fixed S, v is lower among blacks than whitesÞ, ð3Þ theyhave weaker beliefs than whites that cultural capital yields a return ði.e.,different values of m2 in eq. ½6�Þ, or ð4Þ their actual rate of return to cul-tural capital is lower than that of whites ði.e., a lower value of j1 in eq. ½2�even for constantAÞ. In ourmodel, all of these factors lead to different levelsof parental investment in cultural capital ðeq. ½8�Þ and, in the end, differentlevels of educational attainment, as has been reported in empirical research.Social class differences.—Lareau and colleagues argue that cultural cap-
ital mediates social class inequalities in educational success ðLareau 1987,1989, 2003; Lareau and Horvat 1999; Calarco 2014Þ. The argument in thisliterature is that middle-class parents engage in concerted cultivation; thatis, they organize children’s leisure time activities with the intention of in-
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culcating skills and behaviors in children that promote future socioeco-nomic success. In addition to organizing activities outside the home,middle-class parents engage children in conversations and discussion, teaching themto be analytical, reasoning, and argumentative. Working-class parents, bycontrast, are much less likely to engage in these activities and to find themuseful. All these elements speak directly to our dynamic model of parentalinvestments, which can be used to analyze how social class differences inchild-rearing practices and investments lead to educational inequalities.Class differences in the stock of cultural capital are captured in differentaverage values of S. Investments in cultural capital with extracurricular ac-tivities purchased in the market means, in our terms, that vt may exceed S.8
That middle-class parents have stronger beliefs that cultural capital mattersfor educational success would be captured in higher values of m2, and thisbelief might be updated according to the rule described in equation ð9Þ.Lareau and colleagues also argue that middle-class families tend to bemore involved than working-class parents in their children’s schooling, forexample, by volunteering at school events or by requesting special treatmentfor their children. In our model, we may think of these practices as invest-ments over and above those made directly in the child’s cultural capitalðeq. ½5�Þ that either affect teachers’ perceptions of the child ðresulting in ahigher value of J2 in eq. ½4�Þ or, if parents are successful in obtainingspecial treatment, lead to higher teacher inputs in the child ða higher valueof a1 in eq. ½4�Þ. Both strategies lead to higher educational performancein our model and help to explain how cultural capital may mediate socialclass differences in educational success.Institutional differences.—A final example of how our model can be used
to improve the interpretation of results from previous research relates toDiMaggio’s ð1982Þ influential cultural mobility model. DiMaggio arguedthat cultural capital may be a means of upward mobility for children fromdisadvantaged socioeconomic backgrounds. The reason cultural capital isparticularly beneficial for children from disadvantaged backgrounds is thatthey tend to populate educational settings in which there is little culturalcapital, and, compared to children from more advantaged backgrounds,they face less competition when attempting to show off their cultural capi-tal. This model turns Bourdieu on his head by suggesting that returns tocultural capital, if possessed, are higher for those from less advantaged back-grounds than for those from more advantaged backgrounds ðDiMaggio
8The strategy of purchasing extra inputs ðextracurricular activities, tutoring, etc.Þ tosupplement in-house investments in cultural capital is particularly relevant in manynon-Western contexts. For example, research shows that in Japan and South Koreaparents invest extensively in “shadow education” to promote children’s educationalsuccess ðYamamoto and Brinton 2010; Lee and Rouse 2011; Byun, Schofer, and Kim2012Þ.
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1982; Aschaffenburg and Maas 1997; de Graaf, de Graaf, and Kraaykamp2000Þ. DiMaggio’s model is inconsistent with Bourdieu’s ideas but can beaccommodated within our model in which it implies, holding constant re-sources, investments, and beliefs ði.e., S, v, and m2Þ, that returns to cul-tural capital ðvia J2 and a1Þ are higher for children from disadvantaged so-cioeconomic backgrounds than for those from advantaged backgrounds.Our model does not address the question why returns to cultural capitalmight be different for children from different socioeconomic backgrounds,but it could be extended to include such factors. For example, variation inJ2 and a1 by socioeconomic background could arise from differences acrossschooling environments in the mean level of cultural capital in these envi-ronments. In that case, returns might be higher in environments charac-terized by low levels of cultural capital because less cultural capital is neededto stand out relative to one’s peers. In our model we could capture this sce-nario by extending equation ð4Þ to include C̄, where C̄ is the mean level ofcultural capital in the school or class context.
DYNAMIC ANALYSIS OF CULTURAL REPRODUCTION
We have argued that our model can be used to organize findings from re-search on cultural capital and to improve the interpretation of a diversebody of research that has used the theory of cultural reproduction to ac-count for socioeconomic differences in educational success. In this final sec-tion we provide empirical evidence on the dynamic nature of cultural capitalinvestments. Our aim is to illustrate three aspects of our model that havenot been addressed in previous research: ð1Þ parents invest continuously inchildren’s cultural capital, ð2Þ children’s cultural capital affects their edu-cational performance, and ð3Þ parents modify investments in cultural capi-tal in light of the outcomes of previous investments. We use longitudinal datafrom the NLSY-CYA and estimate empirical approximations of equationð5Þ ðdescribing the process through which the child accumulates culturalcapital over timeÞ and equation ð6Þ ðdescribing the process through whichcultural capital is converted into educational performanceÞ. We also providetentative empirical evidence that parents update their beliefs about returnsto investments in cultural capital on the basis of the outcomes of past in-vestments ðas described by eq. ½9�Þ.
Data and Variables
We use data from NLSY-CYA, a panel study conducted biannually be-tween 1986 and 2010, which collects information on all biological childrenof female participants in the National Longitudinal Survey of Youth 1979ðsee CHRR 2006a, 2006bÞ. We use the NLSY-CYA because, unlike other
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available data sets, it includes longitudinal information on cultural capitalfor NLSY 1979 mothers and for children age 10 and older. Our indicatorsof children’s cultural capital are mainly collected from children themselves,and, consequently, we focus on children 10–14 years old, for most of whomwe have three observations. The NLSY-CYA also includes longitudinalinformation on children’s academic achievement and socioeconomic back-ground. Unfortunately, the NLSY-CYA does not include direct measures ofteacher inputs in children, a point to which we return below.We include four types of variables to capture the core ingredients in our
theoretical model. These variables measure ð1Þ the child’s cultural capital,ð2Þ parents’ cultural capital, ð3Þ the child’s educational performance, andð4Þ socioeconomic background and demographic controls. Table A1 pre-sents detailed information and summary statistics for all variables includedin the analyses.Child’s cultural capital.—Previous research has used empirical indica-
tors of highbrow culture, reading behavior, extracurricular activities, cul-tural communication, and educational resources to capture different aspectsof cultural capital ðsee table 1 for a summaryÞ. In the NLSY-CYA we arelimited to including indicators of reading behavior when constructing ameasure of the child’s cultural capital ðC in eqq. ½1�, ½2�, and ½4�–½6�Þ.9Specifically, we construct a composite index that is composed from threeitems: ð1Þ the mother’s report of how much the child reads for enjoyment,ð2Þwhether the child reports that she typically reads a book ormagazine notassigned at school, and ð3Þ whether the child reports that she reads books ormagazines for fun on a usual summer day. This index, which captures thechild’s reading habits, is constructed by first rescaling the indicator of howmuch the child reads for enjoyment to lie in the range 0–1 and then summariz-ing the child’s total score on the three indicators included in the index.In the empirical analysis, we rescale the index to lie in the range 0–1.Parents’ cultural capital.—We construct two indicators of parents’ cul-
tural capital. The first indicator, active cultural investments, is a compositeindex intended to capture how much parents actively invest in transmittingtheir cultural capital to the child ðv in eqq. ½1�, ½5�, and ½6�Þ. It is made up offive items capturing ð1Þ how often in the last year a family member has takenthe child to any type of museum, ð2Þ how often in the last year a familymember has taken the child to any type of musical or theatrical perfor-mance, ð3Þ how many books the child has, ð4Þ whether the family encour-ages the child to start and keep doing hobbies, and ð5Þ whether the childgets special lessons or does extracurricular activities. The index, which com-
9Keeping this limitation in mind, we note that, among the different aspects of culturalcapital that have been included in previous research, reading behavior is the aspect thathas been found to be most strongly correlated with educational success ðe.g., de Graafet al. 2000; Jæger 2009; Gaddis 2013Þ.
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bines indicators of highbrow cultural participation, reading climate, and ex-tracurricular activities, summarizes parents’ response to all five items, and itis rescaled to lie in the range 0–1. The second indicator, passive cultural cap-ital, is intended to capture the influence of cultural capital in the home, netof parents’ active investments ðS in eqq. ½1�, ½5�, and ½6�Þ. We use two indi-cators to create this index: ð1Þ whether the family gets a daily newspaperand ð2Þ whether there is a musical instrument in the home that the child canuse. The index summarizes parents’ responses to these two questions, and itis rescaled to lie in the range 0–1.Educational performance.—The NLSY-CYA includes two time-varying
indicators of the child’s academic achievement, the Peabody IndividualAchievement Tests ðPIATÞ in math and reading recognition. We use thesemeasures as proxies for educational performance ðP in eqq. ½2�–½4� and ½6�Þ.We use percentile scores for each PIAT test, normed to children’s age.Controls.—We include a range of socioeconomic and demographic con-
trol variables ðX in eqq. ½1�–½6�Þ, which are described in appendix table A1.
Analytical Strategy
We use linear dynamic panel data ðDPDÞ models to estimate approxima-tions of equations ð5Þ and ð6Þ in the theoretical model. DPD models are avariant of traditional panel regression models in which present values ofthe dependent variable are treated as dynamic in the sense that they may de-pend on past values of the dependent variable, as well as on present andpast values of explanatory variables ðe.g., Arellano and Bond 1991; Arellanoand Bover 1995; Blundell and Bond 1998Þ. The models we estimate are“reduced form” because they involve statistical estimation of relationshipsthat are derived from our structural model. We interpret the empiricalresults in light of our underlying structural model that specifies the mech-anisms and behaviors that are assumed to generate these results. Likestandard panel regression models, DPD models exploit longitudinal infor-mation in the panel data to control for the effect of unobserved individualcharacteristics that affect the outcomes of interest.We estimate the following reduced form DPD model for the child’s cul-
tural capital ðeq. ½5�Þ:
Ci;t 5 ~g1Ci;t21 1 ~g2vi;t 1~g3Si;t 1 ~g4Xi;t 1 T 1 ui 1 e1i;t; ð10Þ
where Ci,t is the child’s cultural capital ðreading behaviorÞ and where i in-dexes individuals ði5 1, . . . , NÞ and t indexes time ðt5 1986–2010Þ. The ~gare parameters to be estimated, and the tildes are used to indicate thatthese are our empirical estimates of the parameters of equation ð5Þ. The pa-
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rameter ui is a child-specific effect that captures time-invariant unobservedcharacteristics that affect cultural capital.10 In this model the child’s culturalcapital in period t depends on her cultural capital in the previous periodðthus capturing the idea that cultural capital accumulated in the past affectscultural capital in the presentÞ, parents’ active cultural investments and pas-sive cultural capital in the present period ðv and S, respectivelyÞ, and parents’resources in the present period ðXÞ. The model also includes dummies forsurvey year T ð1986–2010Þ to capture time trends and an error term e1.We estimate the following reduced form DPD model for the child’s edu-
cational performance ðeq. ½6�Þ:Pi;t 5 ~m0Pi;t21 1 ~m1Ci;t21 1 ~m2vi;t 1 ~m3Si;t 1 ~m5Xi;t 1 T 1 ui 1 e2i;t; ð11Þ
where the child’s performance on the PIAT math and reading recognitiontests in period t, Pi,t, depends on her performance and cultural capital in theprevious period, parents’ active investments in cultural capital and passivecultural capital in the home, and parents’ resources. We should note thatthis reduced form model is an incomplete representation of our structuralmodel because we do not observe teacher inputs in the child in the NLSY-CYA data. Consequently, rather than estimating the effect of the child’scultural capital on teacher inputs ðwhich is the “catalyst” through whichcultural capital is assumed to be converted into educational performancein our modelÞ, we estimate ~m1, which captures the combined effect of J2
ðthe effect of cultural capital on teacher inputsÞ and a1 ðthe effect of teacherinputs on educational performanceÞ.Finally, we estimate reduced form DPD models to substantiate our as-
sumption that parents adjust their investments in cultural capital in lightof the outcomes of past investments ðdescribed in eqq. ½7�–½9�Þ. We esti-mate the following model:
vi;t 5 ~t1vi;t21 1 ~t2vi;t22 1 ~t3Pi;t21 1 ~t4ðvi;t22 � Pi;t21Þ1 ~t5Si;t
1 ~t6Xi;t 1 T 1 ui 1 e3i;t;ð12Þ
where vi,t is parents’ active cultural investments in the child in period t.11
Parents’ active cultural investment in period t depends on their investmentin the previous period ðvi,t21Þ, their investment two periods ago ðvi,t22Þ, the
10Our theoretical model also includes academic ability, Ac ðeq. ½5�Þ. We control indirectlyfor academic ability via ui, which, among other factors, also captures the effect ofacademic ability on cultural capital.11Note that our indicators of parents’ investments in cultural capital cover the periodwhen the child was 6–14 years old ðand in some cases 0–14 years old; see table A1Þ,which means that we have more repeated observations of parents’ investments thanobservations of children’s cultural capital.
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child’s educational performance in the previous period ðPi,t21Þ, and an in-teraction effect between parents’ investment two periods ago and the child’seducational performance in the previous period ðS, X, T, u, and e are thesame as aboveÞ. The ~t are parameters to be estimated. The idea in thismodel is to test whether, as stipulated in equation ð9Þ, parents adjust theirbeliefs about the returns to cultural capital, and thus their active culturalinvestments in the present, on the basis of the outcomes of past investments.If parents adjust their investments, the coefficient on the interaction term,~t4, should be positive. Parents know how much they invested two periodsago ðvi,t22Þ, they observed the outcome of this investment in the child’s edu-cational performance in the previous period ðPi,t21Þ, and if returns to pastinvestments are positive, parents should update their beliefs so as to investmore in the present ðvi,tÞ. Thus, the coefficient on the interaction effect cap-tures the adjustment in parents’ active cultural investments in the presentthat follows from a combination of investments two periods ago and aca-demic performance one period ago.We estimate the parameters of the DPD models using the one-step
system generalized method of moments estimator implemented in the Stataado xtabond2 ðRoodman 2009Þ. Finally, because the NLSY-CYA includesseveral children from the same family, we adjust all standard errors forclustering of respondents within families.
Results
Table 2 presents results from reduced form DPD regressions of the child’scultural capital and the child’s score on the PIAT math and reading rec-ognition tests. In all models, we use data on three observations for eachchild collected between age 10 and 14.Results from the DPD model for the child’s cultural capital are consis-
tent with the predictions of our theoretical model. We find that the child’scultural capital ðmeasured by reading habitsÞ in period t depends on hercultural capital in the previous period ð~g1 5 :29, P < .001Þ, thus indicat-ing that the child accumulates cultural capital over time. Net of this cu-mulative effect, we also find a positive and statistically significant effectof parents’ active cultural investments in the present period on the child’scultural capital ð~g2 5 :15, P < .001Þ and a positive effect of parents’ passivecultural capital ð~g3 5 :04, P < .01Þ. These results are in line with our argu-ment that the process through which the child accumulates cultural capitalfrom parents is dynamic, and, moreover, parents’ active cultural investmentsand the child’s passive exposure to cultural capital both contribute to theintergenerational transmission of cultural capital.We now turn to the results for the child’s educational performance, as de-
scribed in equation ð6Þ in our theoretical model. Table 2 shows results from
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reduced form DPD regressions of the child’s math and reading ability onthe child and parents’ cultural capital and on the controls. Results are verysimilar for the two measures of academic achievement. In addition to testscores in the present period depending on the test score in the previous periodðreflecting a cumulative effectÞ, math and reading ability in the present pe-rioddependonthechild’sculturalcapital in thepreviousperiod ð~m1math 5 4:52,~m1reading 5 6:31; both P < .001Þ and on parents’ active cultural investmentsin the present period ð~m2math 5 10:64, ~m2reading 5 8:42; both P < .001Þ andpassive cultural capital ð~m3math 5 4:66, ~m3reading 5 4:12; both P < .001Þ. Keep-ing the limitations of the NLSY-CYA data in mind, we find that these em-pirical findings are consistent with our theoretical model. Since we do notobserve teacher inputs, we interpret the positive effect of the child’s culturalcapital on educational performance as capturing the outcome of a two-stageprocess in which cultural capital is converted into teacher inputs, which arethen converted into educational performance. In this regard, our reducedform estimates capture the “rate of return” to cultural capital in terms ofeducational performance, as expressed in our model.Finally, table 3 presents results from reduced form DPD models of par-
ents’ active cultural investments. In equation ð12Þ we stipulate that, in ad-dition to other factors, parents’ active cultural investments in the presentdepend on the outcomes of their investments two periods ago, manifestedin the child’s educational performance one period ago. If parents adjust their
TABLE 2Results from DPD Regressions of Child’s Cultural Capital
and PIAT Math and Reading Recognition Test Scores
Dependent VariableChild’s Cultural
Capital MathReading
Recognition
Child:Lagged academic achievement . . . .13 .30
ð.03Þ*** ð.03Þ***Lagged cultural capital . . . . . . . .29 4.52 6.31
ð.06Þ*** ð1.15Þ*** ð1.12Þ***Parents:Active cultural investments . . . . .15 10.64 8.42
ð.03Þ*** ð2.37Þ*** ð2.19Þ***Passive cultural capital . . . . . . . .04 4.66 4.12
ð.02Þ** ð1.08Þ*** ð1.06Þ***Controls . . . . . . . . . . . . . . . . . . . . Yes Yes YesN . . . . . . . . . . . . . . . . . . . . . . . . . 4,325 4,430 4,443
NOTE.—Estimator is one-step system generalized method of moments. Models also includedummy variables for survey year ð1986–2010Þ. SEs ðin parenthesesÞ are corrected for cluster-ing of respondents within families. See table A1 for list of controls.* P < .05.** P < .01.*** P < .001.
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investments in cultural capital on the basis of the outcomes of past invest-ments, we expect a positive coefficient on the interaction term between activecultural investments two periods ago and educational performance one pe-riod ago. Table 3 shows results from two model specifications that use, re-spectively, PIAT math and reading recognition as the indicators of edu-cational performance. As hypothesized, and net of other factors, we finda positive and statistically significant coefficient on the interaction termsvi;t22 � Pi;t21 in both models ð~t4 5 :004, P < .001Þ. Although our approachis a crude approximation of the theoretical mechanism we propose, theseresults indicate, as implied by equation ð9Þ, that parents invest more incultural capital in the present if higher investments in the past yieldedhigher educational performance.12 In other words, our results are consis-
TABLE 3Results from DPD Regressions of Parents’ Active Cultural Investments
Measure of Educational Performance MathReading
Recognition
Lagged active cultural investments ðt 2 1Þ . . . . . .21 .22ð.02Þ*** ð.02Þ***
Lagged active cultural investments ðt 2 2Þ . . . . . 2.10 2.12ð.06Þ ð.07Þ
Lagged academic achievement:Lagged PIAT math ðt 2 1Þ . . . . . . . . . . . . . . . 2.00
ð.00Þ***Lagged PIAT reading recognition ðt 2 1Þ . . . . 2.00
ð.00Þ***Interaction effect:Lagged active cultural investments ðt 2 2Þ �lagged PIAT math ðt 2 1Þ . . . . . . . . . . . . . . .004
ð.00Þ***Lagged active cultural investments ðt 2 2Þ �lagged PIAT reading recognition ðt 2 1Þ . . . .004
ð.00Þ***Passive cultural capital . . . . . . . . . . . . . . . . . . .09 .09
ð.01Þ*** ð.01Þ***Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yes YesN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10,059 10,044
NOTE.—Estimator is one-step system generalized method of moments. Models also includedummy variables for survey year ð1986–2010Þ. SEs ðin parenthesesÞ are corrected for clus-tering of respondents within families. See table A1 for list of controls.* P < .05.** P < .01.*** P < .001.
12The main effect on parents’ active investments two periods ago is not significant,while the main effect on the child’s educational performance is negative and significant.Taken together with the positive interaction term, this suggests that parents’ investments
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tent with the idea that parents update their beliefs about the returns tocultural capital on the basis of the outcomes of past investments. Naturally,more research, including direct testing, is needed to determine the extentto which parents adjust investments in cultural capital.
DISCUSSION
This article was motivated by what we regard as a discrepancy betweenthe prominent position of the theory of cultural reproduction in socialstratification research and its conceptual and empirical validity. There iswidespread agreement that Bourdieu’s writings on cultural reproductionare unclear with regard to core concepts and mechanisms. We argue thatthis lack of clarity has had a detrimental impact on research on culturalreproduction, which is characterized by little consensus on how to con-ceptualize and measure cultural capital and how to interpret empirical corre-lations between cultural capital and educational success. At present, we arenot convinced that the literature provides a credible answer to Bourdieu’soriginal question: Does cultural capital promote social reproduction?Instead of debating the exact meaning of Bourdieu’s original thoughts,
we present a formal theoretical model of cultural reproduction that encap-sulates what we believe to be the core ideas in his theory. This structuralmodel brings together Bourdieu’s ideas and may be used as a basis for or-ganizing and interpreting results from previous research and as a conceptualstarting point for future research. Our model describes the three componentsthat make up the theory of cultural reproduction: how parents transmit theircultural capital to children, how children convert cultural capital into edu-cational success, and how educational success promotes social reproduction.It extends Bourdieu’s ideas by describing the mechanism through whichparents invest in their children’s cultural capital and the mechanism throughwhich children convert cultural capital into educational performance. Onthe basis of a rational choice perspective, we also propose a flexible set of be-havioral assumptions on the part of parents, children, and institutions thatenables us to interpret the parameters in our structural model.We use our theoretical model to interpret the results of existing empiri-
cal research and use NLSY-CYA data to illustrate the dynamic natureof cultural capital investments and their implications for children’s educa-
in their child’s cultural capital remain unchanged if she performs poorly. If, following lowparental investment, the child performs well, parents reduce their investment further, per-haps because it seems to be unnecessary to their child’s educational success. But if, followingrelatively high parental investment, their child performs well, parents increase their sub-sequent investment because, as we argue, they interpret this to mean that investing in theirchild’s cultural capital pays off.
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tional performance. Our literature review suggests that results from pre-vious research are mostly in line with cultural reproduction theory but alsothat research has yet to test the full implications of the theory and to iden-tify the specific mechanisms through which cultural capital may lead to edu-cational success. Results from our illustrative analysis of the NLSY-CYAdata are consistent with the hypotheses that children accumulate culturalcapital from parents, cultural capital has a positive effect on educationalperformance, and parents adjust their investments in cultural capital on thebasis of the outcomes of past investments.We believe that the main contribution of this article is to propose a new
direction for research that uses the concepts of cultural reproduction andcultural capital to explain persisting intergenerational inequalities in socio-economic outcomes. In our view, there is little doubt that the inequalitiesin socioeconomic outcomes that have been extensively documented in socialstratification research are partly attributable to cultural factors in the familyof origin. The challenge is how to conceptualize these cultural factors andthe ways in which they operate and how to document their implications forpatterns of intergenerational social mobility. We think Bourdieu’s theory ofcultural reproduction represents a starting point for such an investigationbut is ultimately limited by its lack of clarity in several core dimensions.A key advantage of our model is that it can be extended to accommo-
date a richer conceptual setup or new empirical insights. For example, ourmodel assumes that parents have only one child. But how do parents allo-cate investments in cultural capital when they have more than one child?Related research shows that parents allocate resources to each child in thefamily on the basis of the expected costs and benefits of these allocationsand on the basis of observable outcomes of past investments ðSteelman andPowell 1991; Behrman 1997; Ayalew 2005Þ. Lareau’s ð2003Þ qualitative studyillustrates this point. In the Tallinger family—a white middle-class familywith three boys—the parents allocate a disproportionate share of the fam-ily’s resources to the oldest son, Garrett, whom they believe is the mostgifted among the three children. We could extend our model to accom-modate this situation by arguing that, when a family has more than onechild and assuming that there is a limit on the family’s resources, invest-ment in children’s cultural capital ðgiven by vipt, where i indexes childrenÞwill be proportional to parents’ belief about each child’s m2 parameter. Thatis, parents will invest in proportion to how much return their investmentis expected to yield, in terms of educational performance, for each child.Children who more effectively translate parental investments into educa-tional performance will receive greater investment than will their brotheror sister whose performance is less sensitive to parental investment. Fu-ture research should explore whether this type of logic applies in multichildhouseholds.
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Another extension of our model might be to incorporate heterogeneityin returns to cultural capital. Our model assumes that the return to culturalcapital in the form of educational performance, j1 ðor, in the dynamic con-text, J2Þ, is the same for all children. Yet, it may be that j1 varies system-atically by institutional context or by socioeconomic factors. For example,Jæger ð2011Þ found that returns to highbrow cultural capital ðmeasured byfrequency of going to museums and concertsÞ were higher for children fromadvantaged socioeconomic backgrounds than for those from less advan-taged backgrounds. He argued that this difference in the rate of return tohighbrow cultural capital might be due to different institutionalizations ofcultural capital across schooling environments: children from advantagedbackgrounds tend to be in schooling environments that appreciate famil-iarity with highbrow culture, while those from less advantaged backgroundstend not to be in these environments. In a similar vein, Leopold and Shavitð2013Þ found that immigrants from the former Soviet Union in Israel receivea lower return to their cultural capital in Israeli schools than natives becausethey possess the “wrong” type of cultural capital that is not appreciated inmainstream education. In our model we could incorporate these types ofheterogeneity by, for example, letting j1 in equation ð2Þ be a function of aset of institutional or social characteristics. Indeed, many extensions of ourmodel are possible, and we hope that future research will extend, modify,and test the model presented in this article and, in that process, provide aricher understanding of the ways in which cultural capital may contributeto social reproduction.
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APPENDIX
TABLE
A1
DescriptiveStatisticsandSummaryofVariables
Indicator
Respon
seCategory
Age
Ran
geMean/%
SD
N*
Child
’sculturalcapital:y
.56
.33
12,303
How
oftenchild
read
sforenjoym
ent
.........
15
never;25
several
times
ayear;
35
several
times
amon
th;45
several
times
aweek;55
everyday
z6–14
Child
read
sbookor
magazineafterschool
.....
05
no;
15
yes
10–1
4Child
read
sbooksor
magazines
forfunon
asummer
day
.........................
05
no;
15
yes
10–1
4Parents’activecultural
investments:§
.58
.18
12,153
How
oftenin
thelast
year
child
istakento
museum
............................
15
never;2
5on
ceor
twice;35
several
times;45
abou
ton
ceamon
th;55
abou
ton
ceaweekor
moreoftenz
3–14
How
oftenin
thelast
year
child
istakento
concert/theater.......................
15
never;2
5on
ceor
twice;35
several
times;45
abou
ton
ceamon
th;55
abou
ton
ceaweekor
moreoftenz
6–14
Number
ofbookschild
has
.................
15
non
e;25
1or
2books;35
3–9
books;45
10or
morebooksz
0–14
Fam
ilyencourageschild
totakeon
hob
bies
....
05
no;
15
yes
6–14
Child
gets
speciallesson
s/doesextracurricular
activities
...........................
05
no;
15
yes
6–14
Parents’passivecultural
capital:k
.49
.37
11,941
Fam
ilysubscribes
todaily
new
spap
er........
05
no;
15
yes
6–14
Musicalinstrumentav
ailable
inchild
’shom
e...
05
no;
15
yes
6–14
Academ
icachievem
ent:
PIA
Tmath
.............................
Peabod
yIndividual
Achievem
entTest,
5–14
53.47
28.53
11,871
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Indicator
Respon
seCategory
Age
Ran
geMea-
n/%
SD
percentile
scoreð0–1
00Þ
PIA
Tread
ingrecogn
ition
..................
Peabod
yIndividual
Achievem
entTest,
percentile
scoreð0–1
00Þ
5–14
57.81
29.77
11,883
Con
trols:
Fam
ilyincomeðlo
gÞ......................
Log
oftotalfamily
income,
indexed
to1986
10.75
1.71
10,479
Mother’s
education
.......................
Years
ofscho
oling
12.74
2.57
12,268
Mother’s
IQ............................
Mother’s
scoreon
Arm
edForcesQualifi
cation
Test,percentile
scoreð0–1
00Þ
36.09
28.36
12,303
Fam
ilysize
.............................
Total
number
ofchild
renliv
ingin
mother’s
hou
seho
ld2.61
1.21
12,285
Mother’s
race:
White
...............................
Dummyvariable
.43
Black
...............................
Dummyvariable
.30
Hispan
ic.............................
Dummyvariable
.18
Other
................................
Dummyvariable
.10
Child
’ssex
.............................
15
female,
05
male
.51
.50
12,088
Child
’sage
.............................
Child’s
agein
mon
ths
147.46
17.02
12,285
NOTE.—
Allvariableswerecollected
intheyears1986–2010,withthefollo
wingexception
s:child
read
sbookor
magazineafterscho
olð1992–2010Þ,child
read
sbooksor
magazines
forfunon
asummer
day
ð1992–2010Þ,an
dmother’srace
ðcollected
1979Þ.
*Child-by-year
observations
defined
asallob
servationswithvalid
respon
seon
child
’scultural
capital.
yFirstfactor
inprincipal
compon
entan
alysisðPCAÞa
ccou
ntsfor65.1%
ofthecovariance
betweentheitem
sin
theindex
ðestimates
based
onpolychoric
correlationmatrixsince
allindicatorsarecategoricalÞ.
Cronba
ch’s
a5
.484.
zVariable
rescaled
to0–1.
§First
PCA
factor
accountsfor44.7%
oftotalvariance.Cronba
ch’s
a5
.549.
kPolychoric
correlationbetweenitem
sis.168.C
ronba
ch’s
a5
.193.
1111
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