Versión publicada del artículo: BOERTIEN, Diederik; BERNARDI, Fabrizio (2022) “Gendered Diverging Destinies: Changing Family Structures and the Reproduction of Educational Inequalities Among Sons and Daughters in the United States”. Demography, 59 (1), 111-136 (ISSN: 0070-3370). https://doi.org/10.1215/00703370-9612710 Demography (2021) 59(1):111–136 Published online: 17 December 2021 DOI 10.1215/00703370-9612710 © 2021 The Authors This is an open access arti­cle dis­trib­uted under the terms of a Creative Commons license (CC BY-NC-ND 4.0). Gendered Diverging Destinies: Changing Family Structures and the Reproduction of Educational Inequalities Among Sons and Daughters in the United States Diederik Boertien and Fabrizio Bernardi Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 ABSTRACT The prev­a­lence of non­tra­di­tional fam­ily struc­tures has increased over time, par­tic­u­larly among socio­eco­nom­i­cally dis­ad­van­taged fam­i­lies. Because chil­dren’s socio­eco­nomic attain­ments are pos­i­tively asso­ci­ated with grow­ing up in a two-par­ent house­hold, chang­ing fam­ily struc­tures are con­sid­ered to have strength­ened the repro­ duc­tion of social inequalities across gen­er­a­tions. However, sev­eral stud­ies have shown that child­hood fam­ily struc­ture relates dif­fer­ently to edu­ca­tional out­comes for sons than for daugh­ters. Therefore, we ask whether there are gen­der dif­fer­ences in the extent to which chang­ing fam­ily struc­tures have con­trib­uted to the col­lege attain­ment gap between chil­dren from lower and higher socio­eco­nomic back­grounds. We use data from the National Longitudinal Survey of Youth 1979 and 1997 cohorts to esti­mate extended Oaxaca–Blinder decom­po­si­tion mod­els that take into account cross-cohort changes in the prev­a­lence of fam­ily struc­tures and het­ero­ge­ne­ity in the effects of child­hood fam­ ily struc­ture on col­lege attain­ment. We find that the argu­ment that changes in fam­ily struc­tures con­trib­uted to diverg­ing des­ti­nies in col­lege attain­ment holds for daugh­ters but not for sons. This result is due to the dif­fer­ent changes over time in the effects of child­hood fam­ily struc­ture by gen­der and socio­eco­nomic back­ground. KEY WORDS Inequality of oppor­ t u­n ity • Family struc­ture • Education • Gender • Social strat­i­fi­ca­tion Introduction Families in the United States have changed pro­foundly over the last decades. The per­ cent­age of chil­dren liv­ing with a sin­gle par­ent increased from roughly 12% in 1970 to 27% by 2018 (Smock and Schwartz 2020), and many chil­dren live in other “non­tra­ di­tional” fam­ily struc­tures today (defined as chil­dren not liv­ing with two bio­log­i­cal par­ents), includ­ing step­par­ent fam­i­lies (Brown et al. 2016; Cavanagh and Fomby 2019). Changes over time in the prev­a­lence of non­tra­di­tional fam­ily struc­tures have been espe­cially pro­nounced among poor and less edu­cated moth­ers (McLanahan 2004; McLanahan and Jacobsen 2015; Rackin and Gib­son-Davis 2018), and liv­ing in a house­hold with a non­tra­di­tional fam­ily struc­ture is neg­a­tively asso­ci­ated with ELECTRONIC SUPPLEMENTARY MATERIAL The online ver­sion of this arti­cle (https:​­/​­/doi​­.org​­/10.1215/00703370 -9612710) con­tains sup­ple­men­tary mate­rial. 112 D. Boertien and F. Bernardi child out­comes (Amato 2000, 2010; McLanahan et al. 2013). Therefore, var­i­ous authors have argued that child­hood fam­ily struc­tures play an increas­ingly salient role in the repro­duc­tion of inequalities across gen­er­a­tions (Cherlin 2014; McLanahan and Percheski 2008; Putnam 2016). This argu­ment is part of a broader the­sis pos­it­ing that changes asso­ci­ated with the sec­ond demo­graphic tran­si­tion have con­trib­uted to “diverg­ing des­ti­nies” between chil­dren from dif­fer­ent socio­eco­nomic back­grounds (McLanahan 2004; McLanahan and Jacobsen 2015). Parallel to this body of lit­er­a­ture, other research sug­gests that fam­ily struc­ture mat­ters more for edu­ca­tional out­comes of sons than of daugh­ters. The same-sex Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 hypoth­e­sis pos­tu­lates that the absence of a par­ent of the same sex in the house­ hold is spe­cif­i­cally det­ri­men­tal for chil­dren, but this claim has found lit­tle empir­i­cal sup­port (Biblarz and Stacey 2010; Powell and Downey 1997). Departing from this hypoth­e­sis, recent stud­ies sug­gest that the aca­demic achieve­ment of sons is gen­er­ally more sen­si­tive to the char­ac­ter­is­tics of their fam­ily and school envi­ron­ment than the achieve­ment of daugh­ters (Autor et al. 2019; DiPrete and Buchmann 2013; Legewie and DiPrete 2012). In addi­tion, evi­dence sug­gests that sons are more likely to have behav­ioral prob­lems at young ages (Goldin et al. 2006) and to develop anti-school atti­tudes in the pro­cess of the con­struc­tion of mas­cu­line gen­der iden­ti­ties (Legewie and DiPrete 2012), increas­ing the impor­tance of the resources of their fam­ily and school envi­ron­ment for school out­comes. Because non­tra­di­tional fam­i­lies often have less access to a vari­ety of resources than fam­il­ ies with two bio­log­i­cal par­ents, fam­ily struc­ture is expected to have a larger impact on sons’ edu­ca­tional out­comes (Autor et al. 2019; DiPrete and Buchmann 2013; Legewie and DiPrete 2012). In this arti­cle, we build on the body of research that stud­ies the role fam­ily struc­ ture plays in the repro­duc­tion of inequal­ity across gen­er­a­tions (Alamillo 2016; Duncan et al. 2017; McLanahan 2004; McLanahan and Percheski 2008) and incor­po­rate the notion of poten­tial gen­der dif­fer­ences in the impor­tance of fam­ily struc­ture for edu­ ca­tional out­comes. We ask two research ques­tions. First, are there gen­der dif­fer­ences in how much chang­ing fam­ily struc­tures con­trib­uted to changes across cohorts in the col­lege attain­ment gap between chil­dren with lower edu­cated moth­ers and those with higher edu­cated moth­ers? Second, and more gen­er­ally, is the diverg­ing des­ti­nies the­ sis equally valid for sons and daugh­ters? To address these ques­tions, we use a con­cep­tual frame­work based on (1) the prev­ a­lence of non­tra­di­tional fam­i­lies, (2) the pen­alty for edu­ca­tional out­comes related to grow­ing up in a non­tra­di­tional fam­ily, and (3) het­ero­ge­ne­ity in this pen­alty by paren­tal gen­der and paren­tal socio­eco­nomic sta­tus (SES). The diverg­ing des­ti­nies hypoth­e­sis pro­poses that the increas­ing prev­a­lence of non­tra­di­tional fam­ily struc­tures, par­tic­u­ larly among socio­eco­nom­i­cally dis­ad­van­taged fam­i­lies, has led to increased social back­ground dif­fer­ences in chil­dren’s attain­ments (McLanahan 2004; McLanahan and Jacobsen 2015). However, if the pen­alty related to grow­ing up in a non­tra­di­tional fam­ily is sys­tem­at­i­cally dif­fer­ent for sons than for daugh­ters and for chil­dren with low- ver­sus high-SES par­ents, the role of fam­ily struc­ture in strength­en­ing social back­ground dif­fer­ences in attain­ments might dif­fer too. In our empir­i­cal anal­y­sis, we use the National Longitudinal Survey of Youth 1979 and 1997 cohorts, born in the early 1970s and 1980s in the United States. These two cohorts cover a period when fam­ily struc­tures and edu­ca­tional attain­ment changed dra­mat­i­cally. More than 70% of chil­dren still lived with both their par­ents dur­ing ado­ les­cence in the first cohort, but only half did so in the sec­ond cohort. Tertiary degree Changing Family Structures and the Reproduction of Educational Inequalities 113 attain­ment increased from 24% to 33% across cohorts. We employ an extended Blinder–Oaxaca method to decom­pose changes over time in the col­lege attain­ment gap between chil­dren with lower and higher edu­cated moth­ers into the part that is explained by chang­ing fam­ily struc­tures and the part that remains unex­plained. This approach also enables us to fur­ther quan­tify the sep­a­rate con­tri­bu­tions of changes across cohorts in the prev­a­lence of non­tra­di­tional fam­i­lies, changes in the pen­alty related to grow­ing up in a non­tra­di­tional fam­ily, and het­ero­ge­ne­ity in these pen­al­ties. Our con­clu­sions dif­fer con­sid­er­ably from pre­vi­ous research on whether changes in fam­ily struc­tures con­trib­uted to diverg­ing des­ti­nies between chil­dren from dif­fer­ent Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 socio­eco­nomic groups. Earlier stud­ies pro­vided a gen­eral nar­ra­tive that fam­ily struc­ ture changes have inten­si­fied social back­ground dif­fer­ences in edu­ca­tional out­comes of chil­dren (McLanahan 2004; McLanahan and Percheski 2008) or argued that their influ­ ence is small to neg­li­gi­ble based on empir­i­cal esti­ma­tes (Alamillo 2016; Bernardi and Boertien 2017; Duncan et al. 2017). Our find­ings show that changes in fam­ily struc­tures across cohorts increased the gap in col­lege attain­ment between daugh­ters with lower edu­cated moth­ers and those with higher edu­cated moth­ers (although this result is only mar­gin­ally sta­tis­ti­cally sig­nif­i­cant) but decreased the gap in edu­ca­tional out­comes for sons. In other words, we find that changes in fam­ily struc­tures might have con­trib­uted to diverg­ing des­ti­nies for daugh­ters but reduced attain­ment gaps for sons. Prevalence, Penalty, and Heterogeneity: An Analytical Framework In its sim­plest form, the argu­ment that changes in fam­ily struc­ture strength­ened the repro­ duc­tion of inequal­ity across gen­er­a­tions depends on two con­di­tions that hold for the U.S. con­text (McLanahan and Percheski 2008). First, the share of chil­dren grow­ing up in a non­tra­di­tional fam­ily has increased over the last decades, espe­cially among chil­dren in the lower socio­eco­nomic strata (Ellwood and Jencks 2004; Martin 2006; Matysiak et al. 2014; McLanahan and Percheski 2008; Rackin and Gib­son-Davis 2018; Thomson et al. 2014). Second, grow­ing up in a non­tra­di­tional fam­ily is neg­a­tively related to chil­dren’s final edu­ca­tional attain­ment (Amato 2010; McLanahan and Sandefur 1994; McLanahan et al. 2013). Following ear­lier research on pov­erty (Brady et al. 2017), we char­ac­ter­ize the first con­di­tion as refer­ring to dif­fer­ences in the prev­a­lence of fam­ily struc­tures and con­sider the sec­ond con­di­tion to refer to the pen­alty asso­ci­ated with grow­ing up in a non­tra­di­tional fam­ily struc­ture. Recent research find­ings sug­gest that a third con­di­tion should be con­sid­ered: namely, that the effects of fam­ily struc­ture can vary with paren­tal SES (Alamillo 2016; Augustine 2014; Brand et al. 2019; Martin 2012). We char­ac­ter­ize this argu­ment as one about het­ero­ge­ne­ity in pen­al­ties. The notion of prev­a­lence is piv­otal for the gen­eral argu­ment that chang­ing fam­ily struc­tures con­trib­uted to the repro­duc­tion of inequal­ity across gen­er­a­tions. However, it is largely irrel­e­vant in explaining gen­der dif­fer­ences in the role of fam­ily struc­ture because the prev­a­lence of non­tra­di­tional fam­i­lies gen­er­ally does not dif­fer between sons and daugh­ters.1 The notion of het­ero­ge­ne­ity in pen­al­ties is more essen­tial, given that the effects of fam­ily struc­ture on edu­ca­tional out­comes can dif­fer by gen­der and 1 Children’s gen­der appears to have a small effect on sep­a­ra­tion prob­ab­ il­i­ties (Raley and Bianchi 2006) and other fam­ily char­ac­ter­is­tics, such as mar­riage (Lundberg and Rose 2003). These effects, how­ever, are likely to be too minor to affect gen­der dif­fer­ences in the prev­a­lence of fam­ily struc­tures. 114 D. Boertien and F. Bernardi paren­tal SES. In the remain­der of this lit­er­a­ture review, we there­fore focus on how and why the asso­ci­a­tion between fam­ily struc­ture and edu­ca­tional attain­ment might dif­fer across groups. Childhood Family Structure and Educational Outcomes Previous research has shown that, on aver­age, indi­vid­u­als who grew up in a non­ tra­di­tional fam­ily struc­ture fare slightly to mod­er­ately worse on a vari­ety of child Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 and adult out­comes than indi­vid­u­als who grew up in a two-bio­log­i­cal-par­ent fam­ily (Amato 2000, 2010). Associations between fam­ily struc­ture and some out­comes, such as cog­ni­tive abil­ity, are small; the rela­tion­ship between fam­ily struc­ture and other out­comes, such as edu­ca­tional attain­ment and psy­cho­log­i­cal well-being, is stron­ger (Lee and McLanahan 2015; McLanahan et al. 2013). Scholars have debated the extent to which these asso­ci­a­tions reflect causal effects or cap­ture the influ­ence of other preexisting socio­eco­nomic dis­ad­van­tages. Once account­ing for sources of endogeneity, most stud­ies have found that the effects of fam­ily struc­ture are atten­u­ ated but per­sist (McLanahan et al. 2013). Two main types of expla­na­tions for the neg­at­ive asso­ci­at­ion between grow­ing up in a non­tra­di­tional fam­ily and edu­ca­tional out­comes, which are not nec­es­sar­ily mutu­ally exclu­sive, are cri­sis mod­els and resource mod­els. Crisis mod­els focus on chil­dren’s adjust­ments to new fam­ily struc­tures. Most chil­dren liv­ing in a non­tra­di­ tional fam­ily expe­ri­enced a paren­tal sep­a­ra­tion, which might expose them to paren­ tal con­flict and require chil­dren to adjust emo­tion­ally to a new fam­ily arrange­ment (Cherlin 1999; Kalmijn et al. 2007; Pryor and Rodgers 2001; Thomson et al. 1994). Emotional cri­ses asso­ci­ated with paren­tal sep­a­ra­tion can neg­a­tively impact school per­for­mance and, con­se­quently, final edu­ca­tional attain­ment. Several authors have suggested that the sta­bil­ity of fam­ily struc­tures, rather than par­tic­u­lar char­ac­ter­is­tics of given fam­ily forms, is what mat­ters for child devel­op­ment (Bzostek and Berger 2017; Fomby and Osborne 2017; Lee and McLanahan 2015; Mariani et al. 2017; Waldfogel et al. 2010). Resource mod­els sug­gest that dif­fer­ences in par­ent­ing styles and finan­cial resources are pri­mar­ily respon­si­ble for fam­ily struc­ture dif­fer­ences in child out­comes (Amato 2010; McLanahan and Sandefur 1994; Seltzer 2000). Several stud­ies have shown that lower lev­els of eco­nomic resources are largely respon­si­ble for the lower edu­ca­tional out­comes of chil­dren grow­ing up in a non­tra­di­tional fam­ily (Jonsson and Gähler 1997; McLanahan and Sandefur 1994; Thomson et al. 1994). Gender Differences in the Impact of Family Structure on Educational Outcomes The impor­tance of child­hood fam­ily struc­ture can dif­fer by gen­der if the con­nec­tions between fam­ily struc­ture, cri­ses, resources, and edu­ca­tional out­comes vary between sons and daugh­ters. The so-called same-sex hypoth­e­sis (Biblarz and Raftery 1999; Powell and Downey 1997) pos­its that chil­dren ben­efi ­ t par­tic­u­larly from the input of par­ents of the same sex because of pur­ported closer par­ent–child rela­tion­ships between same-sex dyads and the pos­si­bly greater role of same-sex par­ents as role Changing Family Structures and the Reproduction of Educational Inequalities 115 mod­els and author­ity fig­ures (Powell and Downey 1997). Because most chil­dren in non­tra­di­tional fam­i­lies do not live with their bio­log­i­cal fathers, the increas­ing prev­ a­lence of non­tra­di­tional fam­il­ies is expected to have espe­cially affected sons’ out­ comes (Downey et al. 1998). However, very lit­tle empir­i­cal evi­dence sup­ports the notion that chil­dren ben­e­fit more from the input of par­ents of the same sex than from that of par­ents of a dif­fer­ent sex (Biblarz and Stacey 2010). A sep­a­rate body of lit­er­a­ture has focused instead on how sons’ out­comes depend more on their neigh­ bor­ hood, school, and fam­ ily char­ ac­ ter­ is­ tics than daugh­ ters’ out­comes (Autor et al. 2019; Bertrand and Pan 2013; Brenøe and Lundberg 2018; Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 Buchmann and DiPrete 2006; Chetty et al. 2016; Legewie and DiPrete 2012). One expla­na­tion for this obser­va­tion derives from boys’ higher pro­pen­sity toward behav­ ioral prob­lems begin­ning at young ages. For instance, boys have more school dis­ ci­plin­ary prob­lems and are less likely to do home­work than girls (Jacob 2002). The rea­sons for these behav­ioral dif­fer­ences are unclear but might derive from later ages of mat­u­ra­tion for boys than for girls (Goldin et al. 2006). The greater inci­dence of such behav­ioral prob­lems could require more paren­tal invest­ments in sons than daugh­ters. Factors that affect par­ents’ capac­ity to invest in their chil­dren, such as fam­ily struc­ture, are in that case more con­se­quen­tial for sons (Autor et al. 2019). Another expla­na­tion for why envi­ron­men­tal char­ac­ter­is­tics, includ­ing fam­ily struc­ture, mat­ter more for sons than daugh­ters is sim­i­lar but focuses on the con­struc­ tion of gen­der iden­ti­ties (DiPrete and Buchmann 2013; Legewie and DiPrete 2012). Studies tak­ing this per­spec­tive sug­gest that although some con­cep­tions of masculin- ity include anti-school atti­tudes and behav­iors, con­cep­tions of fem­i­nin­ity vary less in the extent to which aca­demic per­for­mance is val­ued (e.g., Legewie and DiPrete 2012). In the pro­cess of constructing mas­cu­line gen­der iden­ti­ties, ado­les­cent boys are there­fore at greater risk of devel­op­ing atti­tudes and behav­iors that lead to dis­en­gage­ ment from school. Environments that pro­mote aca­demic per­for­mance and effort, and thereby shel­ter against dis­en­gage­ment from school, are more ben­e­fi­cial for boys than for girls (DiPrete and Buchmann 2013). Studies focus­ing on edu­ca­tional achieve­ment, non­cog­ni­tive skills, and high school com­ple­tion have indeed reported larger neg­a­tive effects of grow­ing up in a non­tra­di­ tional fam­ily struc­ture for sons than for daugh­ters (Autor et al. 2019; Bertrand and Pan 2013; Buchmann and DiPrete 2006; Chetty et al. 2016). Evidence is less uni­form for gen­der dif­fer­ences in the effects on higher lev­els of edu­ca­tional attain­ment (Duncan et al. 2017; Lundberg 2017) and non­ed­u­ca­tional child out­comes (Amato 2001). Socioeconomic Differences in the Impact of Family Structure on Educational Outcomes The impor­tance of emo­tional adjust­ment to cri­ses and the loss of paren­tal resources for edu­ca­tional out­comes can also dif­fer by fam­i­lies’ SES (Augustine 2014; Martin 2012). Such het­ero­ge­ne­ity in pen­al­ties by paren­tal SES can reduce or amplify the con­tri­bu­ tion of chang­ing fam­ily struc­tures to inequal­ity of oppor­tu­nity (Bloome 2017). Put in extremes, if grow­ing up in a non­tra­di­tional fam­ily affects the out­comes of only those chil­dren with high paren­tal SES, the increas­ing prev­a­lence of non­tra­di­tional fam­ily struc­tures might reduce inequal­ity of oppor­tu­nity, even if dis­ad­van­taged chil­dren more com­monly live in non­tra­di­tional fam­i­lies. Conversely, if child­hood fam­ily struc­tures 116 D. Boertien and F. Bernardi mat­ter for the out­comes of only indi­vid­u­als with low paren­tal SES, the role of fam­ ily struc­tures in cre­at­ing inequal­ity of edu­ca­tional out­comes might be greater than expected. There are two main per­spec­tives on whether and how the impact of grow­ing up in a non­tra­di­tional fam­ily varies with paren­tal SES. On the one hand, high-SES fam­i­lies might have more resources to buffer their chil­dren from the neg­a­tive con­ se­quences of a union dis­so­lu­tion (Grätz 2015). On the other hand, chil­dren whose par­ents have more resources might have more to lose from the absence of a par­ent in the house­hold than other chil­dren (Bernardi and Radl 2014). If eco­nomic resources Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 and other forms of par­ents’ cap­it­al are best accessed through coresidence, chil­dren of high-SES par­ents will lose access to rel­a­tively more resources than chil­dren with low-SES par­ents when a par­ent is not coresiding. For instance, financ­ing a col­lege edu­ca­tion might be more dif­fi­cult for par­ents who have to main­tain two sep­a­rate house­holds (Bernardi and Boertien 2016), and inten­sive par­ent­ing strat­e­gies might be more com­pli­cated within sin­gle-par­ent fam­i­lies (Lareau 2002). That is, the trans­ mis­sion of social, eco­nomic, and human cap­i­tal might be stron­ger among two-par­ent fam­i­lies than in fam­ily forms in which one par­ent is absent from the child­hood home (Coleman 1988). With some excep­tions (e.g., Augustine 2014), stud­ies directly exam­in­ing het­ero­ge­ne­ity in pen­al­ties by paren­tal SES have found that chil­dren from higher SES back­grounds are more affected by grow­ing up in a non­tra­di­tional fam­ily than chil­dren from lower SES back­grounds (Bernardi and Boertien 2017; Martin 2012; McLanahan and Sandefur 1994). Previous stud­ies quan­ti­fied the cross-sec­tional con­tri­bu­tion of var­i­at­ ion in fam­ ily struc­tures to social back­ground dif­fer­ences in edu­ca­tional attain­ment using Oaxaca–Blinder decom­po­si­tion meth­ods (and in this arti­cle, we use an exten­sion of this method to study change over time). These stud­ies found that the impact of the larger pen­al­ties observed for chil­dren with higher edu­cated par­ents can­cels out the impact of the lower prev­a­lence of non­tra­di­tional fam­i­lies among higher edu­ cated par­ents. In other words, once het­ero­ge­ne­ity in pen­al­ties is taken into account, fam­ily struc­ture barely explains any dif­fer­ences in edu­ca­tional attain­ment between chil­dren with low paren­tal SES and those with high paren­tal SES (Alamillo 2016; Bernardi and Boertien 2017). Variation in Nontraditional Family Structures The rela­tion­ship between fam­ily struc­ture and edu­ca­tional attain­ment is com­pli­cated fur­ther by the spe­cific char­ac­ter­is­tics of non­tra­di­tional fam­ily types. For instance, the pres­ence of a step­par­ent can lead to role ambi­gu­ity within fam­i­lies (Sweeney 2010) but increases the paren­tal resources avail­­able (King 2006). Living with a step­­ par­ent can also have dif­fer­ent effects on out­comes for sons than for daugh­ters (King 2009). Similarly, non­res­i­dent par­ents’ increased involve­ment in child-rearing over time has pos­i­tive effects on child out­comes (Bjarnason and Amarsson 2011), which might have changed the rel­a­tive impor­tance of both the cri­sis and resource mech­a­ nisms over time. A full con­sid­er­ation of fam­ily struc­ture types and how their char­ac­ ter­is­tics relate to edu­ca­tional out­comes for sons and daugh­ters from dif­fer­ent social Changing Family Structures and the Reproduction of Educational Inequalities 117 back­grounds is an impor­tant refine­ment that goes beyond the scope of this arti­cle; we return to this issue in the Discussion sec­tion. Hypotheses In short, pre­vi­ous research has shown that the neg­a­tive impact of grow­ing up in a non­ tra­di­tional fam­ily on edu­ca­tional out­comes tends to be larger for high-SES chil­dren. Negative impacts are also expected to be larger for sons, whose aca­demic achieve­ Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 ment is more sen­si­tive to their fam­ily envi­ron­ment. Hence, if paren­tal resources vary with fam­ily struc­ture among high-SES fam­i­lies par­tic­u­larly, and if boys’ col­ lege attain­ment is affected more by paren­tal resources than girls’ attain­ment, we can expect that grow­ing up in a non­tra­di­tional fam­ily entails the larg­est pen­alty for the edu­ca­tional out­comes of sons from high-SES fam­il­ies. In con­trast, pen­al­ties might vary less by fam­ily SES for daugh­ters. The larger the pen­al­ties for the edu­ca­tional out­comes of chil­dren from high-SES back­grounds are rel­at­ive to the pen­al­ties for chil­dren from low-SES back­grounds, the less likely fam­ily struc­ture will strengthen social back­ground dif­fer­ences in edu­ca­tional out­comes (Alamillo 2016; Bernardi and Boertien 2017; Bloome 2017). If the attain­ment of boys, but not girls, from high- SES back­grounds is par­tic­u­larly affected by fam­ily struc­ture, this leads to the main hypoth­e­sis of our study: changes in fam­ily struc­tures across cohorts are less likely to have led to diverg­ing des­ti­nies for sons com­pared with daugh­ters. Data and Methods Data We employ data from two cohorts of the National Longitudinal Survey of Youth (NLSY)—1979 (NLSY79) and 1997 (NLSY97).2 The NLSY cohorts are nation­ally rep­re­sen­ta­tive sam­ples of ado­les­cents who were aged 14–22 in 1979 and 12–18 in 1997, respec­tively. Response rates for all­indi­vid­u­als eli­gi­ble for inter­view in the first sur­vey round were 87% for the 1979 cohort and 91% for the 1997 cohort. By the last waves of data used here—1994 for the 1979 cohort and 2015 for the 1997 cohort—89% and nearly 80% (respec­tively) of the sam­ples interviewed in Round 1 were still pres­ent. Black and His­panic ado­les­cents were oversampled in the study; we use sam­ple weights in the anal­y­sis. We exclude respon­dents who lived with adop­tive par­ents from our sam­ple because they might expe­ri­ence addi­tional obsta­cles to edu­ca­tional attain­ment that are unre­ lated to the fam­ily struc­ture and SES of their adop­tive fam­ily. For our main anal­y­sis, we dis­card cases with miss­ing infor­ma­tion on the var­i­ables used (exclud­ing 16.5% of the sam­ple for the NLSY79 and 10.9% of cases for the NLSY97). In robust­ness checks, we use mul­ti­ple impu­ta­tions to deal with miss­ing val­ues. The final sam­ple sizes used are 7,422 for the NLSY79 and 6,379 for the NLSY97. 2 The rep­li­ca­tion code (Stata) is avail­­able in online Appendix F. 118 D. Boertien and F. Bernardi Variables Bachelor’s degree attain­ment by the time of the sur­vey is our main edu­ca­tional attain­ ment var­i­able, mea­sured when respon­dents reached their early 30s for both cohorts (in 1994 for the 1979 cohort and in 2015 for the 1997 cohort). In robust­ness checks, we also look at high school com­ple­tion (hav­ing a high school diploma or GED) and years of edu­ca­tion com­pleted at the time of the sur­vey. Mother’s highest level of edu­ca­tion is our main indi­ca­tor of paren­tal SES. Even though moth­ers’ edu­ca­tional careers can be affected by fam­ily struc­ture changes at their Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 chil­dren’s young ages, alter­na­tive mea­sures (e.g., income and occu­pa­tion at the time of the sur­vey) are even more respon­sive to fam­ily struc­ture changes. We use mother’s edu­ca­tion rather than father’s edu­ca­tion because the lat­ter is more often miss­ing (9% for fathers vs. 2% for moth­ers), espe­cially for those in non­tra­di­tional fam­i­lies. Changes in the dis­tri­bu­tion of mater­nal edu­ca­tion across cohorts can change the mean­ing of spe­cific edu­ca­tional categories and the extent to which they proxy the broader socio­ eco­nomic posi­tion of the house­hold. For exam­ple, not hav­ing a high school diploma or GED might be a clearer indi­ca­tor of broader socio­eco­nomic dis­ad­van­tage in recent cohorts. Therefore, we cre­ate three mater­nal edu­ca­tion categories of sim­i­lar size for each cohort (bot­tom, mid­dle, and top). At the bot­tom of the mater­nal edu­ca­tion dis­tri­bu­ tion are those who com­pleted grade 8 or less for the 1979 cohort (16.5%) and grade 11 or less for the 1997 cohort (18.3%). At the top of the dis­tri­bu­tion are moth­ers who com­ pleted at least one year of col­lege for the 1979 cohort (21.3%) and at least four years of col­lege for the 1997 cohort (20.7%). Hence, the bot­tom and top categories roughly resem­ble the low­est and highest quin­tile of mater­nal edu­ca­tion within each cohort. The main inde­pen­dent var­i­able of the anal­y­sis is child­hood fam­ily struc­ture. For both data sets, fam­ily struc­ture was mea­sured at age 17. We con­sider four main catego- ries of fam­ily struc­ture: (1) liv­ing with both bio­log­i­cal par­ents, (2) liv­ing with a par­ent and a step­par­ent, (3) liv­ing with a sin­gle par­ent, and (4) not liv­ing with any bio­log­i­cal par­ent. This rather crude clas­si­fi­ca­tion of fam­ily struc­ture is the main lim­it­a­tion of our anal­y­sis. Unfortunately, the NLSY97 pro­vi­des only patchy ret­ro­spec­tive infor­ma­tion on child­hood fam­ily struc­ture, pre­vent­ing us from constructing com­pa­ra­ble mea­sures cap­tur­ing more com­plex child­hood fam­ily struc­ture tra­jec­to­ries. Repeated fam­ily tran­ si­tions are more com­mon among socio­eco­nom­i­cally dis­ad­van­taged groups (Brown et al. 2016). Thus, larger pen­al­ties related to child­hood fam­ily struc­tures among indi­ vid­ua­ ls with lower edu­cated moth­ers even­tu­ally might partly reflect the effects of more fam­ily tran­si­tions expe­ri­enced. For the 1979 cohort, we per­form an addi­tional anal­y­sis for the NLSY79 data using more detailed child­hood fam­ily struc­ture his­to­ries (see the online Appendix A). We elab­o­rate on this issue fur­ther in the Discussion sec­tion. Control var­i­ables included in the anal­y­sis are region (Northeast, North Central, South, and West), age, gen­der, and eth­nic­ity (Black; His­panic; mixed race, non- His­panic; and other, non-Black/non-His­panic). Descriptive sta­tis­tics for these var­ i­ables by sam­ple are displayed in Table 1. Prevalence, Penalties, and the Decomposition Procedure Studying gen­der dif­fer­ences in the con­tri­bu­tion of chang­ing fam­ily struc­tures to the paren­tal SES gap in col­lege attain­ment requires exam­in­ing dif­fer­ences in both Changing Family Structures and the Reproduction of Educational Inequalities 119 Table 1 Descriptive sta­tis­tics of the sam­ples used NLSY79 NLSY97 Variable Daughters Sons Daughters Sons Outcome Variables Bachelor’s degree com­ple­tion (%) 24.0 24.2 37.8 28.9*** High school/GED com­ple­tion (%) 91.1 89.5* 94.0 92.6* Years of edu­ca­tion (mean) 13.4 13.4 14.5 13.8*** Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 Family Structure at Age 17 (%) Living with both bio­log­i­cal par­ents 70.9 73.3* 49.4 54.0*** Living with a par­ent and step­par­ent 8.0 6.9 14.1 14.3 Living with a sin­gle par­ent 14.3 15.1 29.4 26.8* Not liv­ing with any par­ent 6.8 4.7*** 7.1 4.9*** Maternal Education (%) Bottom quin­tile 17.1 15.8 18.6 18.1 Middle 62.2 62.3 61.4 60.7 Top quin­tile 20.7 21.9 20.0 21.2 Control Variables Respondent’s age at inter­view (mean) 33.2 33.1 32.9 33.0 Black (%) 13.3 13.3 15.3 14.6 His­panic (%) 5.9 6.3 11.9 13.0 Mixed race (non-His­panic) (%) N/A N/A 1.1 1.1 Other/non-Black, non-His­panic (%) 80.8 80.4 71.7 71.3 N 3,790 3,632 3,228 3,151 Notes: Sample weights are included. N/A = response cat­e­gory is not avail­­able in the 1979 wave. Respon- dents’ age is assessed in the year that edu­ca­tion is mea­sured. Lower edu­cated moth­ers are those in the bot­tom 17% of the NLSY cohort mater­nal edu­ca­tional dis­tri­bu­tion; mid­dle edu­cated moth­ers are those in the mid­dle of the NLSY cohort mater­nal edu­ca­tional dis­tri­bu­tion; and higher edu­cated moth­ers are those in the top 21% of the NLSY cohort mater­nal edu­ca­tional dis­tri­bu­tion. Asterisks indi­cate sta­tis­ti­cally sig­nif­i­cant dif­fer­ences between sons and daugh­ters within the same cohort. *p < .05; ***p < .001 prev­a­lence and pen­al­ties. We doc­u­ment dif­fer­ences in prev­a­lence through descrip­ tive sta­tis­tics and exam­ine dif­fer­ences in pen­al­ties using lin­ear prob­a­bil­ity mod­ els (LPMs) explaining respon­dents’ bach­e­lor’s degree attain­ment. We esti­mate the com­bined impact of changes in prev­a­lence and pen­al­ties by employing an extended Blinder–Oaxaca decom­po­si­tion approach (Kim 2010; Smith and Welch 1989). We per­form the decom­po­si­tion anal­y­sis sep­a­rately for sons and daugh­ters because the decom­po­si­tion allows study­ing the attain­ment gap between only two groups: in this case, chil­dren with lower edu­cated moth­ers and those with higher edu­cated moth­ers.3 The objec­tive of the decom­po­si­tion is to explain changes in D, which rep­re­sents the abso­lute dif­fer­ence in col­lege attain­ment (Y) between indi­vid­u­als with higher edu­ cated moth­ers (h) and those with lower edu­cated moth­ers (l): D = Yh − Yl . (1) 3 In addi­tional ana­ly­ses, we use a pooled sam­ple of sons and daugh­ters. 120 D. Boertien and F. Bernardi ∆D rep­re­sents the abso­lute change in this group dif­fer­ence between peri­ods 0 and 1: ΔD = (Yh1 − Yl1 ) − (Yh0 − Yl 0 ). (2) In other words, ∆D operationalizes the extent to which social back­ground dif­fer­ences in col­lege attain­ment changed across cohorts. We con­sider four types of child­hood fam­ily struc­ture and define four dummy var­i­ ables distinguishing those who, at age 17, were liv­ing in a fam­ily with two bio­log­i­cal par­ents (f 0), with a sin­gle bio­log­i­cal par­ent (f 1), with a bio­log­i­cal par­ent and a step­ par­ent (f 2), or with­out bio­log­i­cal par­ents (f 3). Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 We then define X s as the weighted share of indi­vid­u­als i liv­ing in each child­hood fam­ily struc­ture type fs (with s = 0, 1, 2, 3), where ωi indi­cates nor­mal­ized sam­ple weights pro­vided with the data: n ∑ ω fs (3) Xs = i = 1 i i . n We esti­mate LPMs to esti­mate the prob­a­bil­ity of bach­e­lor’s degree attain­ment: Yi = α + β1 f 1i + β 2 f 2i + β3 f 3i + δx′i + ε i . (4) In Eq. (4), α expresses the aver­age bach­e­lor’s degree attain­ment for those who lived in a two-par­ent fam­ily. In all­ana­ly­ses, we include con­trols for race, gen­der, and age (δx′i ).4 In addi­tion, X s (with s = 1, 2, 3) cor­re­sponds to the prev­al­ ence of each type of fam­ ily struc­ture, and β s cor­re­sponds to their asso­ci­ated pen­alty com­pared with liv­ing in a two-bio­log­i­cal-par­ent fam­ily (the ref­er­ence cat­e­gory in Eq. (4)). Both X s and Eq. (4) are esti­mated sep­a­rately for each mater­nal edu­ca­tion group (lower and higher) and cohort (cohort 0 and cohort 1). For instance, X sh0 expresses the prev­a­lence of fam­ily type s among those with higher edu­cated moth­ers in cohort 0, whereas β sl1 expresses the pen­alty for those liv­ing in fam­ily type s with lower edu­cated moth­ers in cohort 1. We then decom­pose the change in social back­ground dif­fer­ences in col­lege attain­ ment between cohort 0 and cohort 1(∆D) as fol­lows (for more details, see Kim 2010): ΔD = (α h1 − α h0 ) − (α l1 − α l 0 )     (5a) !### #"#### $ Intercept effect {( ) ( ) }{ ( ) ( + ∑ S ⎡⎣ β sh1 + β sh0 / 2 ⎤⎦ − ⎡⎣ β sl1 + β sl 0 / 2 ⎤⎦ ⎡⎣ X sh1 − X sh0 / 2 ⎤⎦ + ⎡⎣ X sl1 − X sl 0 / 2 ⎤⎦ (5b) !###############"###############$ ) } Effect of general changes in prevalence      ( ) ( ) ( + ∑ S ⎡⎣ X sh1 − X sh0 − X sl1 − X sl 0 ⎤⎦ ⎡⎣ β sh1 + β sh0 + β sl1 + β sl 0 / 4 ⎤⎦ !###########"###########$ ) (5c) Effect of differences in changing prevalence between maternal education groups 4 We include covariates using effect cod­ing for cat­e­gor­i­cal var­i­ables (Jann 2008:9). Our approach dif­fers slightly from Kim’s in that we do not apply the aver­ag­ing method for coef­fi­cients (Kim 2010:627) in the case of our main medi­at­ing var­i­able: fam­ily struc­ture. We use hav­ing lived in a two-par­ent fam­ily as the ref­er­ence cat­e­gory. Therefore, ∑ s sums over the var­i­ous non­tra­di­tional fam­ily struc­tures, and betas indi­cate the effect, with two-par­ent fam­il­ies as the ref­er­ence. Using effect cod­ing also for fam­ily struc­ture would cal­cu­late a coun­ter­­ fac­tual that might be well suited for quan­ti­fy­ing changes in dis­crim­i­na­tion (i.e., the goal of Kim’s approach), but it has a less clear inter­pre­ta­tion in our case. See online Appendix B for a more detailed expla­na­tion. Changing Family Structures and the Reproduction of Educational Inequalities 121 {( ) ( ) }{ ( ) ( + ∑ S ⎡⎣ X sh1 + X sh0 / 2 ⎤⎦ − ⎡⎣ X sl1 + X sl 0 ⎤⎦ / 2 ⎡⎣ β sh1 − β sh0 + β sl1 − β sl 0 ⎤⎦ / 2 !##############"##############$ ) } (5d) Effect of general changes in penalties     ( ) ( ) ( ) + ∑ S ⎡⎣ β sh1 − β sh0 − β sl1 − β sl 0 ⎤⎦ ⎡⎣ X sh1 + X sh0 + X sl1 + X sl 0 / 4 ⎤⎦    (5e) !###########"###########$ . Effect of changing heterogeneity in penalties by maternal education Part (5a) of this equa­tion expresses the changes over time in group dif­fer­ences that can­not be accounted for by changes in the prev­a­lence of fam­ily struc­tures and related Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 pen­al­ties, labeled the inter­cept effect. Parts (5b) through (5e) together quan­tify the over­all change in the con­tri­bu­tion of child­hood fam­ily struc­tures to the cross-cohort change in group dif­fer­ences (∆D). Part (5b) cap­tures the effect of the aver­age cross-cohort changes in the prev­a­lence of the var­i­ous non­tra­di­tional fam­ily struc­tures. If the pen­alty related to grow­ing up in a given fam­ily struc­ture is stron­ger for a spe­cific group, increases in the prev­a­lence of this fam­ily struc­ture type will have a greater impact on that group’s out­comes. In other words, if both groups expe­ri­ence a change from 10% to 50% non­tra­di­tional fam­i­lies, the change will be more con­se­quen­tial for the group with the higher pen­alty of grow­ing up in a non­tra­di­tional fam­ily struc­ture. Therefore, this com­po­nent mul- tiplies the aver­age cross-cohort change in the prev­a­lence of non­tra­di­tional fam­i­lies, ⎡⎣( X sh1 − X sh0 ) + ( X sl1 − X sl 0 ) ⎤⎦ / 2, by the aver­age dif­fer­ences in pen­al­ties related to fam­ ily struc­tures between mater­nal edu­ca­tion groups, ⎡⎣(β sh1 + β sh0 ) / 2 ⎤⎦ − ⎣⎡(β sl1 + β sl 0 ) / 2 ⎤⎦. Part (5c) mea­sures the impact of the unequal changes in the prev­a­lence of fam­ ily struc­ ture types according to mater­ nal edu­ ca­ tion, ⎡⎣( X sh1 − X sh0 ) − ( X sl1 − X sl 0 ) ⎤⎦, weighted by the aver­age pen­alty of grow­ing up in a given fam­ily struc­ture across all­groups and cohorts, ⎣⎡(β sh1 + β sh0 + β sl1 + β sl 0 ) / 4 ⎤⎦. This com­po­nent rep­re­sents the diverg­ing des­ti­nies pre­dic­tion in its sim­plest form: the con­cen­tra­tion of increases in non­tra­di­tional fam­ily struc­tures among lower edu­cated moth­ers ampli­fied the paren­ tal SES gap in col­lege attain­ment. The pen­al­ties related to non­tra­di­tional child­hood fam­ily struc­tures can change across cohorts. Average changes in pen­al­ties across cohorts affect group dif­fer­ences because they will be more con­se­quen­tial for groups with higher shares of indi­vid­u­als liv­ing in house­holds with non­tra­di­tional fam­ily struc­tures. Hence, part (5d) weighs the aver­age change in pen­al­ties across cohorts, ⎡⎣(β sh1 + β sh0 ) / 2 ⎤⎦ − ⎣⎡(β sl1 + β sl 0 ) / 2 ⎤⎦, by mater­nal edu­ ca­tion dif­fer­ences in the prev­a­lence of fam­ily struc­tures, ⎡⎣( X sh1 − X sh0 ) − ( X sl1 − X sl 0 ) ⎤⎦ / 2. Finally, com­po­nent (5e) takes into account that also dif­fer­ences in pen­al­ties between mater­nal edu­ca­tion groups can change across cohorts. It weighs the change in dif­ fer­ences in pen­al­ties between mater­nal edu­ca­tion groups, ⎡⎣(β sh1 − β sh0 ) − (β sl1 − β sl 0 ) ⎤⎦ , by the aver­age prev­al­ence of the fam­ily struc­ture type across groups and cohorts, ⎡⎣( X sh1 + X sh0 + X sl1 + X sl 0 ) / 4 ⎤⎦. The decom­po­si­tion anal­y­sis relies on a rel­a­tively large num­ber of esti­mated terms. To test the robust­ness of the results to indi­vid­ual obser­va­tions, we esti­mate stan­dard errors and con­fi­dence inter­vals for all­terms of the decom­po­si­tion using a bootstrapping method (based on 500 rep­li­ca­tions using boot­strap resampling weights; Efron and Tibshirani 1993). 122 D. Boertien and F. Bernardi Daughters Sons Share With Bachelor's Degree .6 Maternal education .4 Low Middle .2 High Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 .0 NLSY79 NLSY97 NLSY79 NLSY97 Cohort Fig. 1 Bachelor’s degree attainment by cohort, gender, and maternal education. Lower educated mothers are those who did not complete grade 12; middle educated mothers are those who completed grade 12 but less than four years of college; and higher educated mothers are those who completed four or more years of college. Share in Family Structure at Age 17 Lower educated mother Middle educated mother Higher educated mother 100 75 Family structure Both biological parents 50 Other Parent and stepparent 25 Single parent 0 NLSY79 NLSY97 NLSY79 NLSY97 NLSY79 NLSY97 Cohort Fig. 2 Family structure at age 17, by cohort and mother’s education. Lower educated mothers are those who did not complete grade 12; middle educated mothers are those who completed grade 12 but less than four years of college; and higher educated mothers are those who completed four or more years of college. Results Figure 1 dis­plays changes in col­lege attain­ment across cohorts by mater­nal edu­ca­ tion and gen­der. Attainment increased across all­groups but espe­cially among daugh­ ters. The attain­ment gap between sons with lower edu­cated moth­ers and those with higher edu­cated moth­ers increased slightly, from a 47.6-per­cent­age-point dif­fer­ence for the 1979 cohort to a 50.1-point dif­fer­ence for the 1997 cohort. For daugh­ters, the increase in the gap was larger, from a 46.1- to a 58.6-per­cent­age-point dif­fer­ence across cohorts. The main ques­tion to be answered in this empir­i­cal sec­tion is to what extent these changes in the gaps in bach­e­lor’s degree attain­ment can be explained by changes in the prev­a­lence of fam­ily struc­tures and related pen­al­ties. Figure 2 shows changes in the prev­a­lence of four broad categories of fam­ily struc­ture across both cohorts. The prev­a­lence of fam­i­lies with two bio­log­i­cal par­ ents declined, and non­tra­di­tional fam­ily struc­tures became more com­mon among all­ groups con­sid­ered. The decline in fam­i­lies with two bio­log­i­cal par­ents was more pro­ nounced among indi­vid­u­als with lower edu­cated moth­ers, and the gap in this prev­ a­lence between chil­dren of higher edu­cated moth­ers and those with lower edu­cated Changing Family Structures and the Reproduction of Educational Inequalities 123 Daughters, Daughters, Sons, Sons, 1979 cohort 1997 cohort 1979 cohort 1997 cohort 0.1 Effect of Living in Nontraditional Family 0.0 –0.1 –0.2 Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 –0.3 –0.4 –0.5 Lower educated mother (βsh ) Higher educated mother (βsh ) Fig. 3 Penalties related to living in a nontraditional family according to maternal education, gender, and cohort. OLS coefficients are from eight separate models explaining bachelor’s degree attainment—one model for each group defined by maternal education, gender, and cohort. Controls are included for age, ethnicity, and religion. Whiskers indicate 95% confidence intervals. moth­ers increased from 13 to 29 per­cent­age points across cohorts. Among chil­dren liv­ing in a non­tra­di­tional fam­ily, 9% of the 1979 cohort lived with their bio­log­i­cal father, com­pared with 10% for the 1997 cohort (not shown). The con­tri­bu­tion of changes in fam­ily struc­tures to attain­ment gaps also depends on the pen­al­ties related to liv­ing in a non­tra­di­tional fam­ily. Figure 3 dis­plays pre- dicted dif­fer­ences in bach­e­lor’s degree attain­ment between chil­dren who lived in a two-bio­log­i­cal-par­ent fam­ily at age 17 and chil­dren who did not. These predicted dif­ fer­ences are taken from LPM mod­els for each group sep­a­rately by gen­der, mater­nal edu­ca­tion, and cohort, con­trol­ling for age, eth­nic­ity, and region. We find that chil­dren who lived with two bio­log­i­cal par­ents were more likely to attain a bach­e­lor’s degree than chil­dren who lived in a non­tra­di­tional fam­ily among all­groups, but there is great het­ero­ge­ne­ity in the size of this dif­fer­ence across groups. For the 1979 cohort, pen­al­ties observed are sta­tis­ti­cally sig­nif­i­cant only for daugh­ ters with higher edu­cated moth­ers. Statistically sig­nif­i­cant pen­al­ties are vis­i­ble for all­ groups of the 1997 cohort. Effect sizes increased across cohorts, par­tic­u­larly for sons with higher edu­cated moth­ers (with the dif­fer­ence increas­ing from 10 to 34 per­cent­age points across cohorts). For the 1979 cohort, we find quite minor dif­fer­ences in pen­al­ties between sons with lower edu­cated moth­ers and sons with higher edu­cated moth­ers. In the most recent cohort, the pen­alty related to hav­ing lived in a non­tra­di­tional fam­ily is much larger for sons with higher edu­cated moth­ers than for sons with lower edu­cated moth­ers. For daugh­ters, effects related to fam­ily struc­ture became more sim­i­lar across cohorts for daugh­ters with lower edu­cated moth­ers and those with higher edu­cated moth­ers. Table 2 pres­ents results from a model pooling obser­va­tions across all­groups (cohort, mater­nal edu­ca­tion, and gen­der). The model pro­vi­des insights into sta­tis­ ti­cal sig­nif­i­cance and illus­trates what we miss when we do not take gen­der dif­fer­ ences in effects into account. Model 1 con­firms sta­tis­ti­cally sig­nif­i­cant cross-cohort increases in the aver­age pen­alty related to grow­ing up in a non­tra­di­tional fam­ily and a higher pen­alty related to grow­ing up in a non­tra­di­tional fam­ily for those with a higher 124 D. Boertien and F. Bernardi Table 2 Linear prob­a­bil­ity mod­els explaining bach­e­lor’s degree attain­ment Model 1 Model 2 Variable Coef. SE Coef. SE Nontraditional Family (ref. = two-par­ent fam­ily) −0.02† 0.01 −0.01 0.02 Daughter (ref. = son) 0.04*** 0.01 0.01 0.02 Cohort 1997 (ref. = 1979 cohort) 0.12*** 0.02 0.06* 0.03 Mother’s Education (ref. = lower edu­cated) Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 Middle edu­cated 0.14*** 0.01 0.14*** 0.02 Higher edu­cated 0.49*** 0.02 0.49*** 0.03 Nontraditional Family × Cohort 1997 −0.08*** 0.03 −0.05 0.03 Nontraditional Family × Middle Educated Mother −0.06*** 0.02 −0.06* 0.03 Nontraditional Family × Higher Educated Mother −0.17*** 0.04 −0.11* 0.06 Middle Educated Mother × Cohort 1997 0.05 0.03 0.05 0.03 Higher Educated Mother × Cohort 1997 0.06 0.04 0.06 0.05 Nontraditional Family × Middle Educated Mother × Cohort 1997 −0.01 0.04 −0.03 0.05 Nontraditional Family × Higher Educated Mother × Cohort 1997 0.00 0.06 −0.15* 0.08 Nontraditional Family × Daughter −0.02 0.03 Cohort 1997 × Daughter 0.12*** 0.04 Middle Educated Mother × Daughter −0.00 0.03 Higher Educated Mother × Daughter 0.01 0.04 Nontraditional Family × Cohort 1997 × Daughter −0.08 0.05 Nontraditional Family × Middle Educated Mother × Daughter −0.00 0.03 Nontraditional Family × Higher Educated Mother × Daughter −0.13† 0.08 Middle Educated Mother × Cohort 1997 × Daughter −0.02 0.05 Higher Educated Mother × Cohort 1997 × Daughter −0.01 0.07 Nontraditional Family × Middle Educated Mother × Cohort 1997 × Daughter 0.03 0.07 Nontraditional Family × Higher Educated Mother × Cohort 1997 × Daughter 0.33*** 0.11 Constant 0.02 0.02 0.04* 0.02 N 13,801 Notes: Controls included are age, region, and eth­nic­ity. Sample weights are included. Bootstrap stan­dard errors are based on 500 rep­li­ca­tion weights. † p < .10; *p < .05; ***p < .001 edu­cated mother. Model 2 adds inter­ac­tion effects with gen­der, where the changes in pen­al­ties over time (observed in Figure 3) become vis­i­ble. The core find­ing of this model is that the effect of fam­ily struc­ture increased sig­nif­i­cantly more for sons with higher edu­cated moth­ers than for sons with lower edu­cated moth­ers (three-way inter­ ac­tion between fam­ily struc­ture, mater­nal edu­ca­tion, and cohort), but the oppo­site is the case for daugh­ters (as shown by the direc­tion and size of the four-way inter­ac­tion between fam­ily struc­ture, mater­nal edu­ca­tion, cohort, and gen­der). Decomposition Analysis The extent to which fam­ily struc­ture can explain cross-cohort changes in social back­ground dif­fer­ences in col­lege attain­ment depends on the rel­a­tive impor­tance of Changing Family Structures and the Reproduction of Educational Inequalities 125 Table 3 Decomposition anal­y­sis for var­i­ous out­come var­i­ables, with bootstrapped 95% con­fi­dence inter­vals shown in brack­ets Outcome High School Years of Bachelor’s Degree Completion Education Sons Maternal edu­ca­tion gap D in 1979 0.476 0.257 3.43 Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 Change in gap ∆D 0.025 −0.070 0.46    Eq. (5a): chang­ing inter­cept 0.088 −0.075* 0.48 [−0.003, 0.168] [−0.141, −0.005] [−0.07, 1.05]    Eq. (5b): chang­ing prev­a­lence −0.030* 0.004 −0.08 [−0.045, −0.015] [−0.009, 0.013] [−0.18, 0.01]    Eq. (5c): chang­ing prev­a­lence by SES 0.021* 0.006* 0.15*    [0.010, 0.034] [0.001, 0.013] [0.07, 0.26]    Eq. (5d): chang­ing pen­al­ties 0.022* −0.013* 0.17* [0.003, 0.041] [−0.028, −0.001] [0.04, 0.29]    Eq. (5e): chang­ing pen­al­ties by SES −0.075* 0.007 −0.26 [−0.129, −0.016] [−0.038, 0.055] [−0.58, 0.07] Total con­tri­bu­tion, (5b) – (5e) −0.063 −0.005 −0.02 Total con­tri­bu­tion as % of gap D in 1979 −13.2 −1.8 −0.1 Daughters Maternal edu­ca­tion gap D in 1979 0.461 0.227 3.24 Change in gap ∆D 0.125 −0.064 0.84    Eq. (5a): chang­ing inter­cept 0.056 −0.114* 0.22 [−0.034, 0.156] [−0.166, −0.059] [−0.29, 0.83]    Eq. (5b): chang­ing prev­a­lence −0.025* 0.024* 0.01 [−0.042, −0.008] [0.012, 0.036] [−0.08, 0.11]    Eq. (5c): chang­ing prev­a­lence by SES 0.025* 0.014* 0.16* [0.009, 0.043] [0.006, 0.024] [0.07, 0.28]    Eq. (5d): chang­ing pen­al­ties 0.009 0.010 0.05 [−0.020, 0.035] [−0.012, 0.036] [−0.13, 0.24]    Eq. (5e): chang­ing pen­al­ties by SES 0.061 0.003 0.39* [−0.002, 0.128] [−0.044, 0.047] [0.03, 0.79] Total con­tri­bu­tion, (5b) – (5e) 0.070 0.066 0.62 Total con­tri­bu­tion as % of gap D in 1979 15.2 22.2 19.1 Notes: Controls included are mater­nal edu­ca­tion, age, region, and eth­nic­ity; eth­nic­ity is excluded in the sub­sam­ple mod­els. Sample weights are included. D is the dif­fer­ence in out­comes between indi­vid­u­als with higher edu­cated moth­ers and those with lower edu­cated moth­ers in 1979; ∆D is the abso­lute change in D between the 1997 and 1979 cohorts. (5a) = inter­cept effect; (5b) = dif­fer­ence due to the aver­age change in prev­a­lence of fam­ily struc­tures; (5c) = dif­fer­ence due to the change in socio­eco­nomic prev­al­ence dif­fer­ ences; (5d) = dif­fer­ence due to the change over time in aver­age pen­al­ties; and (5e) = dif­fer­ence due to the change in the socio­eco­nomic dif­fer­ence in pen­al­ties. SES = socioeconomic status. *p < .05 changes in prev­a­lence and pen­al­ties. The decom­po­si­tion anal­y­sis allows us to take both trends into account (Table 3). In 1979, the abso­lute gaps in bach­e­lor’s degree attain­ment between chil­dren with higher edu­cated moth­ers and those with lower edu­ cated moth­ers was 47.6 per­cent­age points for sons and 46.1 per­cent­age points for daugh­ters. The increase in these gaps across cohorts was 2.5 and 12.5 per­cent­age points for sons and daugh­ters, respec­tively. Component (5a) indi­cates the part of 126 D. Boertien and F. Bernardi Table 4 Detailed esti­ma­tes of terms used in the decom­po­si­tion anal­y­sis (Eq. (5)) of Table 3 Lower Educated Mothers (l) Higher Educated Mothers (h) Cohort 1979 (0) Cohort 1997 (1) Cohort 1979 (0) Cohort 1997 (1) Sons Shares ( X s )    Two bio­log­i­cal par­ents .66 .42 .78 .69    Biological par­ent and Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 step­par­ent .07 .16 .05 .10    Biological sin­gle par­ent .19 .33 .14 .19    No bio­log­i­cal par­ent .08 .09 .03 .02 Penalties (βs) (ref. = two- par­ent fam­ily)    Biological par­ent and step­par­ent −0.05* −0.05 −0.15 −0.30*** (0.02) (0.04) (0.09) (0.07)    Biological sin­gle par­ent −0.01 −0.04 −0.05 −0.37*** (0.02) (0.03) (0.07) (0.05)    No bio­log­i­cal par­ent −0.04* −0.08** −0.22† −0.25 (0.02) (0.03) (0.11) (0.17) n 881 718 638 563 Daughters Shares ( X s )    Two bio­log­i­cal par­ents .63 .36 .79 .67    Biological par­ent and step­par­ent .08 .15 .05 .10    Biological sin­gle par­ent .16 .34 .14 .21    No bio­log­i­cal par­ent .13 .14 .03 .01 Penalties (βs) (ref. = two- par­ent fam­ily)    Biological par­ent and step­par­ent −0.06** −0.17*** −0.39*** −0.31*** (0.02) (0.09) (0.07) (0.07)    Biological sin­gle par­ent −0.03 −0.14*** −0.16** −0.17** (0.02) (0.07) (0.06) (0.05)    No bio­log­i­cal par­ent −0.03 −0.18*** −0.46*** −0.36* (0.03) (0.11) (0.08) (0.18) n 977 788 617 528 Notes: Shares reflect the weighted share of each fam­ily struc­ture type within each sub­group (Eq. (3)). Pen- alties are taken from sep­a­rate linear probability mod­els with con­trols for mater­nal edu­ca­tion, age, region, and eth­nic­ity (Eq. (4)). Sample weights are included. Standard errors are shown in paren­the­ses. † p < .10; *p < .05; **p < .01; ***p < .001 these cohort dif­fer­ences in gaps that is not explained by changes in the prev­a­lence and pen­al­ties related to child­hood fam­ily struc­tures. Components (5b) through (5e) indi­ cate the parts related to fam­ily struc­ture that con­trib­uted to mater­nal edu­ca­tion gaps in col­lege attain­ment. We dis­cuss the con­tri­bu­tion of each com­po­nent sep­a­rately. The pro­por­tions of chil­dren liv­ing in the var­i­ous child­hood fam­ily struc­tures used in the decom­po­si­tion anal­y­sis (the X s terms of Eq. (5)) are equiv­a­lent to the num­bers presented in Figure 2 but are cal­cu­lated sep­a­rately for sons and daugh­ters. The beta Changing Family Structures and the Reproduction of Educational Inequalities 127 terms (βs) used are equiv­a­lent to the num­bers presented in Figure 3 but are cal­cu­lated for detailed fam­ily struc­ture categories. Table 4 dis­plays the num­bers used in the decom­po­si­tion anal­y­sis. Effect of General Changes in the Prevalence of Nontraditional Families Component (5b) quantifies the con­tri­bu­tion of the aver­age increase in the prev­a­lence of non­tra­di­tional fam­i­lies across cohorts to the mater­nal edu­ca­tion gap in col­lege attain­ment. Because pen­al­ties related to non­tra­di­tional fam­ily struc­tures are greater for Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 chil­dren with higher edu­cated moth­ers, increases in the prev­a­lence of non­tra­di­tional fam­il­ ies across cohorts reduced mater­nal edu­ca­tion gaps in attain­ment. This com­po­nent was related to a 3.0-per­cent­age-point reduc­tion in the col­lege attain­ment gap for sons com­pared with a 2.5-per­cent­age-point reduc­tion for daugh­ters; both con­tri­bu­tions are sta­tis­ti­cally sig­nif­i­cant. Effect of the Changing Maternal Education Gap in the Prevalence of Nontraditional Families Component (5c) operationalizes the diverg­ing des­ti­nies argu­ment regard­ing fam­ily struc­ture in its sim­plest form. It quantifies changes in the attain­ment gap that can be attrib­uted to dif­fer­ences in the increase in non­tra­di­tional fam­i­lies among fam­i­lies with lower edu­cated moth­ers and those with higher edu­cated moth­ers (Figure 2). The more pro­nounced increase in non­tra­di­tional fam­i­lies among chil­dren with lower edu­ cated moth­ers aug­mented the gap in bach­e­lor’s degree attain­ment by 2.1 per­cent­age points for sons and by 2.5 per­cent­age points for daugh­ters. These fig­ures cor­re­spond, respec­tively, to 4% and 5% increases in the bach­e­lor’s degree attain­ment gap; both con­tri­bu­tions are sta­tis­ti­cally sig­nif­i­cant. Effect of General Changes in Penalties Component (5d) quantifies the con­tri­bu­tion of aver­age increases in the pen­al­ties related to child­hood fam­ily struc­ture across cohorts. Because non­tra­di­tional fam­i­lies are more com­mon among chil­dren with lower edu­cated moth­ers, increases in effect sizes across cohorts aug­ment attain­ment gaps between mater­nal edu­ca­tion groups. For sons, increas­ing pen­al­ties across cohorts are esti­mated to have increased the mater­nal edu­ca­tion gap by 2.2 per­cent­age points—5% of the ini­tial gap in 1979—and this con­tri­bu­tion is sta­tis­ti­cally sig­nif­i­cant. For daugh­ters, the cor­re­spond­ing esti­mate is 0.9 per­cent­age points—2% of the gap in 1979—but is not sta­tis­ti­cally sig­nif­i­cant. Effect of Changing Heterogeneity in Penalties by Maternal Education The final com­po­nent (5e) takes into account that the pen­al­ties related to child­hood fam­ ily struc­ture did not change uni­formly for all­groups. Increases in effects were much more pro­nounced for sons with higher edu­cated moth­ers than for sons with lower edu­ cated moth­ers (as also observed in Figure 3). This trend is esti­mated to have reduced 128 D. Boertien and F. Bernardi the mater­nal edu­ca­tion gap in bach­el­or’s degree attain­ment by 7.5 per­cent­age points. In con­trast, for daugh­ters, the pen­al­ties related to non­tra­di­tional fam­ily struc­tures increased only for those with lower edu­cated moth­ers, put­ting them at an addi­tional dis­ad­van­tage com­pared with daugh­ters who had higher edu­cated moth­ers. This trend increased the mater­nal edu­ca­tion gap in years of edu­ca­tion by 6.1 per­cent­age points. These con­tri­bu­tions cor­re­spond to −16% and 13% of the ini­tial mater­nal edu­ca­tion gaps observed in 1979. The con­tri­bu­tion of this com­po­nent is sta­tis­ti­cally sig­nif­i­cant at the 95% level for sons but is only mar­gin­ally sig­nif­i­cant for daugh­ters (p = .056). The dif­fer­ence in the con­tri­bu­tion of this com­po­nent between sons and daugh­ters is sta­tis­ti­ Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 cally sig­nif­i­cant, as evidenced by the non­over­lap­ping con­fi­dence inter­vals. The Overall Contribution of Changes in Family Structures to Inequality in Outcomes Components (5b)–(5e) com­bined indi­cate how changes across cohorts in the prev­ a­lence of fam­ily struc­tures and related pen­al­ties con­trib­uted to mater­nal edu­ca­tion gaps in bach­e­lor’s degree attain­ment. For sons, the over­all con­tri­bu­tion is esti­mated at a 6.3-per­cent­age-point reduc­tion in the gap between mater­nal edu­ca­tion groups across cohorts—13% of the ini­tial gap in 1979. For daugh­ters, all­com­po­nents together are esti­mated to have increased the mater­nal edu­ca­tion gap in bach­e­lor’s degree attain­ment by 7.0 per­cent­age points across cohorts—15% of the ini­tial gap observed in 1979. This result for daugh­ters is sub­stan­tively large, but it relies on a coef­fi­cient that is not sta­tis­ti­cally sig­nif­i­cant at the 5% level. This con­trast in results between sons and daugh­ters is pri­mar­ily pro­duced by com­po­nent (5e). This com­ po­nent depends, first, on the aver­age prev­a­lence of non­tra­di­tional fam­i­lies across groups and cohorts, which dif­fers lit­tle between sons and daugh­ters (Table 4). Sec- ond, the com­po­nent depends on how the dif­fer­ences between chil­dren with lower edu­cated moth­ers and those with higher edu­cated moth­ers in the effects of grow­ing up in a non­tra­di­tional fam­ily changed across cohorts. The detailed over­view of the terms under­ly­ing the decom­po­si­tion shows that the main gen­der dif­fer­ence lies in how pen­al­ties (βs) changed depending on mater­nal edu­ca­tion (and spe­cif­i­cally for chil­dren who lived with a sin­gle par­ent or a sin­gle par­ent and step­par­ent). In the Dis- cussion sec­tion, we review pos­si­ble expla­na­tions for these dis­tinct trends in pen­al­ties between sons, daugh­ters, and socio­eco­nomic groups. Endogeneity Would our con­clu­sions change if we could account for endogeneity? Associations of child­hood fam­ily struc­ture with edu­ca­tional out­comes have been found to over­es­ti­mate actual causal effects (McLanahan et al. 2013). Many of the events mark­ing the tran­si­ tion into non­tra­di­tional fam­ily struc­tures, such as sep­a­ra­tion or child­bear­ing out­side of a union, are driven by dis­ad­van­ta­geous cir­cum­stances or related to fac­tors such as con­flict, stress, or a lack of resources (Edin and Kafalas 2005; Lyngstad and Jalovaara 2010). It is there­fore unlikely that selec­tion into non­tra­di­tional fam­i­lies is pos­i­tive and that the aver­age pen­al­ties in our anal­y­sis under­es­ti­mate actual causal effects. Selection Changing Family Structures and the Reproduction of Educational Inequalities 129 would par­tic­u­larly affect com­po­nent (5c) regard­ing the dif­fer­en­tial change in the prev­a­ lence of child­hood fam­ily struc­ture across cohorts, which depends on the aver­age asso­ ci­a­tions of child­hood fam­ily struc­ture with col­lege attain­ment. Therefore, esti­ma­tes for this com­po­nent should be regarded as upper-bound esti­ma­tes. If the actual impor­tance of this com­po­nent is below these upper bounds, the over­all con­clu­sion for daugh­ters would weaken but the con­clu­sion would be strength­ened for sons. We can be rel­a­tively con­fi­dent that endogeneity is not driv­ing the results for changes over time in how pen­al­ties dif­fer according to mater­nal edu­ca­tion, com­ po­nent (5e), which is the com­po­nent most rel­e­vant for our con­clu­sions. Maternal Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 edu­ca­tion dif­fer­ences in pen­al­ties were sim­il­ar for sons and daugh­ters in the 1979 cohort but changed in oppo­site direc­tions across cohorts (see Table 3). Gender dif­fer­ ences in effects (and trends therein) are com­pli­cated to explain based on endogeneity because sons and daugh­ters gen­er­ally share the same fam­i­lies. In an addi­tional anal­ y­sis, we esti­mate sib­ling fixed-effects mod­els that account for time-con­stant unob­ served fam­ily char­ac­ter­is­tics. We dis­cuss the details and results of this anal­y­sis in the online Appendix C. Even though sib­ling fixed-effects mod­els must be interpreted with cau­tion (Sigle-Rushton et al. 2014), the pat­tern of socio­eco­nomic het­ero­ge­ne­ity in pen­al­ties among broth­ers and sis­ters is in line with the results of Figure 3 based on the com­plete sam­ple: child­hood fam­ily struc­ture mattered more for the col­lege attain­ment of daugh­ters with higher edu­cated moth­ers than for that of their broth­ers in the 1979 cohort. However, child­hood fam­ily struc­ture mattered more for sons with higher edu­cated moth­ers than for their sis­ters in the 1997 cohort. Robustness Checks Table 3 also sum­ma­rizes the results for alter­na­tive out­comes. The results for daugh­ ters using other mea­sures of edu­ca­tional attain­ment are sim­i­lar to our main results. For sons, the equal­iz­ing role of fam­ily struc­tures is not vis­i­ble for high school com­ ple­tion and years of edu­ca­tion across cohorts, pri­mar­ily because dif­fer­ences in the effects of fam­ily struc­ture between mater­nal edu­ca­tion groups did not increase much over time for these edu­ca­tional out­comes, par­tic­u­larly for high school com­ple­tion. Table D1 in the online appen­dix pres­ents results for dif­fer­ent sub­sam­ples. The main devi­a­tion from our main results is observed for His­panic daugh­ters, for whom we find an equal­iz­ing influ­ence of fam­ily struc­ture changes. Note, how­ever, that cell sizes are small for some of the sub­sam­ples stud­ied (with a min­i­mum cell size of 45 cases) and that the results are not sta­tis­ti­cally sig­nif­i­cant. These results pri­mar­ily serve as an illus­tra­tion that fam­ily struc­ture might play a dif­fer­ent role depending on race and eth­nic­ity (Cross 2020). Future research using larger sam­ples is required. Results reported in the online Appendix D show that our main results are robust to using (1) abso­lute instead of rel­a­tive lev­els of mater­nal edu­ca­tion, (2) mul­ti­ple impu­ta­ tions of miss­ing infor­ma­tion, (3) fathers’ edu­ca­tion instead of moth­ers’ edu­ca­tion (while also using mul­ti­ple impu­ta­tions), and (4) lim­it­ing the anal­ys­ is to respon­dents liv­ing with their bio­log­i­cal mother (even though results for daugh­ters become slightly weaker). Finally, we address a pos­si­ble con­cern that our obser­va­tion win­dow does not cover the com­plete period in which impor­tant changes in fam­ily struc­tures took place. Even though this coun­ter­fac­tual sit­u­a­tion does not fit any con­crete his­tor­i­cal period cor­ 130 D. Boertien and F. Bernardi rectly, we sim­u­late a sce­nario in which every­body grew up in a two-bio­log­i­cal-par­ent fam­ily. Similar to our main results, these sim­u­la­tions (online Appendix E) indi­cate that fam­ily struc­ture accounts for 3 per­cent­age points of the mater­nal edu­ca­tion gap in bach­e­lor’s degree attain­ment for daugh­ters (5% of the observed gap in 1997) but that the gap for sons would be 8 per­cent­age points greater if every­one grew up in two- bio­log­ic­ al-par­ent fam­i­lies (15% of the observed gap in 1997). Discussion Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 About 15 years ago, Sara McLanahan (2004) for­mu­lated the diverg­ing des­ti­nies the­ sis, according to which trends related to the sec­ond demo­graphic tran­si­tion inten­si­fied social-class disparities in fam­ily resources. Given that the first gen­er­at­ions of chil­dren whose fam­il­ ies expe­ri­enced these changes have come of age, we asked to what extent changes in child­hood fam­ily struc­tures trans­lated into increased socio­eco­nomic back­ ground inequalities in final edu­ca­tional attain­ment for sons and daugh­ters. We used data from the NLSY to com­pare a cohort that grew up pri­mar­ily in two-par­ent fam­ i­lies with a cohort in which half of the respon­dents lived in a non­tra­di­tional fam­ily at age 17. We performed an extended Oaxaca–Blinder decom­po­si­tion anal­y­sis based on the dis­tinc­tion between the prev­a­lence of fam­ily struc­tures and pen­al­ties related to grow­ing up in a non­tra­di­tional fam­ily. The results revealed that changes in fam­ily struc­ture across cohorts indeed increased mater­nal edu­ca­tion dif­fer­ences in bach­e­ lor’s degree attain­ment by 15% for daugh­ters (although the dif­fer­ence is only mar­gin­ ally sta­tis­ti­cally sig­nif­i­cant, requir­ing con­fir­ma­tion from future research), but reduced inequalities in bach­e­lor’s degree attain­ment by 13% for sons. Hence, we argue that the validity of the argu­ment that chang­ing fam­ily struc­tures con­trib­uted to diverg­ing des­ti­nies varies by gen­der and is not valid for sons dur­ing the period stud­ied. The results of this study sup­port nei­ther the gen­eral nar­ra­tive that fam­ily struc­ ture changes have inten­si­fied socio­eco­nomic inequal­ity of oppor­tu­nity nor ear­lier find­ings that the influ­ence of these changes is small to neg­li­gi­ble (Alamillo 2016; Bernardi and Boertien 2017; Duncan et al. 2017). These dif­fer­ences in con­clu­sions can be attrib­uted pri­mar­ily to the lack of atten­tion to het­ero­ge­neous effects by socio­ eco­nomic back­ground (Duncan et al. 2017) and gen­der (Alamillo 2016; Bernardi and Boertien 2017) in ear­lier research (see Cooper and Pugh 2020 for a sim­i­lar argu­ ment).5 How did includ­ing these con­sid­er­ations lead to con­clu­sions that dif­fer from those of ear­lier research? Our key find­ing is that the effects of grow­ing up in a non­tra­di­tional fam­ily changed very dif­fer­ently across cohorts for sons and daugh­ters. Sons from higher edu­cated back­grounds expe­ri­enced the greatest increases in pen­al­ties related to hav­ing lived in a non­tra­di­tional fam­ily, which narrowed the gap in col­lege attain­ment between sons with lower edu­cated moth­ers and those with higher edu­cated moth­ers. This obser­va­ tion can be aligned with pre­vi­ous research suggesting that indi­vid­u­als from advan­ taged back­grounds have more to lose from liv­ing in a non­tra­di­tional fam­ily (Biblarz and Raftery 1999; Bloome 2017; Martin 2012). The trans­mis­sion of human cap­i­tal 5 As shown in Table D2 in the online appen­dix, we find no con­tri­bu­tion of changes in fam­ily struc­tures to paren­tal edu­ca­tional attain­ment gaps once we pool the sam­ples of sons and daugh­ters. Changing Family Structures and the Reproduction of Educational Inequalities 131 from par­ents to chil­dren is more com­pli­cated for par­ents not resid­ing with their chil­ dren in the same house­hold (Coleman 1988). If time-inten­sive par­ent­ing strat­e­gies have become more impor­tant for edu­ca­tional out­comes across cohorts (Kalil et al. 2012; Lareau 2002), obsta­cles to inten­sive par­ent­ing (e.g., being the only cores­i­dent par­ent) will have increas­ingly larger effects on out­comes. A sim­i­lar argu­ment can be made for the trans­mis­sion of advan­tage through eco­nomic path­ways. If col­lege attain­ment increas­ingly depends on par­ents’ eco­nomic resources (Duncan et al. 2017; Pfeffer 2018; Schneider et al. 2018), events that reduce paren­tal income and wealth (e.g., paren­tal sep­a­ra­tion) might have become increas­ingly con­se­quen­tial across Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 cohorts (Bernardi and Boertien 2016). However, sons and daugh­ters grow up in the same house­holds. If sons from higher socio­eco­nomic back­grounds have increas­ingly more to lose from not coresiding with both par­ents than sons from lower socio­eco­nomic back­grounds, why did we not observe the same for daugh­ters? Earlier research has documented that sons’ edu­ca­tional out­ comes depend more on the aca­demic envi­ron­ment at school and at home than daugh­ ters’ out­comes (Autor et al. 2019; Brenøe and Lundberg 2018; Buchmann and DiPrete 2006; Chetty et al. 2016; Legewie and DiPrete 2012) and that the impor­tance of fathers’ edu­ca­tion for sons’ out­comes has increased over time (Buchmann and DiPrete 2006). A pos­si­ble expla­na­tion for this greater impor­tance of school and home envi­ron­ments refers to the con­struc­tion of gen­der iden­ti­ties in ado­les­cence, with larger var­i­a­tion in how impor­tant aca­demic achieve­ment is for mas­cu­line iden­ti­ties than for fem­i­nine iden­ti­ties (DiPrete and Buchmann 2013; Legewie and DiPrete 2012). More spe­cif­i­ cally, anti-school atti­tudes and behav­iors are part of some con­cep­tions of masculine iden­tity, but this is less true for fem­i­nin­ity. Hence, socio­eco­nom­i­cally advan­taged sons might have the most to lose from not coresiding with one of their par­ents because they are rel­at­ively less shel­tered from the risk of devel­op­ing anti-school atti­tudes. At the same time, the effects of fam­ily struc­ture increased con­sid­er­ably across cohorts for daugh­ters with lower edu­cated moth­ers too. This trend is largely respon­ si­ble for the pos­si­ble con­tri­bu­tion of fam­ily struc­ture to the diverg­ing des­ti­nies observed for daugh­ters. Hence, the com­plete story is more com­plex than suggested by the existing the­o­ret­ic­ al expla­na­tions that focus mainly on sons’ attain­ments. If child­hood fam­ily struc­ture weak­ens the inter­gen­er­a­tional trans­mis­sion of edu­ca­tional advan­tage for sons because of its rela­tion­ship with paren­tal resources, the mech­a­ nisms through which edu­ca­tional advan­tage is trans­mit­ted from par­ents to daugh­ters remain unclear. Future research can fur­ther inves­ti­gate the mech­a­nisms under­ly­ing these results. Overall, this study under­lines that more atten­tion should be directed at why there is het­ero­ge­ne­ity in effects, rather than maintaining a sole focus on the prev­ a­lence of fam­ily struc­ture types (see also Williams and Baker 2021). Our results also speak to the debate on the gen­der rever­sal in edu­ca­tional attain­ ment. The argu­ment that changes in fam­ily struc­tures can explain the rever­sal in the gen­der gap (Bertrand and Pan 2013; DiPrete and Buchmann 2013) has been chal­ lenged by a recent study. Lundberg (2017) used Add Health data to look at the edu­ca­ tional attain­ment of respon­dents born between 1976 and 1984. The find­ings showed that the effects of fam­ily struc­ture on edu­ca­tional attain­ment do not dif­fer by gen­der, a result we also observed when not interacting gen­der with paren­tal edu­ca­tion (see Table E2 in the online appen­dix). Our anal­y­sis shows that rather than changes in the prev­a­lence of fam­ily struc­tures, it is the changes in the pen­alty of grow­ing up in a 132 D. Boertien and F. Bernardi non­tra­di­tional fam­ily that con­trib­ute to increased gen­der dif­fer­ences in edu­ca­tional attain­ment. We leave the ques­tion of how much of the gen­der gap rever­sal can be explained by chang­ing effects of child­hood fam­ily struc­tures to future research. Limitations Our anal­y­sis has two major lim­i­ta­tions. First, our find­ings are lim­ited to edu­ca­tional attain­ment. Studying other out­comes, such as income or occu­pa­tion attain­ment, could Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 pro­vide a more com­plete pic­ture of the role of fam­ily struc­ture in the repro­duc­tion of inequal­ity. Second, data lim­i­ta­tions prevented us from tak­ing into account more com­ plex fam­ily struc­ture tra­jec­to­ries, as well as the num­ber of fam­ily tran­si­tions expe­ ri­enced dur­ing child­hood. The lat­ter fac­tor has received increas­ing atten­tion in the lit­er­a­ture (Cavanagh and Fomby 2019). Children from the 1997 cohort who lived in a non­tra­di­tional fam­ily at age 17 are more likely to have expe­ri­enced sev­eral fam­ily struc­ture tran­si­tions than chil­dren from the 1979 cohort who lived in a non­tra­di­tional fam­ily (Brown et al. 2016). This dif­fer­ence might explain why the pen­alty related to hav­ing lived in a non­tra­di­tional fam­ily gen­er­ally increased across cohorts. However, the num­ber of fam­ily tran­si­tions increased espe­cially among chil­dren from lower socio­ eco­nomic back­grounds (Brown et al. 2016), whereas increases in effect sizes were most pro­nounced for socio­eco­nom­i­cally advan­taged sons. Furthermore, an anal­y­sis look- ing at more com­plex fam­ily struc­ture tra­jec­to­ries for the 1979 cohort (see the online Appendix A) did not show larger pen­al­ties related to tra­jec­to­ries involv­ing at least two tran­si­tions than to tra­jec­to­ries with at most one tran­si­tion. Nonetheless, future research looking at more detailed fam­ily struc­ture types could be fruit­ful. An addi­tional anal­y­sis sep­a­rat­ing the role of sin­gle-par­ent fam­i­lies, step­par­ent fam­i­lies, and other non­tra­di­ tional fam­il­ies shows that changes in effect sizes related to sin­gle-par­ent fam­i­lies are pri­mar­ily respon­si­ble for results for sons, whereas the impor­tance of the var­i­ous non­tra­ di­tional fam­ily types is more equal for daugh­ters (see Table D3 of the online appen­dix). Conclusion The results of this paper are dif­fic­ ult to align with a gen­eral argu­ment that changes in fam­ily struc­ture have increased socio­eco­nomic back­ground inequal­ity in col­lege attain­ment. Our results for sons are in line with Coleman’s (1988) argu­ment that non­ tra­di­tional fam­ily struc­tures pose chal­lenges to the trans­mis­sion of advan­tage from par­ents to chil­dren and are effec­tively an equal­izer (for a sim­i­lar argu­ment on the gen­ eral effects of fam­ily struc­ture on income mobil­ity, see Bloome 2017). Conversely, for daugh­ters, we found that changes in fam­ily struc­tures con­trib­uted to diverg­ing des­ti­nies, largely because the impor­tance of fam­ily struc­ture for col­lege attain­ment increased across cohorts for daugh­ters with lower edu­cated moth­ers. Hence, the results of this arti­cle empha­size that how dif­fer­ent social groups (in our case, defined by gen­der and SES) are affected by events and sit­u­a­tions is equally impor­tant for under­stand­ing inequal­ity of oppor­tu­nity as under­stand­ing why the prev­a­lence of such events and sit­u­a­tions is socio­eco­nom­i­cally strat­ifi ­ ed. ■ Changing Family Structures and the Reproduction of Educational Inequalities 133 Acknowledgments We thank those pres­ent at the oppor­tu­ni­ties we had to pres­ent our work: the Berkeley Demography Brown Bag Series, the Population Association of America 2018 annual meet­ing, the Sociology Seminar Series Mannheim, the Divorce Conference 2017 in Antwerp, and the Inequality Working Group at the Euro­pean University Institute. 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Bernardi Thomson, E., Lappegård, T., Carlson, M., Evans, A., & Gray, E. (2014). Childbearing across part­ner­ships in Australia, the United States, Norway, and Sweden. Demography, 51, 485–508. Waldfogel, J., Craigie, T., & Brooks-Gunn, J. (2010). Fragile fam­i­lies and child wellbeing. Future of Children, 20(2), 87–112. Williams, D. T., & Baker, R. S. (2021). Family struc­ture, risks, and racial strat­i­fi­ca­tion in pov­erty. Social Problems, 68, 964–985. Diederik Boertien (cor­re­spond­ing author) dboertien@ced​­.uab​­.es Downloaded from http://read.dukeupress.edu/demography/article-pdf/59/1/111/1479208/111boertien.pdf by guest on 13 October 2022 Boertien • Centre d’Estudis Demogràfics, Universitat Autònoma de Barcelona, Barcelona, Spain;  https://​​ orcid​­.org​­/0000​­-0002​­-4105​­-8001 Bernardi • Euro­pean University Institute, San Domenico di Fiesole, Italy; https:​­/​­/orcid​­.org​­/0000​­-0002​ ­-5544​­-5184