ASRXXX10.1177/0003122416673598American Sociological ReviewEngland et al. 6735982016

American Sociological Review 2016, Vol. 81(6) 1161­–1189 Do Highly Paid, Highly Skilled © American Sociological Association 2016 DOI: 10.1177/0003122416673598 Women Experience the Largest http://asr.sagepub.com Motherhood Penalty?

Paula England,a Jonathan Bearak,b Michelle J. Budig,c and Melissa J. Hodgesd

Abstract Motherhood reduces women’s wages. But does the size of this penalty differ between more and less advantaged women? To answer this, we use unconditional quantile regression models with person-fixed effects, and panel data from the 1979 to 2010 National Longitudinal Survey of Youth (NLSY79). We find that among white women, the most privileged—women with high skills and high wages—experience the highest total penalties, estimated to include effects mediated through lost experience. Although highly skilled, highly paid women have fairly continuous experience, their high returns to experience make even the small amounts of time some of them take out of employment for childrearing costly. By contrast, penalties net of experience, which may represent employer discrimination or effects of motherhood on job performance, are not distinctive for highly skilled women with high wages.

Keywords motherhood, gender, labor markets, wage trajectories

Being a mother lowers women’s hourly earn- unjust—that the work of mothering is not ings. The mechanisms proposed to explain only unpaid, but also reduces one’s pay when this wage penalty for motherhood include one holds a job. Moreover, given that there is employers’ discrimination against mothers no parallel fatherhood wage penalty, the (Correll, Benard, and Paik 2007), reduced job motherhood penalty contributes to the overall performance due to the demands of mother- gender gap in pay (Waldfogel 1998). This pay hood (Azmat and Ferrer forthcoming), and gap, in turn, reduces the economic well-being the wage growth forgone during any time of single women and their children, and, to spent out of the labor force for childrearing the extent that “money talks” in relationships, (Budig and England 2001). reduces the bargaining power of women in Mothering, the quintessential care work, heterosexual couples (Bittman et al. 2003). produces public goods that many of us enjoy In this article we ask an intersectional as free riders. Although we pay nothing to question about differences between groups of their mothers, we benefit from having women in the size of the penalty they experi- spouses, friends, community members, co- ence for motherhood. Taken as a proportion workers, and employees whose good qualities arose in part through their mothers’ unpaid aNew York University efforts (England 2005). Given the public bGuttmacher Institute goods produced by mothering, many femi- cUniversity of Massachusetts-Amherst nists see it as poignant—indeed, downright dVillanova University

Downloaded from asr.sagepub.com at ASA - American Sociological Association on December 1, 2016 1162 American Sociological Review 81(6) of their wage, is this penalty higher for women leads women to interrupt their employment, it at the top or bottom of hierarchies of cogni- lowers their future wages upon their return to tive skill and wages? Highly skilled women employment (Budig and England 2001; Staff with high wages are privileged in many ways. and Mortimer 2012). Motherhood may also To foreshadow our findings, we find that one adversely affect wages through lowering job aspect of this privilege, their higher rates of performance (Azmat and Ferrer forthcoming; return to experience, has a price—a higher Becker 1985) or through leading women to proportionate wage penalty for motherhood. trade wages for “mother-friendly” jobs. We Although very few of these privileged women are interested in the sum total of all these drop out of employment, the little time some effects of motherhood, which we refer to as do take out is very costly to their future wage, the “total penalty” for motherhood. We also because the wage growth they lose while at examine “net penalties” that are revealed by home or working part-time is substantial. adjusting out any part due to motherhood Thus, when the motherhood penalty is esti- encouraging a loss of experience, tenure, or mated to include that portion of the penalty part-time employment. As is standard, we incurred because of lost experience and ten- express all penalties as a percent of a wom- ure, these privileged women have the highest an’s hourly wage. penalties. The net penalty, tapping employer discrimination or the effect of motherhood on performance, by contrast, does not differ con- Past Research sistently by wage or skill. Are Motherhood Effects Causal? One motivation for our inquiry comes from two articles that, taken together, present Causation is seldom certain outside of ran- a puzzle. Wilde, Batchelder, and Ellwood dom-assignment experiments, but the now (2010) find higher motherhood penalties for mature research on motherhood wage penal- women with higher cognitive skill levels, as ties suggests that associations between moth- measured by test scores, whereas Budig and erhood and wages are not merely reflective of Hodges (2010) find higher penalties at lower differential selectivity of women who are wage levels. This combination of findings is already destined to have low wages into puzzling, given that cognitive skills and motherhood, but rather are, at least in part, wages are positively correlated (Farkas et al. causal (Amuedo-Dorantes and Kimmel 2005; 1997). Moreover, both studies use the same Anderson, Binder, and Krause 2002, 2003; panel dataset, the National Longitudinal Sur- Avellar and Smock 2003; Budig and England vey of Youth (NLSY79), and both use models 2001; Budig and Hodges 2010; Correll et al. with person-fixed effects to remove omitted 2007; Gangl and Ziefle 2009; Glauber 2007; variable bias. In this article, we assess whether Korenman and Neumark 1992; Miller 2011; more advantaged or more disadvantaged Waldfogel 1997; Wilde et al. 2010). Some women—on the dimensions of cognitive skill researchers have assessed causal effects of and wage level—suffer larger motherhood motherhood by using instrumental variables penalties. that plausibly predict fertility but not wages As we use the term “motherhood penalty,” (Amuedo-Dorantes and Kimmel 2005; Kore- it does not imply that all of what we identify nman and Neumark 1992; Miller 2011).1 as a penalty is discrimination against mothers Other work shows evidence of causal effects by employers, although there is strong evi- of motherhood using person-fixed-effects dence that such discrimination exists (Correll models that control for all unchanging, unob- et al. 2007). Another mechanism hinges on served characteristics of women that might the fact that employers reward experience and affect their wages (Anderson et al. 2002; tenure with higher wage rates; thus, even Avellar and Smock 2003; Budig and England absent discrimination, when motherhood 2001; Glauber 2007; Miller 2011; Waldfogel

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1997). One type of selectivity into mother- both before and after controls for experience hood is not adequately dealt with by fixed- are included. Theirs was the first article in the effects models—the selectivity that arises literature on motherhood penalties to deploy when changing events negatively affect a quantile regression, a technique that provides woman’s career trajectory, leading women to separate estimates for how much an inde- decide to have a child. However, Wilde and pendent variable, in this case motherhood, colleagues (2010) present descriptive evi- affects an outcome at different percentiles dence from panel data that women’s wages do (called “quantiles”) of the dependent variable. not tend to fall before, but do often fall after, Standard regression models (sometimes a birth. called “mean regression”) assess how much an increase in an independent variable at its mean is associated with a change in the How Motherhood Penalties Vary by dependent variable at its mean; quantile Women’s Skill and Wage Levels regressions provide much more information. The two articles that prompted our inquiry Because test scores and wages are moder- give very different impressions of whether ately positively correlated (England, Christo- advantaged or disadvantaged women suffer pher, and Reid 1999; Farkas et al. 1997; Neal larger motherhood penalties. The first is a and Johnson 1996), such that many women with National Bureau of Economics Research high wages have high cognitive skills, and vice paper by Wilde and colleagues (2010), using versa, it is unclear what mechanisms would lead panel data from the National Longitudinal to low penalties for women with low cognitive Survey of Youth, begun in 1979. To measure skill but high penalties for women with low cognitive skill, they used a standardized test, wages. We attempt to solve this puzzle by the Armed Forces Qualifying Test (AFQT), examining how penalties differ by various com- administered shortly after the first wave. Such binations of skill and wage level. tests tap the kinds of cognitive skills taught in We use a relatively new statistical model, schools. Nonetheless, the authors believed it the unconditional quantile regression model to be cleaner for causal inference to use the (hereafter UQR), following the lead of Kille- test score rather than education as their mea- wald and Bearak (2014). Budig and Hodges sure of skill; the tests were given shortly after (2010) introduced the use of conditional the first wave, so test scores are thus exoge- quantile regression (hereafter CQR) to the nous to fertility and wage experience thereaf- literature on motherhood penalties. In their ter. By contrast, many women continue comment on Budig and Hodges (2010), Kille- getting more education for years. Combining wald and Bearak (2014) argue that to answer women of all races, Wilde and colleagues the question posed by Budig and Hodges— (2010) find the motherhood penalty to be whether women who have high or low wages much larger for women with higher skills, experience a larger motherhood penalty—one both before and after controls for experience. should use the less well known unconditional No prior paper had examined whether moth- quantile regression, introduced into the erhood penalties vary by women’s cognitive econometric literature by Firpo, Fortin, and skill levels as measured by test scores. A Lemieux (2009). Covariates in UQR models number do consider the related questions of help net out spurious associations between whether women with more education or those motherhood and wages, just as they do in in higher-level jobs suffer larger penalties, but CQR, but in UQR (but not CQR) the inclu- their findings are conflicting.2 sion of covariates in the model has no effect The 2010 article by Budig and Hodges on the wage quantile at which a given obser- reports that, for white women, the proportion- vation falls. In UQR, the quantile of each ate wage penalty for motherhood is much observation is decided by the value of wages larger at low levels of the wage distribution, at various percentiles of the univariate

Downloaded from asr.sagepub.com at ASA - American Sociological Association on December 1, 2016 1164 American Sociological Review 81(6) distribution of wages among the observations analyses that found little variation in mother- in the analysis. By contrast, when using CQR, hood penalties by wage quantiles for black as Budig and Hodges (2010) did, if a model women, and thus limited analyses shown in controls for education, then, for example, a their paper to white women. We too find finding that the motherhood penalty is 5 per- lower penalties for black women than for cent for women whose wage is at the 80th white women, and black women’s penalties quantile informs us about those at the 80th do not vary much by skill and wage quantile. wage percentile of wages among women of Given that we failed to find an explanation of their own education level. Women with low black women’s lower and less variable penal- wages relative to others at their education ties, we limit findings shown in this article to level might still be at a high wage quantile white women; we show findings for black unconditionally—that is, compared to all women in the online supplement, but we sum- women, not just those at their education level. marize them briefly here when discussing our After arguing for the appropriateness of UQR results. to answer Budig and Hodges’s (2010) ques- tion, Killewald and Bearak (2014) re-estimate The Motherhood Penalty and Why It Budig and Hodges’s (2010) simplest baseline Varies by Group: Past Research and model, and they find little difference in moth- erhood penalties by quantile; this contrasts Theory with Budig and Hodges’s CQR findings of Despite strong agreement that, on average, higher penalties for lower-wage women. In motherhood carries a wage penalty, researchers their reply, Budig and Hodges (2014) accept differ in their views about why it occurs, and that UQR is the preferred technique. about why penalties might vary by skill and In this article, we build on the emergent wage level. As mentioned earlier, we will dis- consensus that UQR is the preferred technique tinguish between what we call the “total” moth- for assessing how motherhood penalties vary erhood penalty, estimated in models not across the wage distribution, and we innovate controlling for experience, and the “net” pen- by using UQR to assess whether penalties are alty, estimated in models controlling for experi- lower at low wage levels (as Budig and ence to adjust out any effects that arise because Hodges [2010, 2014] suggest) at all cognitive motherhood takes women out of employment skill levels, and whether penalties are higher (or reduces their hours) for a time. The total for women with high cognitive skill (as Wilde penalty is affected by motherhood-induced and colleagues [2010] suggest) at all wage experience differentials, as well as other fac- levels. That is, we look at how penalties vary tors, such as employer discrimination based on according to skill across wage levels. motherhood or lowered job performance In addition, in an online supplement (http:// because of motherhood. The net penalty is asr.sagepub.com/supplemental), we provide a affected only by mechanisms other than experi- parallel analysis for black women, allowing ence; we thus treat it as the combined effect of us to examine how race affects motherhood discrimination and performance differences penalties as well as racial differences in how among women with the same experience. penalties vary by skill and wage level. Past research shows smaller motherhood penalties Motherhood lowers pay because of for black than white women (Hill 1979; Glau- forgone experience. Some women respond ber 2007, 2013; Waldfogel 1997), but the to having a child by spending some months or differentials remain unexplained.3 Wilde and years out of employment or by reducing the colleagues (2010) included women of all hours they work per week. Although there is races in their analyses without exploring no agreement on whether experience is interactions of motherhood and race, but rewarded with higher wage rates because Budig and Hodges (2010) did preliminary experience increases productivity, as human

Downloaded from asr.sagepub.com at ASA - American Sociological Association on December 1, 2016 England et al. 1165 capital theory posits, or because of institu- If higher cognitive skills allow workers to tional practices undertaken for other reasons, learn more effectively on the job, increasing it is clear that wages rise with experience and their productivity more quickly, and if produc- thus that forgoing experience lowers future tivity affects wages, this will lead more-skilled wages. Some research includes measures of workers to have higher returns to experience, overall years of experience as well as the and thus higher total motherhood penalties. experience one has accumulated with the pre- Some evidence suggests this: Killewald and sent employer (i.e., “tenure” or “seniority”). Gough (2013:484) show higher returns to Most studies show that estimated penalties experience for more-educated women, and are substantially reduced, but not eliminated, Wilde and colleagues (2010) show that, before when models add a control for employment childbearing, women with high cognitive experience and tenure; that is, they explain skills have steeper wage trajectories. part, but not all, of total motherhood penalties What would we expect about penalties (Anderson et al. 2002, 2003; Budig and Eng- varying by wage level? If low-wage workers land 2001; Budig and Hodges 2010; Waldfo- have lower returns to experience, they should gel 1997; Wilde et al. 2010).4 (Staff and also have a lower total motherhood penalty. Mortimer [2012] explain the entire gap with In the 1970s and 1980s, authors theorizing experience-related measures; they examined segmented labor markets posited that firms’ women up to 31 years of age in Minnesota.) low profits and lack of unionization led to Because experience is the mechanism for a jobs that not only paid low starting wages but significant portion of the total motherhood also had little wage growth, because they penalty, we would expect the total penalty to were not attached to the job ladders of inter- be larger in groups that interrupt their employ- nal labor markets (Doeringer and Piore 1971; ment experience for longer periods at home. Edwards, Reich, and Gordon 1975; Tolbert, Thus, we should see higher total penalties for Horan, and Beck 1980). This suggests that women with low wages, because they are low wages often go with low returns to expe- more likely to drop out of employment (Blau rience, but researchers then were working and Kahn 2007). We know of no research on with datasets that lacked measures of experi- whether cognitive skill affects how much ence, so such claims were not tested. If the motherhood reduces women’s employment. claims of an association between low wages But given the correlation between skill and and low returns to experience are correct, education, and the more continuous employ- then we would expect lower total motherhood ment of more-educated women (Byker 2016; penalties in lower-wage jobs. England, Garcia-Beaulieu, and Ross 2004; To summarize, we argued that groups with England, Gornick, and Shafer 2012), we lower experience (including lower tenure) might expect skilled women to suffer lower should have higher total penalties, and groups total motherhood penalties because they stay with higher returns to experience should have employed more continuously. higher total penalties. Indeed, the amount of How much a given amount of time spent any group’s motherhood penalty that is due to out of employment lowers wages depends on experience should be a multiplicative func- the return to experience one would have had tion of the amount of experience they have if one stayed employed. Given this, if we lost to motherhood and their returns to experi- compared two groups with an equal amount ence. This means making predictions about of experience lost to motherhood, we would group differences in total penalties is diffi- expect groups of women with higher rates of cult, because our review suggests that groups return to experience to have higher total that are more advantaged in skill and wage motherhood penalties.5 Predictions about dif- may have higher levels of experience and ferences in penalties between groups defined higher returns to experience. If so, these two by skill or wage follow from this. features of their situations will have

Downloaded from asr.sagepub.com at ASA - American Sociological Association on December 1, 2016 1166 American Sociological Review 81(6) contradictory effects on the size of their total illuminating whether discrimination against motherhood penalties. We thus formulate two mothers varies by skill or wage. In our analy- contrasting hypotheses that differ on which sis, the inference of discrimination will not be part of this multiplicative effect should domi- clear if there is a penalty net of experience, nate group differences in penalties: because the net penalty could also result from the effect of motherhood on women’s perfor- Hypothesis 1: Groups with higher rates of return mance in their jobs. to experience will have higher total mother- Becker (1985, 1993) claimed that mother- hood penalties than groups with lower rates hood reduces women’s productivity on the of return to experience. Women who have job, thus affecting pay; if women do “home high skills and high wages will thus have production” when not on the job, they have higher total motherhood penalties, because they also have relatively high rates of return less energy left for job performance at work. to experience. His argument was theoretical; he had no data with measures of productivity. However, one Hypothesis 2: Groups with lower levels of ex- recent study of a representative sample of U.S. perience will have higher total motherhood lawyers admitted to the bar in 2000 proposed penalties than groups with higher levels of “billable hours” as a measure of productivity, experience. Women with low skills or low which is commonly accepted in law firms wages will thus have higher penalties, be- because of its direct effect on revenue. Using cause they have lower levels of experience. this measure, Azmat and Ferrer (forthcoming) show that gender differences in the number of Motherhood lowers pay because it “billable hours” explain a substantial share of affects performance or because employ- the gender gap in pay, and that having children ers discriminate against mothers. Some reduced billable hours for women but not for mechanisms for the motherhood penalty have men.7 Thus, there is some evidence that moth- nothing to do with levels of, or returns to, erhood lowers productivity, but the hypothesis experience; they affect the penalty estimated is untested for most occupations. net of experience, and they also affect the The productivity portion of the mother- total penalty, because the net penalty is part of hood penalty is undoubtedly also a function of the total penalty. One such mechanism is dis- how gender, family, and jobs are socially crimination against mothers by employers. organized (Acker 1990; Williams 2004; Wil- This discrimination could entail offering liams and Bornstein 2008). For example, lower pay to mothers, less willingness to hire motherhood would be unlikely to affect pro- mothers in high-paying jobs, or offering ductivity in paid work more than fatherhood fewer promotions to mothers. Correll and col- does if gender did not structure who does leagues’ (2007) audit study provides evidence childrearing and associated household work. of hiring discrimination against mothers in Moreover, governmental and employer poli- elite jobs. They sent equivalent résumés as cies may affect the link between motherhood applications to real job ads, varying randomly and productivity. For example, in cases where whether the résumé indicated indirectly that a working long hours is highly rewarded, with woman was a mother by saying she was a little flexibility in which hours are worked, PTA officer. (The alternative “non-mother” women, especially mothers, will be more dis- résumé said the woman was an officer of a advantaged (Cha and Weeden 2014; Goldin neighborhood association.) Résumés of moth- 2014; Herr and Wolfram 2012). Where women ers received significantly fewer calls in are offered paid leave after a birth, this may response to job applications.6 The positions in increase their ability to return to the same Correll and colleagues’ audit study were high- employer, and thus not lose the benefit of their skilled professional jobs and the applicants accumulated tenure (Baker and Milligan 2008; were college graduates. We lack audit studies Waldfogel 1998). In this analysis, however,

Downloaded from asr.sagepub.com at ASA - American Sociological Association on December 1, 2016 England et al. 1167 we are unable to model these variations, or jobs after unanticipated events, such as when even to estimate how much of the penalty childcare arrangements fall through. Budig results from productivity versus discrimina- and Hodges (2010) also argue that low-wage tion averaged across contexts. The closest we women have less income from their own can come is to estimate the net-of-experience earnings to purchase things such as a car or penalty, which is our best estimate of the por- flexible childcare. Thus, when they have chil- tion of the penalty that results from how moth- dren, they may be less able to avoid absences erhood affects how well one actually performs, that get them relegated to even lower wages. or how well, through discriminatory lenses, The predictions just discussed relate to that one is perceived to meet job demands. part of the motherhood penalty not coming Do these net penalties, picking up discrimi- through the effect of motherhood on experi- nation or productivity, differ by skill? Wilde ence, but rather the net penalty, estimated in and colleagues (2010) hypothesized that highly models that control for amount of experience, skilled women suffer higher motherhood penal- and theorized to result from effects of mother- ties because they are in jobs most sensitive to hood on performance, or on employers’ effort. Putting their point more expansively, biased perceptions or discriminatory treat- highly skilled women often hold jobs critical to ment of mothers. This leads to two distinct their organizations’ profits or other goals, so if predictions, one suggesting that advantaged motherhood causes any reduction in effort or women and one that disadvantaged women performance (real or perceived), it may have a have larger penalties: large impact on the organization’s (real or per- ceived) “bottom line,” giving employers an Hypothesis 3: Advantaged women (women with especially large incentive to make wages high skills and high wages) will have higher responsive to performance. Findings by Glass net motherhood penalties. They are more (2004) are consistent with this claim; among likely to be in jobs in which any decline in performance (real or perceived) due to moth- women who have a child and stay with the erhood has a larger effect (or perceived ef- same employer, those who used family-friendly fect) on their organizations’ bottom line. policies, such as reduced hours or working from home, had slower wage growth, a differ- Hypothesis 4: Disadvantaged women (women ence most pronounced for women in profes- with low skills or low wages) will have high- sional and managerial jobs. These patterns er net motherhood penalties. They have less suggest that using family-friendly policies power to negotiate job flexibility and less reduces productivity, or that employees who money to purchase services needed to avoid take employers’ offers of flexibility options are negative effects of motherhood on their per- seen as less productive, and thus are penalized formance (or perceived performance). even if their productivity is not reduced. In contrast to the argument of Wilde and Data And Methods colleagues (2010) that penalties are higher for more cognitively skilled women, Budig and Data Hodges (2010) offer reasons why high-wage Like Wilde and colleagues (2010) and Budig jobs (which typically also entail higher skills) and Hodges (2010), we use nationally repre- would have lower net motherhood penalties. sentative panel data from the National Longi- They suggest that jobs paying lower wages tudinal Survey of Youth 1979 (NLSY79). The are more inflexible, and their incumbents cohort was born between 1958 and 1965 and have little power to negotiate changes that first interviewed in 1979 at age 14 to 21. We would help accommodate motherhood use data through the 2010 interview when the demands. The result may be productivity cohort was age 45 to 52.8 This cohort is, reductions that are reflected in wages, or ter- roughly speaking, the second half of the baby minations that force women to take worse boom, and is now in middle age and largely

Downloaded from asr.sagepub.com at ASA - American Sociological Association on December 1, 2016 1168 American Sociological Review 81(6) through the childbearing years. These data We convert wages to constant 1996 dollars include detailed employment and family and then take the natural logarithm. information collected repeatedly throughout the adult lives of the respondents. Cognitive skill: interacted with all Our main analyses are limited to non-His- other independent variables. We interact panic white women (hereafter called “white”). the cognitive skill variable with all other vari- We limit the main analyses to white women in ables to provide separate estimates of the part to be consistent with the analysis of motherhood penalty by skill. To measure cog- Budig and Hodges (2010), who limited their nitive skills, we use age-adjusted scores from analysis to white women. Another reason for the Armed Forces Qualifying Test (AFQT), limiting the sample to white women is that, administered to all respondents in 1980; this is for the most part, the motherhood penalty the measure Wilde and colleagues (2010) does not differ by skill or wage level for black used. We use women of all races to assess cut- women, but we cannot be sure if this null ting points for thirds to follow Wilde and col- finding is due to limited statistical power, leagues (2010).11 Because preliminary results given the relatively small sample size of showed that motherhood penalties differed black women. We will briefly summarize little between the middle and bottom third, we results for black women here, and we provide dichotomized the variable into the top third regression results in the online supplement. versus the bottom two thirds, which we will, We exclude women of other races because we for brevity, refer to as “high” and “low” skill. do not have enough statistical power for sepa- Our use of AFQT does not imply a belief that rate estimates for these groups. individuals’ scores measure something entirely Our models, discussed in the next sections, determined innately. Scores are potentially take person-years as the units of analysis; affected by genetically inheritable factors; thus, our analytic sample consists of 37,063 socially determined learning environments at person-year observations from 3,216 non- school, at home, and in the community; and Hispanic white women. The online supple- their interactions. Our goal is simply to ascer- ment shows results from a parallel analysis of tain whether motherhood penalties vary by 18,520 person-year observations from 1,442 skill within categories of wage level. Moreover, non-Hispanic black women. To get separate we make no claim that AFQT, or the broader estimates of the motherhood penalty by race, construct of cognitive skills the test taps, are we include one indicator variable for race and the only kind of skills relevant to labor market interact it with all variables.9 success. We do note, however, that this test The person-years in the analytic sample predicts earnings net of education and race, exclude years during which women were and does so for white, black, and Hispanic enrolled in school (secondary school or higher respondents (England et al. 1999; Farkas et al. education), because wages in those years may 1997; Neal and Johnson 1996). be misleading; however, in broad terms, our Why examine how motherhood penalties conclusions are not affected if we retain these vary by skill? Broadly, our motivation is to see person-years (results available upon request).10 whether women toward the top and bottom of job and reward hierarchies experience differ- ent motherhood penalties. We do this in part Variables by examining how penalties vary by wage Dependent variable. Our dependent varia- level, using quantile regression. But skill is ble, consistent with most past research, another aspect of job hierarchies. Although including that of Budig and Hodges (2010, there is no one-to-one match between indi- 2014) and Wilde and colleagues (2010), is the viduals’ skills and the skill demands of their natural logarithm of the hourly wage a woman jobs, these aspects are positively correlated: earned at the time of the given year’s survey. people with more skill are more likely to be

Downloaded from asr.sagepub.com at ASA - American Sociological Association on December 1, 2016 England et al. 1169 hired in jobs requiring more cognitive skill Control variables. Other variables in all (Farkas et al. 1997). Moreover, there is evi- of our models include indicator variables for dence that individual-level skill affects wage each year. We also include respondent’s age differences between individuals in jobs with and its square in the given year.13 We control comparable skill demands, perhaps because for respondent’s geographic location in the skill affects performance (Farkas et al. 1997). given year with indicator variables for four We chose an individual-level measure of cog- regions of the country (Northeast, West, nitive skill to tap this crucial skill dimension South, Midwest), and for whether the respond- of inequality. We do this in part to revisit ent lives in a central city in a Metropolitan Wilde and colleagues’ (2010) analysis, which Statistical Area (MSA), elsewhere in an MSA, used the same AFQT measure. We could have or outside an MSA.14 We also enter education stratified by occupational measures of skill attained by the given year, with indicators for demands, or by broad occupational categories, college or more, some college, or less than and future research could usefully do this. We high school, where high school is the refer- could also have used education as a proxy for ence category.15 We include interactions skill, as other studies have done, with mixed between the age variables and each education results. However, Wilde and colleagues (2010) indicator, allowing us to model the potentially argue that using scores from one test adminis- greater wage gains with age experienced by tered only slightly after Wave 1 of the survey women with higher education. Equation 1 is a better strategy, because this one early includes motherhood and these controls. measurement ensures that the scores are exog- Our next most saturated model, Equation 2, enous to all future fertility and wage experi- adds the woman’s marital status (in three cat- ence. One could similarly ensure exogeneity egories: not yet married; married and still by taking respondents’ education at Wave 1, together; and separated, divorced, or wid- but for respondents who were very young at owed). It also includes her spouse’s annual Wave 1 it is a much worse indicator of ulti- earnings in the previous year, set to 0 if she is mate education than is the skill measure. If not married. The control for marital status instead we used education at each wave to “removes” the effect of these 0s from the coef- measure skill, it might be endogenous to num- ficient on spousal earnings. Spousal earnings is ber of children. also 0 if a woman is married but her husband had no earnings the past year. We include The key independent variable – spousal earnings to control for other income motherhood. Our main independent varia- available in the family, which might affect how ble is motherhood, measured by the number much women will try to maximize earnings. of children a woman has ever given birth to Equation 3 adds person-fixed effects to (or adopted) by the person-year. This way of remove potential selectivity into motherhood measuring motherhood follows the practice on unmeasured variables. In models with of much past research, including Budig and fixed effects, coefficients on measures of England (2001), Budig and Hodges (2010, motherhood reveal the within-person (across 2014), and Killewald and Bearak (2014). As a year) change in wages associated with wom- sensitivity test, in the Appendix we show en’s changes in motherhood, after adjusting results from a specification similar to that for observed covariates that also change used by Wilde and colleagues (2010), which across years. Such models control for all measures the penalty with indicator variables unmeasured, unchanging characteristics of for having been a mother different amounts of persons that contribute additively to the esti- time (relative to not being a mother), with a mation of their wages (Allison 2005). One control variable for number of additional chil- type of selectivity into motherhood is not dren past the first.12 dealt with by fixed-effects models—when an

Downloaded from asr.sagepub.com at ASA - American Sociological Association on December 1, 2016 1170 American Sociological Review 81(6) event that starts a woman upon a negative variable, which treats a year of full-time and wage trajectory also makes her decide to have part-time experience equally. To allow effects a child. If this occurs, models with fixed to be nonlinear, we enter the square of experi- effects will overestimate the negative effect ence as well.16 To measure tenure, we use a of motherhood on wages—attributing to measure of the cumulative number of hours motherhood some negative effects of changes worked for pay since a woman began working that preceded and caused motherhood. Thus, for her current employer, and we include the a key assumption in our claim that our coef- square of this measure to allow effects to be ficients are unbiased is that negative career nonlinear. (As is common practice, we include trajectories do not affect when or if women tenure in the experience measure.) Age, expe- have children. As this is a strong assumption, rience, tenure, and the square of each are also it is fortunate that Wilde and colleagues each interacted with each education dummy, (2010) present a convincing descriptive anal- to adjust for the potentially higher rates of ysis of the path of wages before and after return to experience or tenure obtained by births, showing no evidence that women’s women with high education (Killewald and wages typically fall before a birth; in fact, Gough 2013).17 We enter experience, tenure, wages more typically rise before a birth. the square of each, and part-time status18 in Finally, our most saturated model, Equa- the same model, but examinations (not shown) tion 4, includes work experience, tenure, of models that do not include part-time status whether the current job is part-time versus and tenure show that reductions in the mother- full-time, and the interaction of each of these hood penalty between Equations 3 and 4 come measures with education. To measure experi- largely from the control for experience.19 ence, we use a measure of the cumulative number of hours worked for pay since the first Regression Models wave of the survey for each person-year observation. This measure, also used by Wilde As described earlier, our most saturated and colleagues (2010), is superior to the more model is as follows: customary years (or weeks) of experience

1 1 2 qwττ(ln)ageit =+∑∑ (β01jk kidsijktjβββkττ++ageijktj1 k ageijktj2 kkτ 0 kj == 0

++EDUCATIONijktjββ34kiττage t × EDUCATIONijktjk 2 +aageijkt ×+EDUCATIONMijktjββ53kjττk ARRIAGEijktjβ7 kτ 2 +spouse’’’searningsijktjββ8 kττ+ spousesearningsijktj9 k

+spouses’ earrnings unknownuijktjββ10 kττ++rbanijktj11 k REGIONijktjβ12 kτ 22 +MMSAYijktj++EAR kt ββ13 jkττexperienceijktj14 k + experienceijkt β15 jkτ

+×experienceijkt EDUCATIONijktjβ16 kτ 22 +experienceijkt ×+EDUCATIONtijktjββ17 kττenureEijkt × DUCATIONijktj18 k 2 +tenurreijkt ×+EDUCATIONfijktjββ19 kττulltimeijktj20 k )

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The dependent variable is the natural loga- Computing estimates of the mother- rithm of a woman’s hourly rate of pay in 1996 hood penalty at varying percentiles of constant dollars. We compute separate esti- women’s wage distribution. As mentioned mates for each quantile of the outcome distri- previously, we use unconditional quantile bution, indexed by τ; the method for doing regression (UQR) to estimate separate coef- this will be explained below. The subscript i ficients for a number of quantiles of women’s indexes women; the subscript t indexes the wage distribution. One of the articles that wave of the survey; and the it uniquely iden- motivated our work—Budig and Hodges tify the person-year observations. The sub- (2010)—used conditional quantile regression script j indexes skill category, and the (CQR; see Hao and Naiman 2007; Koenker subscript k indexes race category. Because we 2005; Koenker and Bassett 1978), but we use report findings for black women in the online UQR, which was introduced into the econo- supplement, we interact all variables with metric literature more recently by Firpo, For- race, with white women as the reference cat- tin, and Lemieux (2009). UQR is appropriate egory. To obtain separate penalties by skill if we want to compare motherhood penalties level, we interact all variables with the cogni- between women whose wage levels are high tive skill dichotomy, with low skill as the versus low in an absolute sense, whereas reference. With respect to race, for example, CQR is appropriate if we want to compare for kidsijkt , kidsij0t equals the number of motherhood penalties at different points in children born to woman i by wave t; kidsij1t the conditional wage distribution—that is, is an interaction term and equals the same for across women who differ in whether their black women but is scored 0 for white women. wage is higher or lower than would be Put another way, ij0t indicates a baseline, and expected given their scores on covariates in ij1t an interaction term, with respect to race. the model, for example, whether women with Similarly, but with respect to skill categories, low wages compared to others with similar kids , for ijkt kidsik0 t equals the number of education have higher motherhood penal- children born to woman i by wave t; corre- ties.20 Our interest is in the former, so UQR is spondingly, kidsik1 t is an interaction term and appropriate, as Killewald and Bearak (2014) equals the same for highly skilled women, but suggested, and Budig and Hodges (2014) now 0 for lower-skilled women. Put another way, agree. In UQR, as in CQR, covariates in the i0kt indicates a baseline term, whereas i1kt model help net out spurious associations indicates an interaction term, with respect to between motherhood and wages, but in UQR skill. Other variables are entered as described the inclusion of covariates has no effect on above, with effects estimated for black and which person-years are defined to be at which white women at each skill level by fully inter- quantile of the wage distribution. This means acting everything with skill and race. As that in the series of nested UQR models we mentioned earlier, other variables included in estimate, the same observations are at the all models are age and its square, education 20th and 80th (or any other) quantile across categories, the interaction of the age variables models, which is not true with CQR. with the education categories, year indicators, UQR can be estimated using a simple ordi- and variables capturing geography. A more nary least squares (OLS) regression on a saturated model also includes marital status, transformed dependent variable, the recen- husband’s earnings, and its square. The most tered influence function (RIF), which is saturated model also includes work experi- defined in the following way: ence, its square, tenure, its square, whether the current job is part-time versus full-time, ()τ −≤1{}Yqτ and the interaction of each of these measures RIFY();,qFττY =+q with education. fqY ()τ

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τ is a given quantile. qτ is the value of the Our tables with quantile regression results outcome variable, Y, at the τth sample quan- show coefficients for effects of motherhood at q tile. fqY ()τ is the density of Y at τ . 1 is the the 20th, 50th, and 80th percentile of white indicator function. For example, suppose we women’s logged wage, with the separate effects are interested in the motherhood penalty for at each of these quantiles obtained using UQR women at the 20th quantile of the wage distri- as described earlier. We take the 20th and 80th bution (.τ = 2). The wage at the 20th percen- quantiles to represent low- and high-wage tile in the sample is then qτ . The density of workers, respectively. We did not choose the wage distribution, estimated at the 20th extreme percentiles, as these may be more percentile wage is fq. The indicator func- influenced by measurement error. The online Y ()τ tion 1{}Yq≤ τ creates a dummy variable set supplement shows effects at more detailed to 1 if a given woman’s wage is below the quantiles. Our main emphasis is on results from 20th percentile wage in the sample. The UQR models that show separate effects by wage lev- estimate of the motherhood penalty for els within skill categories, but we also show women at the 20th percentile of the wage results for standard mean regressions (not dif- distribution can then be obtained by OLS ferentiating effects by quantile) for models that regression on the transformed dependent vari- do not interact motherhood (and other varia- able. Effects at other quantiles can be esti- bles) with skill and for models that do neither. mated analogously. Locating the various wage quantiles is done Does UQR make sense with panel in the preliminary stage of UQR regression data? We refer to observations at the 20th and estimation. We use wages across white wom- 80th quantiles as “groups” differing in their en’s person-years to locate the percentiles we wage level. The “groups” near a particular use for analyses of white women, presented quantile are groups of person-years defined by here, as well as analyses of black women, pre- wage, not groups of persons. A question rele- sented in the online supplement. This allows us vant to how to interpret our results is how to compare results to those of Budig and much individual women tend to have approxi- Hodges (2014) and Killewald and Bearak mately the same rank order in wages in differ- (2014), who limited their analysis to white ent years. Let us use the term “rank-invariance” women, and to use common quantiles for our for the extreme situation where no woman white and black analyses, so that, for example, ever changes her rank. Clearly, we cannot the 20th quantile will be the same actual wage require perfect rank-invariance for quantile when we compare black and white women’s results to be meaningful, because if women penalties at that wage percentile. varied in their number of children, but rank- Standard errors are bootstrapped to incor- invariance of wages was perfect, there could porate the uncertainty involved in estimation be no motherhood penalty. But if women’s of the RIF. Each bootstrap simulation repeats rank often changes dramatically across years, each stage of the procedure, starting from the then it may not make sense to think of effects beginning. Coefficients or differences between of motherhood surrounding a particular quan- coefficients are referred to as significant if tile of person-years to be indicative of effects p < .05 on a two-tailed test. experienced by a group of women. Thus, we Our UQR regressions are unweighted, examine the extent of rank-invariance in Fig- given that weights can cause as well as cor- ure 1, which shows the proportion of white rect biases (Winship and Radbill 1994), and women21 whose percentile in the wage distri- we provide separate estimates by race (from bution differed by at least one third (33 per- models fully interacted by race), so that the centage points) or one sixth (17 percentage over-representation of black women in the points) between 1996 (chosen as a year near regressions is not biasing coefficients even if the center of the period) and each other year. effects differ by race. The asymmetry in the curves reflects the

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Figure 1. Proportion of White Women Whose Wage Rank Changes by One Third or One Sixth, Between 1996 and Other Waves well-known fact that wages among young years, to 1 (by definition) for 1996, to a low adults in their first years of employment are in post-1996 years of .59 in 2010. often erratic and less predictive of their later Overall, Figures 1 and 2 show there is a wages; this is why high proportions of women good deal of stability in how a given woman’s deviate at least a sixth or a third from their wage ranks relative to her peers across the 1996 rank in the early years of the survey years. This gives us confidence that referring (they were 14 to 21 years of age in 1979, but to wage “groups” and comparing these years when women had a wage but were also groups’ motherhood penalties is sensible. a student are removed from all calculations). Focusing on the right-hand half of the curves, Computing wage and skill groups’ the “moved > 1/3” curve is at .14 for 2010, rates of return to experience and tenure showing that only 14 percent of women moved from regression results. To explore our at least 33 percentage points in rank between hypothesis that groups with higher rates of 1996 and 2010. The “moved > 1/6” line is at return to experience have higher motherhood .38 for 2010, showing that 38 percent of penalties, we compute the rates of return to women changed their percentile by 17 points experience and tenure for groups defined by or more between 1996 and 2010. If we con- wage quantile and skill from regression sider moving less than a third an acceptable results. Equation 4 includes experience and degree of rank-invariance, it is encouraging tenure (along with all other variables), pro- that in all pairs of years, less than a third of viding rates of return at various quantiles. women moved that far in rank, even when we However, one cannot read these rates of include the early, more erratic years. return directly from regression coefficients, Getting at the same issue a different way, due to complexities of our models—the quad- Figure 2 shows the bivariate correlations ratic form in which experience and tenure are (Pearson R) between a woman’s wage per- entered, and the fact that experience, tenure, centile in 1996 and each other year. The cor- and their squares are each interacted with relations range from a low of .25 in the early education. To obtain an average rate of return

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Figure 2. Correlation between White Women’s Wage Ranks, between 1996 and Other Waves for experience from additive and interactive 80th wage quantiles, separately by combina- coefficients involving experience and in our tions of race and skill. estimated Equation 4, we compute point esti- mates of coefficients for experience and its square for each race-by-skill-by-education Results: How Penalties group at two quantiles of interest, the 20th Vary by Skill, Wage, and and 80th (to represent low and high wages). Race Then, using the coefficients for each experi- Total Motherhood Penalties ence and its square, for each race-by-skill group, at each of the two quantiles (20th and Hypotheses 1 and 2: effects of group dif- 80th), we take a weighted average across the ferences in levels and returns to experi- four education groups, weighting by the race- ence on total penalties. The first two and skill-specific proportion of the sample (of hypotheses disagree on whether disadvan- person-years) that is in each education group. taged or advantaged women will have higher We use these averaged coefficients of experi- motherhood penalties. Hypothesis 1 posits ence and its square for each race-by-skill-by- that advantage is associated with a higher wage group to predict the increase in ln wage return to experience, so any time out of women gain for each group in each succes- employment for childrearing leads to greater sive year of experience, 1 to 30. After com- wage loss upon return and thus higher moth- puting these point estimates, we repeat this erhood penalties. Hypothesis 2, however, process 1,000 times on bootstrapped samples, posits that advantage is associated with lower to compute standard errors, and then repeat penalties, because advantaged women are these steps for each year 1 to 30. For the employed more continuously and have more standard errors of the differences between any experience. two rates of return (e.g., more and less skilled Our test of this begins in Table 1. Equation white women at the 80th quantile), we per- 3, with fixed effects, our preferred specifica- form the analogous procedure, bootstrapping tion for the total penalty, shows that, among the differences. We follow the same proce- white women, highly skilled women with dure to get returns to tenure at the 20th and high wages have the highest motherhood

Downloaded from asr.sagepub.com at ASA - American Sociological Association on December 1, 2016 England et al. 1175 penalty per child. Highly skilled women with mainly due to our use of UQR instead of wages at the 80th percentile lose 10 percent in CQR. Among women with lower skills, we wage for each child, and this penalty is sig- find some hint of their finding, in that the nificantly larger than that for highly skilled penalty is significantly higher for women at women with wages at the 20th percentile, or the 20th than the 80th wage quantile (Table 1, that for less skilled women with wages at Equation 3), but the difference is only 2 per- either the 20th or 80th percentile. These latter centage points (from 5 to 7 percent); moreover, three groups have lower penalties, between 4 an examination of more detailed quantiles and 7 percent. Although we prefer Equation 3 (see Table S1 in the online supplement) shows because fixed effects provide some protection that, among women with lower skills, the from omitted variable bias, in fact, Equations relationship is actually curvilinear, with pen- 1, 2, and 3 all yield estimated penalties of 10 alties slightly larger near the middle wage to 12 percent for highly skilled women with quantiles. high wages (Table 1). Hypothesis 1 describes the higher penalties The conclusion that the highest total penal- for more-skilled women with high wages flow- ties are to women who combine high wages ing from the higher rates of return to experi- and high skill is also supported when, as a ence that advantaged women will have. Figure sensitivity test, we use an alternative specifi- 3 shows that, among white women, more- cation similar to that used by Wilde and col- skilled women do indeed have higher rates of leagues (2010), with an indicator for whether return to experience. The figure shows rates of the woman is eight or more years beyond return to experience for white women in four having a first child (relative to a reference of groups—high- and low-skill women, at the having no child), with a control for number of 20th and 80th quantiles—calculated from the additional children beyond the first. Results quantile regressions in Table 1, Equation 4. for that specification show that penalties Women with high wages and high skill have increase across time (results not shown). For the highest rates of return to experience. At simplicity, Table A2 in the Appendix just every number of years of experience 1 through shows penalties at their highest point at eight 30, their returns are significantly higher than or more years past the birth. In Equation 3, all three other groups (results on significance highly skilled women at the 80th percentile of not shown). Figure S1 in the online supple- wages have a 21 percent penalty, whereas the ment shows that these women also have the penalties for the other three groups (high/low, highest returns to tenure; the four groups have low/high, and low/low) are all lower, between the same rank order in returns to tenure and 6 and 15 percent. experience. Thus, the evidence for white Taking all results together, we conclude women is consistent with Hypothesis 1: white that Wilde and colleagues (2010) were right women with high skill and high wages have that highly skilled women have higher moth- the highest rates of return to experience, erhood penalties, but with the caveat that this whether it is all experience or the portion that is true only if they also have high wages. Of is tenure with their current employer. Their course, highly skilled women are typically high returns to experience and tenure mean earning higher wages; for example, in 1996, that loss of every year of work caused by 64 percent of white women in the top third of motherhood is much more costly for their skills had wages in the top third, whereas only future wages, even in proportionate terms, than 32 percent of white women in the bottom two it is for other groups of women. The remaining thirds of the skill distribution were in the top three wage/skill groups all have significantly third of wages. (Results calculated from the lower rates of return to experience and tenure, observations row of Table 2.) Budig and rates that do not differ dramatically from each Hodges’s (2010) conclusion that lower-wage other. Thus, we do not try to explain these women have higher penalties no longer holds, smaller differences.

Downloaded from asr.sagepub.com at ASA - American Sociological Association on December 1, 2016 *** *** *** *** *** *** *** ** * ** n.s. n.s. –.093 –.059 –.103 –.062 –.084 –.063 –.040 –.024 * ** ** n.s. n.s. n.s. n.s. n.s. \ / / / / \ \ \ Diagonals Mean Regression * * * * **

*** *** n.s. .8−.2 Gradient *** ** *** *** *** *** ** * .8 ** ** *** –.102 –.032 –.118 –.036 –.098 –.045 –.037 –.002 *** *** *** *** *** *** *** .5 n.s. n.s. n.s.

n.s. –.080 –.062 –.085 –.063 –.066 –.080 –.013 –.023 Quantiles *** *** *** *** *** *** *** *** * .2 n.s. n.s. n.s.

–.054 –.060 –.052 –.062 –.044 –.066 –.023 –.031 p < .001 (two-tailed tests). *** p < .01; ** . White Women’s Motherhood Penalty per Child by Skill: At Selected Quantiles and From Mean Regressions . White Women’s Table entries are coefficients from regression models. Entries in the Gradient column show significance tests for differences between at : Table High Skill Difference between Skill Groups Low/Mid Skill High Skill Difference between Skill Groups Low/Mid Skill High Skill Difference between Skill Groups Low/Mid Skill High Skill Tenure, and Tenure × Educational Attainment and Tenure Tenure, Difference between Skill Groups Low/Mid Skill able 1 p < .05; T Educational Attainment, and Age × Attainment Age, Geography, Equation 1: Wave, Earnings Equation 2: All of the Above, Marital Status, and (if married) Spouse’s Equation 3: All of the Above and Woman-Fixed-Effects

Equation 4: All of the Above, Experience, Experience × Educational Attainment, Whether Works Full-Time, Whether Works Full-Time × Educational Attainment, Full-Time Whether Works Full-Time, Equation 4: All of the Above, Experience, Experience × Educational Attainment, Whether Works

Note quantiles .2 and .8. Entries in the Diagonals column show significance tests for coefficients on diagonals: “/” indicates difference between for high-skilled women at quantile .8 and low-to-middle-skilled .2; “\” indicates the difference between coefficients at quantile .2 and low-to-middle-skilled women .8. *

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Top 2006 Wage Third Wage Bottom Middle Top 1996 Wage Third Wage Bottom Middle Top 1986 Wage Third Wage 145 231 272 81 131 369 34 92 286 .531 .320 .279 .889 .740 .659 1.000 .783 .755 .083 .030 .011 .062 .038 .016 .059 .022 .007 .483 .294 .165 .358 .313 .136 .353 .304 .182 .248 .260 .232 .235 .344 .211 .412 .283 .248 .186 .416 .592 .346 .305 .637 .176 .391 .563 .262 .424 .397 .099 .137 .136 .088 .054 .091 .628 .485 .515 .765 .687 .743 .765 .696 .748 .110 .091 .088 .136 .176 .122 .147 .250 .161 .634 .831 .835 .457 .740 .721 .353 .620 .811 5.099 9.074 15.621 5.166 9.132 23.001 5.669 9.089 24.240 4.822 5.660 5.984 11.538 13.383 14.656 17.148 20.028 23.824 1.349 2.102 2.760 2.303 4.880 6.021 3.523 4.954 9.258 Bottom Middle Skill Low/Mid 5.008 8.765 14.820 5.412 8.961 17.779 5.507 8.989 18.670 High Low/Mid .577 .426 .361 .882 .791 .683 .887 .863 .797 Low/Mid .328 .209 .084 .272 .200 .063 .268 .164 .055 High Low/Mid .520 .537 .487 .506 .522 .376 .470 .531 .432 High Low/Mid .125 .168 .225 .171 .206 .270 .202 .233 .313 High Low/Mid .028 .085 .204 .052 .072 .292 .060 .073 .200 Low/Mid .307 .330 .366 .081 .097 .138 .060 .061 .065 Low/Mid .549 .554 .492 .645 .684 .683 .613 .676 .684 High Low/Mid .144 .115 .141 .275 .219 .179 .327 .263 .252 High Low/Mid .598 .829 .764 .572 .756 .815 .577 .779 .816 High Low/Mid 3.959 5.797 6.492 9.818 13.242 14.898 16.404 20.675 23.617 High Low/Mid 1.246 2.470 2.785 2.099 4.517 6.434 2.992 6.810 9.662 High Low/Mid 577 469 191 346 320 319 168 262 310 . White Women’s Means by Wage Third and Skill at Three Selected Waves (1986, 1996, and 2006) Third and Skill at Three Selected Waves Means by Wage . White Women’s widowed Less than high school High High school Some college College Single, not yet married High Married, living together High Separated, divorced, or experience at current job orks full-time able 2 Hourly wage (1996$) High T Mother Educational attainment Marriage W Cumulative years of work Cumulative years of tenure Note: Cumulative work experience and tenure are in years: the sum total of hours worked, divided by 2000. Skill is measured test scores, adjusted for age; cutting points for the thirds refer to weighted sample of all race/ethnic groups women prior any although this table pertains to white women only, deletions. Observations

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Figure 3. White Women’s Return to Experience, by Wage Quantile and Skill Note: Based on results from Equation 4, Table 1. Curves show how much ln wage increases from 0 to each year of experience for each of the four groups. Differences in groups’ initial ln wage levels are not shown, but set to 0 when experience is equal to 0.

Examining the occupations of women/ positions, food service, home health aides, years that are in the highest skill third as well and retail sales. as in the top third of wages22 may help the Why was Hypothesis 2, which said that reader envision the kinds of work in which groups with less experience will have higher women are experiencing high wages, high penalties, not upheld? First, we note that returns to experience and tenure, and high Hypothesis 2 is correct in positing that more motherhood penalties. The 10 most common advantaged women have more experience, as occupations for white women in the top third past research shows. In these data, among of skills and wages are nurses, teachers, ther- white women, highly skilled women with apists, accountants, and managers of various high wages have the highest levels of experi- types (financial, medical and health service, ence. For example, Table 2 shows that in marketing and sales, human resource, manag- 2006, white women in the top third of skills ers of administrative support workers, and a and the top third of wages averaged 24 years; residual category). (Detailed results available white women with low or medium skills, and upon request.) It is a mix of predominantly wages in the bottom third, however, averaged male and predominantly female occupations. only 16 years. Indeed, in later years, the The relatively high rates of return to experi- cumulative experience of women in the top ence and tenure these women enjoy may third of skills is very close to their estimated reflect access to raises and promotion in these potential experience, computed as their age largely professional and managerial occupa- minus 6 more than the years of schooling they tions, compared with occupations the other completed; they are employed quite continu- three groups of women are typically in. The ously, more so than any other wage/skill most common occupations in the other three group (results not shown). Thus, other things groups, featuring either lower skills or low being equal, based on their higher experience wages, are not professional or managerial; levels, we would expect lower penalties for they include secretarial and administrative women who are highly skilled and have high

Downloaded from asr.sagepub.com at ASA - American Sociological Association on December 1, 2016 England et al. 1179 wages, as Hypothesis 2 says, yet we found the general conclusion that more advantaged opposite. This is probably because, to the women have higher penalties, but we are extent that experience is relevant, group dif- unable to offer an explanation of these racial ferences in penalties are a multiplicative differences in penalties. function of group differences in experience levels and in returns. Highly skilled, high- Hypotheses 3 and 4: effects of group wage women have more experience, which, differences in how motherhood affects other things being equal, reduces their penal- productivity or discrimination, and ties; but other things are not equal, as these thus affects penalties net of experience. women also have the highest returns to expe- Hypotheses 3 and 4 concern penalties that do rience. Their high returns appear to dominate not flow through experience but relate to in affecting group differences in penalties other mechanisms, involving performance or through making even the small amounts of discrimination, and are seen net of experi- time taken out of employment for childrear- ence. Hypothesis 3 says that advantaged ing quite damaging to their future wages. women, those with high skills and high The online supplement provides results wages, will have higher net motherhood pen- regarding penalties for black women, which alties because they are more likely to be in we summarize briefly here. We found that jobs in which any decline in performance total penalties are lower for black than for because of motherhood has a large effect (or white women; when we pool across skill perceived effect) on their organizations’ bot- groups and do simple mean regressions, pen- tom line. Hypothesis 4 says that disadvan- alties are 7 to 8 percent for white women but taged women, with low skills or low wages, only 3 to 4 percent for black women (see will have higher net motherhood penalties Table A1 in the Appendix for white women because they have less power to negotiate job and Table S1 in the online supplement for flexibility and less money to purchase ser- black women; Equations 1, 2, and 3). Black vices needed to avoid negative effects of women undoubtedly experience race discrim- motherhood on their performance (or per- ination that white women do not, but it is ceived performance). unclear how this would lead to lower mother- To examine these competing hypotheses, hood penalties. Moreover, black women’s we consider the net penalties from Equation 4 lower total penalties are not due to lower in Table 1, which contains controls for experi- returns to experience or tenure; race differ- ence, tenure, and hours. When these controls ences in these returns are not significant are entered, penalties drop by half or more (results not shown). Black women do have (compare Equations 3 and 4 in Table 1), so lower wages and lower average cognitive this half or more of the motherhood penalty skill (at least as measured by AFQT), but this results from losing experience or tenure.23 does not appear to be the reason for their Hypothesis 3 says that women with high lower motherhood penalties. We conclude wages and high skills suffer the highest penal- this from two findings in the online supple- ties, and Table 1 (Equation 4) shows this is ment (Table S2): (1) Unlike the pattern for true. Their penalty is 4 percent per child, and white women, total penalties do not generally this is significantly more than the near 0 pen- differ significantly for black women by skill alty of women with low skill and high wages. or quantile, suggesting that if their average However, it is not significantly different than wages and skill were to rise, this would not the 2 to 3 percent penalty experienced by increase their penalty. (2) When we compare women at low wage levels and high or low black and white women at the same (white) skill levels, respectively. Our alternative wage quantile and skill level, black women’s specification in Table A2 in the Appendix penalties are generally lower. The lower pen- also shows that the net motherhood penalty is alties for black than for white women fit our largest for women with high skills and high

Downloaded from asr.sagepub.com at ASA - American Sociological Association on December 1, 2016 1180 American Sociological Review 81(6) wages, but this penalty is not significantly return to experience and group differences in larger than that suffered by low-wage women, levels of experience. In the case of highly whether their skills are high or low. 24 Hypoth- skilled white women with high wages, what is esis 4 says that women with low skills or striking is that they have the highest penalties wages have higher penalties. As Table 1 despite the fact that they have the most con- shows, contrary to the hypothesis, the penalty tinuous experience of any group of women, for women with low skill and low wages, 3 which, other things being equal, would reduce percent, is nonsignificantly different from the their penalties. The evidence suggests that penalty for women with high skill and low their penalties are highest because when some wages (2 percent). However, consistent with of these women lose experience to childrear- the hypothesis, among low-skilled women, ing, by dropping out or shifting to part-time penalties do rise significantly as wages go work for a short time, their steep experience- from the 80th to 20th quantile, albeit only wage slopes make even these small amounts from 0 percent to 3 percent. Thus, we find of lost experience very expensive; they lose some support for each of the two conflicting the steep wage growth they would have hypotheses as regards net penalties in our enjoyed had they worked continuously. main specification, but the differences are Revisiting the two articles that inspired our quite small. Overall, we conclude that penal- analysis, we conclude that Wilde and col- ties net of experience and seniority do not leagues (2010) were correct that highly skilled differ consistently or strongly by wage and women have higher total penalties, but with the skill among white women. Moreover, our important caveat that this applies only to analysis in the online supplement (Table S3) women who have high wages as well. Budig shows that net penalties do not differ by skill and Hodges’s (2010) previous finding that or wage for black women. We take these higher-wage women suffer smaller penalties is estimated net penalties to tap effects of modified by our analysis, because we adopt the motherhood on performance or employer appropriate unconditional quantile regression discrimination based on motherhood, and our (UQR) model and examine penalties separately conclusion is that, for the most part, these by skill: among skilled women, high-wage penalties are not distinctive for highly paid women have worse total penalties, the opposite women with high skills. of Budig and Hodges’s finding. Among women with lower skills, total penalties are curvilinear and highest at the middle, although the differ- Conclusions and ence is small and the explanation unclear. Discussion We also estimated net motherhood penal- Who suffers larger motherhood wage penal- ties, those estimated controlling for experi- ties—advantaged or disadvantaged women? ence; these analyses cannot distinguish how We found that, among white women, the total much of net penalties result from employer motherhood penalty is highest—10 percent discrimination against mothers or reduced job per child—for women with high skills and performance due to motherhood. Rather, high wages. This finding is consistent with these two are lumped together in the net pen- our hypothesis that high penalties are associ- alty. This net penalty was not significantly ated with high rates of return to experience; higher (or lower) for women with high skills among white women, highly skilled high- and high wages than it was for women with wage women have the highest rates of return low wages, whether their skill was high or to experience and tenure, as well as the high- low. Thus, there is no clear evidence that this est motherhood penalties. Group differences group suffers any more or less discrimination in the part of the total penalty explained by on the basis of motherhood, or that their job experience will necessarily be a multiplica- performance is more or less affected by tive function of group differences in rates of motherhood.

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Our analysis focused on white women, but of not confusing the disadvantage of we also showed that, taken as a whole, penal- low skill, low wage levels, or membership in ties are lower for black than for white women, a disadvantaged racial group, with the disad- although there are not significant differences vantage of high motherhood penalties. These in the returns to experience between the disadvantages typically afflict different groups. Among black women, penalties did women. Black women have lower wages than not differ significantly by skill or wage. white women, but they have lower total pen- Overall, our analysis shows that privilege alties for motherhood. Among white women, (on race, wage, or skill) has its price—larger those with the highest total motherhood pen- proportionate motherhood penalties. In the alties are in an advantaged group with high case of privilege on wage and skill, the pen- skills and high wages; even after they become alty arises because when highly skilled mothers and suffer the steepest penalty, they women are in high-wage jobs, they have high are typically quite affluent because their own rates of return to experience, and these steep earnings are still high relative to those of wage trajectories make them lose large other women, and many of them are married amounts of wage growth during the typically to relatively high-earning men. Nonetheless, small amounts of time they take out. One when it comes to their own pay, motherhood clear lesson from our results is the importance is the most costly for them.

Downloaded from asr.sagepub.com at ASA - American Sociological Association on December 1, 2016 *** *** *** *** –.030 –.071 –.075 –.069 Mean Regression n.s. n.s. n.s. n.s. .8−.2 Gradient * *** *** *** .8 –.016 –.066 –.062 –.053 *** *** *** *** .5 –.020 –.075 –.071 –.067 Quantiles *** *** *** *** .2 –.028 –.057 –.060 –.058 ix p < .001 (two-tailed tests). d . White Women’s Motherhood Penalty per Child: At Selected Quantiles and From Mean Regressions . White Women’s *** n ppe Attainment, Whether Works Full-Time, Whether Works Whether Works Full-Time, Attainment, Whether Works × and Tenure × Educational Attainment, Tenure, Full-Time Educational Attainment Spouse’s Earnings Spouse’s and Age × Educational Attainment able A1 p < .05; Table entries are coefficients from regression models. Entries in the Gradient column show significance tests for differences between at Note: Table quantiles .2 and .8. * Equation 4: All of the Above, Experience, Experience × Educational Equation 3: All of the Above and Woman-Fixed-Effects T Equation 2: All of the Above, Marital Status, and (if married) A Educational Attainment, Age, Geography, Equation 1: Wave,

1182 Downloaded from asr.sagepub.com at ASA - American Sociological Association on December 1, 2016 *** *** *** *** *** *** *** ** n.s. n.s. n.s. n.s. –.220 –.200 –.126 –.135 –.187 –.133 –.156 –.077 * ** n.s. n.s. n.s. n.s. n.s. n.s. / \ / / / \ \ \ Diagonals Mean Regression * ** ** ** *** n.s. n.s. n.s. .8−.2 Gradient *** * *** * *** * *** * .8 ** *** *** .020 –.275 –.093 –.311 –.097 –.211 –.055 –.146 *** *** *** *** *** *** *** *** .5 n.s. n.s. n.s. n.s. –.202 –.161 –.214 –.163 –.186 –.185 –.097 –.078 Quantiles *** *** *** *** *** *** *** *** .2 n.s. n.s. n.s. n.s.

–.086 –.119 –.089 –.128 –.105 –.148 –.066 –.071 p < .001 (two-tailed tests). *** p < .01; . White Women’s Motherhood Penalty Eight or More Years After the First Birth by Skill: At Selected Quantiles and From Mean Motherhood Penalty Eight or More Years . White Women’s ** Table entries are coefficients from regression models. Entries in the Gradient column show significance tests for differences between at Table High Skill Difference between Skill Groups Difference between Skill Groups Low/Mid Skill High Skill Low/Mid Skill High Skill Difference between Skill Groups Difference between Skill Groups Low/Mid Skill High Skill Low/Mid Skill Tenure, and Tenure × Educational Attainment and Tenure Tenure, able A2 p < .05; Equation 1: Wave, Age, Geography, Educational Attainment, and Age × Attainment Age, Geography, Equation 1: Wave, T Regressions

Equation 2: All of the Above, Marital Status, and (if married) Spouse’s Earnings Equation 2: All of the Above, Marital Status, and (if married) Spouse’s Equation 3: All of the Above and Woman-Fixed-Effects

quantiles .2 and .8. Entries in the Diagonals column show significance tests for coefficients on diagonals: “/” indicates difference between for high-skilled women at quantile .8 and low-to-middle-skilled .2; “\” indicates the difference between coefficients A3. at quantile .2 and low-to-middle-skilled women .8. Models also adjust for additional children; see Appendix Table * Equation 4: All of the Above, Experience, Experience × Educational Attainment, Whether Works Full-Time, Whether Works Full-Time × Educational Attainment, Full-Time Whether Works Full-Time, Equation 4: All of the Above, Experience, Experience × Educational Attainment, Whether Works Note:

1183 Downloaded from asr.sagepub.com at ASA - American Sociological Association on December 1, 2016 ** ** *** ** *** ** n.s. n.s. n.s. n.s. –.060 –.058 –.039 –.063 –.041 –.038 –.016 –.010 * n.s. n.s. n.s. n.s. n.s. n.s. n.s. / / / / \ \ \ \ ** n.s. n.s. n.s. n.s. n.s. n.s. n.s. .8−.2 Diagonals Mean Regression Gradient *** *** .8 n.s. n.s. n.s. n.s. –.053 –.020 –.057 –.022 –.078 –.048 –.011 –.009 * ** ** *** .5 n.s. n.s. n.s. n.s. .011 –.037 –.032 –.039 –.034 –.030 –.049 –.005 Quantiles ** *** ** *** * *** * .2 n.s. n.s. n.s. n.s. –.038 –.039 –.037 –.040 –.021 –.041 –.011 –.019 p < .001 (two-tailed tests). *** p < .01; . White Women’s Motherhood Penalty per Additional Child After the First by Skill: At Selected Quantiles and From Mean Regressions . White Women’s ** High Skill Difference between Skill Groups Low/Mid Skill High Skill Difference between Skill Groups Difference between Skill Groups Low/Mid Skill High Skill Low/Mid Skill High Skill Difference between Skill Groups Tenure, and Tenure × Educational Attainment and Tenure Tenure, Low/Mid Skill able A3 p < .05; Equation 1: Wave, Age, Geography, Educational Attainment, and Age × Attainment Age, Geography, Equation 1: Wave, T

Equation 2: All of the Above, Marital Status, and (if married) Spouse’s Earnings Equation 2: All of the Above, Marital Status, and (if married) Spouse’s

Equation 3: All of the Above and Woman-Fixed-Effects × Educational Attainment, Full-Time Whether Works Full-Time, Equation 4: All of the Above, Experience, Experience × Educational Attainment, Whether Works Table entries are coefficients from regression models. Entries in the Gradient column show significance tests for differences between at Note: Table quantiles .2 and .8. Entries in the Diagonals column show significance tests for coefficients on diagonals: “/” indicates difference between for high-skilled women at quantile .8 and low-to-middle-skilled .2; “\” indicates the difference between coefficients Table A2. at quantile .2 and low-to-middle-skilled women .8. Models also adjust for years since first birth; see Appendix *

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Authors’ Note of 40 hour/week employment. Thus, effects of past part-time (rather than full-time) work are part of our Jonathan Bearak’s affiliation is included for informa- “experience effect.” We also control for whether the tional purposes only; this work was not conducted under current job is part-time in our model assessing net the auspices of the Guttmacher Institute. The views penalties. expressed here are those of the authors and do not neces- 5. It is important to distinguish between the earnings sarily reflect the views of the Guttmacher Institute. forgone during nonemployment (when one is earn- ing nothing), and the forgone increases in one’s Funding post-return wage rate from the same period of non- employment. Our models and our discussion about We are grateful for a grant from the Russell Sage Founda- returns to experience affecting the motherhood pen- tion that funded part of this research. alty refer to the latter, not the former. 6. Correll and colleagues (2007) also present a ran- dom-assignment experiment with undergraduate Notes subjects asked to evaluate candidates for a position 1. See Wilde and colleagues (2010) for a critical dis- and assign a salary. They were given a packet of cussion of the instruments used in this literature. materials on the candidates, including past perfor- 2. Budig and England (2001) find that motherhood mance information, and a mention of whether they penalties differ little by occupational level, and have children. With comparable packets and past Loughran and Zissimopoulos (2009) find no sig- reviews, mothers were treated less favorably and nificant relationship between education and the seen as less able. Correll and colleagues argue that penalty. Amuedo-Dorantes and Kimmel (2005) and this is status-based stereotyping, not merely statisti- Taniguchi (1999) find higher penalties for less edu- cal discrimination, given that substantial informa- cated women, Waldfogel (1997) finds them higher tion on past productivity was available about each among well-educated women, and Anderson and candidate. colleagues (2002, 2003) find them higher at mid- 7. Gallen (2015) provides more indirect evidence that dle levels of education. Buchmann and McDaniel women and men differ in productivity because of (2016) find no motherhood penalty in very recent women’s motherhood burden. Using Dutch data, data for women in high-level male-dominated she finds that firms with a higher proportion of professions (they do not examine nonprofessional women workers had lower revenue, and this differ- women). Pal and Waldfogel (2016) find a com- ential was associated with mothers. plicated pattern of differences between education 8. Respondents in the NLSY79 were interviewed groups in levels and trends in motherhood penalties. annually up to the 1994 survey and bi-annually 3. Recent studies have complicated this finding. Glau- thereafter. We use one more wave of data than ber (2013) used successive Current Population Sur- Wilde and colleagues (2010), and two more than vey cross-sections and reports that black women’s Budig and Hodges, because they were available. motherhood penalties, initially much smaller than However, we did sensitivity tests deleting the last white women’s, increased, moving toward con- two years, and they show this is unimportant to dif- vergence in the 1990s, and then diminished again ferences between our results and those of either set somewhat in the 2000s. Pal and Waldfogel (2016) of authors. report similar findings. These analyses using the 9. Another reason to model interactions between CPS could not control for experience, as the survey motherhood and race is to avoid biased conclu- does not gather this information. Also, we can be sions about how penalties vary by cognitive skills. less sure that motherhood effects in these cross-sec- Because black women average lower test scores, tional analyses are causal than is the case for results and past research has found black women to have from panel data with fixed effects. lower motherhood penalties, the lower penalties 4. Past studies have also found that women earn less Wilde and colleagues (2010) attributed to lower per hour when working part-time, and that, because cognitive skills may actually have been caused by mothers are more likely to work part-time, this some other distinctive features of black women’s explains part of the penalty (Budig and England situations. The additive control for race implicit 2001; Staff and Mortimer 2012; Waldfogel 1997). in fixed-effects modeling does not adequately deal This is presumably because employers often pay with this problem. Given NLSY oversampling, less per hour in such jobs. Working part-time could black women are 28 percent of our analytic sample also have a longer-term influence on wage growth of person-years, but when we divide our analytic if the rate of return to experience in part-time jobs sample into women who are in the top third versus is less than in full-time jobs. As we will discuss, the bottom two thirds of the (all race) AFQT dis- our measures of experience and tenure calibrate tribution, the top third is 6 percent black, whereas them by the hour, such that a week of 20 hours/ the bottom two-thirds is 40 percent black. Thus, week employment counts half as much as a week penalties for the top third reported by Wilde and

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colleagues (2010) are almost entirely penalties using AFQT is not to explain race differences in experienced by white women. Our analyses do not earnings, but to test Wilde and colleagues’ (2010) have this problem, because we produce separate hypothesis that motherhood penalties are higher for estimates by race crossed with skill. women with higher cognitive skills, for both black 10. We exclude person-years in which women were and white women. enrolled in school part-time or full-time in a school 12. Specifically, we enter a set of indicator variables for that gives either a high school degree or a bache- whether, in this person-year, the number of years lor’s or graduate degree. The rationale is as follows: that have passed since the woman first became a effects of motherhood in fixed-effects models reveal mother is less than one year, one year, two to four average within-person wage differences between years, five to seven years, or eight or more years. years before and after motherhood; thus, including The reference category is years by which women years in which women had low-paying, part-time have not given birth. (Women who never have a jobs while in school may lead to underestimation first child, as well as women who have a first but of the motherhood penalty. That is, if women hold never have a second, are scored 0 on the indica- low-paid jobs in school, then graduate and work in tor variable for all their person-years; eliminating higher-paying jobs, then have a child, then return to women who never became mothers changes results work at a wage that reflects some motherhood pen- little.) The analysis allows us to see how the effects alty relative to their post-school, pre-child wages, of being a mother spread out over time. We add a fixed-effects estimation will underestimate this single control variable for the number of additional differential because the “pre-motherhood” wages children (after the first) the woman has had. are an average of their lower and higher pre-child 13. Budig and Hodges (2010) control for age, although wages. not its square, whereas Wilde and colleagues (2010) 11. Another reason for using women of all races to control for potential experience (age minus educa- determine thirds of the AFQT distribution is so the tion minus 5) and its square. cutting points between categories are the same for 14. We also include a category for “MSA not known,” white and black women. This is important, because, which applies to a tiny fraction of cases. although our main analyses are only for white 15. Budig and Hodges (2010) and Wilde and colleagues women, in the online supplement we show results (2010) measure educational attainment in years, for a parallel analysis for black women. Because we forcing the effect to be linear. Our categories are used the full sample of all races to form test score formed from number of years, assuming that less thirds, in our analyses the same test score cuts the than 12 is less than high school, 12 is high school skill groups for both black and white women. But only, 13 to 15 is some college, and 16 or more is are test scores biased for black women? Rodgers and college graduate. Spriggs (1996) use the 1991 wave of the NLSY79 16. Like Wilde and colleagues (2010), we derive years and divide the AFQT into two scales, one that deals of experience from cumulative hours, whereas with reading and another that deals with math. Budig and Hodges (2010) derive it from cumulative They show that reading skills increase the wage weeks, without attention to how many hours/week earned by blacks but not whites, and math skills a woman worked. We control for experience and its increase the wage earned by whites but not blacks. square, like Wilde and colleagues (2010); however, We examined this for our analytic sample of black unlike Wilde and colleagues (2010), we also add and white women’s person-years (through 2010), tenure (with current employer). Budig and Hodges using an OLS regression to predict wage from the (2010) use a linear term for experience and for two AFQT scales, education, year, geography, and tenure. Budig and Hodges (2010) also include the number of children (all variables operationalized respondent’s usual weekly work hours, the number as in our models in Table 1). We found significant of weeks the respondent worked in the prior year, positive effects of the math skill scale for both black and whether the respondent changed employers and white women. The puzzling finding was that between waves; we exclude all of these. Like Budig reading skills, which had significant positive effects and Hodges (2010), we follow standard practice for black women, had significantly negative effects by including tenure in experience. Thus, if an indi- for white women. However, when these scales are vidual has a total of 10 years of employment expe- combined into the overall AFQT measure we use rience, of which 3 are with her current employer, here, it has a significant positive effect on the earn- she is coded as having 10 years of experience and 3 ings of both black and white women and the effects years of tenure. are significantly stronger for black women. Thus, 17. Fortunately, including both age and experience in although we do not know whether AFQT measures the same models does not create problematic col- black women’s skills as accurately as it does those linearity, because women vary substantially in how of white women, we believe it is a meaningful mea- much experience they accumulate with age. One sure of skills that are rewarded in the labor market could, however, be concerned about our inclu- for black as well as white women. Our purpose in sion in our most saturated models of interactions

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between education and experience, given that this the skill and the bottom third of the wage distribu- interaction term might be highly correlated with the tion, and 15 percent are in the bottom two thirds of (also included) interaction between education and the skill and top third of the wage distribution. age. We ascertained that the returns to experience 23. In results not shown, it is apparent that most of this we estimate for wage-by-skill categories among reduction comes from the addition of experience. The white women are virtually identical if we instead small effect of controlling for whether the current job estimate them from a model that excludes the inter- is part-time may be because the experience indicator action of education and experience. (See later text measures cumulative hours worked since the year the for how these experience returns are estimated.) survey began, and thus captures years worked as well 18. Budig and Hodges (2010) also control for whether as how much of past employment was full- or part- the current job is part-time, whereas Wilde and col- time. Adding tenure also leads to little change in the leagues (2010) do not. coefficients on number of children. Thus, having to 19. The failure of the variable indicating whether a move one’s tenure to 0 after a birth is not the main woman is currently working part-time to explain motor of the effects of lost experience. much of the motherhood penalty may arise partly 24. Our alternative specification in Table A2 examines because the measure of hours of experience itself penalties for the first child eight years after the captures directly some of the effects of having birth, controlling for any additional children born worked part-time in the past; working 20 hours/ after the first. Net penalties are largest, 15 per- week over a year will lead to cumulating only half cent, for women with high skill and high wage, but as many hours as working 40 hours/week over the this penalty is not significantly different than that same year. of either women with low wages and low skill or 20. As an example, imagine a CQR with the log of women with high skill and low wages. It is vastly wages as the outcome and just two regressors: and significantly larger than the 2 percent penalty motherhood and education. In such a CQR model, for high-wage women with low skills, however. if the motherhood penalty is 5 percent at the 80th percentile and 15 percent at the 20th percentile, this means mothers who have high wages for their References education level have a smaller wage penalty than Acker, Joan. 1990. “Hierarchies, Jobs, Bodies: A The- do mothers who have low wages for their educa- ory of Gendered Organizations.” Gender & Society tion. Therefore, results from a CQR model cannot 4(2):139–58. be interpreted as the effect of motherhood on high- Allison, Paul D. 2005. Fixed-Effects Regression Models wage and low-wage workers, because, since edu- Using SAS. Cary, NC: SAS Institute. cation strongly affects earnings, even women who Amuedo-Dorantes, Catalina, and Jean Kimmel. 2005. have low wages for their high education level may “The Motherhood Wage Gap for Women in the earn more than many workers whose wages are low United States: The Importance of College and Fer- compared to women overall. tility Delay.” Review of Economics of the Household 21. Figures 1 and 2 on wage rank-invariance are almost 3(1):17–48. identical if black women are included in the compu- Anderson, Deborah J., Melissa Binder, and Kate Krause. tations. 2002. “The Motherhood Penalty: Which Mothers Pay 22. One might be interested in the size of this high- and Why?” American Economic Review, Papers and wage, high-skill group, with its distinctively high Proceedings 92(2):354–58. experience returns, relative to the other three Anderson, Deborah J., Melissa Binder, and Kate Krause. groups. Figure 3 pertains to high or low-to-medium 2003. “The Motherhood Wage Penalty Revisited: (called low) skill groups of women at the 80th and Experience, Heterogeneity, Work Effort, and Work- 20th quantiles of person/years of wages, but there Schedule Flexibility.” Industrial and Labor Relations is almost no one at a single wage percentile, so to Review 56(2):273–94. get an idea of the relative size of groups of observa- Avellar, Sarah, and Pamela J. Smock. 2003. “Has the Price tions that are in the various wage-by-skill groups, of Motherhood Declined over Time? A Cross-Cohort we approximate high wage as the top third (of per- Comparison of the Motherhood Wage Penalty.” Jour- son-years) and low wage as the bottom third. These nal of Marriage and the Family 65(3):597–607. are in turn divided into observations belonging to Azmat, Ghazala, and Rosa Ferrer. Forthcoming. “Gender women in the high- or low-skill groups. We find Gaps in Performance: Evidence from Young Law- that high (top third) wage observations belonging to yers.” Journal of Political Economy. women in the top third of skills make up 18 percent Baker, Michael, and Kevin Milligan. 2008. “How of all person-years. A larger group, 26 percent, are Does Job-Protected Maternity Leave Affect Moth- low on both: these women are in the bottom third er’s Employment.” Journal of Labor Economic of the wage distribution and the bottom two-thirds 26(4):655–91. of the skill distribution. 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Miller, Amalia R. 2011. “The Effect of Motherhood Tim- Paula England is Silver Professor of Sociology at New ing on Career Path.” Journal of Population Econom- York University. Her recent work explores changing pat- ics 24(3):1071–1100. terns of sexuality and family life, and how they are Neal, Derek A., and William R. Johnson. 1996. “The Role structured by class and gender. One project shows the of Premarket Factors in Black-White Wage Differ- rise of bisexual behavior and identity across recent ences.” Journal of Political Economy 104(5):869–95. cohorts of women, and finds much less, if any, analogous Pal, Ipshita, and Jane Waldfogel. 2016. “The Family Gap change among men. Other projects document class dif- in Pay: New Evidence for 1993 to 2013.” RSF: The ferences in cohabitation, nonmarital births, and divorce, Russell Sage Foundation Journal of the Social Sci- and explore reasons for them. In 2014 to 2015 she served ences 2(4):104–127. as President of the American Sociological Association. Rodgers, William M. III, and William E. Spriggs. 1996. “What Does the AFQT Really Measure: Race, Wages, Jonathan Bearak’s research lies at the intersection of Schooling and the AFQT Score.” Review of Black stratification and demography. His published and ongo- Political Economy 24(4):13–46. ing projects address fertility including abortion and Staff, Jeremy, and Jeylan T. Mortimer. 2012. “Explaining unintended pregnancy, marriage, motherhood, adolescent the Motherhood Wage Penalty during the Early Occu- sexual behavior, and school quality. He has published in pational Career.” Demography 49(1):1–21. The Lancet, American Sociological Review, Social Taniguchi, Hiromi. 1999. “The Timing of Childbearing Forces, Demographic Research, Educational Researcher, and Women’s Wages.” Journal of Marriage and the and Contraception. He received his PhD in Sociology Family 61(4):1008–19. from New York University in 2015 and is currently a Tolbert, Charles M., Patrick M. Horan, and Elwood M. Senior Research Scientist at the Guttmacher Institute. Beck. 1980. “The Structure of Economic Segmenta- tion: A Dual Economy Approach.” American Journal Michelle J. Budig is Professor and Chair of Sociology at of Sociology 85(5):1095–1116. the University of Massachusetts. Her research interests Waldfogel, Jane. 1997. “The Effect of Children on include labor market inequalities, wage penalties for paid Women’s Wages.” American Sociological Review and unpaid caregiving, and work-family policy. She has 62(2):209–217. received the Reuben Hill Award from the National Coun- Waldfogel, Jane. 1998. “Understanding the Family Gap cil on Family Relations, the World Bank/Luxembourg in Pay for Women with Children.” Journal of Eco- Income Study Gender Research Award, and is a two-time nomic Perspectives 12(1):137–56. recipient of the Rosabeth Moss Kanter Award for Research Wilde, Elizabeth Ty, Lily Batchelder, and David T. Ell- Excellence in Families and Work. She has provided expert wood. 2010. “The Mommy Track Divides: The testimony on the gender pay gap and the motherhood Impact of Childbearing on Wages of Women of Dif- wage penalty to the U.S. Congressional Joint Economic fering Skill Levels.” NBER Working Paper 16582. Commission and the Massachusetts State Legislature. Williams, Joan C. 2004. “Hitting the Maternal Wall.” Academe 90(6):16–20. Melissa J. Hodges is an Assistant Professor of Sociology Williams, Joan C., and Stephanie Bornstein. 2008. “The at Villanova University. Her work has appeared in the Evolution of ‘FReD’: Family Responsibilities Dis- American Sociological Review and Gender & Society. crimination and Developments in the Law of Ste- She is a past recipient of the Reuben Hill Award from the reotyping and Implicit Bias.” Hastings Law Journal National Council on Family Relations and the Rosabeth 59:1311–58. Moss Kanter Award for Research Excellence in Families Winship, Christopher, and Larry Radbill. 1994. “Sam- and Work. Her research interests include the effects of pling Weights and Regression.” Sociological Meth- children on couple’s earnings within and across house- ods & Research 23(2):230–57. holds and wage penalties for paid and unpaid caregiving.

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