Social Science Research

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1 Social Science Research xxx (2010) xxx xxx Contents lists available at ScienceDirect Social Science Research journal homepage: The myth of the glass ceiling: Evidence from a stock-flow analysis of authority attainment q Zhen Zeng Center for Demography and Ecology, University of Wisconsin-Madison, 1180 Observatory Drive, Madison, WI 53706, USA article info abstract Article history: Received 30 January 2009 Available online xxxx Keywords: Glass ceiling Workplace authority Gender inequality Racial inequality It is apparent to even a casual observer of American society that women and minorities are underrepresented among managers, especially among top-level executives. Past studies, however, have failed to find a consistent pattern of female and minority disadvantages in actual promotions and hiring decisions to account for this underrepresentation. This study aims to resolve this incongruity. Drawing on panel data from a nationally representative sample of scientists and engineers, I analyzed transitions across authority levels for men and women of three broad racial groups: whites, Asian Americans, and underrepresented minorities. There are two main findings. First, downward mobility plays an important role in authority inequality, especially for Asian men and underrepresented minority men and women. Second, while women and minorities face lower rates of upward mobility than white men, their disadvantages are concentrated in the bottom to middle-level transitions. This pattern is inconsistent with the popular notion of a glass ceiling, which implies that women and minorities encounter an unbreakable obstacle in accessing top positions after they have made their way into mid-level management. Ó 2010 Elsevier Inc. All rights reserved. 1. Introduction Originally coined by journalists in the 1980s, the glass ceiling refers to a specific type of labor market disadvantage encountered by women and minorities in advancing to the top positions in organizational hierarchies. The metaphor invokes the image of a subtle, impenetrable barrier that blocks women and minorities advancement in a management hierarchy: they can be promoted below the barrier but not across it. It does not take systematic study to notice that women and minorities are much less likely to occupy top positions in organizations. As of 2006, for example, women and minorities held only 17% and 15%, respectively, of the board seats of Fortune 100 companies (Catalyst, 2008). Similar representational patterns have been reported by numerous studies that examine various types of organizations and industries (e.g., Bullard and Wright, 1993; Tang, 1997), the general labor force (e.g., Elliott and Smith, 2004; Maume, 2004), as well as the working populations of multiple countries (e.g., Wright et al., 1995; Rosenfeld et al., 1998). The glass ceiling claim, however, is not just about an outcome of gender and racial inequality in managerial representation; more importantly, it is a claim about women and minorities adverse experience in the process of advancing to top positions. In contrast to the undeniable evidence of representational inequality, studies that examine promotions, which presumably underlie the shortage of women and minority managers, have failed to find a clear pattern of gender and race variations. Some scholars have reported that women and people of color are less likely to be promoted (Olson and Becker, q An earlier version of this paper was presented at a meeting of the ISA Research Committee on Social Stratification and Mobility, Florence, Italy, May I thank I-Lin Kuo, Yu Xie, Myra Ferree, Rob Mare, the editor, and anonymous reviewers for valuable comments that helped to greatly improve the quality of this article. address: zzeng@ssc.wisc.edu X/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi: /j.ssresearch

2 2 Z. Zeng / Social Science Research xxx (2010) xxx xxx 1983; Maume, 1999; James, 2000; Gjerde, 2002), while others have found either differences in their favor (Powell and Butterfield, 1994, 1997; Petersen and Saporta, 2004) or no differences net of human capital factors and labor force attachment (Yamagata et al., 1997; Booth et al., 2003; Smith, 2005). A recent review article summarized: one-third of the studies found that while gender disparities do exist in relation to position attainment and promotion, these are attributable to differences other than gender (Jackson and O Callaghan, 2009, p. 472). Together, the overwhelming evidence on the shortage of female and minority managers and the mixed findings on promotional inequality create a paradox: if women and minorities are not less likely to be promoted, why are they underrepresented at the top of organizations? From a stock-flow analytic perspective, the labor-market can be partitioned into segments by the amount of workplace authority, with people flowing constantly between segments. At each time, the stock of managers is determined by the accumulation of entrances into, minus exits from, this segment. It then follows that group disparities in managerial representation are due to differences in either entrance rates or exit rates. We can thus infer from the mixed evidence on promotion that the shortage of female and minority managers must be due to more frequent downward mobility from managerial positions. While researchers have given a nod to the possibility of downward mobility (Baxter and Wright, 2000; Cotter et al., 2001), there has been no serious inquiry into this phenomenon. Hence, the primary goal of the current study is to fill in this gap and resolve the glass-ceiling puzzle through an examination of both upward and downward mobility. My second goal is to formally test the hypothesis that women and minorities experience the glass-ceiling barrier. The term, glass ceiling, while amenable to commonsense understanding, does not have a precise meaning as a sociological construct. More than one critic has noted the lack of coherence as to how the glass-ceiling effect is operationally defined and identified (see Cotter et al., 2001; Jackson and O Callaghan, 2009). Some researchers reserve the term for the domain of authority attainment (e.g., Baxter and Wright, 2000) this is the usage adopted in this study while others extend its scope to other labor force outcomes such as wage (e.g., Morgan, 1998) and occupational attainment (e.g., Maume, 2004). Most, however, would agree with two test criteria. First, the glass ceiling is a specific pattern of labor market inequality, characterized by the intensification of inequality at higher levels (Baxter and Wright, 2000). Second, the inequality in representation needs to be distinguished from inequality in advancement into higher levels; a glass-ceiling effect must satisfy the latter criterion (Cotter et al., 2001). Due to data limitations, researchers often use suboptimal tests, making compromises such as inferring promotion rates from distributional patterns of workers across hierarchical levels (e.g., Baxter and Wright, 2000; Elliott and Smith, 2004) and examining the movement from non-managerial occupations to managerial occupations, instead of focusing on upper hierarchical levels (e.g., Tang, 1997; Maume, 1999), etc. This study overcomes these limitations and uses the two crucial test elements to distinguish the glass ceiling from other forms of labor market disadvantage. After first refining the operationalization of the glass ceiling, I test it by comparing gender and racial disparities in workplace advancement at different hierarchical levels. In this study, women and minorities are said to encounter a glass-ceiling barrier if they have lower rates of upward mobility than men and whites, respectively, and their disadvantages exist primarily at higher levels of hierarchies. 2. Workplace authority Workplace authority is the power to participate in and influence the decision-making process regarding an organization s operations and personnel. It can be measured by the extent of supervisory responsibility in hiring, firing, and determining other people s wages, promotions, and work content, or defined simply as a formal position in organizational hierarchies (see Kluegel, 1978 and Wright et al., 1995 for operationalization of workplace authority). The study of workplace authority is an important area of inequality research. Wright et al. (1995) summarized the relevance of authority for analysis of inequality as follows. First, authority is a valued workplace resource because it confers status and is intrinsically rewarding. Second, authority is closely related to the allocation of financial rewards. Last and most important, underrepresentation of women and minorities in management, especially in top managerial positions, is not only an indicator of inequality, but also a potential cause of inequality. It has been suggested that male managers in male-dominated hierarchies are likely to exclude women from positions of power in order to preserve male privileges and advantages hence, authority inequality begets further inequality. 3. Patterns of authority inequality 3.1. Leaky pipelines or revolving doors? It is often assumed that the process of authority attainment consists of a series of upward job transitions, with the higher transitions conditional on the lower ones hence, the analogy to pipelines. Accordingly, many see the shortage of women and minorities at the top as a problem of leaky pipelines : women and minorities face a disadvantage at each step of promotion and leak out on the way to the top. The pipeline perspective is attractive because it prompts researchers to look into where the leakage occurs. However, the approach of seeking the cause of representational inequality in sequential promotions is justifiable only if authority mobility is dominated by upward and lateral moves, with downward moves being the exception. But is it?

3 Z. Zeng / Social Science Research xxx (2010) xxx xxx 3 Although the prevalence of downward mobility in authority has yet to be determined empirically, two casual observations about the labor-market suggest that it must be quite common. First, the managerial structure of the entire labor force is relatively stable over time. The proportion of workers holding managerial jobs in the US, for example, stood at 13 14% throughout the 1990s (Statistical Abstract of the United States, 2010). In a stable authority structure, upward and downward flows must be approximately equal; if this is not true and mobility is dominated by upward flows, we will see an increase of the management sector. Second, although promotion is quite common, most people do not hold managerial positions by the end of their working life. According to the Panel Study of Income Dynamics (PSID), about 2.9% of men and 2.5% of women were promoted from non-managerial jobs to management in a year (Maume, 1999). 1 At this rate, more than half of the workforce would have entered management by retirement. However, when a group of white men in the PSID were tracked from the beginning to the end of their working life, the percentage of managers increased by only 15 points (from 10% to 25%) (Maume, 2004). Hence, most of the entrances into management must have been offset by exits. In a classic study of sex segregation and women s careers, Jacobs noticed a similar paradox: individual mobility among male-dominated, sex-neutral, and female-dominated occupations is common; but the change in the structure of sex segregation is slow, and women s presence in male-dominated occupations remains low. He characterized this pattern of aggregate stability with individual mobility using the metaphor of a revolving door: Every year, for every 100 women employed in male-dominated occupations who were employed in two consecutive years, 90 remained in a male-dominated occupation, while 10 left for either a sex-neutral or female-dominated occupation. At the same time, 11 entered a male-dominated occupation from one of these other occupation groups. Thus, the revolving door sends out 10 for every 11 it lets in. (Jacobs, 1989, p. 4). The revolving-door metaphor describes the dynamics of managerial attainment more aptly than leaky pipelines because it recognizes that mobility is not unidimensional but has many ups and downs. The revolving-door metaphor implies that the net change in managerial structure is small compared to the size of flows in both directions. Thus, if there were less attrition of women and minority managers, there would be more progress toward representational equality Glass ceiling or sticky floor? If the glass ceiling is to have any real meaning, it should be distinguished from plain old labor market discrimination. Although a difference of opinion exists as to what criteria should be used to identify the glass-ceiling effect in empirical research, most scholars agree that the essence is the concentration of inequality in the upper echelons, to be distinguished from both the general inequality that exists at all levels and the inequality that is concentrated at the bottom (Morgan, 1998; Baxter and Wright, 2000; Cotter et al., 2001; Albrecht et al., 2003; Elliott and Smith, 2004; Prokos and Padavic, 2005). The last is referred to in the literature as the sticky-floor effect, which operates to prevent women and minorities from entering managerial hierarchies. As Baxter and Wright (2000) reasoned, since women do reach a point below the glass ceiling but are not promoted above the barrier, the glass ceiling implies a greater female disadvantage at the top of the hierarchy than at lower levels. Specifically, they operationalized the glass ceiling as a greater disadvantage in promotion to the adjacent superior level as women ascend the corporate ladder. Ferree and Purkayastha (2000) challenged this treatment, arguing that it does not take increasing disadvantages at higher levels for female workers at the bottom of a hierarchy to perceive a glass ceiling. They pointed out that, in order to be promoted to the top, candidates usually have to make the cut at all previous levels. Thus, the prospects of making it to the top can be substantially reduced for female candidates, due to cumulative disadvantages. A simple example illustrates the difference between the two viewpoints. To identify a glass-ceiling effect in a hierarchy of three levels level 1 (bottom), level 2 (middle), and level 3 (top), for example Baxter and Wright required that women s disadvantages in promotion from levels 2 to 3 be greater than that from levels 1 to 2, whereas Ferree and Purkayastha only required that women s cumulative disadvantages in being promoted from levels 1 to 2 and then to level 3 be greater than the disadvantages in promotion from levels 1 to 2. 2 While women may perceive a glass ceiling due to cumulative disadvantages, testing a glass-ceiling effect as a cumulative disadvantage is problematic because it fails to distinguish glass ceiling from general disadvantages in promotion. Since promotions typically occur in a stepwise fashion, as Ferree and Purkayastha rightly pointed out, as long as women are less likely to be promoted from the mid-tier to the top than men, the cumulative probability for a woman at the bottom to make it to the top will necessarily be smaller than the probability of reaching the mid-tier. The problem with Ferree and Purkayastha s conception is that it fails to discriminate between patterns of disadvantages. Using their criterion, general inequality that exists at all levels can be called a glass ceiling; worse yet, even a sticky-floor effect can pass the test. Therefore, following Baxter and Wright, I operationalize the glass-ceiling effect as a greater disadvantage in reaching the adjacent superior level, as women and minorities ascend organizational hierarchies. 1 The PSID rates refer specifically to promotions crossing the line between non-managers and managers. General promotion is much more common. According to the National Longitudinal Survey of Youth, one third of men and women aged received a promotion in the 2-year period of Eighty percent of those promotions involved an increase of responsibilities, and 90% were accompanied by a raise (Cobb-Clark and Dunlop (1999)). 2 Baxter and Wright s criterion of an increasing disadvantage at higher levels identifies the most important feature of the glass ceiling (Baxter and Wright (2000)). However, as the number of levels within a hierarchy increases, this criterion becomes unnecessarily stringent, as the glass ceiling is understood as a phenomenon taking place at the top; most definitions of the glass ceiling are silent on the pattern of discrimination at lower levels.

4 4 Z. Zeng / Social Science Research xxx (2010) xxx xxx Table 1 The SESTAT definition of scientists and engineers. Source: 1993 National Survey of College Graduates. Notes: The SESTAT definition of scientists and engineers include people in the shaded cells. Those who did not hold S/E degrees but were working in S/E occupations (2%) are excluded in this study because their mobility in-and-out of S/E occupations creates coverage gaps in longitudinal analysis Data The data for the current study comes from the Scientists and Engineers Statistical Data System (SESTAT) Sponsored by the National Science Foundation, SESTAT is a longitudinal database of the employment, education, and demographic characteristics of scientists and engineers in the US. The surveys of SESTAT were conducted biannually from 1993 to SESTAT has several attractive features for studying authority attainment. First, it has a very large sample size (n = 126,721 in 1993), large enough for estimating the rates of transition into and out of managerial positions for minorities. Second, it measures supervisory responsibilities and managerial status in sufficient granularity to distinguish three levels of managerial authority. This latter feature is critical because, as explained earlier, in order to identify the glass-ceiling effect we need to compare the probability of advancing to the adjacent higher level at different hierarchical levels. This requires that authority be measured with at least three levels. Yet another advantage of SESTAT is that it utilizes a national, population-based random sample, which permits inferences about mobility patterns for US workers. Due to data limitations, many authority studies are restricted to a single firm or a single labor market segment (e.g., DiPrete and Soule, 1988; Yamagata et al., 1997; Cohen et al., 1998; Barnett et al., 2000). Since organizations differ in their promotion schemes and practices, case studies as such do not allow us to make inferences about the average behavior of US employers. In addition, case studies typically focus on internal promotions and do not follow employees who leave the focal firms for better (or worse) positions elsewhere. Since authority may be attained through either internal promotions or external job shifts (Barnett et al., 2000), studies that fail to account for both avenues of advancement cannot fully address women and minorities underachievement in authority. Although SESTAT represents a much broader population than many firm-based studies of authority, one might still be concerned that results from a sample of scientists and engineers are not generalizable. However, because scientists and engineers are rather broadly defined by the NSF, the SESTAT sample covers much more than the two occupational groups. The NSF s definition of scientists and engineers consists of two groups: (a) people with science and engineering (S&E) degrees, regardless of their occupation, and (b) college graduates who do not have S&E degrees but are working in an S&E occupation. 3 In other words, a college graduate can qualify as a scientist or engineer either by field of study or by occupation. Because the proportion of college graduates with S&E degrees exceeds those with S&E jobs in the population by over three-to-one 45% vs. 13%, according to the 1993 National Survey of College Graduates (NSCG) the SESTAT sample consists predominantly of the former group (see Table 1). Over 70% of the sample falling under the NSF s definition of scientists and engineers were employed in non-s&e occupations. Hence, the study population is not nearly as selective as we might first assume. To better understand the sample selectivity of SESTAT, I compared college graduates with S&E degrees to those without S&E degrees in the 1993 NSCG. The results are presented in Appendix Table A1 and Fig. A1. Despite differences in demographic characteristics, educational attainment, and employment sectors, the two populations are actually quite similar in authority distribution and pattern of authority inequality. Hence, while not generalizable to the entire US workforce, the results of this study may nonetheless be applicable to the college-educated population. In fact, given this study s interest in the glass-ceiling phenomenon in upper management, it is quite appropriate to target the college-educated rather than the general population. Unfortunately, the NSCG only followed the S&E sample for longitudinal study; therefore, my study utilizes the S&E sample from SESTAT. 4 For this study, analysis is limited to those who held a post-secondary degree and were between the ages of 21 and 60 during Two groups of people are excluded: (a) those who did not have an S&E degree and (b) post-secondary teachers. The first group consists of 4454 respondents who did not have an S&E degree but were included in SESTAT because they held a job in an S&E occupation sometime during These people are excluded because the occupational mobility of this group creates coverage gaps in panel analysis, due to the way scientists and engineers are defined in SESTAT. The second group of post-secondary teachers, 5 consisting of 21,814 individuals, are excluded not because a possible 3 The NSF s definition of a scientist or engineer requires a bachelor s degree or higher; those working in S&E occupations who do not have college degrees (e.g., individuals with associate degrees in any field) are not covered by SESTAT. 4 Those who were identified by the 1993 NSCG as scientists and engineers became part of the SESTAT panel and were followed up on in 1995, 1997, and Post-secondary teachers are over-sampled in SESTAT.

5 Z. Zeng / Social Science Research xxx (2010) xxx xxx 5 glass-ceiling effect does not exist in higher education, but because the measure of managerial authority used in this study (see two paragraphs below) does not capture professors authority status well. (If we were to study this group exclusively, rank and tenure status would be more appropriate measures.) The final sample consists of 271,006 observations on 129,529 respondents. My analysis focuses on the comparison of six demographic groups: white men and women, Asian-American men and women, and underrepresented minority (hereafter URM) men and women. Blacks, Hispanics, and American Indians are grouped together in the public-use SESTAT for the protection of respondent confidentiality. The dependent variable is three-level managerial authority. The control variables used in this study are: (1) the type and major of the highest academic degree received, (2) work experience measured as years since attainment of the highest degree, (3) hours of work (full time vs. part time), and (4) employment sector. Table A2 in the Appendix lists sample statistics by race and gender. Managerial authority is inferred from two variables: (1) whether the respondent belonged to the category of top and mid-level managers, executives, and administrators people who manage other managers, and (2) whether the respondent supervised the work of others as part of her or his job. In the surveys, supervisory responsibilities are defined as assigning duties to workers and recommending or initiating personnel actions such as hiring, firing, or promoting. I classified respondents into the following three tiers: (a) Level 1 workers: those who did not belong to the group of top and mid-level managers and did not supervise the work of others; (b) Level 2 supervisors: those who did not belong to the group of top and mid-level managers but did supervise the work of others; and (c) Level 3 managers: those who belonged to the group of top and mid-level managers and supervised the work of others. Rarely did top and mid-level managers report no supervisory responsibilities only 4% of them did. These managers are excluded from analysis because they were probably lame-duck managers with no real power, whom organizations could not or would not get rid of for some reason. From now on, I will refer to the three levels in this classification scheme as L1, L2, and L3, and to people at these levels simply as workers, supervisors, and managers. To validate the measure of authority, I examined the relationship between authority and salaries. Managers and supervisors earned on average 82% and 39% more than workers, respectively. After adjusting for human capital factors and employment sectors, the differentials stood at 48% and 18%. More importantly, change in authority level is associated with wage growth. People who moved down the hierarchy over a two-year period averaged a wage growth of 3%, while those who remained at the same level and those who upgraded their status experienced wage growth of 11% and 19%, respectively. Although we can entertain the possibility that people sometimes voluntarily move down in authority for higher pay, the positive association between change in authority and change in wage suggests that trading authority for pay is not a common phenomenon; rather, authority and pay generally go hand in hand. 4. Methods Three sets of analysis are conducted here to investigate gender and race differences in authority attainment. First, in order to replicate the well-documented shortage of female and minority managers in the SESTAT data, I model authority levels using a multinomial logit regression specified as follows: Pða i ¼ jþ ¼ expðb jx i þ Z 0 i c jþ Pj expðb jx i þ Z 0 i c jþ ; ð1þ where P(a i = j) is the probability that person i has authority level j (j = 1, 2, or 3), X i denotes gender and race of i with white males as the reference group, and Z i is a vector of the control variables, which include degree, major, experience, sector, hours of work, and observation year. Eq. (1) is estimated on the employed sample using pooled cross-sectional data from 1993 to Robust standard errors are used to account for the clustering of observations within individuals. Next, I investigate the mechanisms underlying the pattern of managerial representation uncovered in the first analysis by examining transition rates across four states: three authority levels (L1, L2, and L3), plus the state of unemployment (denoted by L0). While the focus of this study is on upward mobility and downward mobility of the employed population, I also examine transitions into and out of employment as an additional source of female and minority disadvantages in managerial representation. The model used to estimate the transition probabilities the probability that person i who was observed in state k ended up in state j two years later P(a i,t+2 = j a i,t = k) has the same form as Eq. (1). However, the data for the transition analysis consists of paired observations a starting state and an ending state 2 years apart for the same people. The transition probabilities are conditional on the starting state. That is, four separate models are estimated one for each starting state. The glass-ceiling hypothesis is tested by comparing a group s disadvantage in the mid-to-top-level upward transition (L2? L3) to its disadvantage in the bottom-to-mid-level upward transition (L1? L2).

6 6 Z. Zeng / Social Science Research xxx (2010) xxx xxx Women and minorities may face a disadvantage in both upward and downward mobility, as well as experience lower employment stability relative to white men. In the third analysis, I conduct a demographic projection to compare the impacts of these mechanisms. The procedure is outlined below. Step 1: Using the models from the transition analysis, I predict experience-specific transition probabilities across four states L0, L1, L2, and L3 for each group. All other independent variables in the models degree, major, sector, hours of work, and observation year are held constant at the sample mean in the prediction. Step 2: A set of starting distributions across the four states i.e., the distributions of new graduates are obtained for each group. This is done by using a model similar to Eq. (1), but with an added state of unemployment. Again, covariates are adjusted for in the prediction. Step 3: Treating authority attainment as a Markov Chain process, I trace the state distribution of each group as they age by applying the experience-specific transition probabilities from step 1 to the starting distributions from step 2. Step 4: The proportions of working life (from age 21 to 60) that each group would spend in each state are calculated from its age profile of state distribution from step 3. Step 5: For each female or minority group, I then modify the transition probabilities for three hypothetical scenarios and repeat steps 3 and 4. The three scenarios are: (1) the group experiences the same upward transition rates as white men; (2) the group experiences the same downward transition rates as white men; (3) the group experiences the same in-and-out-ofemployment transition rates as white men. I refer to the three scenarios as same up, same down, and same in/out, respectively. Modification of the three sets of rates was introduced one at a time. Meanwhile, the likelihood of making no transitions (e.g., L2? L2) is adjusted accordingly to keep the sum of the conditional transition probabilities at unity. By observing the changes in duration times brought on by the three hypotheticals, an inference can be made about the relative importance of upward mobility, downward mobility, and labor force attainment in authority inequality. It should be noted that the projection is based on the Markovian assumption that the next state depends only upon the current state. Furthermore, the projection assumes that people experience the prevailing rates of the period throughout their life. The results are, thus, synthetic: that is, they summarize the behavior of all age groups in the population during , rather than trace a cohort through its lifetime. 5. Results 5.1. Cross-sectional analysis of managerial representation Let us begin with a comparison of managerial representation by gender and race. Fig. 1 plots group differences in the likelihood of being supervisors and managers expressed as relative risk ratios. The results for white females, for example, indicate that their probabilities of being a manager and a supervisor relative to the probability of being a worker P(a = 3)/ P(a = 1) and P(a = 2)/P(a = 1) are, respectively, 0.53 and 0.76 times those for white men, all else being equal. The 95% confidence intervals are also shown. Women and minorities are less likely to be manager and supervisors and than comparable white men, as evidenced by coefficients ranging from 0.2 to 0.8. In accordance with the glass-ceiling hypothesis, the underrepresentation is more severe Relative Risk Ratio Asian female Asian male URM female White female URM male Manager Supervisor Fig. 1. Likelihoods of being managers and supervisors estimated from multinomial logit regression. Source: SESTAT Notes: The model controls for the type and major of the highest degree, potential work experience in quadratic specification, employment sector, hours of work (full time vs. part time), and year of observation. Whiskers represent confidence intervals at 95% level.

7 Z. Zeng / Social Science Research xxx (2010) xxx xxx 7 Table 2 Weighted 2-year transition rates across authority levels (%). n L0? L0 L0? L1 L0? L2 L0? L3 Total (A): From the state of L0 (unemployment) All 21, White male White female Asian male Asian female URM male URM female n L1? L0 L1? L1 L1? L2 L1? L3 Total (B): From the state of L1 (worker) All 105, White male 51, White female 24, Asian male 11, Asian female URM male URM female n L2? L0 L2? L1 L2? L2 L2? L3 Total (C) From the state of L2 (supervisor) All 83, White male 48, White female 15, Asian male Asian female URM male URM female n L3? L0 L3? L1 L3? L2 L3? L3 Total (D) From the state of L3 (manager) All 25, White male 15, White female Asian male Asian female URM male URM female Source: SESTAT among managers than among supervisors. This holds for all but URM men, who face similar shortages of 0.77 and 0.81 at L3 and L2, respectively. Fig. 1 also reveals an interesting racial and gender pattern in authority attainment. Of the five disadvantaged groups, URM men are the most likely to be supervisors and managers, while Asian women have the smallest probabilities of occupying those positions. The groups in the middle white women, URM women, and Asian men have roughly the same managerial representation. Along the dimension of race, we see that Asian Americans face a greater disadvantage than URMs; the pattern holds for both sexes. While this result may seem incongruous with Asian Americans reputation as the model minority, it nonetheless agrees with Tang s (1997) study of scientists and engineers in the 1980s and the general observation by Asian-American scholars that, although Asian Americans have surpassed whites in major socioeconomic indicators, such as education, income, and overall occupational status, they continue to face a disadvantage in accessing managerial positions. Within each racial group, men have higher authority attainment than women. Furthermore, while the effects of race and gender are largely multiplicative for Asian women, that is not the case for URM women, who do considerably better than predicted by their double minority status in the likelihood of being a manager. 6 This pattern of gender race interaction is in line with the well-documented finding that the gendergap in many socioeconomic indicators is smaller among blacks than among whites Rates of upward and downward mobility Although Fig. 1 lends prima facie evidence to the glass-ceiling hypothesis except for the case of URM men, additional investigation is necessary before we can draw any conclusions. First, we need to determine whether women and minorities 6 This is tested with a differently parameterized version of Eq. (1), where group indicators are replaced by dummy variables for race, gender, and their interactions. The only statistically significant interaction term, is gender URM for the manager outcome (P = 0.006).

8 8 Z. Zeng / Social Science Research xxx (2010) xxx xxx underrepresentation is due to slower upward mobility or to greater downward mobility. Second and central to the identification of the glass ceiling if the underrepresentation is indeed due to slower upward mobility, are the disadvantages greater at the top than at the middle? To address these questions, we now examine transitions across authority levels. Table 2 presents crude, 2-year transition rates across four states (L0, unemployed; L1, worker; L2, supervisor; and L3, manager), conditional on the starting state. The rates are calculated for the whole sample first, and then by race and gender. For example, 60.6% of the people who were not working at time t remained unemployed 2 years later, 27.9% of them started working as workers, 9.6% became supervisors, and 2.0% made it to the managerial level. Because SESTAT measures employment status at only four points the week of April 15th in 1993, 1995, 1997, and 1999 status changes within those two-year intervals are not captured. If a worker is first promoted to L2 and then demoted to L1 or if he makes a lateral move at L1 within the two years between survey dates, he will show up as a case of no transition in this table. As Table 2 shows, approximately 60 70% of the employed population exercise the same level of authority two years later. Transitions across authority levels are quite frequent in both directions, except that those at the bottom rarely made it to the top (L1? L3) in 2 years. As expected, downward mobility is common and apparently has higher incidence rates than upward mobility. For example, the transition rates out of managerial positions, L3? L1 and L3? L2, are 8.2% and 19.6%, respectively; while the rates for the reverse transitions L1? L3 and L2? L3 are 1.9% and 8.7%, respectively. As mentioned earlier, this disparity can be explained by the stability of authority distribution. At each wave, approximately 13% of the people are managers, and another 34% are supervisors. Because there are fewer managers than workers and supervisors, downward transition probabilities must be larger than upward transition probabilities for the proportions of the three levels to remain stable. Comparing the transition rates across all six groups, we observe with one exception that white men always exhibit the highest rates of upward mobility and the lowest rates of downward mobility; in addition, they are the least likely to enter, and the most likely to exit, the state of unemployment. The notable exception to the white male advantage is the transition critical for testing the glass-ceiling effect L2? L3. Asian and URM male supervisors apparently enjoy a slight advantage in advancing to management (9.4% and 9.2%, respectively, compared to 9.1% for white men), contrary to the glass-ceiling hypothesis. To formally test group differences in transition rates, we now turn to the results from multinomial logit models of transition. These models control for human capital variables and employment characteristics. To save space, only race and gender effects are presented in Table 3. The coefficients are relative risk ratios, with white men and no transition as reference categories. For example, the results in Panel A indicate that, for white women who were unemployed at time t, the transition probability into L1 two years later relative to the probability of remaining unemployed P(a t+2 =1 a t = 0)/P(a t+2 =0 a t = 0) is only 35% of that for non-working white men, while their relative probabilities of transitioning to L2 and L3 are only 24% and 8% of those for white men, respectively. After controlling for covariates, group differences in upward mobility as seen in the previous analysis remain. Women and minorities are less likely to advance from L1 to L2 than comparable white men, with relative risk ratios ranging from for Asian women to for URM men. In addition, white women and Asian Americans but not URM face a sizable disadvantage in advancing directly from L1 to L3. 7 However, there are no significant gender or race differences in the L2? L3 transition. Although Asian females experience a lower transition rate from L2 to L3 than white men (0.791), the gap is not statistically significant and apparently smaller than the one they face in L1? L2 (0.629). Hence, we do not even need to formally test group disparities in L1? L2 and L2? L3 transitions to reject the glass-ceiling hypothesis. On the other hand, since women and minorities do face a disadvantage in the L1? L2 transition, it can be said that the sticky-floor metaphor aptly describes the pattern of authority inequality they encounter. Turning to group differences in transitions of L2? L1, L3? L2, and L3? L1, it is worth noting that women and minorities disadvantage in downward mobility is more systematic than in upward mobility. Eleven out of the 15 coefficients (five demographic groups with three transition types) representing disparities in downward mobility are statistically significant at the 0.05 level and all 15 are in the expected direction, compared to eight statistically significant coefficients for upward mobility and 12 in the expected direction. Table 3 also displays group differences in labor market attachment. The results for exiting the labor-market are listed under L1? L0, L2? L0, and L3? L0, and those for (re)entering the labor-market under L0? L1, L0? L2, and L0? L3. Overall, women and minorities are more likely to exit employment and less likely to return than white men. As we might expect, the pattern is more conspicuous for women than for minority men. We also note that gender disparities in labor market attachment are greater among supervisors and managers than among workers: that is, while women are more likely to flow out of employment than white men overall, those in supervisory and managerial positions leave disproportionately more often. For example, the relative risk ratio for white females to leave employment increases from among workers to over 2.5 among supervisors and managers. In addition, when women return to work, they tend to start at a lower level than do white men, as evidenced by their decreasing relative risk ratios from L0? L1, to L0? L2, and to L0? L3 in Panel A. This suggests that off time may take a heavier toll on women than on white men with regards to authority attainment. In sum, the transition pattern between unemployment and the three employment states leads to the expectation that women and, to a lesser 7 Although Asian Americans appear to face greater barriers in advancing to L3 than to L2 from L1, this result is difficult to interpret because we do not know whether the L1? L3 transitions involve an unobserved intermediate step in L2. In any case, this type of transition is rare, observed in only 1.9% of the personperiods.

9 Z. Zeng / Social Science Research xxx (2010) xxx xxx 9 Table 3 Selected coefficients from multinomial logit regression of transition in authority level. L0? L0 L0? L1 L0? L2 L0? L3 (A) From the state of L0 (unemployment) White male Ref. Ref. Ref. Ref. White female Ref ** ** ** Asian male Ref ** Asian female Ref ** ** ** URM male Ref URM female Ref ** ** ** L1? L0 L1? L1 L1? L2 L1? L3 (B): From the state of L1 (worker) White male Ref. Ref. Ref. Ref. White female ** Ref ** ** Asian male Ref ** ** Asian female ** Ref ** ** URM male * Ref * URM female ** Ref ** L2? L0 L2? L1 L2? L2 L2? L3 (C): From the state of L2 (supervisor) White male Ref. Ref. Ref. Ref. White female ** ** Ref Asian male * ** Ref Asian female ** ** Ref URM male ** ** Ref URM female ** ** Ref L3? L0 L3? L1 L3? L2 L3? L3 (D): From the state of L3 (manager) White male Ref. Ref. Ref. Ref. White female ** ** Ref. Asian male * ** Ref. Asian female Ref. URM male * Ref. URM female ** ** Ref. Source: SESTAT Notes: The models control for the type and major of the highest degree, potential work experience in quadratic specification, employment sector, hours of work (full time vs. part time), and year of observation. Two-sided tests. * p < 0.05 ** p < extent, minority men not only spend less time working, but their lower labor force attachment also hinders authority attainment Demographic projection Fig. 2 displays the results of the demographic projection intended to compare the roles of downward mobility, upward mobility, and labor market attachment in authority inequality. The vertical line at 0.13 represents the projected proportion of working life white men would spend in the state of manager, and the line at 0.52 gives the proportion they would spend in the states of supervisor and manager combined. Four projection series are shown for women and minorities. The first projection was conducted using estimated transition rates for that group. The next three series, labeled same up, same down, and same in/out, were carried out after each group s disadvantages in upward mobility, downward mobility, and in-and-out-of-employment transitions relative to white men were eliminated, respectively. The series for the hypothetical scenarios are sorted by duration time in the state of manager. In comparing the three types of transitions, I focus on their effects on duration in the state of manager, since representational inequality at the top is more severe and of greater concern. Taking white women as an example, according to their estimated transition rates, they would spend of their life in L3. In the scenarios of same down, same up, and same in/out, the proportion of time in L3 would increase to 0.079, 0.086, and 0.091, respectively. That is, white women would see the largest increase in managerial representation if they had the same in-and-out-of-employment transition rates as white men. Thus, it can be inferred that lower labor force attachment is a major bottleneck to equal managerial representation for white women. As the figure shows, for white and Asian-American women, the disadvantage in upward mobility plays a more important role than that in downward mobility. For the other three groups, the reverse is true: equalizing downward mobility rates alone eliminates at least half of the gaps in managerial representation for Asian men and URMs. This is congruous with

10 10 Z. Zeng / Social Science Research xxx (2010) xxx xxx White female Asian male Asian female URM male URM female Estimated rates Same down Same up Same in/out Estimated rates Same in/out Same up Same down Estimated rates Same in/out Same down Same up Estimated rates Same up Same in/out Same down Estimated rates Same in/out Same up Same down Fig. 2. Projected proportions of working life in the states of manager and supervisor. Source: SESTAT Note: This bar chart displays projected proportions of working life spent in the states of manager and supervisor based on estimated transition rates across authority levels as well as between employment and unemployment. The vertical lines display the results for white men, who are projected to spend 13% of their working life in the state of manager and 39% of their working life in the state of supervisor. Four projection series are presented for women and minorities. The first series, labeled estimated rates, uses their estimated transition rates. The other three series, labeled Same up, Same down, and Same in/out, pretend that they had the same upward mobility rates, downward mobility rates, and in-and-out-employment rates as white men, respectively. The three hypothetical series are sorted by duration time in the state of manager. the results in Table 3 that white and Asian-American women appear to face more systematic barriers in upward mobility than the other groups. The effect of group differences in in-and-out transitions on authority inequality is much smaller than what we might expect based on the magnitudes of the coefficients in Table 3. Although all five groups exhibit lower labor force attachment than white men in Table 3, Fig. 2 demonstrates that only white and Asian-American women s duration in the state of manager is affected visibly. There are two explanations for the lack of effect. First, lower labor market attachment reduces duration in all three employment states, not just in the state of manager. Only in the cases of white and Asian-American women did we see a pattern of in-and-out transitions that is clearly not authority-neutral i.e., a pattern that reduces time in L3 more than in L1. Second, the overall impacts of group differentials in upward, downward, and in-and-out transitions on authority inequality depends not only on the size of those differentials, but also on the frequency of that type of transition. It is possible that group disparities in in-and-out transitions are large when expressed as relative risk ratios, but their effects are negligible because the overall rate of transition into the state of unemployment is low. 6. Discussion The analysis of this study prompts the question: why are female and minority managers less likely to hold onto their positions than their white male counterparts? For female managers, the primary reason is probably the differential impacts of fertility and work-family conflicts on men and women. There is substantial evidence from prior research that women are more likely to experience job interruptions for family related reasons (Phipps et al., 2001; Erosa et al., 2002). Women in high positions face more intense work-family conflicts not only because their jobs are more demanding but also because many of them are married to fellow professionals, who face the same pressures and overloaded work schedule as they do. While recent literature has focused on the opt out phenomenon i.e., professional women in high-power positions choosing to quit after giving birth it is conceivable that some women may instead opt down to jobs with fewer responsibilities and lower authority in order to better handle work-family conflicts (Stone, 2007). The underrepresentation of Asian Americans in managerial positions should be considered alongside their overrepresentation in professional and technical occupations. Compared to whites, Asian Americans are not only more likely to hold professional jobs, but, among those holding professional jobs, they are overrepresented in the more technical occupations, such as medicine, computer programming, and scientific research. The pattern of white-asian differences in occupations closely mirrors that in academic fields of study: Asian Americans are more likely to major in engineering, mathematics, and the physical sciences, and less likely to major in social sciences, the humanities, and other non-s&e fields. Insofar as the choice of major indicates a person s occupational aspirations, we may speculate that Asian Americans prefer professional occupations to managerial occupations, causing them to exit managerial positions in pursuit of professional careers in greater numbers than whites.