Job-shift differences between men and women in the workplace

SOCIAL

SCIENCE RESEARCH

11,

l-29 (1982)

Job-Shift Differences between Men and Women in the Workplace CHARLES

N.

HALABY

University of Wisconsin-Madison Until now causal analyses of male-female career differences have been based on the standard attainment model and have focused on differences in career outcomes, namely status and earnings. This paper departs from this practice by using the career lie-cycle model of achievement as a framework for the analysis of sex differences in the job mobility experiences of management personnel of a large corporation. The paper focuses not on sexual differences in the level of career rewards, but on differences in the rate of job shifts as the career unfolds. The models are based on the mean-value function of a Poisson arrival process. The principal findings are: (1) Male and female job-shift regimes are similar in form and described by the mean-value function of a nonstationary and heterogeneous Poisson arrival process; (2) the parameters governing mate and female job-shii regimes are significantly different; (3) parameter differences indicate sexual inequities with respect to the rate of return to productive resources, but not with respect to structural opportunities to shift; (4) for men and women alike, schooling increases the rate of job shift, while labor force experience prior to being hired and entry-level achievement decrease the rate of shift.

The causalanalysis of careerdifferencesbetweenmen and women has become an increasingly important part of stratification researchon socioeconomic achievement.Until now, however, virtually all studieshave been formulated exclusively in terms of the conceptual and methodological framework of the standardattainment model. Whetherone considers research pertaining to the labor market as a whole (Suter and Miller, 1973;Treiman and Terrell, 1975;Feathermanand Hauser, 1976), or between- (Stafford and Johnson, 1974;Talbert and Bose, 1977)and within-employer studies(Malkiel and Malkiel, 1973;Halaby, 1979a),the approach has always been the same: a static application of the linear regressionmodel to the analysis of male-female differencesin the level of career rewards (e.g., statusor earnings).This paperdepartsfrom this This research was supported by a grant from the University of Wisconsin-Madison Graduate School Research Committee. Address reprint requests to Charles N. Haiaby, Department of Sociology, University of Wisconsin, 1180 Observatory Drive, Madison, WI 53706.

2

CHARLES

N. HALABY

tradition and takes a distinctly different approach to the problem of male-female careerdifferences.Rather than using the attainment model and focusing on disparitiesin careeroutcomes,I usethe careerlife-cycle model of achievementas a framework for the analysis of male-female differencesin job-shift behavior. The career life-cycle model does not replacethe attainment model so much as augmentit. The attainment model is primarily a framework for the causal analysis of the relation between career inputs and career outcomes,not for the causalanalysisof the interveningprocessof career mobility. Due largely to the work of Sorensen(1974,1977)and Spilerman (1977),the careerlife-cycle approachemergedto challengethe attainment model for its failure to attend to and incorporateelementsof the process of changein achievement.The challengeis conceptualas well as methodological, and rests on the revival of the idea of a work career as representinga discontinuous sequenceof jobs unfolding over the life cycle. From this perspective, the basic mechanismdriving the achievement trajectory traced from initial entry to the labor force to somelater point in an individual’s work history is a successionof job shifts, usually involving movement from lower, less rewarding to higher, more rewarding positions. Within this framework variation in achievement is traced to variation in the rate, pattern, and outcomes of job shifts; in Sgrensen’s(1974)words, “Job shifts representelementary acts of mobility.” A central researchtask is to assesshow a variety of factorsindividual and structural-shape achievementtrajectories through their impact on thejob-shift process.This approachtherebyjoins the interest of mobility analysts in movement among differentially rewarding positions (Hodge, 1966; McGinnis, 1968; McFarland, 1970;White, 1970; Stewman, 1975)to the interest of attainment researchersin background causes(seeTuma, 1976). The application of the careerlife-cycle model to sexualdifferencesin achievement processescan profitably proceed along the same lines as attainment studies of reward inequality. Aggregateanalysespertaining to the labor market as a whole are obviously necessary,but must be supplementedby studies of between-and within-employer sexual disparities in career mobility. Only by proceedingon each of these fronts will it be possibleto gaugethe extentto which careermobility differences between men and women are due to either (1) the operation of external labor markets and the unequal distribution of the sexes between employers with systematically different mobility structures, or (2) the operation of internal labor markets and the within-employer “tracking” of men and women along distinctly different mobility regimes. This paper initiates this researchagendaby examining aspectsof the sexual differentiation of mobility regimes in an internal labor market. The crux of the paper is a causal analysis of the processesgoverning

JOB-SHIFT

DIFFERENCES

3

the job mobility experiencesof male and female personnel of a large corporation. In contrast to previous employer-basedstudies, the issue is not male-female differencesin the level of earningsor status attained in the workplace career, but differencesin the rate of occurrenceof job shifts as the career unfolds. Real and notable gains in achievementin a bureaucratic setting dependon position changes,so that an emphasis on job shifts is an especially appropriatemeans of assessingthe distinguishingfeaturesof male and female careerprocesses.Indeed, the very concept of the “bureaucratic career” is frequently defined not only in terms of career rewards, but in terms of movement among positions (Weber, 1958,p. 203). This shift in focus brings a distinctly different methodological approach. Although basedon cross-sectionaldata, the analysis presented here issues from an explicitly dynamical conceptualizationof the jobshift process.’ The models around which the analysis is organizedare basedon hypothesesregardingthe rate of job shifts. The principal issues concern sexual differentiation on two relateddimensionsof the job mobility process. As detailed later, the job-shift processis conceptualized as the product of two functions: onegoverningthe arrival of opportunities to shift and assumedto be a stable structural property of the workplace career system; and a second governing the impact of individual characteristics on the probability of being chosenfor a shift opportunity, and assumed to reflect the terms of the employer-employee exchangeof productive resourcesfor inducements,The central aim of the analysis is to assessthe relative significanceof the opportunity structure and the exchange relation in generating male-female differences in job-shift processes. The vast literature on male-female career differencesdoes not shed much light on this issue.To be sure,the well-documentedsex differences in achievementgive groundsfor assumingthat women shift at a slower rate than men. Similarly, becauseof the extent to which both betweenand within-employer sex differencesin achievementissuefrom job segregation, it is reasonableto assume that job segregationis associated with and may even generatethe sexual differentiation of job-shift processes.But even assumingthat job segregationresults in slower rates of shift for women than for men, there remains the question whether ’ Because it brings a dynamical interpretation to cross-sectional data, ours is a so-called synthetic cohort analysis. Although there are well-known pitfalls with this type of analysis, the fact is that much of the evidence we have regarding the dynamics of achievement issue from this type of analysis, and squares quite well with the findings of longitudinal studies. When the “true” model of a phenomenon is dynamical, synthetic cohort analyses of crosssectional data are no more “synthetic” than static analyses; both are based on potentially erroneous assumptions. For the phenomenon under investigation here, a priori reasoning suggests that a synthetic cohort analysis is subject to less specification error than a static analysis.

4

CHARLES

N. HALABY

this is becausewomen are disadvantagedwith respect to the rate of arrival of shift opportunities, or becauseof the exchangerelation and the lower rates of return women receive for their productive resources. Becauseour data come from a company characterizedby a high degree of job segregationalong sexuallines, our analysis will speakdirectly to this issue. MODELS OF JOB SHIFTS

We begin by laying out an analytical framework within which the job mobility experiencesof males and females may be compared. The exposition draws on but is more comprehensivethan Sorensen’s(1975, 1977)work on job mobility in the occupational structure. The models are presentedwithout regard for sex differences,and may thereforebe viewed as a series of hypothesespertaining to males and females alike. The following section discussesthe details of incorporating sex differentials into the parametrizationof the job-shift process. It is assumedthat job mobility is a discrete state processevolving in continuoustime. Job shifts occur in discretejumps of unit increment and at any point in time. Furthermore, the shift experiencesof different individuals are assumedto be stochastically independent.*With these assumptions,we specify a generalparametrizationof thejob-shift process from which the specific models of interest may be derived. Let {N,, t 2 0) be an integer-valuedcounting processregisteringthe number of job shifts undergoneby the ith individual in t yearsof service in the workplace (Nit = 0, t = 0). Also let all individual characteristics on the job-shift behavior of the ith individual be arrangedin a vector Xi, and define the mean-valuefunction of the job-shift processas M(X,J) = E(NJXj) (1.1) = A (Xi)G(t).

The function M(X,,t) gives the expected number of job shifts for an individual with attribute profile Xi and t years of employment in the workplace. The mean-valuefunction is written as the product of two other functions, each controlling a different aspect of the mobility process. The ’ This assumption is probably false, although to an unknown degree. As White (1970) has argued, the movement of one person will, through the creation of a vacancy, affect the movement of others. In their analyses of job shifts both Sorensen (1977) and Tuma (1976) assume independence on the ground that it may hold approximately in a large open system like the occupational structure. The degree to which independence is approximated in a large, highly differentiated company like the one from which the data analyzed here come is hard to say. In order to circumvent the enormous methodological difficulties which would otherwise ensue, I will follow convention and treat the data as if departures from independence may be safely ignored.

JOB-SHIFT

DIFFERENCES

5

function G(t) is some transformation of time representinga clock by which we reckon the arrival of opportunitiesto shift jobs. It is assumed that G(t) is not influenced by individual characteristics,but rather is a property of the opportunity structure of the workplace, and reflects both the rate at which vacanciesare createdand the distribution of jobs (see Sorensen, 1977).’On the other hand, the effect of individual characteristics on the job shift processis registeredvia h(X,). The function X(Xi) controls the extent to which an individual with attribute profile Xi takes advantageof or is chosen for the opportunities for shifts exogenously created in G(f). Stated differently, A(Xi) is the rate at which the ith individual shifts per unit of time in G(t). A second quantity of interest is the intensity function of the job-shift process, defined as

(suppressingthe i subscript). This function gives the meanrate at which shifts occur in real time t. To expressthe intensity function in terms of A(X) and G(t), substitute from (1.1) into (1.2), yielding v(X,t) = A(X)?

+ G(t) y.

Now, if we make the simplifying assumptionthat the elementsof X, are fixed at the time of initial employment, and that the parametersof A( ) are constant over time, the last term drops out, giving v@,t) = W&(t), (1.4) where g(t) = (d/dt)G(t). This equation shows how the rate of shift in real time dependson the interaction of individual (A(X)) and structural (g(t)) factors. Later we will ask whether the sexualdifferentiation of the job mobility process occurs via A(X) or g(f). For now it is enough to ’ Whether G(r) is interpreted in terms of the opportunity structure or in terms of the accumulation of human capital through work experience is ultimately arbitrary. The latter interpretation is justified by the human capital theory of achievement, while the former rests on Sfirensen’s mathematical theory of job mobility in a fixed structure of inequality. We prefer to interpret G(t) in terms of structural opportunities because it is consistent with a theory which is specifically tailored to the job shift phenomenon, and because it allows us to draw on a powerful repertoire of statistical models. ’ The assumption that individual resource endowments and attributes are tixed at the time of initial employment is not as strong as it appears. Fist, all of the individual background factors that are of interest to sociologists and that we shall consider are in fact tixed at the time of entry. Second, the only resource variable for which the assumption is doubtful is “experience” in the workplace, but this is usually measured in terms of length of service and is implicitly incorporated as an index parameter in our models. As for the assumption that the parameters of A( ) and G( ) do not vary over historical time, this is of course the premise of a synthetic cohort analysis.

6

CHARLES

N.

HALABY

observe that once A(X) and g(t) are specified, the resulting expression for v(X,t) may be integratedto obtain M(X,t), which in turn may be used as an estimating equation with Nit on the left-hand side. Model I: Poisson process. All of the models consideredare variations on the Poisson arrival process (Cinlar, 1978, Chap. 4; Parzen, 1962, Chap. 4). The simplest starting point is the homogeneous,stationary Poisson process. If to the assumptionsstated earlier we add that A(X) = A and that for any t, s, N,,, -N, is stochasticallyindependentof {N,, u c t} (the so-calledMarkov assumption)and of t, then it can be shown that g(t) is unity and the intensity function is v(X,t) = A, A 2 0. (1.5) This states that the rate of job shifts is constant. The job-shift process {Nit, t 3 0) correspondingto this intensity function is said to be homogeneous,asagainstheterogeneous,becausethe rate of shift is constant acrossindividuals with different characteristics(v(X,t) is not a function of Xi). Furthermore, the job-shift processis stationary, as againstnonstationary, becausethe rate of shift is constant through real time; individuals shift at the same rate at all points in the workplace career. The mean-valuefunction of this processis M(X,t)

=

v(X,u)du I = ir,

(1.6)

so that the expected number of shifts undergoneby an individual is proportional to length of service. Model ZZ: Nonstationary Poisson process. A common initial departure from the simple Poisson process involves relaxing the stationarity assumption in favor of a model which allows time dependenceof the intensity function. This means that the number of shifts N,+,-N, occurring in a time interval of length s would dependnot only on s, as is true of Model I, but also on t. By relaxing the stationarity assumption one hypothesizes,in effect, that job shifts may be more likely at some points in the workplace career than at others. The first question to arise concerns the functional form of the time dependence.Past efforts to introduce time dependencein models of mobility in the occupationalstructure have assumedthat transition rates are declining functions of time, where time has been defined variously in terms of job duration (McGinnis, 1968;Tuma, 1976),age (Mayer, 1972;Sflrensen,1975)and labor force experience(Sgrensen,1977).This assumption is consistent with the empirical observation that individual rates of mobility do indeed slow down. We assumethat the rate of shift is a monotonically declining function

JOB-SHIFT

DIFFERENCES

7

of length of service in the workplace. The rationale is threefold. First, Sorensenhas obtained a reasonablygood fit using this assumption to model shifts in the occupational structure. Second, this form of time dependenceis consistent with the shapeof observedcareer attainment trajectories, which show rapid rates of increasein attainment early in the career, followed by slower rates later on. Third, a declining rate of shift reflects the idea of structural barriers to mobility, and is derivable from some fairly reasonableand commonly madeassumptionsabout the shape of reward distributions (Sorensen, 1977; Simon, 1957; Lydall, 1959). Assume, then, that opportunities to shift arrive at an exponentially declining rate, and write5 g(t) = eb’, b < 0. Therefore, the intensity function of the job-shift processis

(1.7)

v(X,t) = Aeb’, A > 0, b -C 0, (1.8) where the homogeneity feature of Model I is retained. This equation states that the rate of job shift is constant across individuals with the same length of service, but declines at a constantrate as length of time in the workplace increases.Note that if b = 0, Eq. (1.7) becomesthe intensity function of Model I, so that the rate of shift would remain constant throughout the career. Hence, the hypothesis b < 0 as against b = 0 is a precise specificationof the idea of structural barriers to job mobility. On hypothesis (1.7), the expectednumber of shifts is given as M(X,t) = J;v(u)du (1.9) = !$!?ceb’- I), where (eb’- 1)/b = J&(u)du = G(t). Model ZZZ: Heterogeneous Poisson process. Another way of allowing for departuresfrom the simple Poissonprocessis to retainthe stationarity assumption but introduce heterogeneityvia A(X). Assume that opportunities to shift arrive at a constant rate throughout the career,but that the ability of individuals to avail themselvesof the opportunitiesdepends on their attribute profile Xi. Specifically, if h(X) = ZCjXv, then the intensity function is linear,6 ’ This function has been used previously in a similar context by Sorensen (1975, 1977) and Mayer (1972), and is a common initial departure from stationarity in the stochastic processes literature (e.g., Parzen, 1%2, p. 125; Cox and Lewis, 1966, p. 45). 6 One small problem with the linear specification is that the intensity function is not constrained to be nonnegative for each individual, as it must be. On this count a preferable

CHARLES N. HALABY

v@,O =

(1.10)

ZCjX(j,

and the mean-valuefunction is Mow

= ~c,&tJ,

(1.11)

where the first element of X.j is X.O= 1 and the cj, j = 1,2, . . . , are parameterscontrolling the effect of X, on the rate of shift in real time .1.

Model IV: Heterogeneous time-dependent Poisson process. The final model relaxes both the homogeneity and stationarity assumptions by combining Models II and III. We assumethat for individuals with a given length of service the rate of shift is a function of their attribute profile Xi. and that for a given individual the rate of shift exponentially declines as the careerunfolds. Letting A(X) be linear and g(t) = eb’,the intensity function can be written as v(X,t) = Zc,{X,eb?. (1.12)

This equation implies that the effect of individual attributes on the rate of shift is greatestearly in the career and thereafter declines as 1eRgth of serviceincreases.’The expectednumber of job shifts by an individual with t years of service and profile Xi is M(X,t)

=

tx c,(X&b?dt I0

which can be used to estimate the parametersof A(X) and g(t).’ Resources, entry-level achievement, and job shifts. These models establish a framework for comparing male and female mobility regimes. specificationwould be v(X,r) = Pm, which is always nonnegative. However, we found no need to go to this specification,nor was there a s&a&ant improvement in fit when we did. The results reported later are based on the linear specilkation. ’ This can be seen by taking the partial derivative of v(X,r) with respect to X,, say, yielding

av(xr) aX, = @'. Since b < 0, the effect of X, on the rate of shift is an exponentially decreasingfunction of length of service. * If the linear specificationof v(X,r) yields negative values, then an exponential specification would be preferred; in which case the mean value function would be M(X,t)

= ecfi(ebr-

1)lb.

JOB-SHIFT

DIFFERENCES

9

But before incorporating sex differences into this framework we need to give empirical content to the models by specifying the sources of heterogeneityin A(X). Because it has been assumedthat G(f) is a relatively stable property of the workplace, in a given workplace individual differences in rates of shift will be a function of differencesin Xi and thus in A(X). The conceptualizationof the job-shift processgiven here is tentatively assumedto hold for men and women alike. Our reasoning regardingthe sources of heterogeneityis based on a number of assumptionsabout the functional significanceof job shifts in the employer-employee exchangerelation. First, it is assumedthat job shifts function largely as a mechanism for the exchangeof increased productive contributions for increasedrewardsor achievement.’Second, there exists an optimum or equilibrium point beyond which exchanges and thus job shifts ceaseto occur. From the employee’s standpoint,this optimum representsthe highestlevel of achievementattainablegiven his resourcesand the opportunity structure of the workplace; from the employer’s standpoint, this optimum representsthe maximum productive contribution that can be expectedof an employee with a given resource endowment. In a given workplace the optimum point of exchangeis a function of (1) the length of time an individual remains exposedto the opportunity structure; and (2) individual productive resourcesthat are fixed upon entry to the workplace and which at that time exist largely as future potential. Hence, the exchangeof productive contributions for achievementat the start of the workplace careerwill nearly always fall short of the equilibrium or optimum point of exchange. Within this framework job shifts are a vehicle for closing the gap between the entry-level and optimum point of exchange.Job shifts are the means by which an employer can realize the complete productive capacity of an employee, and an employeecan realize his or her optimal level of achievement. Assuming that the incrementsin productive contributions and achievementproducedby a job shift representa constant proportional increase over previous levels (see Simon, 1957; Lydall, 1959),then over a fixed span of time the greater the gap between the optimum and entry-level point of exchange,the higher the rate of job 9 I wish to emphasize that this statement is indeed an assumption, since the measure of number of shifts introduced later does not distinguish shifts which yield a gain in achievement from those which do not. While this assumption may be problematic in a societal context, not so in an organizational context. To be sure, not all shifts result in a gain even in an organizational context, but it is probable that all but a very small proportion do. In fact, independent analyses of the company data used here suggest that the assumption is correct in the present case. Specifically, I have found that for men and women alike, dynamic models of earnings attainment fit significantly better when indexed on job number rather than on length of service, thereby indicating that job shifts typically yield gains in attainment.

10

CHARLES

N. HALABY

shifts.” Looked at from the employee’s viewpoint, for a given level of entry achievement,the greater the productive resources,the higher the optimal-level achievement, and thus the higher the rate of job shifts neededto attain it. Conversely,for a given level of productiveresources, the higher the entry-level achievement,the lower the rate of job shifts. Finally, consider the fact that employeesmay come to a particular workplace at different points in their careertrajectories. Somemay enter at the very beginningof their careers,while othersmay be further along. Other things equal, such differenceswill changethe relation betweenthe optimum and entry-level point of exchange,and thus affect the rate of job shifts. The optimum point of exchangedependsnot only on the productive resources of the individual but on the length of time the individual remains “exposed” to the opportunity structure of the workplace, and this will tend to be less for employeeswho are further along in their careersthan for those at the beginning.Conversely, entry-level achievementwill depend on the productive contributions an employee can make when hired, and this will tend to be higherfor individuals with prior labor force experience than for those without. Hence, previous experienceaugmentsan individual’s productive value at time of entry to the workplace, but depleteshis or her potential long-run productive contributions, thereby reducing the optimal attainablelevel of achievement. On balance then, individuals who are more advancedin their socioeconomiccareerswhen hired will tend to have lower rates of job shift thereafter than thosejust starting out. In sum, the main factors entering X(X) are entry-level achievement, productive resources,and time in the labor force prior to entering the workplace.” At this point it is assumedthat these factors operate in similar ways for males and females.The predictionsregardingthe effects of these factors may be summarized and incorporatedinto the various models as follows. Let N be the number of job shifts, LS the length of service, PROD a measure of productive resources, LF a measure of time in the labor force prior to entering the workplace, and ENT a measure of entry-level achievement. Then the models and predictions may be written as Model I N = ALS,

A > 0.

I0 This scenario may be contrasted with S@ensen’s (1975’) model, in which the job shift function is homogeneous but the achievement gain per shift is heterogeneous. ‘* It should be mentioned that the models preseked later originally included measures of father’s occupation, father’s education, religious group atIiliation, and nativity. Because these variables taken singly or together failed to improve the fit of the models, they were excluded from the analysis.

JOB-SHIFT

11

DIFFERENCES

Model II N = (X/b)(exp(b(LS))- 1.O),

A > 0, b < 0.

Model III N = c&S -I- c,PROD*LS

-I- c,LE*LS c3

-I- c,ENT*LS,

< 0.

co, Cl ’ 0, c21

Model IV N = (co + c,PROD

+ c,LF + c&NT)*(exp(bLS) > 0, c2, c3, b c 0.

- 1.0)/b),

co, cl

(Note that all models exclude an intercept term, so that N is zero when length of service is zero, as desired.) PARAMETRIZING

SEX DIFFERENCES

IN JOB MOBILITY

At the start we askedwhetherthe sexualdifferentiationof job-mobility processes occurred with respect to the structure of opportunity, the employer-employee exchangerelation, or both. This is tantamount to asking whether a sex difference in the rate of shift occurs via G(t), via h(X), or via both. Sex differencesgeneratedvia G(r) would indicate that the opportunities to shift arrive at a different rate for malesand females; differencesgeneratedvia A(X) would indicate that the terms of the exchangeof inducementsfor contributions differ for males and females. Such sex differentials may be incorporatedinto all of the models discussedabove, but it is enoughto state the relevant alternativesin terms of the general model v(X,t) = h(X)g(t). Ho: No sex differences in job-shift processes’: VW) = A mm. (2.0) H8: Male-female differencesin the terms of exchangebut not in opportunity structures: vAX,O = WOgW,

(2.1)

where k = male/female. &: Male-female differencesin opportunity structures but not in the terms of exchange: ML0 = UXk,(O. (2.2) HE: Male-female differences in both opportunity structure and the terms of exchange: Vk,(X, f) = h(XkM.

(2.3)

12

CHARLES

N. HALABY

The analytical procedure is straightforward. For each of the four models we test Ho against the global alternative H, to determine the magnitude of the overall sex difference in mobility processes.” At the same time we will be interested in comparing for both males and females the goodness of fit of Models I-IV. Once these issues are resolved we will asssess the extent of sexual differentiation on each of the two dimensions of the job-shift process. DATA AND METHODS The data pertain to management personnel of a California-based firm that was at the time of the study the largest single enterprise of a major public utility holding company in the United States.” Questionnaires were distributed to all 2198 managers of the firm; 1649 (75%) usable signed questionnaires were returned. A comparison by salary, sex (1242 men and 405 women), and position revealed a close correspondence between the sample distributions and the respective “population” distributions. The analysis that follows is based on listwise deletion of missing data, which leaves I1 15 observations on men and 363 observations on women. The dependent variable is the number of changes of position (number of positions minus one) an individual has experienced since starting with the company.‘4 Length of service is measured in years. Data on length of service came to me coded in four 5-year intervals. For this analysis I2 This procedure is better than starting with separate tests of Ho against Ha and Hbr since it is possible to accept Ho in both instances and yet reject Ho when tested against Hc. I3 The data were collected by Oscar Brusky in 1960. Although somehwat dated, it is not clear just what bearing this has on the analysis. After ah, all data are “dated” in one sense of the term. The only reasonable ground for prefering new to old data is that the intervening years have brought important changes, but this already presupposes the accumulation of studies which span a wide range of years and indicate that historical time is relevant. But there are no such studies of sexual differentials in within-employer job mobility. Our analysis therefore constitutes a valuable baseline against which to assess historical change as findings from other studies accumulate. The data represent a period prior to the advent of the women’s liberation movement and well before the adoption and full-scale implementation of aflirmative action legislation. Furthermore, they precede in time the increases in female labor force participation witnessed in the mid- and late 1960s and continuing into the 1970s. I’ A position is defined in terms of the official job titles of the firm. Data on the dependent variable come from individual self-reports of the number of positions held since joining the company. While studies in the societal context have also relied on retrospective selfreports to measure number of shifts (Tuma, 1976; Sorenson, 1973, this mode of measurement probably yields more accurate data when applied in an organizational context. In a bureaucratic setting individuals count positions with reference to a common, shared, and standardized listing of jobs, and this helps reduce the error that may be due to interindividual variation in the definition of a job shift.

JOB-SHIFT DIFFERENCES

13

respondentswere assignedthe midpoint of the interval into which they fell.” Managerial productive potential is measuredby education, coded on a 6-point scale correspondingto years of schooling (see Blau and Duncan, 1967, p. 165).“j Two measuresof work experience prior to coming to the firm were used. The first is starting age, estimated as current age minus length of service. The secondis the total number of positions held previously in other companies.Entry-level achievement is indicated by the hierarchical level in the company at which a manager began his or her organizationalcareer. This is measuredby a 7-point scale representinga classification of the company’sjob titles according to the authority and responsibility associatedwith them; for details consult Grusky (1%6). The statistical methods used to estimate and test the various models are not without interest in their own right. To fix ideas,write the meanvalue function of the various models in generalform, ww

= MXJi,%

(3.1)

where the subscript refers to the ith individual, 0 is a set of unknown parameters,and the remaining notation is as previously defined. Under the assumptionspresentedearlier the N, (conditionalon Xi) will be Poisson distributed with mean and varianceequal to M(X,,t,$), and with the probability of the ith individual experiencingNi job shifts in t, years of service given by P(N,,t,)

= exp[ - M(X~~ti~e)l(M~,,t~,e))Ni . N,!

(3.2)

Equation (3.1) is a regressionfunction, but unlike the usual regression functions used in sociological work the dependentvariable is assumed to be Poisson rather than normally distributed. Furthermore, in two instancesthe models posited earlier involve regressionfunctions which are nonlinear in the parameters.The analysis is based on techniques developed for the linear and nonlinear regressionanalysis of Poissondistributed data (Jorgensen,1961; Weber, 1971;Frome, Kutner, and Beauchamp, 1973). ” The length of service midpoints are 2.5, 7.5, 12.5, and 17.5. The use of groups rather than ungrouped data on length of servicedefmitely reducesthe efficiencyof our parameter estimates, so that the procedure described later is not quite equivalent to maximum likelihood estimation. However, it is doubtful that the actual parameter estimateswould have been very diiercnt had we gone to the trouble to alter the estimation procedure to accomodate grouping on length of service. ” The schooling codes arc: lessthan high school-l; some high school-2; high school graduate-3; some college-4; collegegraduate-5; postgraduateworkd. These intervals correspond to approximately 2 years of schoolingand will be interpreted accordingly.

14

CHARLES

N. HALABY

The estimation techniqueemployed here is an interatively reweighted least-squaresprocedurewhich yields maximum likelihood estimators of the parameters.The procedureinvolves minimizing the following weighted sum of squareswith respect to 8, S(e) = C%Vi[Ni-M(Xi,ti,BS]‘, (3.3) I

where Okis the estimateof 8 obtainedon the kth iteration and the weights are the reciprocals of consistent estimatesof the variance of n, Wi = [m(Xi,ti,Ok-‘)]-I. The minimization procedure begins with a set of estimates 8” of 8. When M( ) is linear theseinitial estimatesare obtained by ordinary least squares;when M( ) is nonlinearthe investigatorsupplies a set of starting values for the parametersand the Gauss-Newton method is used to solve the nonlinear normal equationsfor first-round estimates of 6. In both cases the initial weights are set to unity. The estimatesof 8 thus obtainedare usedto form the weights for the second round of iterations. This iterative process continuesuntil Ok= Ok-’ by some convergencecriterion.I7 At this point the least-squaresnormal equations are identical to the maximum likelihood normal equations based on (3.2). Indeed, using the Gauss-Newton method as indicated above is equivalent to the Fisher scoring algorithm for maximum likelihood estimation (Jennrich and Moore, 1975).In order to obtain the Fisher scoring estimates of the standarderrors of the coefficients, the least-squaresstandard errors are transformed by resealing the mean squareresidual to unity (Jennrich and Moore, 1975). Within this estimation framework there is a number of ways to formulate tests of significance and statistical comparisons of different models. Tests of significancefor a single parameterestimate are based on the Wald test statistic W = (@/SQ,where Sij is the information theory estimate of the variance of 6j’ and W is asympototically distributed as x2 with one degreeof freedom. For hypothesesrelating to several parameters the likelihood ratio test is used. To test the goodnessof fit of the various models we use the residual weighted sum of squaresgiven in (3.3). Note that when ek = f3*-‘, (3.3)is distributed as x2with degrees of freedom equal to the number of observationsminus the number of parametersin 8. A more graphic measureof goodnessof fit is obtained by comparing the empirical marginal frequency distribution of shifts to the predicted distribution generatedby the model yielding the smallest residual weighted sum of squares. ” The convergence criterion used was a relative change in a parameter of less than lo-‘. The models were estimated using NREG, a package of nonlinear regression routines put out by the Madison Academic Computing Center at the University of Wisconsin-Madison. Nonlinear regression is discussed by Draper and Smith (lP66, Chapter 10) and Maddalla (1979; pp. 171-176).

JOB-SHIFT

DIFFERENCES

15

FINDINGS The sexual differentiation of the job-mobility process. Before identifying the sources of male-female differences in mobility regimes, we need to assess the degree to which the job-shift process is differentiated along sexual lines. This may be done by fitting a given model to all observations and to separate sets of observations on men and women. If fitting a model to male and female observations separately achieves a large enough reduction in residual error, we can conclude that the job shift regimes governing the mobility of men and women are different. Table 1 gives the parameter estimates and residual sum of squares obtained for Models I-IV. With the exception of the “total” and “male” equations of Model I, all of the residual sums of squares fall short of the critical region defined by the relevant x2 statistic, thereby indicating an acceptable fit. More importantly, in each of the four cases fitting the model separately to males and females yields a substantial reduction in the residual sum of squares. In a more formal vein, Table 2 presents the likelihood ratio test statistics bearing on the hypotheses of equality of male and female job-shift regimes. These statistics forcefully indicate that regardless of the specific model, the hypothesis of equality must be rejected. The best-fitting model of the job-shif process. Knowing that men and women follow different job-shift regimes does not tell us which model best represents the nature of the underlying mobility process. What it does do is allow us to compare the different models separately for men and women. As a point of departure Model I may be compared to Model IV. According to Model I, which assumes homogeneity and stationarity, opportunities to shift arrive at a constant rate throughout the workplace career, and the ability of individuals to take advantage of these opportunities is constant with respect productive resources, entry-level achievement, and time spent in the labor force prior to entering the company. Because Model IV relaxes both the homogeneity and stationarity assumptions, contrasting Models I and IV yields a simultaneous test of these assumptions. For both males and females Model I must be rejected in favor of Model IV. For males relaxing the stationarity and homogeneity assumptions reduces the residual sum of squares from 1200 to 1049, and yields a statistically significant log likelihood ratio x2 value of 138; for females the residual sum of squares drops from 381 to 333, and the log likelihood ratio x2 value of 34 (p < .OOl). For males and females alike, then, Model IV gives a better representation of the job-mobility process than Model I. Indeed, analogous tests indicate that Models II and III may also be rejected in favor of Model IV. In this limited sense then, the job-shift processes governing the mobility of men and women are basically similar in form and described by Model IV.

-

Females

Females

Males

44s (.025) (ii

-

Males

II. N= (X/b)(e” - 1) Total

-

K

-.068* ww - .07-l* (011) - .074* (.OI8)

(.-if; .295* Low .228f WV

Length of service Education

Previous positions

of

Entry level

Coefficients Starting age

1476 1113 361

1077 342

362

1114

1477

df

1489

381

1200

1631

Residual sum of squares

.05)

1192 >$=406

>x’=

>x2= 1567

>x* =408

>)(I= 1193

>x*= 1569

(p =

Critical region

TABLE 1 Estimates of the Parameters of Models of Job Shifts, for All Personnel (N = 1478) and for Males (N = 1115) and Females (N = 363)

I. N=Xt Total

Models

Maximum Likelihood

F z

9

E z

r

2 %

y

(@I-

1)

.437* (.038) .502* (.053) .411* (.071)

- .054* ww - .066* (.012) - .068* (.018)

.300* (.020) .312* (.023) .284* (.039)

.029* (.ow .027* (.007) .Oll (.013)

(.OW

.024* (.ow .025* C.004) .oos

(.oW

.002 (.@w - .OOl (.003) .005

.003 (.003) .OOl (.003) .008 (.005)

’ The information theory standard errors appear in parentheses. * Statistically significant at less than the .OOl level by the Wald test. ** Statistically significant at less than .05 level.

Female

Male

Total

=

-

Females

N

-

Males

Iv.

-

(&,tJ

III. N=Pc, Total

- .040** (.016)

(.OW

- .030* (.ow - .037*

- .017* (.ow - .018* (.ow - .024** (.OlO)

- .003* (.ool) - .003* (J-w - .002 (.ool)

- .002** (.ool)

(.@w

- .003* (.ool) - .003*

357

1109

1049 333

1472

358

1110

1473

1440

363

1123

1525 1189

1564

1188 z-x*=402

>g=

>x*= 1563

>x2 = 403

>x’=

>g=

18 Likelihood

CHARLES

N. HALABY

TABLE 2 Ratio (6) x2 Statistics for Tests of Equality of Male and Female Parameter Vectors, Models I-IV

Models

Me)

- 21n@)

4

Critical region

I. N = At II. N = (X16)(eb’- 1) III. N = Xc, (X&

-30 -37 -23

60 14 46

1 2 5

>$(.Ol,l) = 6.6 >&.01,2) = 9.2 >xZ(.01,5) = 15.0

IV. N = y

-30

60

6

>x*(.O1,6) = 16.8

(e”-l)

The relative signijcance of structural and individual factors. Before examining the actual parametersof the male and femalejob-shift equations, it pays to considerthe relative contribution of nonstationarityand heterogeneityto the increased explanatory power achieved in moving from Model I to Model IV. Nonstationarity refers to the function G(t) governingthe arrival of job-shift opportunities, and is assumedto be a stable structural property of the workplace; heterogeneityrefers to the function A(X) governingthe exchangeof inducementsfor contributions, and reflects the impact of individual characteristicson the rate of job shifts. An assessmentof the explanatory power attributable to each of these sourceswill enable us to gaugethe degreeto which job mobility is shapedmore by structuralopportunitiesor by individualcharacteristics. The relevant statisticsmay befound in Table 1.The explanatorypower due to nonstationarity (assuminghomogeneity)is given by the reduction in the residual sum of squaresbetweenModels I and II; the explanatory power due to heterogeneity(assumingstationarity) is given by the reduction in the residual sum of squaresbetweenModels I and III. Among men, relaxing the stationarity assumption reducesthe residual sum of squaresfrom 1200to 1077,while relaxing the homogeneityassumption reduces the residual variation from 1200to only 1123.Among women we find the same pattern: nonstationarity reducesthe residual variation from 381 to 342, while the reduction due to heterogeneityis from 381 to 363.‘* Hence, even without taking account of the disparity in the degreesof freedom associatedwith nonstationarity (df = 1) and heterogeneity(df = 4), it is clear that the former is the primary source of departurefrom the simple Poisson model of job shifts. In his analysis of job shifts in the occupational structure Sgrensen (1977)conjecturedthat introducingnonstationarityin the arrival function would absorb much of the heterogeneityin the rate of shifts across I8 These comparisons may be carried out more formally by using a likelihood ratio test, but a good and easier alternative is to observe that the mean square residual of the alternative model is approximately unity in each case, so that the reduction in the residual sum of squares per degree of freedom wiII be distributed approximately as an F statistic.

JOB-SHIFT

DIFFERENCES

19

individuals. The results above support this conjecture in the workplace context and for both men and women. More importantly, the results buttress the argumentsof Sorensen(1977),and Spilerman (1977)concerning the relative significanceof structural as againstindividual background factors in the job mobility process.” This does not mean that individual characteristicscontribute nothing to the rate of shift once account has been taken of nonstationarity. On the contrary, the results (Table 1) for Model IV (comparedto Model II) indicate that individual factors still make a difference, albeit more for men than for women. The male equation shows that three of the four individual characteristicshave a significant impact on the rate of shift, the one exception being the numberof positions held in other firms. The significant coefficients indicate, as expected,that schoolingtends to acceleratethe rate of shift, while entry-level achievementand starting age tend to reduce it. For the female equation only the coefficient of entrylevel achievement is significant and negative as expected. Among the other three variables, only the negative coefficient of starting age even exceedsits standarderror. Sexual differentiation: Disparities in structural opportunities or terms ofexchange? Of paramountimportanceis the contrastbetweenthe values

of male and female coefficients.Although we have establishedthat male and female mobility processestake the sameform, we have also seen that the parametersgoverning theseprocessesdepart significantly from equality. By examining the actual coefficients we may determine the source of the departure from equality, be it disparities in the rate of arrival of structural opportunities to shift, or in the terms of the employer-employee exchangerelation. The figures in Table 1 are quite clear regarding the source of the differentiation of male and female job-shift regimes: differencesin the terms of the exchangerelation are far more important than differences in structural opportunities. Indeed, there is virtually no sex difference on the latter dimension. The male value of the parametergoverningthe arrival function is b = - .066, indicating that the rate of shift declines at an averagepercentagerate of 6.6% per year of service. The correspondingfigure for women is b = - .068, so that the decline in the rate of shift as the career unfolds is only slightly greaterfor women than it is for men. Virtually all of the sex difference in mobility regimes is due to differences in the parametersof the function A(X) governing the exchange relation, and most of this differencecan be traced to two sources.First, ‘9 Another way to compare to the explanatory power of these two sets of factors would be to compare the reduction in residual sums of squares attributable to length of service and to individual background variables. By this criterion, too, structural opportunities would be judged more significant than individual attributes.

20

CHARLES

N.

HALABY

women are at a sizeable disadvantage with respect to the impact of schooling on the rate of shift. For men the schooling coefficient is ,027, but for women the figure is .Oll and less than its standard error. Second, women are at a sizeable disadvantage with respect to the intercept, or what might be viewed as the effect of unmeasured productive resources. The male value of 302 is 22% higher than the female value of .411. The nature of Model IV is such that the male advantage engendered by these differences tends to be greatest in absolute terms early in the career, and declines as length of service increases. Components of the male-female shift rate differential. These results indicate that the male-female difference in rates of shift cannot be due to differences in the rate of arrival of structural opportunities, since this rate is approximately equal for males and females. This leaves only two systematic sources of the rate-of-shift differential: the differences observed above in the parameters of the exchange relation, or differences in levels of productive resources, entry-level achievement, and time spent in the labor force prior to entering the firm. In order to gauge the relative extent to which differences in the rate of shift at various points in the workplace career are attributable to these two sources, we proceed as follows. The curves describing the observed average rate of shift of males and females as the career unfolds may be written as v,(%J)

= A,(S,,~~,,~f,k,)ebm’,

and

where s is average schooling, fsp is average number of previous positions, E is average entry level, A is average starting age, A,,, and A, are the estimated male and female exchange relations, b, = br = - .067 are the arrival rates, and t = 0,1,2, . . . , is length of service. To determine how much of the average difference in rates of shift (v, - VJ is due to differences in terms of exchange (A,,, - AJ and to differences in average levels of “resources” (8, - J&), we need only generate hypothetical shift-rate curves by varying each component while holding constant the other. Hence, the expected rates of shift of women who follow their own job-mobility regime but have male levels of resources is VAX,,.,,?) = AXS,,I’P,,~~,A,)e-.067’ for t = 0,1,2 . . . . On the other hand, the expected rates of shift of women who follow the male mobility regime but have their own levels of resources is v,(X,,t) for t = 0, 1, 2. . . .

= A,(Sf,~~b~f,Af)e-.067’

21

JOB-SHIFT DIFFERENCES

The numerical results are given in Table 3 and graphedin Fig. 1. Reading from left to right, Table 3 gives the values of v,(&,,), v&r), v&J, and v,&) for different values of length of service. The first two columns indicate that women are at a sizeabledisadvantagewith respect to the rate of shift, with the female rate amountingto about 75% of the correspondingmale rate. While male and female rates decline in similar fashion, the decline for women comes about 5 yearsearlier in the career than it doesfor men. For example,women with 5 yearsof seniority shift at a rate of .253, which is approximately the same as the rate of shift of men with 10 years of service. The figures in column 3 of Table 3 are the expectedrates of shift of women who follow their own mobility regime but have male levels of resources.These hypothetical rates are approximately equal to the observedfemale rates, thereby indicatingthat noneof the male-female rate differential is accounted for by male-female differences in levels of schooling, entry achievement, previous positions, or starting age. In contrast, the figures in the last column of table 3 tell a very different story. As a comparison with the observedmale rates will verify, these figures indicate that if women retainedtheir own levels of resourcesbut followed the male mobility regime, they would shit at approximatelythe samerate as men. In other words, the male-femaledifferencein observed rates of shift is due entirely to differencesin mobility regimes. Drawing on previous findings, we can be even more specific than this: virtually all of the sex difference in rate of shii is due to differencesin exchange relations-women are at a serious disadvantagewith respect to the returns to unmeasuredresourceendowmentsand to schooling-not arrival functions. Observed and predicted marginal frequency distributions of shifts. It is instructive to consider what the respective male and femaIe models imply for the overall marginal frequency distribution of individuals by TABLE 3 Estimated Rates of Job Shift by Ungth of Service Observed

Length of service 0 5 10 15 20

Hypothetical

Males

Females

Female regimehale resources

Male regime/ female resources

A67 ,336 .242 .174 .125

.355 .253 .181 .129 .092

.355 253 .180 .128 392

.459 .330 .237 ,171 .123

22

CHARLES

N. HALABY

.45

.40

.35

5 f B 2 %

3

.25

.20

.15

.iO

.-

3

qv Length

FIG. 1. Observed and hypothetical

of

15

20

Service

rates of job shift by length of service.

numberof shifts. Comparingthe observedfrequencydistribution of shifts to the predicted distribution yields a graphic means of assessingthe fit of Model IV. Table 4 gives the predictedand observedfrequencydistributions. Considering the male figures first, the predicted distribution derived from Model IV yields a reasonablygood fit throughout the observed distribution except at the upper tails, where it underestimatesthe number of nine-shift movers and overestimatesthe number of movers exceeding nine shifts. Since this pattern exhibits both over- and underprediction, it is diicult to fashiona theoreticalaccount.A more likely explanationalthough I cannot verify it-is that the disparity is due to the fact that the observedupper tail was actually generatedby aggregatingfrequencies acrosscategoriescorrespondingto nine or more shifts.MIf the predicted m The reason I suspect aggregation is because the original data file as it came to me was designed such that all variables were coded using a single character occupying a single column of an IBM card. I think that shifts of 10 or more were probably assigned “9” to

JOB-SHIFT

23

DIFFERENCES

TABLE 4 Predicted and Observed Frequency Distribution of Individuals Males and Females

by Number of Shifts, for

Males Number of job shifts Total 0 1 I

L

3 4 5 6 I 8 9 Above 9 X2 x2 (aggregating frequencies for 9 shifts and above)

Observed 1115 26 106 161 182 188 145 125 99 41 42 0

Females Predicted

Observed

Predicted

1115 36.1 %.l 153.7 188.6 196.3 162.8 120.5 78.3 45.4 23.7 19.5

363 7 96 89 66 33 36 16 13 5 2 0

363 30.8 65.2 78.5 70.7 52.1 32.8 18.0 8.8 3.8 1.5 0.1

46.1

45.5

12.5

44.7

frequencies are aggregatedin a similar fashion, an expectedfrequency of 40.9 results, a value quite close to the observedfigure of 42. After aggregationthe recomputed x2 value is 12.5,indicating a very good fit. But even without aggregationthe fit is good, since the bulk (73%)of the original x2 value of 46 is due to a lack of fit that is confinedto the upper tail, while the fit of the rest of the distribution is remarkably good. Moreover, if the pattern of over- and underprediction throughout the distribution is considered,we find an arrangementwhich, by a runs test, would be expected 65% of the time on the hypothesis of randomness. By this criterion too, the predicted distribution fits the empirical distribution well. The results pertainingto women indicatethat the predicteddistribution fits the empirical distribution about as well as it did for men. The x2 statistics for the female comparison are about the same as the preaggregationvalue of 46 for men. However, it is clear that the lack of fit detectedby the x2 statistic cannot be due to aggregationof the upper tail. On the contrary, the distribution derived from Model IV fits both the upper tail and middle of the empirical distribution quite well. In contrast to the male comparison, the bulk (73%) of the x2 value is due maintain a F 1.0 format and to facilitate calculations at a time when computer technology and software were not what they are today. Fortunately, the chances are that fewer than 2% of the male observations may have been affected by this procedure.

24

CHARLES

N.

HALABY

to a lack of fit in the lower endof the distribution. Model IV underpredicts the frequency of women making one shift and overpredictsthe number making zero shifts. Although it is impossible to say for sure why this disparity at the lower end of the distribution should be observed for women but not men, it may reflect some ambiguity or discontinuity, especiallyat ports of entry to the company, in thejob assignmentprocess as it applies to women. Still, the overall fit is adequate;in fact, the pattern of departuresof predicted from observedfrequenciesyields an arrangementwhich would be expected83%of the time on the hypothesis of randomness. SUMMARY AND CONCLUSION

In this paper I have departedfrom the usual attainment approachto male-female career differences and have used instead the career lifecycle model as a framework for the causalanalysis of sexual disparities in the rate of job shift in an internal labor market. The careerlife-cycle model assumesthat achievementis a dynamic processof change,and that job shifts are the fundamentalunits of mobility. Careerachievement is conceptualized as a discontinuous sequenceof employer-employee exchangesof increasedinducementsfor increasedcontributions, and it is assumedthat the major behavioral manifestationof these exchanges is a successionof job shifts. Finally, the approachassumesthat the job shift process itself incorporatesthe effects of both individual resource endowmentsand structural opportunities on careermobility. Theseassumptionshavethoroughly informed the analysis.The models around which the analysis was organized were based on the intensity function of a Poissonarrival process,and explicitly representedjob-shift rates in terms of the interplay of individual resourcesand structural opportunities. The job-shift processwas parametrizedas the product of two functions: one controlling the impact of individual characteristics on the mobility rate and reflecting the terms of the employer-employee exchangerelation; and another controlling the arrival of exogenously generatedopportunities to shift and assumedto representa stable property of the workplace. The generalaim of the analysiswas to determine whether sexual disparities in the rate of mobility were due to (1) differences in the “returns” males and females received to their productive resources,or (2) differences in the rate of arrival of structural opportunities (as indexed by the coefficient of length of service) to shift. The findings may be summarizedas follows: 1. Regardlessof the assumptionsmade about the underlying mobility process,the evidencepoints decisively to the differentiation of job-shift regimesalong sexuallines. For all four models,the hypothesisof equality of male and female parametershad to be rejected.

JOB-SHIFT

DIFFERENCES

25

2. Despite differences in parameter values, the best-fitting male and female job-mobility regimes have the samefunctional form. 3. Job mobility is shapedmore by structural opportunities than by individual characteristics. For men and women alike, the rate of shift respondedmore to nonstationarity in the function governingthe arrival of structural opportunitiesthan to heterogeneityin the function governing the employer-employee exchangerelation. 4. Despite the overriding significanceof structural opportunities, individual factors still affect the rate of shift, albeit more for men than for women. For both sexes, schooling tends to increasethe rate of shift, while entry-level achievementand starting age tend to reduce it. 5. The sexual differentiation of job-mobility regimes is due more to differences in the terms of the exchangerelation than to differences in structural opportunities to shift. 6. The difference in exchangerelations accounts for virtually all of the male-female difference in averagerates of shift. Male-female differencesin averagelevels of schooling, entry rank, number of previous positions, and starting agehave no net effect on the shift-ratedifferential. Of paramount significance is the result that sexual inequities in the rate of job-shift issue largely from the exchangerelation and the lower value the reward system assignsto the resourcesof women compared to men. With respect to structural opportunities, men and women face rates of arrival that are equal. Moreover, the structural communalities obtaining between male and female job-shift processesextends even further than this. As the figures in the last two rows of Table 1 show, the effect of entry rank on the rate of mobility is about the same for men (- .037)and women (- .040).Although entry-rank was treated formally as an individual characteristic, it is clearly not of a piece with schooling, previous positions, and starting age.Rather, entry rank could have beentreated as a structuralfactor, sinceit representsnot a personal attribute, but a location in the organization’s hierarchical structure of inequality. From this perspective,then, the equality of male and female coefficients of entry rank also support the conclusion that the structural barriers to mobility faced by men and women are equivalent. Some care should be taken in interpreting this last conclusion. Just becausethe values of certain parametersreflectingthe role of structural factors in the job shift processare equal for men and women, it cannot be inferred that men and womenface the su17te barriersto mobility within a sexually undifferentiatedstratification structure. Indeed, in the present casejust the opposite is true. The stratification system of the company consideredhere showsa large measureof segregationalong sexuallines, with women crowded into the lower-payingjobs and ranks (seeHalaby, 1979a,Table 7). Moreover, the positions to which women are confined span a much narrower range of rewards than do the positions of men.

26

CHARLES

N. HALABY

Still, such sexual segregationobviously does not necessarilyentail disparities in the structural componentsof the job-shift process, since no such disparities were found.” What such segregationdoes entail, or perhapsreflect, are differencesin the exchangerelation governing the effect of individual productive resourceson the rate of job shift. At this point it is worth consideringwhether the patterns found for male and femalejob-shift processesin the company studied here can be generalizedto other internal labor markets. While the best basis for judgment would be a direct comparison to similar analyses in other organizationalsettings, this will have to await the accumulationof future studies. However, if job shifts are the mechanismsunderlying gains in achievement, evidencebearing on the typicality of male-female differences in achievement in this company should shed some light on the typicality of our findings pertaining to job shifts. In this connection, the results of other analysessuggestthat this firm’s reward practicesare not atypical of other, especially large, employers. Analyses of sexual inequality in career rewards show that the overall male-female earnings ratio, the overall male-female differencein earningsstructures,and the male-female differencesby marital status observedin this firm are remarkably comparableto thoseobservedmore recently in aggregateanalyses basedon representativenational samples(Halaby, 1979a).**Moreover, the pattern and sourcesof earnings inequality in this company coincide with thosefound in a companywhich otherwisediffers in major respectsfrom the one consideredhere (Halaby, 1979b,p. 125).While these results may not prove that our findings on sexual differencesin job-mobility processesare generalizable,they do shift the burden of proof to those who would claim otherwise on grounds other than the strictly statistical or conjectural. Another issue worth keepingin mind when assessingtheseresults has to do with selectivity bias. Employer-specific researchtypically must make do with observationsonly on those individuals (stayers)who are members of the workforce at the time of the study; observationsare ” This finding is quite consistent with theoretical expectations. For example, Sorenson’s (1977) mobility theory posits that the rate of arrival of shift opportunities is a joint function of the rate of creation of vacancies and the distribution of jobs with respect to reward levels, so that male-female differences on the latter dimension do not necessarily imply differences in structural opportunities. 22 Commenting on this similarity, I wrote in another paper, “if one were to assume that the structure of sexual inequality in this firm is typical of other employers, then one would expect to find aggregate patterns of inequality very much like those actually observed.” After reading this, Professor Barbara Bergmann reported to me (personal communication, 1978) that research in progress on employers in a number of different industries is coming to the same conclusion. This suggests that the mean pattern of within-employer inequality has not changed much since 1960, and that there may be remarkably little variation around this mean.

JOB-SHIFT

DIFFERENCES

27

usually unavailable for individuals (leavers)who were members of the organization during the time period spannedby the youngestand oldest cohorts in the sample, but who have since left. Now if there is a systematic relationshipbetweenleaving the organizationand, in the present case,job-shit behavior, then regressionsfor stayersalone would yield biasedestimatesof the parametersof a modelpertainingto the population of both stayers and leavers. While our results are probably subject to some selectivity bias, the real questionis whether the bias has severely distorted the male-female contrasts.23 Although the data neededto assessthe effect of selectivity bias are not available, the magnitudeof the problem may be guagedby treating current members of the workforce as either stayers or future leavers. If a variableindicating an individual’s propensityto leavethe organization can be defined, then some insight into the nature and extent of sample selection can be gleanedfrom the associationbetweenthis variable and the residuals from Model IV. To measurethe propensity to leave the organization I used an item indicating whether an individual would take a job with another company if it meant a raise in salary (coded 1 = definitely no to 4 = definitely yes). The correlationbetweenthis variable and the residualsfrom Model IV is - .09for males and - .08for females, thereby suggestingthat for males and females alike, samplesof stayers overselect individuals with many job shifts. I also calculated these correlations for the different length of service groups. For men the correlations are, in ascendingorder of length of service, .13, - .02, - .12, and - .11; for women the figures are .Ol, - .07, - .13, and - .02. These figures suggestthat samplesof stayers underrepresentindividuals with many shifts in the youngestcohort, but overrepresentindividuals with many shifts in the remaining cohorts. The important thing is that the pattern and magnitude of these correlations are similar for men and women. This arguesagainstthe hypothesisthat the male-female differences in job-shift processesfound here are artifactual and due to differencesin the extent and nature of selectivity bias. In the final analysis issuesof generalizabilityand selectivity will hinge on future employer-basedanalysesof the sexual differentiation of jobshift processes.The analysis presentedhere initiates this researchprogram and yields results which may serve as a baselineagainstwhich to assessthe findings of other studies as they accumulate. REFERENCES Blau, P., and Duncan, 0. D. (1%7), The American Occupational York.

Structure, Wiley, New

u It should be said that selectivity bias is not intrinsically more serious than any other kind of bias resulting from missing data, and that in other contexts taking account of selectivity has revealed only minor biases (Heckman, 1974, 1976; Fligstein and Wolf, 1978).

28

CHARLES

N. HALABY

Cinlar, E. (1975), Introduction to Stochastic Processes, Prentice-Hall, Englewood Cliffs, N.J. Cox, D. R., and Lewis, P. A. W. (1966) The Statistical Analysis of Series of Events, Methuen, London. Draper, N. and Smith, H. (1966), Applied Regression Analysis, Wiley, New York. Featherman, D. L., and Hauser, R. M. (1976), “Sexual inequalities and socioeconomic achievement in the U.S., 1%2-1973,” American Sociological Review 42, 462-483. Fligstein, N., and Wolf, W. (1978), ‘Sex similarities in occupational status attainment: Are the results due to the restriction of the sample to employed women,” Social Science Research 7, (June), 197-212. Frome, E., Kutner, M., and Beauchamp, J. (1973), “Regression analysis of Poisson-distributed data,” Journal of the American Statistical Association 68, (December), 935-940. Grusky, 0. (1966), “Career mobility and organizational commitment,” Administrative Science Quarterly 10, 489-502. Halaby, C. N. (1979a), “Sexual inequality in the workplace: An employer-specific analysis of pay differences,” Social Science Research 8, (March), 79-104. Halaby, C. N. (1979b), “Job-specific sex differences in organizational reward attainment: Wage discrimination vs. rank segregation,” Social Forces 58, (September), 108-127. Heckman, J. J. (1974), “Shadow prices, market wages and labor supply,” Econometrica 42, (July), 679-694. Heckman, J. J. (1976), “The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models,” Annals of Economic and Social Measurement 514, 475-492. Hodge, R. (1966), “Occupational mobility as a probability process,” Demography 3, 19-34. Jennrich, R. I., and Moore, R. H. (1975), “Maximum likelihood estimation by means of nonlinear least squares,” in Proceedings of the Statistical Computing Section, American Statistical Association. Jorgenson, D. W. (1961), “Multiple regression analysis of a Poisson process,” Journal of the American Statistical Association 56, (June), 235-245. Lydall, H. F. (1959), “The distribution of employment incomes,” Econometrica 27, 110-115. Maddalla, G. S. (1979), Econometrics, McGraw-Hill, New York. Malkiel, B. G., and Malkiel, J. A. (1973), “Male-female pay differentials in professional employment,” American Economic Review 63, 693-705. Mayer, T. (1972), “Models of intragenerational mobility,” in Sociological Theories in Progress (J. Berger et al., eds;), Vol. 2, pp. 308-357, Houghton-MifBin, Boston. McFarland, D. D. (1970), “Intragenerational social mobility as a Markov process: Including a time-stationary Markovian model that explains observed declines in mobility rates,” American Sociological Review 35: 463-476. McGinnis, R. (1%8), “A stochastic model of social mobility,” American Sociological Review 33, 712-722. Parzen, E. (1%2), Stochastic Processes, Holden-Day, San Francisco. Simon, H. A. (1957) “The compensation of executives,” Sociometry 28, 32-35. Sorensen, A. B. (1974), “A model for occupational careers,” American Journal of Sociology 80, 44-57. Sorensen, A. B. (1975), “The structure of intragenerational mobility,” American Sociological Review 40, 456-471. Sorensen, A. B. (1977), “The structure of inequality and the process of attainment,” American Sociological Review 42, %5-978. Spilerman, S. (1977), “Careers, labor market structure, and socioeconomic achievement,” American Journal of Sociology 83, (November), 593.

JOB-SHIFT DIFFERENCES

29

Stafford, F. P., and Johnson, G. E. (1974), “The earnings and promotion of women faculty,” American Economic Review 64, 888-903. Stewman, S. (1975), “Two Markov models of open system occupational mobility: Underlying conceptualizationsand empirical tests,” American SociologicalReview 48, 298-321. Suter, L. E., and Miller, H. P. (1973). “Income differences between men and women,” American Journal of Sociology 78, %2-974. Talbert, J., and Bose, C. E. (1977), “Wage-attainment processes:The retail clerk case,” American Journal of Sociology83 (November), 403-424. Treiman, D. J., and Terrell, K. (1975) “Sex and the process of status attainment: A comparisonof working women and men,” American SociologicalReview 48,174-200. Tuma, N. B. (1976), “Rewards, resources, and the rate of mobility: A nonstationary multivariate stochastic model,” American SociologicalReview 41, (April), 338-360. Weber, D. C. (1971), “Accident rate potential: An application of multiple regressionanalysis of a Poissonprocess,” Journal of the American StatisticalAssociation66, (June), 285-288. White, H. (1970), Chains of Opportunity, Havard Univ. Press,Cambridge, Mass.