A HIERARCHICAL THEORY OF OCCUPATIONAL SEGREGATION AND WAGE DISCRIMINATION.

BALDWIN, MARJORIE L. ; BUTLER, RICHARD J. ; JOHNSON, WILLIAM G. 等

WILLIAM G. JOHNSON [*]

Becker's model of discrimination is extended to the case where men exhibit distastes for working under female managers. The distribution of women in the resulting occupational hierarchy depends on the number of women in lower occupations, the wages of male workers in lower occupations, and male distastes for female management. Thus, there exists an occupational sorting function, related to wages, that determines the occupational distribution of women. We integrate this sorting function into a standard wage equation to derive a new decomposition of male-female wage differentials and apply it to a sample of insurance industry workers from the 1988 CPS. (JEL J71)

I. INTRODUCTION

This article describes and tests a model that relates wage discrimination to occupational segregation. The model is based on the hypothesis that labor market discrimination against women depends more on the positions of men and women in job hierarchies than on a reluctance of men to work with women. Stated simply, we assume that men are reluctant to work for women even if they do not object to working with women. We believe the hierarchical model more directly represents the social history of attitudes toward female workers than the usual models of tastes for discrimination based on physical or social distance.

The hierarchical model also permits us to derive an empirical measure of the effect of occupational segregation on wage differentials that is directly linked to theory. In particular, the model predicts that the proportion of women declines exponentially as one moves up the job hierarchy. Therefore, there exists an occupational sorting function related to wages that determines the occupational distribution of women. We integrate this occupational sorting function into a standard wage equation to derive a new wage decomposition that accounts for occupational segregation.

The model extends the analysis of discrimination against women beyond predictions of occupational segregation by recognizing that abilities to acquire managerial skills vary among individuals of both sexes. Thus, even in the presence of discrimination, the comparative advantage of some women as managers more than offsets the costs incurred to compensate for the tastes of the men whom the women supervise.

We apply the new decomposition formula to a sample of insurance workers from the 1988 Current Population Survey (CPS). The results imply that, for this sample, approximately one-third of the male-female wage differential can be attributed to the occupational segregation of women.

The article is organized as follows. Section II summarizes the literature on female work roles that is the basis for our hypothesis of male discrimination against female supervisors. The hierarchical theory of discrimination is developed in section III. Section IV presents simulations, based on the hierarchical model, to derive the prediction that the relative proportion of females declines exponentially as one moves up the job ladder. Section V derives the new wage decomposition, and section VI presents results from the CPS data. Section VII concludes.

II. THE SOURCE OF HIERARCHICAL DISCRIMINATION

There is a considerable literature that supports the assumption of hierarchical, gender-based discrimination. [1] Although the evolution, nature, and sources of men's attitudes toward working women are topics beyond the scope of this article, the principal findings of the research can be briefly summarized as follows. Women's traditional role in society was to manage the home and nurture children, leaving their spouses free to work for wages. Men were expected to be dominant in the world of work, whereas women were expected to support but not direct men's work activities as indicated in Bergmann (1986) and Fuchs (1988). Thus, female managers violate traditional work roles when they supervise men. [2]

Goldin (1990) indicates that before 1950 it was typical for women to work for wages only until they married. With few exceptions, work by a married woman was considered evidence of her husband's inability to provide adequately for his family, as indicated in Blau and Ferber (1992).

The occupational structures that were developed by firms throughout the years before 1950 were premised on the prevailing assumption that women would not become managers. The institutionalization of these attitudes and their widespread acceptance for more than half of the twentieth century suggests that they will not be quickly replaced by more recent concepts of workplace equality between the sexes as noted in Bergmann (1986). The most extensive study of occupational segregation at the firm level--that of Bielby and Baron (1984)--found that 90% of jobs were segregated in 1979.

The assumption of male distastes for female managers is intuitively appealing. In the next section, we explore its theoretical implications by setting forth a model of hierarchical discrimination against women and deriving its equilibrium conditions.

III. THE MODEL

We begin with a model of the demand for male and female workers in a firm with a simple technology, assuming there is hierarchical discrimination against women. Although the effects of discrimination on the demand for labor are well known, they are presented here in a different context. We then extend the model to more complex technologies and derive the implications of hierarchical discrimination for the supply of male and female workers. Becker (1971) does not consider the effects of discrimination on the supply of labor, because he assumes all workers are homogeneous. When we extend the model to consider hierarchical discrimination, we assume workers vary in their ability to acquire the human capital necessary to move up the management hierarchy. Supply becomes important because labor supply elasticities may vary across workers. We derive a sorting equilibrium for the model and show that technological constraints, costs of acquiring human capital, and male tastes for discrimination determine unique distri butions of men and women across the occupational hierarchy.

Hierarchical Discrimination in a One-Supervisor Firm: Demand

Consider a profit-maximizing firm that hires [L.sub.M] male workers and [L.sub.F] female workers, at a wage [W.sub.L], and one supervisor at a wage [W.sub.S], where [W.sub.S] [greater than] [W.sub.L]. Assume that male workers' distastes for female supervision are measured by [delta]([delta] [greater than] 0). [3] If the firm hires a female supervisor, male workers demand a wage, [W.sub.L](l + [delta]), that includes a compensating differential, and total costs of labor are

(1) [C.sub.1] = [L.sub.M][W.sub.L](1 + [delta]) + [L.sub.F][W.sub.L] + [W.sub.S].

Firms minimize costs by hiring a male supervisor unless all workers to be supervised are female. Firms will be segregated except at the lowest entry-level jobs.

A female supervisor may be hired to supervise males if she accepts a wage penalty to compensate her employer for the sum of the discriminatory wage differentials paid to male workers. Let p equal the wage penalty imposed on a female supervisor, expressed as a fraction of a male supervisor's wage. Then, costs of labor are

(2) [C.sub.2] = [L.sub.M][W.sub.L](1 + [delta]) + [L.sub.F][W.sub.L] + [W.sub.S](1 - p)

when the supervisor is female. The firm is indifferent between a male or female supervisor when the female wage penalty exactly offsets the costs of male tastes for discrimination, that is, when

(3) [W.sub.S]p = [L.sub.M][W.sub.L][delta].

The wage reduction imposed on a female supervisor is the product of the number of male workers supervised, their wage rate, and their tastes for discrimination. The only situation in which a woman is likely to be hired to supervise men is one in which the wage differential between the supervisor and her workers is relatively large and the number of men to be supervised is small. Staff positions, such as public relations, in many large organizations meet these requirements. Managers in these positions may have a great deal of responsibility, but, unlike managers in line positions, only a few employees report to them.

Hierarchical discrimination reduces the mean wages of women in two ways: fewer women are employed in managerial positions (an occupational effect) and, in each management level, female wages are reduced by the implicit compensation the female manager pays to the firm to cover the discriminatory employment costs (a wage effect).

Hierarchical Discrimination in a Multisupervisor Firm: Supply

Market Assumptions. To develop the implications of hierarchical discrimination on the supply of male and female workers, consider a management hierarchy based on a Leontief production function (y = min[4E, 2S, L]). That is, our example is a cost-minimizing firm with a strict hierarchical structure in which one executive (E) manages two supervisors (S), who each manage two laborers (L) (Figure 1). [4] All firms have this identical hierarchical structure, and nonhuman capital is ignored. The labor market is assumed to be competitive, and, once human capital investments are made, all workers are equally productive in their management positions. Hence, the coefficients of the Leontief production function completely characterize the technology.

If we assume, as did Mincer (1974), that workers are of equal ability and that wage differences between each level in the management hierarchy are just sufficient to compensate workers for the investment they make to be promoted to the next level, then women will not manage men. Because no one earns rents and men exhibit positive distastes for female supervision, women have no incentive to take wage cuts to manage male workers and, therefore, only supervise other women. Wages are equalized across sex by occupation, and females move up the management hierarchy only in segregated lines.

A more interesting scenario occurs if workers vary in ability. The supply of workers to different levels in the hierarchy is governed by their comparative advantage in skill acquisition and by the intensity of tastes for discrimination against female managers. To move above the laborer level in the management hierarchy, human capital must be acquired at a cost [c.sub.s] to become a supervisor or [c.sub.e] to become an executive.

Our model is static, with human capital investments made at the beginning of the period. Each worker knows his own costs of acquiring different types of management capital and the distribution of costs for all other workers. We assume, for every worker, the investment costs of becoming an "executive" (who manages supervisors) are higher than the investment costs of becoming a "supervisor" (who manages laborers). Thus, for each individual "i," [c.sub.s,i] [less than] [c.sub.e,i]. While this ranking is strict for each individual, it is possible that [c.sub.e,i] [less than] [c.sub.s,j] if i [neq] j, because more able workers can acquire the human capital necessary to become managers at lower cost.

Labor market competition ensures that wages are equalized within each level of the management hierarchy. Although wages are equal, more able male managers earn rents because they are able to achieve the same managerial level at lower cost than less able managers.

Hierarchical Equilibrium with No Tastes for Discrimination. If men do not object to female managers, equilibrium wages and employment for the hierarchical management structure described above are shown in Figure 2. The disks in Figure 2 represent the bivariate distribution of ability for becoming supervisors and executives. Panel A describes the case where there is a positive correlation between the ability to become a supervisor or executive (that is, the least-cost executives are also the least-cost supervisors). Panel B describes the opposite case of a negative correlation between the ability to become a supervisor or executive. [5]

In the sorting equilibrium for a given technology, workers self-select into the occupation where they have a comparative advantage and have no incentive to change occupations. In Panel B, for example, able executives are not able supervisors, and each worker's comparative advantage is clear: Those in the northwest part of the distribution tend to be supervisors, and those in the southeast tend to be executives. Each technology determines a unique proportion of workers in each occupation in the hierarchy, and occupations and wages are determined by the equilibrium investment costs, denoted by [[c.sup.*].sub.c] and [[c.sup.*].sub.s]. In our example of the Leontiefi technology shown in Figure 1, [[c.sup.*].sub.e] and [[c.sup.*].sub.s] must be such that one-seventh of the workers are below the [[c.sup.*].sub.e] line, two-sevenths are to the left of the [[c.sup.*].sub.s] line, and the remaining four-sevenths are laborers between those two lines.

The distribution in Panel A is more complex than that in Panel B because more able workers who can acquire the human capital necessary to become an executive at low cost can also acquire the human capital necessary to become a supervisor at low cost. To identify the occupations of these workers, add the "equal rents line" to the diagram. The "equal rents line" is parallel to the 45[degrees] line, and indicates those points for which the rent earned as an executive exactly equals the rent earned as a supervisor. Clearly, workers above the equal rents line but left of the [[c.sup.*].sub.s] line maximize their rents as supervisors, whereas those below the equal rents line and beneath the [[c.sup.*].sub.e] line maximize their rents as executives.

Note that, for either positive (Panel A) or negative (Panel B) correlation of ability, the following equilibrium conditions are satisfied at [[c.sup.*].sub.e] and c: (1) the technology constraints are met; (2) the least-cost principle is satisfied, that is, workers who can become managers at least cost do so; and (3) no one has an incentive to change occupations. [6]

Hierarchical Equilibrium with Tastes for Discrimination. Now assume men insist on a compensating wage differential to be supervised by women. If there are enough women to fill the laborer ranks, no wage differentials are paid, managerial lines are completely segregated by sex, and we can superimpose the female and male distributions over one another to determine [[c.sup.*].sub.e] and [[c.sup.*].sub.s].

Assume instead that the underlying distributions of managerial costs are the same for men and women, but women have self-selected into the workforce because women, unlike most men, have the alternative of pursuing household work as their primary activity. This self-selection is such that the number of women in the labor force is smaller than the number of men, so that, at the margin, some female executives must manage male supervisors, and some female supervisors must manage male laborers. To move up the managerial ranks a woman incurs the costs of human capital investments and the costs of compensating male workers' tastes for discrimination. Thus, the female distribution of managerial costs is shifted to the northeast, parallel to the 45[degrees] line, by an amount [theta], the additional cost associated with assigning a female to manage male workers. The shift of the female distribution is indicated in Figure 3, where the relatively smaller disk for females reflects their self-selection into the workforce so that there are fewer female workers than male workers.

The additional employment cost, [theta], associated with hiring a woman to manage male workers is the product of the workers' wage rate, the number of men supervised, and the strength of male distastes for female supervision, as discussed in the previous section (equation (3)). For pedagogical reasons, we assume the cost, [[theta].sub.e], of hiring a female executive over male supervisors equals the cost, [[theta].sub.s], of hiring a female supervisor over male laborers. Then, the female cost distribution is simply shifted northeast by the amount [theta] on either axis as pictured in Figure 3. [7]

In competitive markets with effective tastes for discrimination, female managers' net wages decrease by [theta], and the only female managers are those for whom [[c.sup.*].sub.s] ([[c.sup.*].sub.e]) is greater than [c.sub.s,i] + theta]([c.sub.e,i] + [theta]). Note that, at the margin and on average, female managers are more capable than male managers because discriminatory costs exclude all but the most capable females from management positions.

From Figures 1-3 and the accompanying discussion, we conclude that:

1. High-ability men in management positions earn rents equal to the difference between [[c.sup.*].sub.s] ([[c.sup.*].sub.e]) and [c.sub.s,i] ([c.sub.e,i]). On average, these rents are higher than the rents earned by high-ability women. Relatively few women earn rents, because their rents have been appropriated by hierarchical discrimination.

2. Effective tastes for discrimination depend on the entire distribution of ability for both males and females, technology, and tastes for discrimination, which may vary by level of supervision. [8]

3. An increase in tastes for discrimination lowers the average female salary by decreasing the number of females employed as managers, and by decreasing the wages paid to female managers relative to nondiscriminatory wages and relative to male wages.

4. Hierarchical discrimination can persist in competitive markets so long as male distastes for female supervision are prevalent because the entire costs of discrimination are borne by female managers. Such discrimination produces wage differentials at all levels of the job hierarchy: female managers pay the costs of male distastes for female supervision, male laborers receive compensating wage differentials.

5. The equilibrium conditions set forth above are satisfied.

IV. RELATIVE OCCUPATIONAL DISTRIBUTION OF WOMEN

It is intuitively plausible that when men exhibit distastes for female supervision the proportion of female to male workers declines as one moves up the occupational hierarchy. Analytical expressions for the occupational distribution of men and women are not available, however, even for the case of bivariate normally distributed investment costs. Therefore, we simulate the equilibrium for various employment costs, [theta], where [theta] takes the values: .25[sigma], .50[sigma], .75[sigma], [sigma], with [sigma] representing one standard deviation of the investment cost distribution. We assume managerial investment costs ([C.sub.e], [C.sub.s]) are drawn from bivariate normal distributions with the following values of the correlation coefficient: .9, .5, .25, 0, -.25, -.5, -.9. Thus, for each technology we simulate, there are 28 equilibria to calculate. The equilibria are computed for three specifications each of the Leontief and Cobb-Douglas technologies using a grid search method. [9]

Table 1 presents regressions showing how well the exponential function fits the simulation results. The regressions summarize the fit of the exponential decline in the relative proportions of female to male workers as one moves up the management hierarchy. That is,

(4) (proportion female)/(proportion male)

= [alpha] exp(-[psi]h)

yields a simple log-linear model in which the log of the relative proportions of female and male workers is regressed on a constant and the variable h, where h is the hth occupation in the management hierarchy. [10] For all six technologies, we reject the alternative of a random distribution of women across the job hierarchy in favor of the hypothesis that the relative proportion of women declines exponentially as one moves from laborer to supervisor to executive. The rate of exponential decline in the relative proportions of female to male workers is given by [psi] [congruent] 0.6.

The regressions in Table 1 can be viewed as a descriptive summary of the results for the individual simulations. In fact we estimated the exponential function given in equation (4) for each of the 28 simulations we computed for each of the 6 technologies. In every case, we find that the relative number of females declines exponentially as one moves up the job hierarchy. [11] In the next section, we derive a new decomposition of male-female wage differentials that takes advantage of this exponential result.

V. WAGE DECOMPOSITIONS INCLUDING SEGREGATION

Empirical studies of wage discrimination typically use variations of Oaxaca's (1973) technique to separate minority-majority wage differentials into two parts: a nondiscriminatory part measured by between-group differences in human capital endowments, and a discriminatory part measured by between-group differences in the returns to those endowments and a residual. The wage equation is sometimes modified to account for the effect of occupational segregation on the wage differential by adding a set of occupational dummies. Then the decomposition formula produces three results, namely, the parts of the wage differential attributed to differences in endowments, differences in occupational distributions, and wage discrimination within occupations. [12]

There are, however, serious limitations to this approach. Between-group differences in occupational distributions can be interpreted as either discriminatory effects of the occupational segregation of women, or nondiscriminatory differences in endowments. Absent a direct link between empirical methods and theory, there is no way to determine the extent to which differences in the occupational distributions of men and women are discriminatory. Moreover, the portion of the wage differential attributed to occupational differences increases with the number of occupational variables included in the wage equation (Polachek [1987]). An extremely fine division of workers into occupational groups could, for example, attribute most of the wage differential to occupational differences. Again, the absence of a theoretical basis for the specification of occupation variables severely limits the value of estimates of this type.

Our model predicts that the relative proportion of females declines exponentially as one moves up the job ladder when there is hierarchical discrimination. We integrate the exponential occupational structure directly into maximum likelihood estimates of the wage distribution to create new wage decompositions that estimate the impact of hierarchical discrimination on the male-female wage differential. The new decomposition avoids the problem of having to specify ex ante the appropriate number of occupational categories for the wage equations. We first consider the case in which intraoccupational wages are fixed, and then generalize to the case where intraoccupational wages can vary.

Fixed Wages within Occupations

Let there be an infinite number of occupations arrayed by the mean male wage in each occupation. Denote a given occupation by "h," and let [f.sub.M]([W.sub.h]) be the distribution of male wages. The hierarchical theory of discrimination implies that the relative proportion of females in an occupation, [(proportion of females).sub.h]/[(proportion of males).sub.h], decreases as h increases. The form of this "discriminatory sorting" function, therefore, implies a distribution of female wages given the male wage distribution. By estimating the male and female wage distributions and the implicit discriminatory sorting function simultaneously, we can decompose mean wage differentials into a part attributed to occupational segregation and a part attributed to within-occupation wage differences. We derive the procedure for several common distributions.

Consider the generalized gamma distribution, special or limiting cases of which include the lognormal, the Weibull, and the gamma distributions. Assume that male wages have the following generalized gamma distribution,

(5) [f.sub.M]([W.sub.h]) = a[[W.sup.ap-1].sub.h] exp[-[([W.sub.h][beta]).sup.a]/[[[beta].sup.ap][gamma](p)]

where a, [beta], and p are parameters and [gamma] is the gamma function. Then, assume that for gamma-distributed wages, the relative proportion of females declines exponentially as wages increase (note that each wage rate represents a different occupation in this analysis) according to the following function:

(6) g([W.sub.h]) [equivalent] [(proportion females).sub.h]/[(proportion males).sub.h] = [[pi].sub.0] exp(-[([W.sub.h]/[lambda]).sup.a]).

In equation (6) [[pi].sub.0] is the "constant of integration" that makes the female wage distribution a proper probability density function. At successively higher levels of a management hierarchy, male incomes increase and the relative proportion of females declines. The rate of decline is given by the magnitude of [lambda]. As [lambda] approaches infinity, the wage distributions equalize and there is no occupational segregation.

Multiplying [f.sub.M]([W.sub.h]) by g([W.sub.h]) yields the implied wage distribution for females, [13]

(7) [f.sub.F]([W.sub.h] = a[[W.sup.ap-1].sub.h] exp[(-[W.sub.h]/[[beta][lambda]/[([[beta].sup.a] + [[lambda].sup.a]).sup.1/a]).sup.a]/{[([beta][lambda]/[([[beta].sup.a] + [[lambda].sup.a]).sup.1/a]).sup.ap] [gamma](p)}

The difference in mean wages is then

(8) [W.sub.M] - [W.sub.F] = [[gamma] (p + 1/a)/[gamma](p)]X[beta]{1 - [[lambda]/[([[lambda].sup.a] + [[beta].sup.a]).sup.1/a]}.

Because we have assumed wages at the hth job level are equalized by sex, the wage differential in equation (8) is attributed entirely to the occupational segregation term.

Variable Wages within Occupations

Now we generalize the formulae derived above to allow wage differentials within occupations. Recall that, in the framework of the hierarchical theory of discrimination, there is a competitive wage function relating wages to human capital within occupations, but male workers' distastes for female management also create wage differentials between male and female managers and compensating wage differentials for male workers.

Assume that female wage rates within each job are a fraction, [delta], of male wage rates. Let "[W.sub.h]" continue to denote male wages at the hth job, but now let "[Z.sub.h]" denote female wages in the hth job such that [Z.sub.h] = [delta][W.sub.h]. Substituting [Z.sub.h] for [W.sub.h] in equation (4) yields

(9) [f.sub.F]([Z.sub.h])

= a[[Z.sup.ap-1].sub.h] exp (-[[Z.sup.a].sub.h]/[[[delta][beta][lambda]/[([[beta].sup.a] + [[lambda].sup.a]).sup.1/a]].sup.a])/{[[[delta][beta][lambda]/[([beta] .sup.a] + [[lambda].sup.a]).sup.1/a]].sup.ap][gamma](p)}.

Now the difference in mean wages can be written in the following form:

(10) [W.sub.M] - [W.sub.F] = [[gamma] (p + 1/a)/[gamma](p)[beta]] -

{[[gamma]( p + 1/a)/[gamma](p)][beta][delta] X [[lambda]/[([[lambda].sup.a] + [[beta].sup.a]).sup.1/a]]}

= [[gamma](p + 1/a)/[gamma](p)][beta] - [[gamma](p + 1/a)/[gamma](p)][beta][delta] + [[gamma](p + 1/a)/[gamma](p)][beta][delta] X {1 - [[lambda]/[{[[lambda].sup.a] + [[beta].sup.a]).sup.1/a]]}.

To relate this to the usual wage decomposition, assume the scale parameter ([beta]) of the gamma distribution varies with worker characteristics but the shape parameters (p, a) do not. Then, [beta] = [X.sub.M][[delta].sub.M] and [beta][delta] = [X.sub.F][[delta].sub.F]. Substituting into equation (10) and rearranging, the first two terms on the right correspond to Oaxaca's decomposition, and the last term measures the wage differential attributed to occupational segregation. [14]

Table 2 presents decomposition equations for the lognormal and generalized beta, as well as the generalized gamma, distributions. [15] As Table 2 shows, decompositions based on the hierarchical tastes model account for occupational segregation and discriminatory wage differentials and allow the use of flexible distributional forms for the analysis.

The next section uses data for a sample of insurance workers from the CPS to demonstrate how the decomposition formula can be estimated. Where there are interesting differences, the results are compared to estimates obtained from a standard Oaxaca decomposition.

VI. EMPIRICAL RESULTS

The hierarchical model of discrimination provides three empirically testable hypotheses concerning occupational segregation, namely: (1) more narrowly defined occupations will exhibit a higher degree of occupational segregation, (2) the relative number of females declines exponentially as one moves up the job ladder, and (3) the relative number of females declines in occupations with increasingly higher wages. We cannot fully test all the predictions of the model without firm-specific data on occupations and wages. We can, however, test the prediction of an exponential decline in the relative proportion of women as one moves up the management hierarchy and estimate the impact of hierarchical discrimination on wages using the decomposition formula derived above.

We apply the new decomposition formula to estimates from a sample of fulltime insurance workers who participated in the 1988 CPS. [16] The sample is restricted to white men and women, at least 18 years old, who report positive annual earnings. Fulltime workers are defined as those who work at least 50 weeks per year and at least 30 hours per week. Characteristics of the sample are described in Table 3. Nearly two-thirds of the insurance workers (63%) are men. On average, men in the industry have about two more years of education and work experience than do women. The female-male earnings ratio is 0.55, considerably lower than the ratio for all U.S. workers.

The insurance industry was selected for its large size and hierarchical management structure. As the hierarchical theory of discrimination suggests, females are concentrated in the lowest-paying occupations. Two out of three females are employed as adjustors or in technical support positions, compared to one in five males. The industry-level data are, however, likely to substantially understate the extent of occupational segregation. Bielby and Baron (1984) demonstrate that substantial occupational segregation exists within firms even in industries where industry-wide measures of occupational segregation are quite low.

To see how well the insurance sample satisfies the predictions of the hierarchical tastes model, we fit equation (4) (including mean wage as an independent variable) to the h = 6 occupational categories shown in Table 3. The coefficients have the expected signs, indicating that the relative proportion of women declines exponentially as one moves up the occupational hierarchy. The model is not significant at the usual levels (F 3.4, df = 1) but this should be viewed as a very strict test of the prediction of the hierarchical tastes model since we use so few occupational categories.

The new decomposition formula derived above (equation [10]) is estimated for the sample of insurance employees, assuming that wages have a gamma distribution. The results are presented in Table 4. [17] In the first specification (columns 1 and 2) the parameter "a" has been restricted to one (gamma distribution), but in the second specification (columns 3 and 4) it is unrestricted (generalized gamma distribution). The "mean" parameters for each sex ([beta] for males, and [beta][delta] for females) vary linearly with education and experience, and are estimated with other parameters of the model by maximum likelihood techniques. [18]

The education and experience variables are jointly significant at the 1% level (Table 4, row 9). The coefficients of these variables change slightly as we move from a gamma to a generalized gamma wage distribution. The marginal impact of schooling is higher for males than for females in the gamma model, and this differential increases in the generalized gamma model. For both gamma specifications, male wages initially increase more quickly with experience than do female wages. The effect of experience peaks for both sexes at about 33 years, slightly higher than in the OLS model (reported in Appendix Table 2).

The lower panel of Table 4 uses the gamma results to decompose the male-female wage differential (as suggested in equation [10] and note 14) into parts attributed to endowments, discrimination, and occupational segregation. The endowment effects are nearly identical in the two models. Allowing the parameter a to vary, however, produces a larger estimate of [lambda] in the generalized gamma model. [19] As a result, the part of the wage differential attributed to occupational segregation decreases.

Estimates of the endowment effect from the gamma models are greater than estimates from the ordinary least squares (OLS) model: slightly more than one-third of the male-female wage differential is attributed to differences in the human capital variables. The most important difference between the OLS specification and the gamma models, however, is in the proportions of the wage differential attributed to discrimination and to occupational segregation. The discriminatory part of the wage differential falls from more than 60% in the OLS model to about 25% in the gamma model and 33% in the generalized gamma model. The part of the wage differential attributed to occupational segregation increases from 19% in the OLS specification to 38% in the gamma model and 31% in the generalized gamma model. [20]

The results from the gamma models are preferred to the OLS results because they do not require an a priori specification of occupational categories. A likelihood ratio test indicates no significant improvement in the gamma estimates when the parameter a is allowed to vary. [21] We conclude that the gamma model provides valuable estimates of the effect of occupational segregation on the wages of women in the insurance industry.

VII. CONCLUDING COMMENTS

This article develops a model of labor market discrimination based on a simple but compelling assumption concerning attitudes toward women in the workplace. The assumption is that males object to being supervised by females. By defining discriminatory tastes in this manner, we develop a model in which discrimination in the workplace depends on the positions of males and females in the job hierarchy rather than on physical distance. The model enables us to predict the circumstances under which female workers will be admitted into job hierarchies, and provides the first theoretical linkages between occupational segregation and wage discrimination.

One of the most important predictions of the model is that the relative proportion of females declines exponentially as one moves up the job hierarchy. We integrate this exponential function into the wage equation to derive a new decomposition of male-female wage differentials and provide estimates for a sample of insurance workers from the CPS. Although the results generally support the predictions of the model, they are more a demonstration of how the model can be applied than an analysis of occupational segregation. An adequate analysis of the model's predictions requires firm-level data with information on wages and occupations, more narrowly defined than the CPS categories. These data would also permit a test of the prediction that women in upper management positions will be disproportionately assigned to staff functions, such as human resources and public relations departments, rather than line management positions.

This article demonstrates that more adequate definitions of "tastes for discrimination" can yield important insights into how discrimination affects employment opportunities for minority groups. We hope the article stimulates further investigation of the relationship between occupational segregation and the nature of "tastes for discrimination."

Baldwin: Associate Professor, Department of Economics, East Carolina University, Greenville, NC 27858-4353. Phone 1-252-328-6383, Fax 1-252-328-6743, E-mail baldwinm@email.ecu.edu

Butler: Professor of Economics, Brigham Young University, Provo, UT 84602. Phone 1-801-378-1372, Fax 1-801-378-2844, E-mail richardbutler@byu.edu.

Johnson: Professor of Health Administration and Economics, School of Health Administration and Policy and Department of Economics, Arizona State University, Tempe, AZ 85287-4500. Phone 1-602-965-7442, Fax 1-602-965-6654, E-mail william.g.johnson@asu.edu

(*.) We appreciate comments on an earlier draft from Meghan Busse, Ron Ehrenberg, James Heckman, Mark Killingsworth, Peter Kuhn, Olivia Mitchell, Joel Sobel, and John D. Worrall and comments made in workshops at Brigham Young University, Cornell University, East Carolina University, Rutgers University, and the University of Chicago.

(1.) See, for example, Bergmann (1986), Blau and Ferber (1992), Fuchs (1988), and Goldin (1990) for studies of the changing economic roles of women, and Bradley (1989) for a sociological history of the sexual division of labor. Analyses of internal labor markets by Doeringer and Piore (1985) and Bielby and Baron (1982), and case studies of women in the insurance industry as in Hartmann (1987) and management as in Ferber and Green (1991) also support the hierarchical discrimination model. We do not suggest that other forms of discrimination against women do not exist but rather that hierarchical discrimination is the most important source of workplace discrimination against women. Other minorities may be subject to hierarchical discrimination as well. See Dewey (1952), for example, for references to hierarchical discrimination against blacks.

(2.) Examples of the stereotyping of male and female work roles in management hierarchies can be found in court records of discrimination cases. A 1972 complaint against the Bell System, for example, notes that "women were given some of the lower-level management jobs that involved supervising other women but had almost no chance of penetrating into the higher management levels," as cited in Bergmann (1986, 83). At Western Electric, "The company provided supervisors with a requisition form to be used when they had a position to fill, which had a place where they could ask for a male, or a female or could express no preference. ... On requisition forms for grade 32 openings, supervisors said they wanted a female in 87 out of 96 cases. On requisition forms for higher-level positions, supervisors asked for males for 263 out of 292 openings," as cited in Bergmann (1986, 85).

Some firms have developed elaborate mechanisms to preserve appropriate roles for male and female employees. In a classic study of the restaurant industry, Whyte (1949, 306) reports, "On the main serving floor ... waitresses wrote out slips which they placed on spindles on top of a warming compartment separating them from the countermen. The men picked off the order slips, filled them, and put the plates in the compartment where the waitresses picked them up. In most cases there was no direct face-to-face interaction between waitresses and countermen, and, indeed, the warming compartment was so high that only the taller waitresses could see over its top. ... One of the countermen described earlier experiences in other restaurants where there had been no such barrier and let us know that to be left out in the open where all the girls could call their orders in was an ordeal to which no man should be subjected. ... Most restaurants consciously or unconsciously interpose certain barriers to cut down waitress ori gination of action for countermen."

(3.) We recognize that the attitudes toward female managers described above can be shared by employers and workers, but we assume, for simplicity, that employers have no tastes for discrimination against women. Our empirical results do, however, separate wage discrimination by employers from hierarchical discrimination by co-workers.

(4.) The firm is characterized by a strict hierarchical structure in which the executive is directly responsible for the work of the supervisors, and each supervisor is directly responsible for the work of the laborers who report to him or her. Male distastes for female supervision are directed toward the immediate superior only.

(5.) In either the case of positive or negative correlation of investment costs, the distribution lies above the 45[degrees] line. This follows from our assumption that, for each individual, the cost of acquiring the human capital to become an executive is greater than the cost of acquiring the human capital to become a supervisor.

(6.) In general, extending the model to n + 1 levels of supervision does not create any additional problems for the analysis. For the (n + 1)-level technology, n values of [[c.sup.*].sub.z] are determined as above. The "equal rents" line becomes an n-1 dimensional facet whose sides meet the axes at 45[degrees] angles; the "edges" of the facets are where the [[c.sup.*].sub.s] and [[c.sup.*].sub.e] lines meet. The conclusions derived above continue to hold.

(7.) If costs of discrimination differ for executives and supervisors, the female distribution will not shift parallel to the 45[degrees] line but will be tilted away from the direction in which those costs are greater. For example, if [theta], is greater than [[theta].sub.e] (perhaps because supervisors manage more males than do executives), then the female distribution will be shifted further along the [c.sub.s] axis than along the [c.sub.e] axis. This tilts the distribution away from the [[c.sup.e].sub.s] line and makes it even less likely that women will become supervisors.

(8.) Tastes may also vary across male workers. Regardless of the correlation between discriminatory tastes and managerial ability, however, comparative advantage in "marketing" tastes implies that, among the males to be managed, those with lowest tastes for discrimination will be managed by females first. Thus, effective tastes for discrimination are a monotonically nondecreasing function of the relative number of female managers. No high-ability male manager with weak tastes for discrimination will ever exchange places with a lower-ability male with strong tastes for discrimination who is working for a female. This follows because transfers between inframarginal managers and laborers increase firm costs and eliminate managerial rents. Exchanges between a marginal laborer and a marginal manager are inconsequential in their cost impact. Hence, allowing for varying tastes across males does not change the analysis above, except to make the shifts in the female cost distribution both not parallel to the 45[degre es] line and a more complex endogenous function of the wage and employment determination process.

(9.) The (E = 1 S, = 2, L = 4) technology is the one discussed extensively above, the (E = 1, S = 2, L = 8) technology is "labor intense," and the (E = 1, S = 4, L = 8) technology is "middle-management intense." The Cobb-Douglas technologies, Y = [AE.sup.e][S.sup.s][L.sup.l] with e + s + l = 1, represent: equal product shares to each input (e = s = l = .33); a greater product share to managers (e = .6, s = .3, l = .1); and a greater product share to laborers (e = s = .25, l = .5). Across all simulations the proportion of females to males in the labor force is held constant at .667. Simulation results are available from the authors.

(10.) Because the analysis is restricted to technologies with three levels in the management hierarchy, h = 1 for laborers, h = 2 for supervisors, and h = 3 for executives.

(11.) Estimated slope coefficients for the individual regressions are summarized in Appendix Table 1.

(12.) Allowing for variations in human capital and in the occupational distribution, let [W.sub.i] = [X.sub.i][beta] + [Y.sub.i][gamma] + [[epsilon].sub.i] where [W.sub.i] is the natural log of the wage of the ith worker, [X.sub.i] is a vector of variables measuring human capital endowments, [Y.sub.l] is a set of occupational dummies, [beta] and [gamma] are corresponding vectors of coefficients, and [[epsilon].sub.i] is a mean-zero, random disturbance term. Then, the average male-female wage differential can be decomposed as follows:

[W.sub.M] - [W.sub.F] = [([X.sub.M] - [X.sub.F])([d[beta].sub.M] + (1 - d)[[beta].sub.F])] + [([Y.sub.M] - [Y.sub.F])(d[[gamma].sub.M] + (1 - d)[[gamma].sub.F])] + [([[beta].sub.M] - [[beta].sub.F])(d[X.sub.M] + (1 - d)[X.sub.F]) + ([[gamma].sub.M] - [[gamma].sub.F](d[Y.sub.M] + (1 - d)[Y.sub.F])]

where d (the proportion of the employed labor force that is male) is the weight used to represent the nondiscriminatory wage structure. The first term on the right represents endowment effects, the second term represents occupational segregation, and the third term represents wage discrimination within occupations.

(13.) The requirement that [integral] [f.sub.F]([W.sub.h])d[W.sub.h] = 1 implies [[pi].sub.0] = [([[lambda].sup.a] + [[beta].sup.a]).sup.p]/[[lambda].sup.ap], which upon substitution into equation (6) and multiplication by [f.sub.M]([W.sub.h]) yields equation (7).

(14.) As indicated in Table 2 (row 6) for the various distributions, the difference in mean wages is just

[[gamma](p+1/a)/[gamma](p)][[beta]-[beta][delta]+[beta][delta]{1 - [lambda]/[([[lambda].sup.a]+[[beta].sup.a]).sup.1/a]}]

=[[gamma](p+1/a)/[gamma](p)][[X.sub.M][[delta].sub.M] - [X.sub.F][[delta].sub.F]+[delta][beta]x{1 - [lambda]/[([[lambda].sup.a]+[[beta].sup.a]).sup.1/a]}]=[[gamma](p+1/a )/[gamma](p)]x[[X.sub.F]([[delta].sub.M] - [[delta].sub.F])+([X.sub.M] - [X.sub.F])[[delta].sub.M] + [beta][delta] x {1 - [lambda]/[([[lambda].sup.a]+[[beta].sup.a]).sup.1/a]}]

where the three terms in the final, right-hand-side brackets have the following interpretation: the term on the left is the usual discrimination or "differences in coefficients" term, the middle term is the "differences in means" or the endowment effect, and the term on the right is the part of the wage differential attributable to occupational segregation.

(15.) The equations given in Table 2 encompass most of the distributions used in empirical research on income and wage distributions. Special or limiting cases of the generalized beta function include the generalized gamma, Beta type 2 (generalized pareto), Burr-12 (Singh-Maddala), Burr-3 (generalized logistic), Lomax, Fisk, and F-distributions. Special or limiting cases of the generalized gamma distribution include the log-normal, Weibull, exponential, and gamma distributions. See McDonald (1984) for details.

(16.) Insurance workers are identified by industry code 711.

(17.) Although the addition of employer tastes for discrimination of the Becker type can be readily accommodated in the model, employee tastes for discrimination cannot. Employee tastes for discrimination, as commonly interpreted, refer to male-female relationships as co-workers rather than relationships in the job hierarchy. Note that without firm-specific data on hierarchical lines, we cannot sort discriminatory wage differences into (a) compensating differences for female supervision or (b) discriminatory components that reflect employer tastes for discrimination. These will be confounded in the empirical discrimination component reported below.

(18.) Using maximum likelihood techniques also allows us to control for truncation of annual wages at $100,000 in the CPS data.

(19.) When the parameter a is restricted to equal one, the weights in the decomposition formula (equation [10]) reduce to p. When a is allowed to vary with the male-female wage differential fixed, one of the following must be true as a increases: returns to the human capital of males and females ([beta] and [beta][delta]) diverge, the degree of occupational segregation of women increases ([lambda] decreases), or the parameter p increases.

(20.) Note that the coefficients of the occupational dummies in the OLS model provide additional support for the hierarchical discrimination model. The returns to women in administrative and supervisory positions are much lower than the returns to men. Although men and women in professional occupations earn nearly equal returns, 66% of the professional workers in our sample are employed as systems or operations analysts, actuaries, or lawyers, jobs that do not usually involve supervisory responsibilities.

(21.) The [[chi].sup.2] statistic equals 0.12 (df = 1). The gamma estimates also have lower standard errors than the generalized gamma estimates because there are fewer parameters to estimate in the gamma model.

REFERENCES

Becker, G. The Economics of Discrimination. Chicago: University of Chicago Press, 1971.

Bergmann, B. R. The Economic Emergence of Women. New York: Basic Books, 1986.

Bielby, W. T., and J. N. Baron. "A Woman's Place Is with Other Women: Sex Segregation within Organizations," In Sex Segregation in the Workplace, edited by B. Reskin. Washington: National Academy Press, 1984, 27-55.

-----. "Organizations, Technology and Worker Attachment to the Firm." In Research in Social Stratification and Mobility, Vol. II, edited by D. J. Treiman and R. V. Robinson. Greenwich: JAI Press, 1982, 77-113.

Blau, F. D., and M. A. Ferber. The Economics of Women, Men, and Work. Englewood Cliffs: Prentice Hall, 1992.

Bradley, H. Men's Work, Women's Work. Minneapolis: University of Minnesota Press, 1989.

Dewey, D. "Negro Employment in Southern Industry." Journal of Political Economy, August 1952, 279-93.

Doeringer, P., and M. Piore. Internal Labor Markets and Manpower Analysis. Lexington: D. C. Heath, 1985.

Ferber, M. A., and C. A. Green. "Occupational Segregation and the Earnings Gap." In Essays on the Economics of Discrimination, edited by E. P. Hoffman. Kalamazoo: W. E. Upjohn Institute, 1991, 145-65.

Fuchs, V R. Women's Quest for Economic Equality. Cambridge: Harvard University Press, 1988.

Goldin, C. Understanding the Gender Gap: An Economic History of American Women. New York: Oxford University Press, 1990.

Hartmann, H. I. "Internal Labor Markets and Gender: A Case Study of Promotion." In Gender in the Workplace, edited by C. Brown and J. A. Pechman. Washington: Brookings Institution, 1987, 59-92.

McDonald, J. B. "Some Generalized Functions for the Size Distribution of Income." Econometrica, May 1984, 647-63.

Mincer, J. Schooling, Experience and Earnings. New York: National Bureau of Economic Research, 1974.

Oaxaca, R. "Male-Female Wage Differentials in Urban Labor Markets." International Economic Review, October 1973, 693-709.

Polachek, S. W. "Occupational Segregation and the Gender Wage Gap." Population Research and Policy Review, 1987, 47-67.

Whyte, W. F. "The Social Structure of the Restaurant." American Journal of Sociology, January 1949, 302-10.

ABBREVIATIONS

CPS: Current Population Survey

OLS: Ordinary Least Squares

 Regressions of the Relative Number of
 Females in the Management Hierarchy
 Coefficient Estimates and
 Absolute t-Statistics
 Leontief Technologies Cobb-Douglas Technologies
 E = 1 E = 1 E = 1 e = .33
 S = 2 S = 2 S = 4 s = .33
 L = 4 L = 8 L = 8 l = .33
Intercept .902 .840 1.002 .837
 (7.81) (6.12) (8.18) (6.30)
h -.611 -.694 -.722 -.551
 (11.44) (10.93) (12.73) (8.95)
[R.sup.2] .61 .59 .66 .49
 e = .25 e = .6
 s = .25 s = .3
 l = .50 l = .1
Intercept .834 1.409
 (5.98) (10.49)
h -.654 -.668
 (10.13) (10.74)
[R.sup.2] .56 .58

Notes: The dependent variable is 1n (proportion females in occupation h/proportion of males in occupation h) generated from simulations of the Leontief or Cobb-Douglas technology. There are 84 (7 values of the correlation coefficient x 4 values of investment costs x 3 occupation levels) "observations" for each regression.

 Generalized Wage Decompositions
Equation Number Lognormal Distribution
 5
(Male wages) 1/[[W.sub.h][sigma][square root]2[pi]
 exp (-[(log[W.sub.h] - [micro]).sup.2]/
 2[[sigma].sup.2])
 6
(Proportion female/ [gamma]exp(-([[gamma].sup.2] - 1)log
 [W.sub.h]/2[[sigma].sup.2](log
 [W.sub.h]/exp(2[micro]/[gamma]+1)))
 proportion male (equalize as [gamma] [right arrow] 1)
 7
(Female wages) 1/[W.sub.h]([sigma]/[gamma])[square
 root]2[pi]exp(-[(log[W.sub.h] -
 [micro]/[gamma]).sup.2]/2[([sigma]/
 [gamma]).sup.2])
 8
(Mean differences) 1n[W.sub.M] - 1n[W.sub.F] = [micro]
 ([gamma] - 1/[gamma])
 - occupational segregation)
 9
(Female wages if within 1/[Z.sub.h]([sigma]/[gamma])[square
 root]2[pi]exp(-(log [Z.sub.h] - [(
 [gamma]1n[delta] + [micro]/[gamma]).sup.
 2])/2[([sigma]/[gamma]).sup.2])
 occupation differentials)
 10 [micro] - (1n[delta] + [micro]/[gamma])
(Mean differentials) = [micro] - (1n[delta] + [micro]) +
 [micro]([gamma] - 1/[gamma])
 - occupation segregation where:
 + within occupation [micro] = [X.sub.M][[gamma].sub.M]
 differentials) (1n[delta] + [micro]) = [X.sub.F]
 [[gamma].sub.F]
Equation Number Generalized Gamma Distribution
 5
(Male wages) a[[W.sup.ap-1].sub.h] exp(-[([W.sub.h]/
 [beta]).sup.a])/[[beta].sup.ap][gamma]
 (p)
 6
(Proportion female/ [[pi].sub.0]exp[(-[W.sub.h]/[lambda])
 .sup.a]
 proportion male (equalize as [lambda] [right arrow]
 [infinity])
 7
(Female wages) a[[W.sup.ap-1].sub.h]exp[(-[W.sub.h]/
 ([beta][lambda]/[([[beta].sup.a] +
 [[lambda].sup.a]).sup.1/a])).sup.a]/[(
 [beta][lambda]/[([[beta].sup.a] +
 [[lambda].sup.a]).sup.1/a]).sup.ap]
 [gamma](p)
 8
(Mean differences) [W.sub.M] - [W.sub.F] = [phi]([beta]1 -
 [lambda]/[([[lambda].sup.a] + [[beta].
 sup.a]).sup.1/a])
 - occupational segregation) where [phi] = [gamma](p + 1/a)/[gamma]
 (p)
 9
(Female wages if within a[[Z.sup.ap-1].sub.h]exp(-[[Z.sup.a].
 sub.h]/[([delta][beta][lambda]/[([
 [beta].sup.a] + [[lambda].sup.a]).sup.
 1/a]).sup.a])/[([delta][beta][lambda]/
 [([[beta].sup.a] + [[lambda].sup.a]).
 sup.1/a]).sup.ap][gamma](p)
 occupation differentials)
 10 [varphi][beta] - [varphi][delta][beta]([lambda]/
 [([[lambda].sup.a] + [[beta].sup.a]).
 sup.1/a])
(Mean differentials) = [varphi][beta] - [varphi][beta][delta] +
 [varphi][delta][beta]([lambda]/[([[lambda].
 sup.a] + [[beta].sup.a]).sup.1/a])
 - occupation segregation where:
 + within occupation ([beta]) = [X.sub.M][[gamma].sub.M]
 differentials) ([beta][delta]) = [X.sub.F][[gamma].sub.
 F]
Equation Number Generalized Beta Distribution
 5
(Male wages) a[[W.sup.ap-1].sub.h]/[[beta].sup.ap]B
 (p,q)[(1 + [([W.sub.h]/[beta]).sup.a]).
 sup.p+q]
 6
(Proportion female/ [epsilon][[W.sup.ap([epsilon]-1)].sub.h]
 [(1 + [([W.sub.h]/[beta]).sup.a]/1 +
 [([[W.sup.[epsilon]].sub.h]/[beta]).
 sup.a]).sup.p+q]
 proportion male (equalize as [epsilon] [right arrow] 1)
 7
(Female wages) [epsilon]a[[W.sup.[epsilon]ap-1].sub.h]/
 [[beta].sup.ap]B(p,q)[(1 + [([[W.sup.
 [epsilon]].sub.h]/[beta]).sup.a]).sup.
 p+q]
 8
(Mean differences) [W.sub.M] - [W.sub.F] = [omega][beta](B
 (p + 1/a, q - 1/a) - [beta]1-[epsilon]/
 [epsilon]B(p + 1/[epsilon]a, q - 1/
 a[epsilon])/B(p + 1/a, q - 1/a))
 - occupational segregation) where [omega] = B(p + 1/a, q - 1/a)/
 B(p,q)
 9
(Female wages if within [epsilon]a[[Z.sup.[epsilon]ap-1].sub.h]/
 [([delta][beta]1/[epsilon]).sup.
 [epsilon]ap]B(p,q)[(1 + [([Z.sub.h]/
 [delta][beta]1/[epsilon]).sup.[epsilon]
 a]).sup.p+q]
 occupation differentials)
 10 [omega][beta] - [omega][delta][beta] +
 [omega][beta](B(p + 1/a, q - 1/a) -
 [[beta].sup.1-[epsilon]/[epsilon]]B(p +
 1/a[epsilon], q - 1/a[epsilon])/B(p +
 1/a, q - 1/a))
(Mean differentials)
 - occupation segregation where:
 + within occupation ([beta]) = [X.sub.M][[gamma].sub.M]
 differentials) ([beta][delta]) = [X.sub.F][[gamma].
 sub.F]
 Descriptive Statistics for the CPS
 Sample of Insurance Workers
 Means and Standard Deviations
 Males Females
 (N = 674) (N = 399)
Annual wage 36,868.5 20,160.7
 (21,773.9) (9,599.1)
Education 15.02 13.21
 (2.11) (1.71)
Experience 18.99 17.07
 (12.04) (11.46)
[Experience.sup.2] 505.18 422.71
 (580.74) (507.96)
Occupation dummies
 Administrative .203 .144
 (.403) (.351)
 Professional .063 .031
 (.243) (.174)
 Supervisory .135 .067
 (.343) (.250)
 Sales .356 .105
 (.479) (.307)
 Technical .100 .472
 (.301) (.500)
 Adjustors .100 .177
 (.301) (.382)

Notes: Selected from the 1988 CPS tape, industry code = 711 (for last year's longest job). Restricted to those working at least 50 weeks during the previous year, at least 30 hours per week (those whose hours were coded 99 were deleted), and with positive wages. Occupational dummies were coded as follows (where occupation refers to last year's longest job): Administrative (33 [less than or equal to] occ [less than or equal to] 37), Professional (43 [less than or equal to] occ [less than or equal to] 199), Supervisory (occ = 243), Sales (occ = 253), Technical (203 [less than or equal to] occ [less than or equal to] 389, excluding 243 and 253), and Adjustors (occ = 375).

 Wage Decompositions from the Gamma Model
 Coefficient estimates
 Gamma Regressions
 Males Females
Intercept -6,343 -5,550
Education 688.9 669.1
Experience 367.0 232.6
Experience [2] -5.46 -3.60
a (1.00) [R]
p 4.567
[lambda] 23,497
\log likelihood\ 11,321.87
[ae.sup.2] 228.80
 Generalized Gamma Regressions
 Males Females
Intercept -7,048 -5,428
Education 762.6 678.1
Experience 410.7 233.9
Experience [2] -6.14 -3.64
a 1.024
p 4.321
[lambda] 31,165
\log likelihood\ 11,321.81
[ae.sup.2] 209.00
 Wage Decompositions
 Components of the Wage Differential
 Gamma Generalized Gamma
Endowment .372 .364
Discrimination .250 .331
Segregation .378 .305
Notes: R = the "a" parameter is restricted
to have a value of 1 in the gamma regressions.
 APPENDIX TABLE A1
 Summary of the Rate Exponential Decline
 in the Relative Number of Females in the
 Management Hierarchy
 Leontief Technologies
 E = 1 E = 1 E = 1
 S = 2 S = 2 S = 4
 L = 4 L = 8 L = 8
Mean -.599 -.459 -.520
Standard deviation .355 .186 .186
Minimum -1.276 -.713 -.713
Maximum -.115 -.087 -.120
 Cobb-Douglas Technologies
 e = .33 e = .25 e = .6
 s = .33 s = .25 s = .3
 l = .33 l = .50 l = .1
Mean -.475 -.476 -1.183
Standard deviation .370 .210 1.321
Minimum -1.052 -1.360 -6.825
Maximum -.735 -.805 -.208
Note: Mean of [psi] (equal 4) in regressions for each of 28
(7 values of the correlation coefficient x 4 values of investment costs)
simulations for each technology.
 OLS Wage Equations and Decompositions
 with and without Occupational Controls
 OLS Estimates and Absolute t-Values
 No Controls
 Males Females
Intercept -21,589 -11,546
 (2.56) (3.96)
Education 2,782.1 1,899.8
 (5.57) (9.41)
Experience 1,531.2 692.1
 (5.22) (7.37)
[Experience.sup.2] -24.52 -12.32
 (4.04) (5.84)
Administrative -- --
Professional -- --
Supervisory -- --
Sales -- --
Technical -- --
Adjustors -- --
[R.sup.2] .129 .168
n 399 674
F 40.9
 Occupational Controls
 Males Females
Intercept -14,735 -6,475
 (1.69) (1.19)
Education 1,856.1 1,307.5
 (3.54) (6.53)
Experience 1,255.6 526.6
 (4.37) (5.86)
[Experience.sup.2] -20.63 -9.40
 (3.49) (4.68)
Administrative 20,413 7,861
 (3.63) (1.63)
Professional 10,691[degree] 11,977
 (1.63) (2.34)
Supervisory 11,706 8,976
 (2.05) (1.83)
Sales 9,774 9,392
 (1.85) (1.94)
Technical 4,288 1,574
 (0.74) (0.33)
Adjustors 76 2,888
 (0.01) (0.60)
[R.sup.2] .204 .283
n 399 674
F 15.3
 Components of the Wage Differential
 Without Occupational Controls With Occupational Controls
Endowment .308 .212
Discrimination .692 .602
Segregation NA .187
Note: Endowment = ([X.sub.M] - [X.sub.F])
(0.63[[beta].sub.M] + 0.37[[beta].sub.F)].