college major choice and changes in the gender wage gap

COLLEGE MAJOR CHOICE AND CHANGES IN THE GENDER WAGE GAP

ERIC EIDE*

The distribution of college majors changed markedly between the 1970s and 1980s as fewer students completed degrees in low-skill jields such as education and letters and more graduated in high-skill jields such as engineering and business. "his shift was most dramatic for females, who previously were concentrated in low-skill jields relative to those of males. This paper examines how this education-related skill upgrade, as represented by changes in the major distribution, affected the gender wage gap for college graduates during the 1980s. The results show that convergence in major distribution between males and females contributed to a decline i n the gender wage gap for college graduates.

I. INTRODUCTION

The gender wage gap narrowed markedly during the 1980s after remaining stagnant for the previous two decades. Studies analyzing Current Population Sur- vey data show that over this time span the average wage of women relative to that of men rose by about 8 percent (see Bound and Johnson, 1992; Katz and Murphy, 1992; ONeill and Polachek, 1993). Disag- gregating by education level reveals that the decline in the wage gap between male and female college graduates was substantially less than the corresponding fall for high school graduates. Bound and John- son (1992, table 1 column v) show that for male and female college graduates with less than 10 years of labor market experience, the log hourly wage differential fell

*Assitant Professor, Department of Economics, Brig- ham Young University. This is a revised version of a paper presented at the Western Economic Association International 68th Annual Conference, Lake Tahoe, Nev., June 21, 1993, in a session organized by Philip Ganderton, University of New Mexico, and Peter Griffin, California State University, Long Beach. The author is grateful to Jeff Grogger, Jack Hou, Steve Trejo, and two anonymous referees for helpful comments.

Contemporary Economic Policy Vol. XI, April 1994

by 1 percentage point between 1979 and 1988, while for high school graduates the differential closed by 10 percentage points.

Previous analyses make the implicit as- sumption that male and female college graduates' relative skill levels remained constant over time. However, the skills that recent college graduates bring to the labor market are likely to depend on the distribution of fields of study. Changes in male and female major distributions therefore would lead to changes in the typical male and female college graduate's relative skill levels. If the returns to college differ by major, then changes in relative male-female skills could lead to changes in the gender wage differential for college graduates (see Blakemore and Low, 1984; Daymont and Andrisani, 1984; Jacobs, 1989; Paglin and Rufolo, 1990; Polachek, 1978; and Rumberger and Thomas, 1993, for studies on differences in male-female major choice).

U.S. Department of Education (1989) data show that between the mid-1970s and mid-1980s, the major distribution moved away from low-skill fields such as education and social science and toward high-

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@Western Economic Association International

56 CONTEMPORARY ECONOMIC POLICY

skill fields such as engineering and business. For example, the proportion of males graduating in education and social science fell from 27 percent to 18 percent, and the proportion of males graduating in business and engineering increased from 34 percent to 49 percent. Changes were even greater for women. The proportion of female graduates majoring in education and social science fell from 42 percent in 1976-1977 to 27 percent in 1984-1985, while the proportion of females graduating in engineering and business rose from 9 percent to 27 percent during that period. These data suggest that the typical male and female college graduate’s relative skills were not constant over time (see Grogger and Eide, 1994; Jacobs, 1989; and O’Neill and Polachek, 1993, for other studies describing changes in the major distribution).

The move of females away from tradi- tionally female majors towards tradition- ally male majors suggests an upgrading of skills relative to male college graduates. If the male-female wage gap is partly due to differences in relative skills, as reflected by relative major distributions, then convergence in major distribution should reduce the gender wage gap. The purpose of this paper is to examine how major distribution changes affected the gender wage differential for college graduates.

11. DATA

The analysis here uses two longitudinal surveys conducted by the U.S. Depart- ment of Education. The National Longitu- dinal Study of the High School Class of 1972 (NLS72) is a longitudinal survey of roughly 21,000 high school seniors who graduated in 1972 (see National Center for Education Statistics, 1981). Information about respondents’ family backgrounds and educational performance was collected in the 1972 base year survey. Re- spondents also took a set of achievement tests during the base year. Subsequent waves of interviews collected data on

respondents‘ work and educational expe- riences since leaving high school. The analysis here uses wage data from the 1979 interview, the first for which earnings data on college graduates are available.

The High School and Beyond (HSB) survey is a similar panel of about 12,000 members of the high school class of 1980 and was intended as a follow-up to the NLS72 (see Center for Educational Sta- tistics, 1987). Similar background data were collected in the base year survey, and a test battery was explicitly de- signed to be comparable to the 1972 test battery (see Hilton, 1992). Estimates in the analysis here involve using wage data from the 1986 interview.

The sample includes male and female college graduates who are working full time, are not enrolled in school, and par- ticipated in the base year survey and the follow-up interview from which data were drawn. The sample includes only persons whose hourly wage was between 1 dollar and 100 dollars. All monetary values are in 1986 dollars, deflated by the CPI.

The dependent variable in the analysis is the logarithm of the hourly wage. The independent variables include college major dummies, educational achievement measures, family background variables, potential experience, and race dummies.

All fields of study fall into one of six majors: business, engineering (including computer science), science (including mathematics), social science (including economics), education and letters, and other. Controlling for the presence of postgraduate degree recipients involves including a dummy variable equal to one if the individual has earned a postgraduate degree and equal to zero otherwise.

Educational achievement measures consist of achievement test scores and high school grades. The analysis includes three achievement tests: a math test, a vocabulary test, and a “mosaic” test that measures perceptual speed and accuracy. Two dummy variables were constructed

EIDE: COLLEGE MAJOR CHOICE AND CHANGES IN THE GENDER WAGE GAP 57

from base year self-reports of the student’s high school grades. The first equals one if the student earned mostly As and Bs in high school and equals zero otherwise. The second indicates that the student earned mostly Bs and Cs.

Family background variables include parental income and education. The potential experience measure gives the num- ber of years since the respondent last at- tended school full-time. The marital status indicator equals one if the respondent was married at the follow-up interview date and equals zero otherwise. Finally, the mutually exclusive race categories are white, black, Hispanic, and other.

Panel A of table 1 presents summary data on male-female ratios for hourly wage and test scores. Row 1 shows that the ratio of male to female wages fell slightly from 1.125 in 1979 to 1.120 in 1986. This result is consistent with the small decline in gender wage gap for college graduates reported earlier.

The test score ratios show that male college graduates received higher math scores than did female college graduates and that difference grew slightly between cohorts. Females in the early cohort scored higher on both the vocabulary and mosaic tests. By the later cohort, females lost their advantage in vocabulary scores and increased their advantage in mosaic scores by a small margin.

The previous comparison of ability-related skill measures suggests that female college graduates of the later cohort declined in ability, as measured by standard- ized test scores, relative to male college graduates. If these changes in relative ability had been substantial, then a feasible conclusion would be that ability-related skill differences have been a factor in the lack of gender wage gap convergence for c o 1 leg e grad u a t e s . How ever, these changes were modest, and it is unlikely that changes in ability-related skill differences influenced changes in the wage gap.

Much larger changes occurred in relative education-related skill, as reflected in changes in the male and female major distributions shown in panel B of table 1. Half of the NLS72 male college graduates earned degrees in the high-skill fields of business, engineering, or science, while less than one-third of female college graduates majored in those fields. In contrast, over 60 percent of NLS72 female college graduates received degrees in the low-skill fields of social science or education and letters, while only 43 percent of males graduated in those .areas. College graduates of the HSB cohort majored in business and engineering in larger proportions than did their NLS72 cohort predecessors. The percent of males in high-skill fields rose to about 70 percent, and the percent of females in those majors increased to nearly half. The largest of all changes was the increase in the proportion of female business majors, which grew by over 18 percentage points. These substantial changes in the male and female major distributions clearly show that relative education-related skill of the typical male and female college graduate was not constant during the 1980s.

111. ESTIMATION

A. Regression Specification Estimating log wage regressions sepa-

rately for males and females of each cohort involves using the equation

(1) Y1= xi p + ui

where Y, is the log of hourly wage for individual i, Xi is a vector of individual characteristics, p is a vector of parameters to be estimated, and ui is an unobserved zero mean disturbance term. The variables in Xi consist of college major dummies, a postgraduate attainment indicator, ability


TABLE 1 Summary Statistics

A. Male-Female Ratiosa

NLS72 HSB Changes Variable (1) (2) (21-P)

Hourly Wage 1.125 1.120 -0.005

Math Test 1.097 1.106 0.009

Vocabulary Test 0.949 1.011 0.062

Mosaic Test 0.979 0.966 -0.013

B. Major Distributions as a Percent of Same-Sex College Graduates

Field

NLS72 HSB Males Females Males Females

(1) (2) (3) (4)

Business 0.243 0.094 0.325 0.276

Engineering 0.116 0.011 0.210 0.089

Science 0.137 0.210 0.140 0.097

Social Science 0.283 0.269 0.184 0.233

Education and Letters 0.151 0.339 0.095 0.248

Other 0.068 0.077 0.046 0.057

aTest score means based on sample restricted to respondents with non-missing test scores. Note: Based on weighted data.

measures, race dummies, potential experience, a marital status indicator, and family income dummies. Table 2 presents the results from OLS estimation of equation (1). Section IIIC discusses these estimates.’

1. Since the sample analyzed here is composed of college graduates who are working full-time, it may not be a random sample, and thus O E estimation of equation (1) may yield biased estimates. Testing for selectivity bias for men in choosing to graduate college involves using Heckman’s (1979) technique. The analysis also tests for selectivity bias for women in the joint decision to graduate college and participate in the labor market using Fishe et al.’s (1981) approach. The parameter estimates for the selection models were similar to the OLS estimates in table 2. Therefore, the analysis focuses on the OLS results.

B. Simulations The regression estimates simulate how

the gender wage differential would have changed under various regimes. The first simulation asks what the log wage differential would have been if females had the same major distribution as males in each cohort but also had their own major-specific returns. The next simulation asks what the log wage differential would have been if females had the same major coefficients as males in each cohort but also had their own major distribution. These simulations first ask how the log wage differential would have changed (i) if there had been total convergence in major dis-


TABLE 2 OLS Wage Regression Resultsa

NLS72 HSB Males Females Males Females

Variable (1) (2) (3) (4)

Business

Engineering

Science

Social Science

Other Major

Postgraduate

Math Test

Vocabulary Test

Mosaic Test

As and Bs in High School

Bs and Cs in High School

Constant

Adjusted R2

Observations

0.178 (0.041)

0.351 (0.049)

0.121 (0.046)

0.119 (0.039)

0.172 (0.056)

0.239 (0.051)

0.006 (0.003)

-0.002 (0.004)

0.003 (0.002)

0.096 (0.051)

0.035 (0.049)

1.793 (0.080)

0.08

1119

0.219 (0.045)

0.223 (0.124)

0.232 (0.035)

0.071 (0.032)

0.130 (0.050)

0.226 (0.042)

0.002 (0.003)

0.001 (0.004)

0.000 (0.002)

0.084 (0.064)

0.021 (0.063)

1.839 (0.086)

0.08

997

0.227 (0.064)

0.440 (0.068)

0.217 (0.078)

0.093 (0.070)

0.072 (0.106)

0.668 (0.165)

0.006 (0.005)

0.001 (0.006)

-0.005 (0.002)

0.117 (0.108)

0.043 (0.105)

1.685 (0.138)

0.20

403

0.046 (0.045)

0.210 (0.063)

0.125 (0.057)

(0.046)

0.128 (0.076)

0.013 (0.1 26)

0.011 (0.003)

-0.007 (0.005)

0.001

-0.023

(0.002)

0.091 (0.103)

-0.019 (0.1 04)

1.505 (0.127)

0.12

551

'Regressions control for race, experience and experience squared, marital status, and family

Note: Standard deviations in parentheses. income categories. Omitted college major is education and letters.

tributions and (ii) if there had been total convergence in major-specific returns to college. These simulations shed light on how much of the differential is due to differences in relative education-related skill and how much is due to male-female differences in earnings by major.

Table 3 presents estimates of these simulations. Row 1 shows that the OLS differential based on observed sample means fell by about 1 percentage point. Using the OLS differentials as baseline comparisons reveals that substituting the male major distribution for the female major distribu-


TABLE 3 Predicted Male-Female Log Wage Differentials for College Graduates

1979 1986 Change Type of Differential (1) (2) (2)-(1)

Observed Sample Meansa 0.129 0.121 -0.008

Females with Male Major Distributionb Females with Male Major Coefficientsc

0.093 0.088 -0.005

0.136 0.079 -0.057

aComputed by substituting weighted sample means of explanatory variables for each

bComputed same as (a) except male means for the major dummies are substituted for

‘Computed same as (a) except male major coefficients are substituted for female major

gender into the OLS regression equation for that gender.

female major means.

coefficients.

tion reduces the log wage gap in 1979 from 0.129 to 0.093 and in 1986 from 0.121 to 0.088. Differences in major distribution between males and females therefore account for about 27 percent of the wage gap in each cohort.

Substituting male major coefficients for female major coefficients widens the wage differential in 1979 from 0.129 to 0.136 and narrows it in 1986 from 0.121 to 0.079. Thus, applying the male earnings structure for college majors to females in 1979 widens the gap. However, in 1986 differences in major coefficients account for 35 percent of the wage gap.

If there had been complete convergence in major distribution between males and females and the major coefficients for males and females in each cohort were as observed, the wage differential would have declined by nearly a third (from 0.129 to 0.088) between 1979 and 1986. If there had been complete convergence in major coefficients and the major distribution was as observed, the wage differential would have declined by almost 40 percent (from 0.129 to 0.079) between 1979 and 1986. These comparisons suggest that gender differences in both major distribution

and major coefficients were important factors in determining male and female college graduates’ relative wages during the 1980s.

C. Decomposition Decomposing the change in the gender

wage gap into changes in mean characteristics and changes in regression coefficients of females relative to males reveals the under- lying determinants of changes in the gender wage gap for college graduates. Calculating the decomposition involves using the OLS estimates from table 2.

One can express the wage gap in a given year (dropping individual subscripts) as

where the m andfsubscripts refer to males and females, respectively; is the mean of the logarithmic wage; x is a vector of mean values of explanatory variables; and B is a vector of estimated coefficients. Choosing female means and male coefficients as weights is arbitrary. The results using male means and female coefficients


as weights are similar. One can express equation (2) more compactly as

(3)

where

Bj .

The first term in equation (3) measures the part of the wage gap accounted for by mean differences in observable characteristics and often is referred to as the ”explained” portion. The mean difference in male-female characteristics is weighted by the male coefficients and thus applies the male wage structure to both males and females. The second term measures the portion of the wage gap not explained by mean differences in characteristics. This “unexplained” or “residual” component often is attributed to labor market discrim- ination and differences in unobserved characteristics.

Following Sorensen (1991), one can generalize equation (3) to decompose the change in the wage gap between years t and t’,

These two components represent a decomposition of the change in the male-female wage gap into parts due to changes in the residual and changes in the mean difference in male-female characteristics. One can further decompose the second term in equation (4) as

(5)

The first expression in equation (5) allows the convergence in male-female mean characteristics to be weighted by the same weight, as opposed to different weights as in equation (4). The second expression in equation (5) is the part of the decline in the gender wage gap due to a change in the male earnings structure. Interpreting the second term in equation (5) involves applying the male earnings structure to both males and females. The decline in ihe differential then would be (B, pmu - hx, b,,), the second term in equation (4) above. If the male earnings structure did not change, then the wage diiferential change would equal (AT,. - at) Pmt Thus, (A 57,. AB,) is the difference between these scenarios and accounts for the portion of the change in the gender wage gap attrib- utable to a change in the male earnings structure. One thus can express the change in the wage gap between years t and t’ as

+ (fit I - a,) B,,,, + (hx,. AS,,, )

The subscripts t and t’ refer to the years 1979 and 1986, respectively.

The estimates in table 4 decompose the decline in the gender wage gap. Thus, a variable with a negative sign contributed to the decline, and a variable with a posi- tive sign widened the gap. Table 4 does not report the individual components of the residual. For dummy variables, the decomposition depends on which category was omitted. For continuous variables, the results depend on the zero point chosen (see Jones, 1983). However, the total for the residual would not change (see below).

The results from the last row of table 4 show that changes in mean characteristics significantly widened the wage gap between male and female college graduates by 0.019. Changes in the male earnings


TABLE 4 Decomposition of Changes in the Male-Female

Log Wage Differential for College Graduates: 1979-1986 Male Earnings

Groups of Variablesa Mean Structure

College Major Business -0.015 0.002

(0.004) (0.004)

Engineering

Science

Social Science

Other Major

Ability Measures Math Test

Vocabulary Test

Mosaic Test

High School Grades

Demographics Race

Marital Status

Family Income

Control Variables

0.008 (0.001)

0.013 (0.005)

-0.007 (0.002)

(0.0002) -0.001

0.001 (0.0001)

(0.002)

(0.0002)

-0.001

-0.002

0.010 (0.005)

0.002 (0.002)

(0.0001) -0.001

-0.004 (0.004)

0.016 (0.015)

0.011 (0.010)

0.004 (0.004)

0.001 (0.004)

0.001 (0.001)

0.000 (0.008)

0.000 (0.001)

(0.001) 0.008

-0.001 (0.003)

0.002 (0.002)

(0.002) -0.002

0.004 (0.004)

-0.007 (0.007)

Total 0.019 0.023 (0.009) (0.019)

aThe control variables are experience and experience squared, the postgraduate indicator, and a

Note: Standard errors in parentheses. dummy variable which accounts for missing test score data.


structure widened the gap by 0.023, but not significantly. The change in the residual component (not reported in table 4) was -0.051 with a standard error of 0.189. The total change in the wage gap therefore was -0.009 (=[-0.051 + 0.019 + 0.0231). Thus, changes in the residual component narrowed the gap. However, changes in mean characteristics and in the male earnings structure in favor of males mostly off- set this decline.

Examining the individual components of table 4 shows that for the subgroup of college major, convergence in major distribution led to a decline in the gender wage gap of -0.002 (the sum of the individual mean components for college major). This was predominantly due to the large increase in proportion of female business majors. Although female college graduates of the 1980s moved into high-skill fields (table l), the move was not as pro- nounced as for males, with the exception of business. Thus, there was divergence in the major distribution for engineering and science majors. Moreover, changes in the major distribution were significant for each major. As the simulations demon- strate, the difference in major distribution accounts for a substantial portion of the wage gap. If higher proportions of females had graduated in these high-skill fields, the wage differential decline would have been greater, holding the returns to college major constant.

For the ability measures, there was convergence in mean test scores for the mosaic and vocabulary tests but a widening

in the difference between male and female mean math scores.

This decomposition analysis shows that convergence in major distribution between male and female college graduates and a decline in the residual portion of the wage differential led to a narrowing of the gender wage gap. On the other hand, divergence in other mean characteristics and a change in the male earnings structure in favor of males contributed to a widening of this differential. The net effect was a small decline in the wage gap.

IV. CONCLUSION

Substantially greater proportions of college graduates in the mid-1980s earned degrees in high-skill fields, and much lower proportions earned degrees in low-skill fields relative to their mid-1970s counter- parts. Decomposition analysis shows that major distribution convergence contributed to a decline in the gender wage gap during the 1980s. The simulation exercise demonstrates that if there had been total convergence in major distribution, the observed wage gap would have been markedly lower.

These findings have important policy implications. Increasing the proportion of females in high-skill majors to the same proportions as males would lead to a substantial decrease in the gender wage gap for college graduates. However, this wage differential is not likely to disappear com- pletely if pay disparity exists between males and females from the same major.


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college major choice and changes in the gender wage gap

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