paglin, m., & rufolo, a. m. (1990). heterogeneous human capital, occupational choice, and...

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Heterogeneous Human Capital, Occupational Choice, and Male-Female Earnings DifferencesAuthor(s): Morton Paglin and Anthony M. RufoloSource: Journal of Labor Economics, Vol. 8, No. 1, Part 1 (Jan., 1990), pp. 123-144Published by: The University of Chicago Press on behalf of the Society of Labor Economists andthe NORC at the University of ChicagoStable URL: http://www.jstor.org/stable/2535301 .

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Heterogeneous Human Capital, Occupational Choice, and Male-

Female Earnings Differences

Morton Paglin, Portland State University

Anthony M. Rufolo, Portland State University

Human capital models have mainly focused on the rate of return to investment in a homogeneous stock of capital. Yet individuals have different initial attributes that determine comparative advantage in producing different types of human capital. We find that mathematical ability is an important determinant of field choice for college students and that differences in earnings across fields are largely explained as a return to the use of scarce quantitative abilities in the production of each type of human capital. The model successfully accounts for the observed male-female differences in earnings and occupational choices of recent college graduates.

I. Introduction

Human capital models have largely focused on estimating the rate of return to investment in a homogeneous stock of capital measured by years of schooling and experience. However, there are clear differences in the apparent rate of return to investment in the various types of human capital. Some of these differences have been addressed by treating human capital

We gratefully acknowledge partial financial support from the Hoover Institution and the competent research assistance of Marvin Horowitz.

[Journal of Labor Economics, 1990, vol. 8, no. 1, pt. 1] ? 1990 by The University of Chicago. All rights reserved. 0734-306X/90/0801-0001$01.50

123



124 Paglin/Rufolo

as being heterogeneous once it is produced. Those who follow this approach try to explain differences in earnings across occupations as some form of equalizing difference based on the characteristics of the occupation or of the human capital used in an occupation (e.g., Polachek 1981; McDowell 1982; Blakemore and Low 1984; and Willis 1986). Thus, human capital in the field of education may receive a lower return because of high demand for the shorter work year. Similarly, some occupations may receive high returns because the training becomes obsolete rapidly. However, there is another major reason for differences in earnings across occupations. All people are not equally well equipped to enter each occupation, and they self-select on the basis of their comparative advantage for the occupation. Further, the choices made over time alter a person's human capital, and the heterogeneous nature of the capital accumulated also influences the set of options that are available for further investment.

Since all occupations do not require the full range of skills, the choice of occupation may make some skills redundant. Thus, a particular skill or attribute may be very valuable in some occupations and of no value in others. This complicates empirical work since the value of any characteristic may depend on a person's whole set of characteristics. For example, increases in physical strength are likely to be associated with increases in earnings for athletes but not for physicists. Alternatively, mathematical training is rewarded for physicists but not for athletes. Thus, empirical analysis might find that individual characteristics have little explanatory power when looking at occupations and earnings over the population as a whole.'

The notion of comparative advantage influencing occupational choice and earnings goes back at least to papers by Roy (1951) and Tinbergen (1951). Willis and Rosen (1979) find that comparative advantage partly determines who goes to college and who does not. Further, there has been research into whether occupational differences in earnings in the manu- facturing sector can be explained by the returns to some unobserved differences in productive factors among workers (Welch 1969). In the present study we deal with students who have chosen to go to college; hence we focus on the second stage of their decision process, choice of college major.

Each college program has different requirements and promises different rewards when the student completes the degree. The question we address is whether the theory of comparative advantage offers any insight into the choice of field. Within this narrow context it may be presumed that the major factors that affect choice of field are relatively few in number. If we look across fields, we would expect to find that the highest-paying field required more of some scarce attribute than did other fields. If so, the returns to the education will reflect an implicit return to these scarce attributes. Whether the return will be equalized across fields is an empirical

' For a good general discussion of the issues see Rosen (1974).



Male-Female Earnings Differences 125

question. Unfortunately, the equalization of returns to factors that are not traded is far from certain. There are several reasons why the return to skills might vary across occupations. The most important one is that the different occupations may not make use of the same skills. However, there are circumstances in which a simple hedonic relationship between characteristics and price will result (e.g., see Muellbauer 1974), and a finding of equalization of returns to a particular factor would be strong support for the comparative advantage approach to choice of occupation.

There are three basic hypotheses that come out of the comparative- advantage approach to field choice. The first is that we can estimate the return to various inputs in the production of human capital. The second is that the return to education will differ across fields depending on the value of the inputs needed to produce a particular type of human capital. (The widely observed empirical evidence supporting this is often treated as a shortcoming of the human capital model-see, e.g., Blaug [1976].) The third is that the attributes of the individual are an important determinant of the choice of occupation.

We focus on the measured quantitative and verbal abilities that are often used in determining admission into colleges. Since these characteristics are of importance in almost all college fields, they are most likely to register as quantitatively significant in this setting. Our results show that comparative advantage influences the observed choice of college major and that quantitative ability is one of the most important factors in this choice. Viewed in this context, it is not surprising to find differences in return among the college-based occupations. Such variation reflects the range of inputs of scarce quantitative abilities used in producing the many types of human capital.

Section II of this article reviews the data and shows the high correlation between quantitative attributes of those in a field and mean starting salaries of college graduates in the field. Regression results yield a measure of the implicit market value of quantitative ability as measured on standardized tests. Section III presents more direct tests of the sensitivity of the choice of major to a person's likelihood of success in specific fields and the results support the model. In Section IV, the model is applied to the issue of male-female occupational choice and the earnings differences of recent college graduates. The model is highly successful in accounting for such differences.

II. Attributes, Types of Educational Capital, and Earnings

Assume that the production of human capital is different for each type of human capital that is produced. Each production function requires a set of inputs, some of which are traded on markets and some of which are not. Each individual has an endowment of the nontraded inputs. If some of the nontraded inputs are scarce and are used to produce a~type of human capital that is in high demand, then we would expect these attributes to



126 Paglin/Rufolo

earn a rent in equilibrium. Thus, capital that requires large amounts of these inputs would have a higher price than other forms of capital that do not require much of the scarce inputs.

An exceptional endowment of a specific attribute does not uniformly affect the ability to produce all types of human capital. Thus, a keen sense of pitch and rhythm would offer a significant advantage in producing musical capital but provide little benefit in engineering. Possession of these attributes would raise the probability of choosing an education in music relative to other fields.2

The choice, then, is not simply to maximize the present value of the lifetime earnings by choosing the amount of education. Rather, the maximization of lifetime earnings is a joint choice of type and amount of educational capital to produce. Further, differences in initial endowment of abilities will alter the production opportunities available to an individual. Hence, different people would rationally make different choices based on their endowments and the relative wage differences. There will be a ten- dency to sort among occupations on the basis of the amount of ability the student has. Thus, students with low endowments of certain types of ability could go into occupations that make intensive use of this factor in producing human capital, but it would take them longer, and/or they would end up with a lower quantity or quality of capital at the end of their education. Clearly, depending on the "price" of various types of human capital, the student may be better off choosing to produce a type of human capital that has less value per unit because the student could produce more units in a given amount of time.

It is not necessary to distinguish between natural endowments and in- termediate types of human capital in generating empirical tests of the model since they are both used as inputs into the production function. It is certainly true that choices made in high school and earlier will have an important influence on the measured level of mathematical and verbal ability and also on the potential to successfully complete a field of study. However, it appears farfetched to argue that such choices are made in anticipation of differences in field requirements and earnings. Thus, it does not appear to be necessary to determine whether tests of verbal or mathematical ability test native ability or learning. The important question is whether they measure a significant input into the production process. Of course, it would be desirable to separate the ability component from the learning component since ability will determine something about the rate of increase in human

2 In practice, different universities have different standards for awarding the degree. Hence, we should account for both the choice of educational institution and the choice of field. This greatly complicates the analysis because each institution provides a different mix of market inputs and generates a different amount or type of human capital. While this is an important distinction for many purposes, it does not appear to be relevant in an aggregate cross-section analysis since there is a broad range of institutions in each field.




capital, but this is not necessary for simply testing the implication of the model.

In the data presented here we concentrate on students who have completed (or are about to complete) a 4-year college program, thus holding years of schooling fixed. We focus on the differences in attributes of those completing different educational programs as an explanation of mean earnings differences by educational or occupational groups.

In order to differentiate human capital goods by the attributes typically required as inputs, we draw on two large-scale tests given annually by the Educational Testing Service: the Scholastic Aptitude Test (SAT) taken by high school seniors, and the Graduate Record Exam (GRE) usually taken 4 years later by college seniors. Both tests have components that measure analytical-mathematical ability and language-compositional ability. Since students who take the GRE indicate their undergraduate major (and their intended graduate major), we have a national pool of students with about 4 years of college whom we can identify by undergraduate major and by their verbal and mathematical attributes. There were over 180,000 GRE test takers in the 1981-82 academic year, and a computer tape of these data was used in the present study. Students were classified by the testing service into 11 broad subject disciplines and 98 subdisciplines.

When classified by undergraduate major, we found very significant mean quantitative and verbal score differences in the 98 subdisciplines as well as in a broader grouping by 11 disciplines. To cite some contrasts: physics majors averaged 680 points in the GRE-Quantitative test (GRE-Q), education majors had a mean of 442. In the GRE-Verbal test (GRE-V), physics majors averaged 514 points, education majors 440. Figure 1 shows a 2-dimensional attribute plane with the attribute levels typical of each discipline. Of course there are variations around the means, so we have rather a group of overlapping tents or distributions on the attribute plane. It is important to note that the pattern of these attribute differences is very stable: year-by-year serial correlation (using the complete 98 subdiscipline classification in the Graduate Record Exam questionnaire) yielded r values between .98 and .99 for adjacent years and only fell slightly (r = .96) as we correlated mean values 5 years apart. Hence we find that 180,000 to 200,000 students independently taking these tests each year have sorted themselves by major in a remarkably consistent way. They appear to be choosing their major with regard to their own attributes and the typical attributes required by the educational discipline they select.

For the type of comparisons we are making, GRE scores are not ideal since they measure characteristics when the field is completed and since the exams are taken only by those contemplating graduate school rather than immediate employment. Thus, there is some possibility of bias due to different percentages of people in each field taking the exam and differences between those taking the exam and those taking jobs, but there are no obvious expectations with respect to such biases. Another possibility



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is that the GRE scores are, in some sense, a measure of the human capital the students acquired during their education. Thus, the year-by-year sim- ilarity in the pattern of scores across fields would result from the education process rather than as a result of self-selection. However, there is a high degree of correlation between SAT results (taken before college) and GRE scores. For example, in a sample of Oregon college students the mean SAT scores by major fields correlated highly (r = .90) with the national mean GRE scores by major.3 This indicates that the field pattern of GRE scores is more a consequence of student attributes at the time they enter college than it is of skills acquired during college.

The sorting among fields is further highlighted by the data shown in figure 2. Here we see (retrospectively) that students with different levels of mathematical ability exhibited sharply different patterns of choice: 71% of students in the highest GRE-Q interval selected and completed a major in the math-physical science-engineering group whereas only 2.6% chose to major in education-social science. By contrast, 37.4% of students in the lowest group (GRE-Q scores of 300-400) chose education-social science while only 1.2 percent chose the math-physical science-engineering option. Note that for these two field groupings the percentage of students entering and completing each field is a monotonic function of the GRE-Q score, with science-engineering positively sloped and education-social science negatively sloped. The third curve shown (biological and health sciences) first rises, reaching a maximum at the GRE-Q interval of 600-650, and then declines.4

The regression results were

GRE-Q = -80.94 + 1.17 (SAT-M), (-1.3) (9.5)

corrected r2 = .82;

N = 21 disciplines common to both the SAT and GRE test data; t-values are in parentheses. SAT scores were based on students who were in their third year of college and for whom SAT scores were on a computer tape of admissions files. This correlation is further confirmed by a national sample of students who took the SAT and, 4 years later, the GRE (see College Entrance Examination Board 1963, p. 2). The individual SAT-M scores correlated with the GRE-Q scores (r = .84), and the SAT-GRE verbal scores showed a similar r = .85. The least-squares equation relating SAT to GRE scores was also similar to ours: GRE-Q = -1.45 + 1.04 (SAT-M).

4 As noted, students were grouped by their scores on the GRE taken at the end of their college studies. But if these same students were grouped by their SAT scores, the curves in fig. 2 would look very similar. This is supported by the correlation between SAT and GRE scores cited above and by a replication of fig. 2 using SAT scores and subject majors of students in the Oregon State University system. Oregon data were taken from a computer tape of student records described below in Sec. III.



130 Paglin/Rufolo

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0 200- 301 - 351- 401- 451- 501- 551- 601- 651- 701- 75 1 - 300 350 400 450 500 550 600 650 700 750 800

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FIG. 2.-Probability of major by GRE-Q. Probabilities in each GRE-Q interval would total 100% if all subject majors were shown. Source.-Derived from Educational Testing Service data, tape of all test takers in academic year 1981-82 (see Goodison 1983). * Education and social science (excludes economics); * biological and health sciences; 0 engineering, math, and physical sciences.

The larger data set of all SAT test takers is less useful for our purposes. Although prospective college students indicate their first and second choice of possible majors, many switch majors within the first couple of years of college and some do not enroll at all or do not complete a 4-year program. Hence the nationwide data set of SAT test takers (unlike the set of GRE test takers) cannot be used to identify the attributes of those who have completed a specific major. However, SAT data taken from the records of university students who have completed 3 years of college work, who indicate their major, and for whom high school and college grade-point averages also were available, provided additional support to this approach. The results are reported in the next section.5

Table 1 shows a regression of mean starting salaries of recent college graduates, grouped by educational major, and mean GRE-Q scores of students in the respective undergraduate major.6 The results provide striking

5 Such data can be obtained only from the records of each college or university. For our study, a computer listing of students in their third year at the University of Oregon and Oregon State University (spring term, 1984) was obtained.

6 The data on starting salaries for new college graduates, identified by academic program, were taken from national surveys conducted by the College Placement Council (CPC) (1983). This organization regularly collects information from 160 college placement offices across the country on the number of job offers and salaries




Table 1 Mean Starting Salaries and GRE-Q Scores by Discipline (Dependent Variable = Monthly Starting Salary, 1982; t-Ratios in Parentheses)

Data Set Constant GRE-Q Adjusted R2

(1) College Placement Council (July 1982) -603 3.99 .82 (-2.45) (9.68)

(2) Langer and Associates (1982)* -55 3.85 .79 (-2.16) (8.98)

NOTE.-The College Placement Council (CPC), in classifying job offers by students' undergraduate major, uses the same system for coding the academic disciplines as the Educational Testing Service. Hence we were able to match salary data wit% the appropriate test scores. For some job categories, there was no direct match, e.g., "other social sciences" or "other physical and earth sciences," so we used the weighted average test scores of the subdisciplines indicated by the CPC code sheets as being subsumed in those job categories. In the business fields with no GRE-Q scores, GMAT-Q scores were converted to GRE-Q equivalents by means of a regression, using data from some 30 fields in which both were available (see Graduate Management Admission Council 1982, pp. 66-67, and Goodison 1983, pp. 93-96). The equation was GRE-Q = -15.04 + 20.08 (GMAT-Q) with an adjusted R2 of 0.94.

* Reported by Scientific Manpower Commission (n. 6 in text).

confirmation that the market recognizes the varying levels of a scarce attribute (in this case mathematical ability) embodied in the different types of educational capital. The relationship is linear with an adjusted r2 =.82. The unequal returns to educational capital (as conventionally measured) reflect the equalization of returns per unit of the scarce attribute required to produce such capital. Equation (1) in table 1 tells us that for every 100- point increase in the attribute "quantitative ability" (as measured by GRE- Q scores) the educational capital goods that embody this attribute yield about $399 per month more in (1982) earnings. The intercept value of -$603 also seems reasonable since the test scores have a theoretical range of 200-800. Hence an academic discipline that required no quantitative or analytical ability would still yield a low monthly salary of $195. There is, of course, no academic discipline with a mean score of 200, and alternative jobs that require only physical labor (and no educational investment) would usually be preferred.

received by recent college graduates with little or no experience. The CPC salary data for July 1982 was based on over 58,000 job offers. The jobs are classified into 24 groups reflecting conventional academic majors such as engineering (several subgroups), math, physical sciences, chemistry, economics, social sciences, health sciences, humanities, accounting, marketing, finance, and so on. A second source of salary data was taken from a summary of a report by Langer and Associates who make annual surveys of hirings of new college graduates as reported by the firms or institutions that hired them. These are also grouped by academic disciplines similar to, though not identical with, the categories used by the CPC. The Langer and the CPC data are conveniently summarized in the annual report of the Scientific Manpower Commission (1983).

There is no reason to expect that a simple linear relationship is appropriate since the unit of measure is, in some sense, arbitrary. However, we did not try to fit other forms because this result appears to be sufficient confirmation of the equalization of returns to attributes.



132 Paglin/Rufolo

Even if the returns to a particular ability or skill are equalized across individuals, there is a problem in interpreting the value of the skill. There may be a direct return to that skill as part of one's wages, and there may be an indirect return owing to the more valuable capital that was created. The effect through capital formation cannot be separated from the direct wage effects when everyone in the sample has the same amount of schooling. However, the results can be interpreted in this context. Variation in the other major inputs was largely held constant by taking people with the same amount of time spent on education. Further, variations in the value of capital formed owing to variations in a personal attribute are a form of return to the personal attribute, so the regression results do rep- resent the returns to the attributes.

A similar regression test using GRE-Verbal means of the academic disciplines and the same salary data as above showed no significant correlation. This suggests that verbal ability is not sufficiently scarce (among college graduates accumulating educational capital) to yield a rent to those who major in a subject requiring higher than average levels of this attribute. Multiple regression using GRE-Q and GRE-V as independent variables also showed no significant contribution by the GRE-V variable.8 These findings probably reflect the supply and demand conditions of our tech- nological age. In Elizabethan England, high verbal skills may have been the scarce factor, while in fifteenth-century Florence artistic attributes probably commanded rents.

III. Explaining Choice of Educational Fields

The results based on the GRE scores are subject to two potential problems: the test may measure output rather than input, and there may be bias caused by different-size groups taking the test in each field. Thus, we next look at two tests of student choices among alternative educational investments that are not subject to these biases.

Changing Field

Our first test focuses on students who change field after they complete their undergraduate degree. The data set is drawn from the national Grad- uate Record Examination (GRE) tape of 180,000 test takers in the 1981- 82 academic year. Since the students indicate both their undergraduate major and their intended graduate field, we can observe those who shift

8 It is interesting to note another piece of evidence that students sort more on the basis of quantitative ability than on the basis of verbal ability. The standard deviation of mean GRE-Q scores across the 98 fields was 71.4, while the standard deviation of GRE-V scores was only 45. Hence, there is much greater variation in Q scores across fields than there is in V scores. For individual scores, the standard deviation of the Q scores ( 134) was only slightly larger than for the V scores, 122.




fields and note the relationship of these shifts to the attributes of the students who make them. Some 30% of the test takers, or 54,000 students, indicated a change in field. This group was divided into two subgroups: those intending to enter doctoral programs and those intending to go on with graduate work below the doctoral level.

Is there a systematic relationship between the attributes of those who move to a new field and the distance and direction of their move? Students should evaluate their probability of success in a graduate field by comparing their attributes with those of their peer group. We would expect that those who move down the scale to a less mathematically demanding field would be below the mean Q-score of their original field. Those who move up to a more demanding (and higher-paying) field would be expected to have Q-scores above the mean of their group.

We measure the distance between any two fields by the difference in the mean GRE-Q scores of intended graduate students in each field. We used the 11 major disciplinary fields shown in the GRE Summary Report (Goodison 1983, tables 32-35). An example here may be helpful. All students with an undergraduate major in behavioral sciences had a mean GRE-Q of 521. The students in this group who switched their graduate field to mathematical sciences (a field move of +151 points) had a mean Q score of 637 (+116 Q points above the mean of their original group) while those who moved down the scale to do graduate work in education (a field move of -55 points) had a mean Q score of only 475 (-46 Q points below the mean of their original group). To test for this relationship we set up the following equation:

(FN - Fo) = a + b(SN - SO),

where

FO = the mean GRE-Q score of all students intending to do graduate work in the original field of study;

FN= the mean GRE-Q score in the new graduate field to which the student is migrating;

So = the mean undergraduate GRE-Q score in a student's original field; and

SN = the mean GRE-Q score of the subset of students who migrate to a new field N from field 0.

For both groups (doctoral studies and less than doctoral studies), the regressions strongly support the comparative-advantage hypothesis. The equations, with t-statistics in parentheses, are shown in table 2 for each group.

The GRE-Verbal attributes also influence the change in field. For example, engineers who switch to humanities (which includes architecture)



134 Paglin/Rufolo

Table 2 Quantitative Abilities and Change of Field

Doctoral Studies Group

(FN- FO) -7.2 + 1.60 (SN - SO) (-1.2) (14.5)

r = .83 corrected r2 = .68

Less than Doctoral Studies Group

(FN- FO) -28.1 + 1.51 (SN - SO) (-5) (13.6)

r = .78 corrected r2 = .61

NOTE.-N = 1 0 groups; t-ratios are in parentheses. For def- inition of variables, see text, Sec. III.

have lower average GRE-Q scores than their cohorts in engineering but higher GRE-V scores, closer to the average verbal attributes of the students in their new field. We have concentrated on the horizontal (GRE-Q) moves since they have greater economic significance, but we could use a similar regression model to explain vertical moves on the GRE-V axis, though we would expect weaker results.

Expected Earnings

The next test of the model focuses on the relationship between students' attributes and the type of educational capital they decide to produce. The sample here is drawn from a computer tape of all junior-level students at the University of Oregon and Oregon State University (spring term, 1984) for whom there was a complete record of math and verbal SAT scores, high school grade-point average, cumulative college grade-point average, and gender. Generally, the record was likely to be complete for students who entered the university as freshmen rather than as transfer students. We want to see if students select a college major that will maximize the expected value (or expected utility) of their future income, given the current information on salaries paid to graduates in each field and the academic attributes of each student.

The first step in the analysis was to determine if student attributes, namely, SAT scores, high school grade-point average (GPA), and gender could predict degree of success in a given academic major, with success measured by the cumulative college grade-point average in all college courses taken. The results of the multivariate analysis were statistically significant (see the Appendix for details). Using the regression coefficients, we could then simulate the grade-point average that each student could expect to achieve in all the alternate fields of study. If these were high compared with the GPA of students actually in the field, then this would indicate a high probability of success in that subject area; if the predicted




cumulative GPA was low, then the probability of succeeding in the program would, of course, be low. The specific derivation of the probability of success from predicted GPAs is described in the Appendix. The expected value (EV) of the return to each type of educational capital was simply the probability of success in each field times the average salaries new college graduates were offered in each field as reported in Section II of this article.

Low probability of success could be interpreted in two ways, both consistent with the test used here. If predicted GPA in a field is low, the probability of successfully completing the major is reduced; even if completed, the low class rank may lead to poor job offers, well below the mean salary of average graduates in that field. In either case, the EV of the return to investment in this type of educational capital would be reduced. For each student we derive the EV of the return to each possible type of educational capital. If the EV of the major actually selected is higher than in the other fields (even if salaries are higher in some alternate fields), then the model has correctly predicted the student's choice of field.

Of course, no theory with so few variables can predict choices very well in narrowly defined fields, especially insofar as many people can do almost as well as in several fields. Although using nine subject matter groupings gave us predictions well above chance, it seemed best to focus on two groups of students with significantly different (mean) attributes, namely, those majoring in (1) humanities, education, or social sciences, and (2) mathematics, sciences, or engineering.9 Using this division, which also shows a sizable difference in mean starting salaries, our model gave a clear answer to the question why students persist in choosing educational programs in group 1 when they seemingly can get much higher salaries by opting for degrees in group 2. The probability of success in alternative fields, not just salaries, determines choices. The results are shown in table 3. The model is sufficiently robust to hold up in terms of maximization of expected values (EV) or expected utility (EU).

9 We thank Robert Tamura and Gustavo Bamberger for pointing out that the kappa-statistic is the most appropriate way to test for agreement between the model's predictions and the students' actual choices. Using an unweighted test of first-field choice among nine possibilities, the kappa-values were .04 and .05 for the expected utility and expected value models, respectively. Since kappa should vary between zero and one for this test, the explanatory power does not seem great, yet the t- ratios are 3.39 and 3.47. Part of the difficulty is that many fields are similar in characteristics, and the kappa-statistic treats the choice of the second field as an error. It is possible to adjust for this by assigning weights to the seriousness of the disagreement between the model and the actual choice. When the fields were weighted by the differences in the average math scores in each field, the weighted kappa-values were .21 and .16 for the expected utility and expected value models respectively, with t-ratios of 7.07 and 5.33. Finally, we ran separate comparisons using the two-field model noted in the text for each university separately. The expected value kappas were .49 and .17 with t-ratios of 13.03 and 3.12, while the expected utility kappas were .43 and .49 with t-ratios of 11.27 and 11.49. For an explanation of the kappa and weighted kappa statistics, see Everitt (1968).



136 Paglin/Rufolo

Table 3 Actual and Predicted Student Choices

Predicted

Predictions Actual N Field I Field 2 % Correct

University of Oregon: 509 Field 1:

EV 381 289 92 75.9 EU 381 297 84 78.0

Field 2: EV 128 75 53 41.4 EU 128 28 100 78.1

Total: EV 509 364 145 67.2 EU 509 325 184 78.0

Oregon State University: 537 Field 1:

EV 246 190 56 77.2 EU 246 216 30 87.8

Field 2: EV 291 81 210 72.2 EU 291 126 165 56.7

Total: EV 537 271 266 74.5 EU 537 342 195 70.9

NOTE.-EV is expected value and EU is expected utility. Field 1 consists of humanities, education, and social science for both universities, while field 2 consists of math and physical science for both universities and also engineering for Oregon State. For evaluation of results see n. 9, in text.

IV. An Application to Male-Female Earnings Differences

Recently, much attention has been focused on the failure of the traditional human capital model to explain persistent differences in earnings between men and women. Some people conclude that any differences not explained by the human capital model must be due to discrimination. However, part or all of such differences may simply be due to specification errors in the human capital model; hence an improved specification should reduce the amount of unexplained difference.

If women differ from men in the kinds of educational capital they produce, then our theory should account for part of the observed differences in earnings. Since we have identified mathematical reasoning ability (measured by SAT-M or GRE-Q) as a key variable determining differential rental rates on human capital, it is appropriate to examine male-female differences in the distribution of this variable and the resulting differences in the kinds of educational capital accumulated.

The attribute differences are shown in table 4 for both SAT-M and GRE- Q. We see that, in both tests, men have much higher relative frequencies than women in the top intervals, from 600 to 800, while women have a much higher proportion at the low end of the distribution. We also note that the high-paying fields-engineering, physical sciences, mathematics,




Table 4 Male-Female GRE-Q and SAT-Math Distributions

Scores Male Female on GRE-Q GRE-Q Male Female % GRE-Q, Relative Relative GRE-Q GRE-Q Female % Female SAT-M Frequency Frequency Nos. Nos. GRE Q* SAT-Math*

200-300 3.6 7.8 2,985 7,522 71.6 66.1 301-350 3.3 7.2 2,761 6,951 71.6 63.4 351-400 5.5 11.1 4,556 10,658 70.0 60.3 401-450 7.2 13.2 5,966 12,627 67.9 56.8 451-500 10.7 15.7 8,875 15,036 62.9 52.7 501-550 12.8 14.8 10,652 14,251 57.2 48.7 551-600 14.6 12.6 12,164 12,110 49.9 43.6 601-650 13.0 8.2 10,802 7,876 42.2 38.6 651-700 12.8 5.5 10,613 5,325 33.4 32.3 701-750 10.2 2.8 8,469 2,670 24.0 25.2 751-800 6.2 1.0 5,188 980 15.9 16.4

Totals 100.0 100.0 83,031 96,006 53.6t 51.7t

NOTE.-A similarly striking disparity in male/female frequencies at the high end of the distribution shows up in the SAT-math test given to some 10,000 mathematically gifted seventh- and eighth-grade boys and girls prior to the onset of differential course taking. "These data show that large sex differences in mathematical aptitude are observed in boys and girls with essentially identical formal educational experiences" (Benbow and Stanley 1980, p. 1262).

* Based on absolute frequencies. t Average % female. Source.-Educational Testing Service. GRE data are from a tape of 1981-82 test

takers. SAT data for 1983 are from the College Entrance Examination Board (1983b).

and computer science draw a large proportion of their candidates from the high end of the distribution, while the low-paying fields-education, social science, and humanities-draw a large proportion of their candidates from the low end of this distribution (see figs. 1, 2). Looking at the male- female attribute distributions, one can see an important reason for the differences in male-female participation rates in these academic programs.

It is important to note that women (as well as men) with high SAT-M and GRE-Q scores, show high participation rates in the sciences. In almost every discipline, average male and female GRE-Q scores are very similar; they show a correlation of r = .93.1O Thus, it appears that if we wish to increase the proportion of women in the sciences, we must do something to change the underlying mathematical-attribute distribution. As pointed out by Berryman (1983) in a recent Rockefeller report, this requires changes in curriculum choices made by girls in high school.

Although the mean scores of men and women by discipline are similar, their frequencies within each discipline are strikingly dissimilar. If we plot proportion of female participants (in each discipline) against mean GRE- Q scores (in the respective discipline) we get a negatively sloped function with a correlation of -.74. This now provides us with a market-based

10 The data show women have slightly lower mean scores in the physical sciences and engineering-even though they constitute a smaller, more selective segment of the female distribution than do the males of the male ability distribution.



138 Paglin/Rufolo

explanation for the concentration of women in the lower-paying (lower- Q-score) fields-without dependence on a model of exclusion or crowding because of explicit discrimination. Our market-based explanation would hold that fields with a high proportion of women are not lower paying than other fields because of "crowding" brought on by discriminatory exclusion; they are lower paying because the human capital in these fields can be produced with less of an important scarce attribute (quantitative ability). And, as we have seen in the attribute distributions, women are much more numerous than men at the lower end of the attribute scale. Similarly, graduates in physical science and engineering are not paid more because of the high proportion of men in these fields but because the production of human capital in these areas requires a much higher than average level of mathematical ability. Males dominate in these fields because they are two to five times as numerous as females in the top three intervals of the SAT-M and GRE-Q distributions.

We have developed the above explanation in stark terms in order to show how this model can be applied to the issue of male-female occupational and earnings differences. We certaliydo not rule out the historical impact of earlier discrimination on the educational choices girls make in high school (e.g., a smaller proportion opting for math and science courses, which, in turn, affect their SAT-M scores and their choices in college).11 However, the choices made in terms of college major appear to reflect the reasonable maximization of expected earnings based on existing characteristics and abilities.

Finally, we can make a simple calculation of the effects of the 81-point GRE-Q difference between males and females on average starting salaries of college graduates. The College Placement Council data (cited in Sec. II) show that the mean starting salaries for males and females in each narrowly defined field are very close. The unweighted average in all fields shows females earning 97.3% of male salaries. It is only when we consider the differences in male-female frequencies in each educational-occupational class that the average of female salaries as a percent of male salaries drops.

We can use our earlier regression equation (1) in table 1 (1982 monthly salary =-603 + 3.99 GRE-Q score), and the mean GRE-Q scores for males (569) and for females (488), to predict average male and female salaries and the resulting salary ratio. The equation yields a monthly mean salary of $1,667 for males and $1,344 for females, and a female-male salary ratio of .806.

" That is, a smaller proportion going into the scientific fields than their mathematical-ability distribution would indicate. Additional math courses have a positive effect on SAT scores, but it is much too small to explain the very large male-female differences at the high end of the SAT-M or GRE-Q distributions. See Benbow and Stanley (1980), pp. 1263-64.




Since we have used one equation to predict male and female salaries, we are postulating that both receive the same rate of return on quantitative ability. We can easily test this assumption since we have 1982 CPC salary and GRE-Q test data broken down by sex. The new regressions are as follows (t-statistics are in parentheses).

m m h i -507 + 3.80 GRE-Q, male monthly salaries = (-1.67) (7.59)

adjusted r2 = .73;

female monthly salaries 584 + 4.03 GRE-Q, (-1.98) (7.96)

adjusted r2 = .75.

The male and female equations clearly show very similar returns to the quantitative attribute (GRE-Q scores) with the market slightly favoring females-a result possibly attributable to affirmative-action hiring policies. For example, males would earn 2.2% more if their average quantitative skills were rewarded using the female equation, while average females would earn 1.5% less if compensated by use of the male regression equation. This difference is not statistically significant, and therefore we may conclude that male-female earnings differences are due to differences in attribute levels, not to differences in rates of return. Furthermore, using any of the three equations, along with the male and female attribute values to derive salaries and the salary ratio, gives the same result: females are predicted to earn 80 or 81/% of the male average salary. Our prediction matches almost exactly the actual earnings ratio of .80 for the 18-25-year-old cohort (Po- lachek 1984, p. 40). These findings support the proposition that explicit market discrimination in the setting of starting salaries for male and female college graduates is not presently a significant factor, and that the returns to scarce attributes tend to be equalized across gender groups.

Clearly, our results are based on a specific subset of the population, college seniors who took the SAT or GRE exams. Yet the results suggest that the model can be applied as well to earnings differences that are un- related to education. The key is to identify personal attributes that are sufficiently scarce to command a premium for jobs requiring those attributes. For example, it may be that physical strength commanded a premium over much of our history. If this is true, then it would explain some of the earnings differences that have existed in occupations requiring little or no education. Faced with the choice of low-paying unskilled work that did not require physical strength, or higher-paying work that did, those with the physical strength attribute would be more likely to choose the latter. Those without this attribute would not have such a choice. Thus, men



140 Paglin/Rufolo

(being stronger) would, on average, have higher wages than women in all occupations since only those men anticipating high wages from human capital investments would choose to acquire an education or skill. This is put forward as a hypothesis, not an explanation. If it is a correct hypothesis, then a number of implications follow from it. For example, men who lacked physical strength should have lower average earnings overall than those with physical strength since they would have a more restricted op- portunity set. Further, since it appears that the value of strength is declining over time, the premium for it in the unskilled occupations should also be declining.

V. Summary and Conclusions

The human capital model is based on the insight that investments in human beings produce an intangible form of capital that is significant in analyzing production. Differences in the amount of a person's human capital explain many of the commonly observed differences in both productivity and earnings. Despite the obvious improvement in our understanding of the wage-setting process that the traditional model provides, there is much that the model could not account for, and this frequently was taken as evidence that such phenomena were not explainable as market outcomes. We have shown here that the explanatory shortcomings of the model arise at least partly because most researchers treat human capital as being produced by spending time learning, with all types of capital essentially being produced with the same resources, using the same production function.

In this article, human capital is treated as a variety of heterogeneous outputs produced by a combination of time and other resources. The other resources include both market inputs and personal characteristics. The relative scarcity of different types of characteristics then determines the value of each characteristic. Production functions that make relatively heavy use of scarce characteristics will produce an output which, in equilibrium, has a higher value than similar capital produced using relatively less of the more valuable inputs.

The model provides a number of testable implications. The first is that it is returns to certain scarce factors of production that will tend to be equalized in equilibrium, not returns to human capital as conventionally measured. Preliminary work on the returns to mathematical and verbal abilities indicates that mathematical ability yields high returns while variation in verbal ability seems relatively unimportant in explaining interfield earnings differences in the college groups we studied."2 Equalization of returns to mathematical ability imply that students who work in areas

12 This does not imply that levels of verbal ability are unimportant. Rather, it implies that variations in this attribute are not as important in determining field choice as is math ability.




requiring a greater degree of mathematical ability will achieve a higher rate of return to their investment in human capital than students who generate a type of human capital that makes less use of mathematical ability. This is the second testable implication of the model, and it is confirmed by the data.

The third testable implication of the model is that people will sort themselves out among occupations according to the amounts of each type of characteristic they have. On average, people with relatively little of the scarce characteristics needed to produce a certain valuable type of human capital will not choose to produce that type of human capital, given a high probability that they would be unsuccessful or that large amounts of time and other resources would be needed to achieve success. Data on the GRE scores of people majoring in specific subjects show that there is remarkable consistency over time in the pattern of characteristics of students choosing particular areas of concentration. Further, SAT scores and high school GPAs have a good predictive ability of success within fields. Using these predictions of probability of success by field, it is shown that student choice of field is consistent with an earnings-maximization or utility-maximization view of field choice. Finally, the data are also consistent with the movements observed among students who choose to pursue graduate studies in a field different from the field of their undergraduate degree. Those with GRE quantitative scores that are above the average for their undergraduate field are more likely to switch to fields having higher average scores, while those with scores below the averages for their undergraduate fields are more likely to move to new fields with lower average scores. This demonstrates that students do, indeed, consider their individual attributes and the typical requirements of a field when deciding what type of educational capital to produce.

In conclusion, this formulation of the human capital model provides a closer parallel with the treatment of physical capital and shows that certain issues that could not be adequately addressed by the traditional treatment are nevertheless amenable to analysis. In particular, it appears that at least some of the previously unexplained differences between men and women in both occupational choice and earnings are due to differences in the distribution of scarce quantitative abilities.

Appendix

In order to determine a person's expected earnings or expected utility in a field other than the one actually chosen, it is necessary to construct an index of probability of success in these other fields. Since we have no information on the student's performance in any field not chosen, we constructed a probability index based on the person's characteristics and the coefficients of a regression model that relate these characteristics to grade-point average (GPA) in each major field of study. For each



142 Paglin/Rufolo

field we regressed the 3-year college GPA on SAT scores, high school GPA, and sex for those students who declared that field as a major. (The coefficient for sex was usually not significant, weakly positive or negative depending on field. However, on average women have higher GPAs than would be predicted on the basis of SAT scores and high school GPA, so we decided to include the variable.) We then simply inserted the student's characteristics into the regression equation for the field of interest. This gave us a method of predicting GPA by field for each student. The predicted GPA was used to construct a probability of success in the field for that student.

The equations to predict GPA gave a fairly good fit within fields, and somewhat better than typical results reported by the Educational Testing Service (ETS).'3 (Using nine fields, our multiple correlation coefficients averaged .60 vs. .55 for ETS.) Our results may be better because we are using data on 3 years of performance (rather than just first year) and are looking at students after they have more definitely been sorted out by fields. For example, our regression results indicate that SAT-math scores are a good predictor of grade performance for engineering and physics majors but are only weakly related to performance for English and political science majors. For SAT-verbal scores, the inverse would be true. Thus, students with the same characteristics will perform very differently in different fields.

Despite the good fit, there are some statistical problems with our regressions. There are no data on students who actually failed in any field. Thus, our data set is truncated within the field. This tends to bias coefficients toward zero and would lead us to underestimate the relationship between GPA and SAT scores. In particular, we would seldom predict an outright failure within any field since failure is defined as a GPA of less than 2.0, and this (except for a few probationary students) is outside the range of observations of our fitted sample. We expect that the pattern of unobserved failures varies dramatically across fields and that any attempt to correct for this might introduce other biases. Hence, we arbitrarily redefined failure within a field as being a score more than one-half standard deviation below the mean of the students in the field. Thus, about 30% of the students in a field are treated as failing. The effect of this is to increase the amount of variation in the probability of failure among the students in the sample.

The probability of success was created as follows. We estimated a grade for each student in each field. We treated the estimated GPA as being the midpoint for a distribution of possible grades, and the standard error of the regression defined the dispersion parameter. The portion of the distribution above the failure point then determined the probability of success in the field for that student.

For the expected value calculations, the probability of success was simply multiplied by the mean earnings in the field to get expected earnings by field. Our prediction was simply that each person would

13 The College Entrance Examination Board (1983a), pp. 21-22.




choose the field with the highest expected value. Using this method on all fields, we predicted field choice at a rate significantly above chance.'4

For the expected utility calculations, it was assumed that people are somewhat risk averse. Thus, we used the square root of mean starting salary times probability of success to determine field choice. This effectively reduced the weight on mean earnings differences in field choice and increased the weight on probability of success. The results were essentially unchanged.

Our method of defining probability of success may appear to be somewhat arbitrary. However, it is the differences in expected GPAs across fields that is important. These differences are determined by the regressions. We simply chose a cutoff point that would allow the estimated probability of success to reflect the variation in expected GPAs. This would not happen if the transformation found that all students had very high probabilities of passing all fields.

References

Benbow, C. P., and Stanley, J. C. "Sex Differences in Mathematical Ability: Fact or Artifact?" Science 210 (1980): 1262-64.

Berryman, Sue E. Who Will Do Science? New York: Rockefeller Foundation, 1983.

Blakemore, Arthur E., and Low, Stuart A. "Sex Differences in Occupational Selection: The Case of College Majors." Review of Economics and Statistics 66 (February 1984): 157-63.

Blaug, Mark. "Human Capital Theory: A Slightly Jaundiced Survey." Journal of Economic Literature 14 (September 1976): 827-55.

College Entrance Examination Board. ATP Guide for High Schools and College, 1983-84. Princeton, N.J.: Educational Testing Service, 1983. (a)

. National Report on College Bound Seniors, 1983. Princeton, N.J.: Educational Testing Service, 1983. (b)

Using Scholastic Aptitude Test Scores in Counseling Prospective Graduate and Law Students. Statistical Report SR-63-62. Princeton, N.J.: Educational Testing Service, October 1963.

College Placement Council. CPC Salary Survey: A Study of 1982-1983 Beginning Offers. Formal Report no. 3. Bethlehem, Pa.: College Placement Council, July 1983.

Everitt, B. S. "Moments of the Statistics Kappa and Weighted Kappa." British Journal of Mathematical and Statistical Psychology 21 (May 1968): 97-103.

Goodison, Marlene B. A Summary of Data Collected from Graduate Record Examination Test Takers during 1981-1982. Data Summary Report no. 7. Princeton, N.J.: Educational Testing Service, June 1983 (also computer tape of above data).

14 Logit regressions were run for the two-field choices and were entirely consistent with the results presented here.



144 Paglin/Rufolo

Graduate Management Admission Council. A Demographic Profile of Can- didates Taking the Graduate Management Admission Test during 1980- 81. Princeton, N.J.: Educational Testing Service, 1982.

McDowell, John M. "Obsolescence of Knowledge and Career Publication Profiles." American Economic Review 72 (September 1982): 752-68.

Muellbauer, J. "Household Production Theory, Quality, and the 'Hedonic Technique.' " American Economic Review 64 (December 1974): 977-94.

Polachek, Solomon W. "Occupational Self-Selection: A Human Capital Approach to Sex Differences in Occupational Structure." Review of Eco- nomics and Statistics 63 (February 1981): 60-69.

. "Women in the Economy: Perspectives on Gender Inequality." In Comparable Worth: Issue for the 80's, vol. 1. Washington, D.C.: U.S. Commission on Civil Rights, 1984.

Rosen, Sherwin. "Hedonic Prices and Implicit Markets: Product Differ- entiation in Pure Competition." Journal of Political Economy 82 (January/ February 1974): 34-55.

Roy, A. D. "Some Thoughts on the Distribution of Earnings." Oxford Economic Papers 3 (June 1951): 135-46.

Scientific Manpower Commission. Salaries for Scientists, Engineers, and Technicians, 11th ed. Washington, D.C.: Scientific Manpower Com- mission, 1983.

Tinbergen, Jan. "Some Remarks on the Distribution of Labour Income." International Economic Papers 1 (1951): 195-207.

Welch, Finis. "Linear Synthesis of Skill Distribution." Journal of Human Resources 4 (Summer 1969): 311-27.

Willis, Robert J. "Wage Determinants: A Survey and Reinterpretation of Human Capital Earnings Functions." In Handbook of Labor Economics, vol. 1, edited by Orley Ashenfelter and Richard Layard, pp. 525-62. Amsterdam: North-Holland, 1986.

Willis, Robert J., and Rosen, Sherwin. "Education and Self-Selection." Journal of Political Economy 87, no. 5, pt. 2 (October 1979): S7-S36.



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