SOME EVIDENCE ON NEGATIVE RETURNS TO GRADUATE EDUCATION

LYNN MAXWELL University of Wyoming

The evidence provided in this paper indicates that the private rate of return for males with doctor’s degrees and females with master’s degrees is positive, bur the private rate of return for males with master’s degrees is negative. Until recently, the estimation of private rates of return for graduate schooling has been limited by the fact that Census data classifies all graduate schooling in one category of “five or more years of college.” Faced with insufficient Census data, Orley Ashenfelter and Joseph Mooney used a cohort of Woodrow Wilson fellows to estimate private rates of return for some graduate education [ 1 1 . Their results indicated that the point estimates of private rates of return for males with M.A. degrees varied from 1.6 to 7.5 percent, while those for Ph.D.’s ranged from 3.5 to 10.8 percent.

In order to determine the private rates of return presented here, infor- mation on age, sex, schooling, place of residence and earnings was gathered from a questionnaire mailed to former University of Nebraska students. This survey provided a cross-sectional sample of 627 males and 168 fe- males with full-time earnings for the year 1967. The sample has three important limitations: (1 ) The interaction of ability and income could not be controlled. (2) The degrees of the respondents represented a het- erogeneous group of fields of study. Of the doctor’s degrees thirty-seven percent were Ph.D.’s, thirty-four percent were D.D.S.’s, and the others were professional degrees equivalent to a doctorate granted in the College of Law. (3) The data are based on schooling at the University of Nebraska; hence conclusions in regard to rates of return may not be valid for similar cohorts elsewhere in the United States.

The important feature of the sample is that the respondents ranged in age from twenty-four through sixty-five. Thus, it was possible to estimate complete ageearnings profiles for the specified degree levels.’ Four pro- fdes were estimated from multiple regression equations using the standard least-squares technique. Each regression equation contained two quanti- tative variables, the dependent variable representing annual earnings (Y, ) and the age variable (XI ) . The remaining variables, representing degrees earned (X2 - X4) and place of residence (X, - X,), were dummy variables. Equation (1) was fitted to data for males up through age 30. Equation (2) was fitted to data for males between 31 and 65 years of age and specifies

1. Details of the sample. which represented approximately 40 percent of the individuals who were mailed qucatbnnaires. can be found in 121, from which the numerical results in this paper are taken.

186

MAXWELL: RETURNS TO EDUCATION 187

Equation Constant

Males:

N= 125

N = 502 Females:

N=29

N = 139

(1) -9712

(2) -21837

(3) -2542

(4) -2282

a nonlinear relationship between earnings and age. This method permitted the estimation of a complete nonlinear ageearnings profile where the earnings differentials (as represented by the difference between the re- gression coefficients of the schooling variables) were smaller during the early years in the labor force than in later years. Equations (3) and (4) were used in the same manner to determine the ageearnings profiles for females with master’s degrees. Estimates of annual earnings could not be made for females with Ph.D.’s because of insufficient data. Each age- earnings profile was adjusted for future growth in real income per capita.2

The results of the regressions are presented in Table 1 . The substantial size of the standard errors indicates a large degree of variability in the earnings estimates and hence in the private rates of return based on them.

Table 1 -CONSTANTS AND REGRESSION COEFFICIENTS FOR EQUATIONS USED TO ESTIMATE ANNUAL EARNINGS

Age

X I (Xd2

641* (107) 1473* -15* (157) (1.8)

315* (102)

(112) (1.2) 328* -4*

Degree Bache- h4aa- Doc- lor’s ter’s tor’s

x2 x3 x4

1467 862 3229+ (830) (1129) (1451) 2921* 424 8789+ 1191) (1339) (1335)

1167 1308 (588) (641) 2292* 2886* (813) (860)

Region North- South West east

xS x6 x7

536 376 1487 (1119) (730) (676) 4116*1292 2024.

(1323) (862) (679)

-2066* 498 -16 (804) (513) (633) 3058* 113 2408* (834) (703) (495)

R 2

(SYJ

.38 (2754)

.3 1 (6746)

.48 (994)

.30 :2472)

Standard errors are noted in parentheses under the regression coefficients. A star indicates that the regression coefficient is significant at the five percent kvel.

For each year in the labor force, income differentials were estimated from the ageearnings profiles. Males with a doctorate were assumed to have completed a four-year program and t o receive earnings from age twenty-seven through age sixty-five. Persons with a master’s degree were assumed to have completed a one-year program and to have earnings from age twenty-four through sixty-five. The extra income attributable to a higher degree was found by subtracting each income in the age- earnings profile for a bachelor’s degree from the corresponding income

2. The income estimate for each age was multiplied by (1 + .022)‘, where .022 h the yearly average rate of growth of per capita real personal income, 1947-65, computed from (5, p. 1561, and 2 is the number of years in the labor force. Becaw of the poaoible discontinuity at ages thirty and thirty-one. a nine-year moving average w a s wed to provide a continuous poflle.

188 WESTERN ECONOMIC JOURNAL

for the higher degree level. Table 2 shows income differentials at selected ages for residents of the North Central United state^.^ Table 2-ESTIMATED ANNUAL INCOME DIFFERENTIALS BY AGE FOR MALES

AND FEMALES IN THE NORTH CENTRAL REGION WHO COMPLETED THEIR SCHOOLING AT THE UNIVERSITY OF NEBRASKA IN 1967

Males Females Master's Doctor's Master's

Age Desrw Degree Degree

25 -810 -3 35 -3406 5166 525 45 -4612 6531 720 55 -5739 8200 93 1 65 -6966 10852 1237

Source: [ 2, pp. 79-82]

An iterative computer technique was then used to solve for the rate of discount, r , that would equate private costs of schooling, K, with the present value of the expected stream of income differentials. The private costs of schooling, assumed to be incurred in the year preceding receipt of the degree, were estimated as the direct cost of tuition and fees ($433 for one year of full-time work), plus opportunity costs, estimated as the earnings of individuals with a bachelor's degree at the same ages. The private costs were $33,216 for males with a doctor's degree, $7,040 for males with a master's degrde, and $6,457 for females with a master's degree.

The two positive rates of retutn were computed by the formula

t = 1.2, . . . n

where (Y,, - YBt) is the earnings differential in the f-th year during the n years that individuals with graduate degrees receive earnings. The results were:

Males, doctor's degree . . . . . . . . 12.6% Females, master's degree . . . . . . 6.3%

Since the net addition to income for males from a master's degree was negative: the private rate of return would also be negative. This result

3. Two of the dummy variable6 had to be eliminated to estimate the equation parameters. " h o e eliminatnd vmre (1) undergraduate study of 1 4 yevr without the awnrdmg of a degree and (2) residence in the North Central region. Income differenthla for the other regions of the U.S. are given in 12, pp. 79-82].

4. The podtive wniny differential. found by M e n f e l t a and Mooney [ 11 and Tolla and Mdichu [ 31 m not ddctly comparable, beawe Aahonfelter and Mooney were concerned only wlth M ~ t s r of M a dopea, and Toner m d Mellchar atlmated duy differentials from the 1966 National Re-r of Scientifi and Technical PenonneI.

MAXWELL: RETURNS TO EDUCATION I89

may be due to the occupational mix of the sample, where fifty-six per- cent of the men with master’s degrees were in the field of teaching, many of them at the elementary or secondary level. Since this field has tradi- tionally been a low-income occupation [4, p. 3531, the overall earnings estimates for males with a master’s degree may be biased downward by the large percentage of teachers in the sample. The University of Nebraska, however, did not award an especially high percentage of master’s degrees to males in education. The figure for males in 1967-68 was 31.1 percent [7, pp. 41-85] as compared with 27.2 percent for all institutions in the United States and 33.0 percent for all public institutions [ 6 , pp. 8-91. These figures would be indicative of the possible percentage of U.S. men with master’s degrees in education who are teaching, were it not that some males with this degree do not teach, while others teach without it. If this second group is added to the percentage for all institutions, then the percentage of U.S. males with master’s degrees who are teaching could approximate the percentage in the sample. If this is the case, then it is more likely that the private rate of return for males with master’s degrees in the U.S. is negative.’

The two positive rates of return estimated from the sample are con- sistent with other estimates. For females with a master’s degree, the rate is comparable to estimates using Census data for females with five or more years of college [2, p. 1011. The rate of return for males with a doctor’s degree is approximately the same as that indicated by Ashenfelter and Mooney.

5. An alternative explanation of the negative rate of return for the master’s degree is that the degree is sometimes granted t o those who fail t o make the grade in a Ph.D. program. This type of master’s degree is not specifically granted at the University of Nebraska. Nonetheles, for other m w n s average ability a t the master’s level might be lower than that at the bachelor’s level.

REFERENCES 1. 0.Ashenfelter and J. D. Mooney, “Some Evidence on the Private Returns to Graduate Educa-

tion,” So. Econ. Jour., Jan., 1969, 35, 247-56. 2. L. Maxwell, The Rate of Rerum from Schooling at the Unlwrsity of Nebmtka. Unpublished

doctoral dissertation. Univ. of Nebraska, 1969. 3. N. A. Tolla and E. Melichar, “Studies in the Structure of Economists’ Salaries,” Am. Econ.

Rev., Dec. 1968, 58 (5) Supp. Pt. 2, pp. 56-69. 4. U.S. Department of Commerce, Bureau of Census, V.S. Census ofPopulationr 1960, Summary

Report, PC(1)-1C. Washington 1964. 5. U.S. Department of Commerce, Office of Business Economics, The National Income and Prod-

uct Accounts of the United States. Washington 1966. 6. U.S. Department of Health. Education, and Welfare. Office of Education, Earned Degrees Con-

f e n d . Part A, Summary Report. Washington 1969. 7. -, Earned Degmes Conferred. Part 9, Institutional Data, Washington 1969.