Tuition Growth and the Value of a College Degree
Antony Davies, Ph.D.[1]
Research Fellow, Mercatus Center, Capitol Hill Campus
Associate Professor of Economics
Duquesne University
Pittsburgh, PA 15282
Thomas W. Cline, MBA, Ph.D.
Associate Professor of Business and Economics
Alex G. McKenna School of Business, Economics, and Government
Saint Vincent College
Latrobe, PA 15650
JEL Classifications: G12, I21, I22, I28
Keywords:Costs, Human Capital, Rate of Return, Student Financial Aid, State and Federal Aid, Economic Impact, Education
Abstract
Much dispute over the value of a college degree arises from the mistreatment of tuition as an expense rather than as an investment. Using tools typically employed in the evaluation of financial investments, this paper compares the cost of a college education to the expected return from holding a college degree. For each of the past twenty-seven years, we look at information available to 18-year-olds at the time that they would choose between entering the workforce and pursuing a college degree. We measure expected differences in earnings, earnings growth, unemployment, and labor participation to determine the ex ante expected value of holding a college degree. We find that, although tuition and fees have been growing at better than twice the rate of inflation, the expected monetary return from holding a college degree has been growing even faster. The result is that, for the median student, the expected value of a college degree, net of tuition and fees, has almost doubled in present value terms.
1. Introduction
Numerous studies have found evidence of moderate to high returns to higher education. These studies agree in direction, if not magnitude, across countries. Among these are studies of earnings and education data from Norway (Alstadsæter, 2004), China (Heckman and Li, 2003), Taiwan (Chuang and Chao, 2001), Germany (Daly et al., 2000), Australia (Miller et al., 1995), Canada (Doiron and Riddell, 1994), the United Kingdom (Hough, 1994), and the United States (Cohn and Hughes, 1994).[2] These and other studies employ one or more of three methodologies for assessing the value of education: (1) the so-called “short-cut” method, (2) the Mincer method, and (3) the internal rate of return method.
The short-cut method gives the rate of return per year of education as
(1.1)
where Em is the mean earnings for people with m years of education, and r is (approximately) the growth rate per year of education.[3]
The Mincer method (Mincer, 1974) employs a simple linear regression model wherein the log of wages is regressed on years of education, years of work experience, and other wage determinants.[4] The value of the coefficient attached to years of education is taken as the rate of return per year of education (cf. Psacharopoulos, 1994).
The internal rate of return method employs the traditional IRR function wherein the present discounted value of the earnings due to the education are set equal to the present discounted costs. The resulting discount rate is the internal rate of return.
This paper expands on the previous literature by examining (1) differences in total compensation (i.e. wages plus benefits) versus wages alone, (2) differences in expected wage growth over an average worker’s career, and (3) differences in the probabilities of unemployment and labor force participation for high school versus college graduates, and by (4) calculating expected return in terms of breakeven, internal rate of return, and net present value measures, and (5) computing the relative risk of a college degree as an investment. Also, this paper shows the earnings the median high school graduate and median college graduate could expect to earn, ex ante, over his/her career. By employing the data in an ex ante fashion, our estimates of the value of a college degree are based only on information that was available to students at the points in time that they would have made the decisions to enter the workforce or to go on for higher education.
2. Issues in Measuring the Value of Education
Previous studies have identified issues involving measuring the value of education: private vs. social returns, selection bias, male vs. female and white vs. black, and survey data collected from firms vs. households. This paper focuses on the individual’s decision to pay for a college education in light of the individual’s expectation of the financial rewards that accrue to the education. As such, I look at private returns – i.e. the net return of higher education to the individual.[5] Selection bias presents a significant problem when evaluating the impact of education on earnings. Specifically, one can argue that those with traits that would, a priori, result in higher earnings (e.g. greater intelligence, self-discipline, etc.) will be more likely to attend college. A partial counterargument is that the value lies not solely in the education, but partially in the degree-as-signal (Belman and Heywood, 1997; Altonji and Pierret, 1996). Thus, there are three possible arguments: (1) that the value of a degree lies in increased labor productivity due to the education, (2) that the value of a degree lies in the signal that the degree conveys, and (3) that the degree has no signaling value and that those who obtain degrees would have earned more regardless of the education.
We find the last argument untenable, as the argument requires irrationality on a massive scale – that every year millions of students would spend multi-billions of dollars on a product that imparts no value. We do not distinguish between the first two arguments, as the purpose of this analysis is to examine the financial value of a college degree, not a college education. While of interest from a causal perspective, from a financial perspective the student’s decision to pursue a degree hinges on the fact of the degree’s value, not on the source of the degree’s value. To draw an analogy, a stock that is guaranteed to yield a constant 10% annual return is a good investment. While interesting from a managerial perspective, why the stock earns a guaranteed 10% return is irrelevant to the investment decision.
Using earnings data for different age cohorts for each year from 1977 through 2003, we construct estimates of the earnings an 18-year-old could have expected to earn both with a college degree and with a high school degree only over the course of his/her career. The two anticipated earnings streams represent the reasonable expectations of 18-year-olds at each year from 1977 through 2003.
While studies have shown marked differences in earnings for males vs. females (Oaxaca 1973; Paglin and Rufolo 1990) and blacks vs. whites (Card and Krueger 1993), the focus of this paper is on earnings of college graduates vs. high school graduates aggregated across gender and race. Psacharopoulos and Patrinos (2002) argue that, in measuring earnings, household survey data is preferable to firm survey data as, when surveying firms, there is a bias toward surveying larger organizations that, by extension, will tend to be located in urban environments. Analyses in this paper are based on household survey data reported by the Bureau of the Census.
3. Financial Benefits of a College Degree
In 1976, tuition and fees at the average private 4-year college were less than 20% of median household income, and tuition and fees at the average public 4-year college were less than 5% of median household income. By 2003, tuition and fees had risen to over 45% of median household income for 4-year private colleges and 11% for 4-year public colleges.[6] Over the past thirty years, tuition and fees inflation has averaged just under 8% annually for both public and private institutions.[7]
We identify four economic benefits to a college degree: (1) Starting compensation. In 2003, the average 25-year-old full time worker with a college degree earned annual wages of $58,500 versus $33,500 for the average 25-year-old full time worker with a high school education.[8] Over the period 1991 through 2003, wages and salaries have averaged only 72% of employee compensation.[9] Adding in employer-paid benefits, the difference in compensation for the 25-year-old college graduate versus the 25-year-old high school graduate in 2003 was almost $35,000. (2) Wage growth. Since 1977, the median income for full time workers with college degrees rose 1.1% more per year than for full time workers with high school diplomas.[10] This difference in growth rates caused the earnings gap between high school and college educated workers to more than quadruple (in real terms) over the past thirty years. (3) Likelihood of unemployment. Since 1970, college graduates have experienced unemployment rates (2.3%) that are less than half those of high school graduates (6.1%).[11] (4) Likelihood of labor participation. Factors that cause workers to drop out of the labor force include work-preventing injuries and prolonged unemployment. It is more likely that a college-educated worker would be able to compete for a job with a high school educated worker than is the reverse. Because college educated workers are less likely to be employed in manual labor jobs, they will also be less likely to suffer on-the-job injuries. In addition, because of the difference in the range of jobs for which they are respectively suited, the likelihood of a given injury being work-preventing for a high school graduate is greater than the likelihood of that same injury being work-preventing for a college graduate. Due to these factors, one would expect the likelihood of labor participation to be greater among college-educated workers than among high school educated workers. Over the period 1976 through 2003, 86% of college graduates, but only 75% of high school graduates, were labor force participants.[12]
For the median 18-year-old at time t, let and be, respectively, the median compensations at year t for college educated workers and high school educated workers who are s years older than the 18-year-old at year t. Let , , , and be, respectively, the probabilities of labor participation (for college and high school educated workers) and unemployment (for college and high school educated workers) at year t. At year t, let and be the annual compensation the 18-year-old can expect to earn s years in the future, after completing a college degree, and with a high school diploma, respectively. For the 18-year-old at year t who chooses to pursue a college degree, the expected stream of future compensations is given by
(1.2)
where we assume, conservatively, that the student does not work while in college and does not work after age 65. Similarly, at year t, the 18-year-old can expect to earn
(1.3)
for each year, s, of his/her career if s/he skips college and goes directly into the labor force. Intuitively, (1.2) and (1.3) imply that the 18-year-old forms his/her expectation by (a) looking at workers older than s/he, and (b) assuming that, when s/he reaches the same age as those workers, s/he will be earning (in terms of purchasing power) the same amount as those workers are earning now. Thus the expectations in (1.2) and (1.3) are measured in constant (year t) dollars. Unlike other studies in which earnings are compared ex post, (1.2) and (1.3) represent the median ex ante earnings the student can expect at the time the student makes the decision as to whether or not to attend college.
College vs. High School Earnings Gap
Combining these four economic benefits to a college degree, one can measure the expected earnings gap, or the difference between what the median college graduate and the median high school graduate can expect to earn. In 1977, the median 18-year-old with a high school diploma could expect to earn total compensation (in 1977 dollars) of $700,000 over the course of his/her career – i.e. .[13] By comparison, the median 18-year-old anticipating attaining an undergraduate degree and then entering the workforce could expect to earn total compensation of $1.1 million. The anticipated career-spanning benefit of the college degree in 1977 was the difference of $400,000 (in 1977 dollars). By 2003, the median 18-year-old with a high school diploma could expect to earn total compensation of $1.5 million (in 2003 dollars) over the course of his/her career. But, with a college degree, that same worker could expect to earn $3.4 million. Thus, by 2003, the anticipated career-spanning benefit of a college degree had increased almost five-fold to $1.9 million. Table 1 shows the expected compensations as perceived by the median 18-year-old in 1977, , and . Table 2 shows expected compensations as perceived by the median 18-year-old in 2003,, and .
[Insert Table 1 here]
[Insert Table 2 here]
Evaluating College as an Investment
We employ the three typical methods for evaluating a financial investment: (1) breakeven point – the number of years required for the income generated from an investment to pay for the investment (assuming no time-value adjustments), (2) internal rate of return – the effective interest yield the investment generates, and (3) net present value – the amount of cash-in-hand today that, if invested at current interest rates, would yield a stream of payments over time identical to the income stream generated by the investment. While previous studies have used IRR in valuing a college degree, IRR is inappropriate when comparing investments of different magnitudes. For example, a $100 investment that yields an IRR of 50% would be considered by most to be inferior to a $10,000 investment that yields an IRR of 25%. As the cost of education has changed significantly, the net present value is a more appropriate measure for comparing the value of a degree over time. Looking at these three measures for evaluating an investment, we find that despite increases in tuition, the value of a college degree has been steadily rising.
Breakeven point. In 1977, the cost of tuition and fees for four years at an average 4-year college plus foregone income from delayed entry into the workforce totaled almost $47,000 for private institutions and $39,000 for public institutions.[14] A student who graduated college at age 22 could expect to earn enough additional income as a result of the degree to completely pay off the investment approximately 9.6 years after matriculation.[15] By 2003, the average cost of four years’ of tuition and fees plus foregone earnings had risen to $167,000 at private institutions and $106,000 at public institutions. But, the additional income the college graduate could expect to earn had risen even faster so that the average college graduate could expect to pay off the investment within 9.1 years of matriculation (see Figure 1).
Let the expected tuition and fees for one year of college at year t + s be Tt+s. Let the year t + s cost of attending college (tuition, fees, and foregone compensation) be:
(1.4)
The ex ante expected breakeven period, bt, for the sequence of expected net cash flows associated with attaining a degree is:
(1.5)
[Insert Figure 1 here]
Internal Rate of Return: In 1977, the median student could expect the increased compensation from holding a degree to yield the equivalent of a 15% real rate of return on the price of a private college education and 17% on the price of a public education. By 2003, the median student could expect the real return to be 16% on the price of the private education and 21% on the price of the public education. Over the past 27 years, the rate of return on an investment in a college degree has averaged 2.3 times the return on the Dow Jones Industrial Average and 1.7 times the return on the NASDAQ (see Figure 3). For an anticipated career (including years of college) of n years, we calculate the ex ante internal rate of return, rt, as:
(1.6)
[Insert Figure 2 here]
[Insert Figure 3 here]
Net Present Value: In 1977, the average 18-year-old could equate the increased earnings over time resulting from a degree less the cost of the degree to $160,000 cash-in-hand (in 1977$), or a net present value of $472,000 in 2003$.[16] Specifically, if we took two identical 18-year-old high school graduates in 1977, gave one of the equivalent of $472,000 (in 2003$) and sent him into the job market, gave the other nothing and told her to go to college and pay her own way, by the end of their careers, the two would have been equally well off financially. By 2003, the net present value of a degree had increased to over $800,000 (in 2003$). The ex ante expected net present value (NPV) at age 18, is given by:
(1.7)
where is the long-term riskless real interest rate. As we have accounted for risk via incorporating the probabilities of labor participation and unemployment, and have accounted for inflation by using current wages of older workers as forecasts for the 18-year-old’s future earnings, the appropriate discount rate is the long-term riskless real interest rate. For the discount rate, we use the average return (over the period 1977 through 2003) on 20-year Treasury Bills (7.3%) less average inflation (4.3%).
[Insert Figure 3 here]
Relative Risk: An asset’s beta as defined in the Capital Asset Pricing Model (CAPM) gives us a traditional measure of a firm’s risk relative to the market as a whole. Using our estimates of the internal rate of return on a college degree from 1977 through 2003 as the return on the “security” (rt), 1-year constant maturity Treasury Bill rates as the riskless rate (), and the annual growth in the S&P 500 from year t – 1 to year t as the market return (), we estimate the “beta” for a college degree via constrained OLS applied to the CAPM:
(1.8)
We obtain a beta of 0.16 using the average cost of private colleges and 0.23 using the average cost of public colleges. This indicates that the risk associated with an investment in a college degree is significantly less than the risk associated with an investment in the market as a whole. One might argue that since wage income comprises the lion’s share of GDP, the beta on the returns to a college degree should be close to one. This argument suffers from aggregation bias. During recessions, high school graduates bear a greater unemployment burden than do college graduates. In fact, over the period 1970 through 2001, the standard deviation of annual unemployment rates for high school graduates was 2.7 times that for college graduates. Thus, one should expect the risk associated with an investment in a college degree to be strictly less than overall market risk.[17]
4. Conclusion