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College degree for everyone?

Introduction

In 2007-2008, the United States experienced a bubble bursting in the housing market, causing one of the largest recessions in its history. While the U.S. economy is still facing a long recovery to the pre-recession levels, there is already an ongoing discussion in the literature and popular press on the next asset bubble to burst and the market for higher education is a likely candidate. There are two sides to this discussion. Studies by Avery and Turner (2012) and OECD (2013), among others, state that a college degree is a worthy investment and a rise in tuition costs is well justified by a corresponding rise in the wage-premium, at least over the lifecycle of a worker. Avery and Turner (2012) show that for an average student, college education in the U.S. is always a positive lifetime net present value investment. OECD (2013) provides similar evidence for OECD countries and shows that the earning differential between college and high school graduates has increased in recent years.

At the same time, a study by Owen and Sawhill (2013) claim that while a college is indeed a worthy investment for some students, it may not be so for all the students, stressing the importance of selecting the right major and the right school. They document a lot of variation in the returns to education, depending on many factors including college, major, and student individual characteristics. Former Secretary of Education William Bennett, in his interview to Yahoo! Finance (Lyster 2013) publicly expressed his concern about the worthiness of college education for all students and essentially supported the Owen and Sawhill (2013) study. Fie argued that based on his rate of return calculations, only 150 of 3500 colleges in the U.S. are worth the investment. Furthermore, he stresses that about half of all students who start a four-year university do not finish it. Hence, students should only go to college if they are committed and plan to study a marketable major or attend a top-tier school. In addition, many popular news sources (e.g. Economist 2011, 2012) as well as countless blogs speculated and warned readers about the possible existence of a bubble in higher education.

In this paper, we add to this discussion and show that it is possible to have, on average, a positive net wage premium of a college degree over a high school diploma over the lifetime of a worker. We estimate that a sizeable fraction of the population that acquired a college degree would be better off by not getting a college degree. This proportion depends on tuition costs, opportunity costs of going to college, and survey year. For example, in our benchmark year, 2010, we estimate this proportion to be around 13 %. Our estimates are in line with the recent data on delinquency rates on student loans. In 2010, 8.97 % of all student loans were 90+ days delinquent. (1) Lending against improper valuation of an asset can cause serious damage to the functioning of the financial system with the consequential severe distress to the whole macroeconomy.

What makes education valuation especially troubling is the fact that unlike past asset bubbles, bankruptcy does not erase student debt. Hence, the wage premium and return on college education are important factors to prospective students deciding whether or not to pursue higher education. If college is overvalued, students may shy away from paying top dollar for education, choosing less costly education, trade school, or entering the workforce. Also, wage premiums and returns are important to institutions of higher education. Those institutions that do not have much endowment to cushion a reduction in prices could begin to cut unnecessary educational spending, or shift to a more online educational model where they can benefit from economies of scale (Cronin and Horton 2009). On the other hand, if education is fundamentally valued, colleges should feel safe about continuing to raise tuition prices.

In this paper, we estimate and compare distributions of fundamental values of a college degree and a high school diploma. We define fundamental values of a college degree and a high school diploma as their corresponding net present discounted values. We use lifetime earnings of college graduates, tuition costs, and opportunity costs of going to college to estimate a net present discounted value of a college degree, and lifetime earnings of high school graduates to estimate a net present discounted value of a high school diploma. We show that the median net present discounted value of a college degree is greater than the median net present discounted value of a high school diploma, regardless of the assumptions about tuition costs, opportunity costs for going to college and survey year, supporting Avery and Turner (2012). At the same time, we show that lower percentiles of net present discounted value of a college degree are smaller than corresponding percentiles of net present discounted value of a high school diploma. In other words, college graduates located at the lower tail of the wage earnings distribution would be strictly better off by not going to college, supporting Owen and Sawhill (2013). Finally, our estimate of the proportion of the students that are worse off by going to college is in line with the data on delinquency rates on student loans and depends on tuition costs, opportunity costs of going to college, and survey year.

Our study relates to the general literature on the evaluation of pecuniary returns to education. (2) Hansen (1963), in his seminal work, estimates the present value and internal rate of return for different levels of education and finds that four years of college is the most profitable option. Goldin and Katz (1995) examine the wage premium for high school education between 1890 and 1940. They show that the wage premium declined from 1890 to 1930, and then remained constant from 1930 until 1940. Grogger and Eide (1995) employ the National Longitudinal Survey of Youth 1979 data set to show that college wage premium rose sharply in the 1980s and attribute 25 % of the rise to a shift from low-skill to high-skill majors. (3) Recent studies by Goldin and Katz (2007) and Avery and Turner (2012) claim that both earnings and employment prospects for college graduates remain better than for high school graduates. At the same time, Owen and Sawhill (2013) show that there is large variation in the return to education depending on the institution attended, field of study, and student individual characteristics. The main goal of our study is to demonstrate that it is possible to have, on average, a positive net premium to a college degree and at the same time to show that a significant fraction of college graduates are strictly better off by not going to college. Essentially we extend the Avery and Turner (2012) approach to take into account opportunity costs of going to college (indirect costs), and variations in the tuition costs: both public and private institutions (direct costs of going to college).

Motivation

We begin our discussion by exploring in more detail three characteristics of the market for higher education. First, we examine the price of higher education (tuition costs).

Second, we discuss the financing in the market for higher education (amount of student loans). Third, we examine how successful individuals are in repaying their student loans (delinquency rates on student loans).

In general, asset bubbles arise if the price of an asset irrationally deviates from its fundamental value. In Fig. 1, we plot several price indexes: average tuition costs, average housing prices, and CPI for the period 1987 to 2010. Both tuition costs and housing prices have risen by more than 300 % since 1987. (4) While home prices collapsed from their peak in 2006 and caused the Great Recession, tuition costs have continued their steadily rise reaching 336 % in 2010.

In Fig. 2, we plot the dynamics of total debt balances in the three largest consumer credit markets: mortgages, student loans and credit cards for the period 20032013. The mortgage market (right scale) is still the largest in terms of the size, though it experienced a large decline from its peak value in the third quarter of 2008. We observe a similar trend with the credit card debt (left scale), which peaked in the fourth quarter of 2008, and then slowly declined. Both declines can be attributed to the recent recession. At the same time, we observe a different development in the student debt market. Student debt has continued to steadily rise throughout the recent recession, eventually surpassing credit card debt in the second quarter of 2010 and becoming the second largest consumer credit market after the mortgage market.

Next, we discuss how successful individuals are in paying back their student loans. In Fig. 3, we plot the delinquency rates in the three largest consumer credit markets. (5) Delinquency rates in both mortgage and credit card markets behave similarly to their corresponding debt markets (Fig. 2). Delinquency rates on mortgages peaked to 8.89 % in the first quarter of 2010, and declined rapidly reaching 4.31 % in the third quarter of 2013.

Similarly, delinquency rates on credit card debt peaked to 13.27 % in the second quarter of 2010, and then declined to 9.36 % in the third quarter of 2013. However, the dynamics of delinquency rates on student loans is different than on mortgages and credit cards. They have continued their steady rise reaching 11.83 % in the third quarter of 2013, surpassing delinquency rates on both mortgages and credit card debt. It is worth noting that in the third quarter of 2013 the delinquency rate on student loans is equal to 11.83% and it is already higher than the delinquency rate on credit card loans for the same quarter, and higher than the peak delinquency rate on mortgages during the recent recession, that reached a maximum of 8.89 % in the first quarter of 2010.

We document several warning signs in the higher education market. First, the price of higher education has risen dramatically in recent years (Fig. 1). While the price itself does not imply the existence of an asset bubble per se, all of the past asset bubbles were characterized by sharp increases in the asset prices. Moreover, for the period 1987-2010, tuition costs have already risen by a larger percentage (336.6 %) than housing prices (336.4 %) in their pre-recession peak in 2006.

Second, similar to the housing market, higher education is often financed with debt, which is now the second largest type of consumer debt in the U.S. economy, with more than $1 trillion of student loans outstanding in the third quarter of 2013. The Federal Advisory Council recently warned the Fed that the growth in student loan debt "parallels to the housing crisis." Third, a large proportion of students who took out these loans are not able to pay them back. Moreover, the share of loans that are delinquent in the student debt market is already larger than in any other consumer credit market. All these facts suggest that the U.S. market for higher education may display not only symptoms of an asset bubble, but probably already the beginning of the bubble bursting. In the next section, we will apply the classical theory of asset pricing to the market for higher education and estimate what a college degree is really worth.

Model

The classical definition of the fundamental value of any asset is the present discounted value of future cash flows generated by this asset. We treat a college degree as an asset and the fundamental value of this asset should be equal to the present value of all future cash flows generated from a college degree. To be more formal, we set this fundamental value equal to the present discounted value of future wages of a college graduate minus the tuition cost and minus the opportunity cost of attending a college. In order to determine whether it pays off to go to college, we compare this value to the present discounted value of future wages of a high school graduate. Extending Avery and Turner (2012), we define the fundamental value of a college degree as:

[MATHEMATICAL EQUATION NOT REPRODUCIBLE BY ASCII], (1)

where [FV.sub.college] is the fundamental value of a college degree, [MATHEMATICAL EQUATION NOT REPRODUCIBLE BY ASCII] is present value of wage earnings for a college graduate, T is a number of working years, [beta] is a discount factor, and exp is the level of experience of a college graduate. We assume that all students spend four years in college. Hence, we multiply [MATHEMATICAL EQUATION NOT REPRODUCIBLE BY ASCII] by

1/[[beta].sup.4] to account for a four-year delay before students can enjoy the earnings of a college graduate. The second term, [MATHEMATICAL EQUATION NOT REPRODUCIBLE BY ASCII] is the present value of tuition costs, where

Tuition is per year real tuition at a four-year institution either public or private. The last term, OpportunityCost is defined as lost wages while in college.

Our definition of the present value of going to college is an extended version of the one used by Avery and Turner (2012). First, we consider both private and public tuition, while Avery and Turner (2012) use only public tuition costs. (6) Second, to the best of our knowledge, we are the first study to introduce and estimate the opportunity cost of going to college.

We set the opportunity cost of going to college equal to the present discounted value of the wage earnings of a high school graduate that she would have earned by working for four years instead of going to college. We define it as:

OpportunityCost = [MATHEMATICAL EQUATION NOT REPRODUCIBLE BY ASCII] (2)

The fundamental value of a high school diploma is given by:

[FV.sub.High School] = [MATHEMATICAL EQUATION NOT REPRODUCIBLE BY ASCII] (3)

where [FV.sub.High School] is the fundamental value of a high school diploma, [MATHEMATICAL EQUATION NOT REPRODUCIBLE BY ASCII] is the present value of wage earnings for a high school graduate, T is a number of working years, [beta] is a discount factor, and exp is the level of experience of a high school graduate.

Data and Methodology

We use March Current Population Survey (CPS) (King et al. 2010) for the period between 1965 and 2011 and restrict our sample to white male workers with either a high school diploma (12 years of schooling), or a college degree (16 years of schooling) that worked more than 35 hours per week and no less than 40 weeks in the prior year, were not students in the prior year, and had no allocated earnings. (7) Following Avery and Turner (2012), we employ the following estimation procedure:

Step 1: For each survey year, education category, and individual worker we transformed nominal annual wage earnings into real wage earnings using the 2008 gross domestic product (GDP) Personal Consumption Expenditures (PCE) Price Index. Then, we re-weight these real earnings using the sampling weights provided by CPS.

Step 2: For each survey year, we divide our sample into two: one with only high school graduates and one with only college graduates.

Step 3: Following Avery and Turner (2012), we define experience in the earnings year (which is a previous calendar year), as the minimum of age minus years of education minus seven, and age minus seventeen. We set number of working years, T equal to 38 and then divide each sample into T experiences. Essentially, for each survey year, each education category, and each experience we have a separate sample.

Step 4: For each experience in each education category and survey year, we compute 99 percentiles of real wage earnings.

Step 5: Using percentiles obtained in Step 4, we compute 99 percentiles of fundamental values of college degree and high school diploma for each survey year using Eqs. (5) and (6):

[MATHEMATICAL EQUATION NOT REPRODUCIBLE BY ASCII] (5)

[MATHEMATICAL EQUATION NOT REPRODUCIBLE BY ASCII] (6)

where [P(*).sub.i],i denotes i-percentile and i = [bar.1,99]. To put it differently, Eqs. (5) and (6) are rewritten Eqs. (1) and (3) in percentiles form.

Results and Discussion

Following our estimation procedure we compute distributions of the fundamental values of a college degree and a high school diploma (all 99 percentiles) for calendar years 1964 and 2010 and plot them in Figs. 4 and 5. (8) We use a dotted line to denote the distribution of the fundamental value of a high school diploma. A solid line denotes the distribution of the fundamental value of a college degree when all costs of going to college are zero. In between, we have distributions of the fundamental values of a college degree with different assumptions about the costs. We use a long dashed line to denote the distribution of the fundamental value of a college degree with public tuition only (opportunity costs of going to college are zero), a short dashed line for private tuition only (opportunity costs of going to college are zero), a square dotted line denotes the distribution of the fundamental values of a college degree with public tuition and non-zero opportunity costs of going to college, and finally a long dashed dotted line denotes the distribution of the fundamental value of a college degree with private tuition and non-zero opportunity costs of going to college. In order to determine for which individuals it pays off to go to college, we need to establish the relationship among those distributions. If the distribution of the fundamental value of a high school diploma (dotted line) is located below all other distributions, it would imply that it pays off to go to college for everybody regardless of the costs. However, if a black solid line (high school) is above any other line for at least some percentiles, it implies that some students would be better off by not going to college.

In Fig. 4 we plot these distributions for 1964. We infer that the distribution of the fundamental value of high school graduates is strictly below the distribution of the fundamental value of college degree regardless of our assumptions about the costs of a college degree. Hence, in 1964 it paid off to acquire a college degree. However, in 2010 the relative position of these distributions, which are plotted in Fig. 5, is different. We can conclude that the distribution of the fundamental value of a high school diploma is above the distributions of fundamental values of a college degree at lower percentiles.

In Fig. 6, we plot just the first 25 percentiles from Fig. 5. The fundamental value of a high school diploma is below the fundamental value of a college degree only when costs are either zero or equal to public tuition. In other words, in 2010 a college degree is net positive investment only for students who paid public tuition and experienced no opportunity costs of going to college. This result is in line with Avery and Turner (2012). They consider only public tuition, and show that a college degree is net positive investment for all students. (9) However, when we introduce opportunity costs of going to college to public tuition, or consider private tuition, instead of public, some of the students would be strictly better off by not going to college.

For example, the lowest 13 percentiles of college graduates that experienced opportunity costs and paid private tuition costs would be strictly better off by not going to college. This result is in line with the data on delinquency rates on student loans plotted in Fig. 3. In 2010, around 9 % of all student loans were 90+ days delinquent. If we assume that students pay public tuition costs and incur opportunity costs, then students at the second and third percentiles would be better off by not going to college. (10) It is also worth noting that regardless of the assumptions about the costs, it always pays off to go to college for any individual located at the median of the distribution. Furthermore, the average return to higher education is also always positive.

Since both direct (tuition costs) and indirect costs (opportunity costs of going to college) affect the returns to education, especially for college graduates located at the lower tail of the earnings distribution, we compare the changes in both costs between 1964 and 2010. In Table 1, we display these changes. (11)

A few observations emerge from Table 1: First, different percentiles of opportunity costs have changed by different amounts between 1964 and 2010 with larger variations in the tails of the distribution. Second, both public and private tuitions have risen by larger percentages than opportunity costs, with the exception of the lower tail of the distribution of opportunity costs. Third, opportunity costs are similar in size to direct costs and hence students should take them into account when making a decision to go to college. For example, for 2010 public tuition is below the 25th percentile of opportunity costs, while private tuition is below the 90th percentile. (12)

Conclusion

In this study, we show that both direct costs and indirect costs do affect and may significantly reduce the returns to higher education. While in 1964, a college degree was still a positive net investment regardless of the costs, it was no longer the case in 2010. We demonstrate under reasonable assumptions that up to 13 % of college graduates would be better off by not going to college, supporting recent data on the delinquency rates on student loans. Our results are consistent with the recent literature. We demonstrate that higher education is on average a net positive investment (Avery and Turner 2012). At the same time, we show that some students are worse off by going to college (Owen and Sawhill 2013).

Essentially, we treat college education as an asset, and evaluate the net monetary value of this asset. However, some individuals may decide to go to college for different reasons than just financial gains. For example, they may seek unique college experience, social interaction with their peers or access to consumer credit markets. Hence, there exists a different approach to valuing education, which is based on the individual non-pecuniary returns or broad social returns to education. These non-monetary returns capture the impact of education on local communities, individual health outcomes, individual family outcomes and overall health of the economy. For example, Moretti (2004) shows that the number of college graduates increases the wages of high school graduates in the local communities. Mirowski and Ross (2003) show the positive link between college education and health outcomes. However, as they point out the causality of the effect is unclear. Brand and Davis (2011) show that college education reduces the fertility rates. Finally, Schwartz (2010) shows that higher education improves family stability for college graduates. These non-pecuniary benefits may have non-trivial effects on the value of education and hence may alter our results. However, a proper identification and evaluation of non-pecuniary returns would require a much richer dataset than CPS. Furthermore, when considering non-pecuniary benefits, we would also need to take into account non-pecuniary costs (negative spillovers) of higher education, in particular the non-pecuniary costs experienced by the college graduates who are in default on their student loans. We already stressed that bankruptcy does not erase student debt. Hence, we believe that the effects of a college degree on health outcomes and family stability can be quite different for the students in default. Furthermore, the social costs may also be non-trivial. For example, some riskaverse students who should go to college would choose not to attend because they realize that default rates on student loans are at their historic highs. Hence the quality of students may be lower than the socially optimal level. Fundamentally, a policy maker faces a trade-off: on one hand the social benefits of higher education may outweigh any individual costs in the long run, and on the other hand it is not clear what to do with so many students defaulting on their student loans in the short ran. Should a policy maker take them into account, especially with elections every 4 years? We believe that it is a very important and interesting question, and worth further investigation.

One of the shortcomings of our paper is that we assume a perfect correlation between percentiles of fundamental values of college degrees and high school diplomas. For example, if a worker with a high school diploma is located at the 10th percentile of the earnings distribution, this worker would also be located at the 10th percentile of the earnings distribution of college graduates. In reality, it may not be the case. For instance, a college graduate located at the 10th percentile of the earnings distribution may be located at the 25th percentile of the earnings distribution of high school graduates. Thus, this would significantly decrease the net return to higher education for that student. The opposite can also be true. Hence, when we compare lifetime returns of a college degree to lifetime returns of a high school diploma, some individuals may have more to lose than it seems by going to college.

DOI 10.1007/s11294-015-9527-y

References

Avery, C., & Turner, S. (2012). Student loans: do college students borrow too much or not enough? Journal of Economic Perspectives, 26(1), 165-192.

Brand, J. E., & Davis, D. (2011). The impact of college education on fertility: evidence of heterogeneous effects. Demography, 48(3), 863-887.

Cronin, J.M., & Horton, H. H. (2009). Will higher education be the the next bubble to burst? The Chronicle of Higher Education. May 22. http://chronicle.com/article/Will-Higher-Education-Be-the/44400. Accessed 12 2014.

FRBNY. (2013). Quarterly report on household debt and credit, Federal Reserve Bank of New York, November 2013. http://www.newyorkfed.org/research/national_economy/householdcredit/ DistrictReport_Q32013.pdf. Accessed 12 August 2014.

Goldin, C., & Katz, L. F. (1995). The decline of non-competing groups: Changes in the premium to education, 1890 to 1940. NBER Working Papers, No. 5202, August 1995.

Goldin, C., & Katz, L. F. (2007). The race between education and technology: The evolution of U.S. educational wage differentials, 1890 to 2005. NBER Working Papers, No. 12984, March 2007.

Grogger, J., & Eide, E. (1995). Changes in college skills and the rise in the college wage premium. Journal of Human Resources, 30(2), 280-310.

Hansen, W. L. (1963). Total and private rates of return to investment in schooling. Journal of Political Economy, 77(2), 128-140.

Hout, M. (2012). Social and economic returns to college education in the United States. Annual Review of Sociology, 38, 379-400.

Katz, L. F., & Autor, D. H. (1999). Changes in the wage structure and earnings inequality. In O. Ashenfelter & D. Card (Eds.), Handbook of labor economics (Vol. 3, Part A, pp. 1463-1555). Amsterdam: Elsevier.

King, M., Ruggles, S., Alexander, J. T., Flood, S., Genadek, K., Schroeder, M. B., Trampe, B., & Vick, R. (2010). Integrated public use microdata series, current population survey: Version 3.0. [Machinereadable database], Minneapolis: University of Minnesota.

Lyster, L. (2013). Only 150 of 3500 U.S. Colleges Are Worth the Investment: Former Secretary of Education. Yahoo! Finance. December 23. http://finance.yahoo.com/blogs/daily-ticker/only150-3500-u-collegesworth-investment- former-132020890.html. Accessed 12 August 2014.

Mirowski, J., & Ross, C. E. (2003). Education, social status, and health. Hawthorne: Aldine Transaction.

Moretti, E. (2004). Estimating the social return to higher education: evidence from longitudinal and repeated cross-sectional data. Journal of Econometrics, 727(1-2), 175-212.

OECD. (2013). Education at a glance 2013: OECD indicators. OECD Publishing. doi: 10.1787/eag-2013-en.

Oreopoulos, P, & Petronijevic, U. (2013). Making college worth it: a review of the returns to higher education. The Future of Children, 23(1), 41-65.

Oreopoulos, P., & Salvanes, K. G. (2011). Priceless: the nonpecuniary benefits of schooling. Journal of Economic Perspectives, 25(1), 159-84.

Owen, S., & Sawhill, I. (2013). Should everyone go to college? Center on children and families atbrookings. CCF Brief # 50. Washington, DC: Brookings Institution.

Schwartz, C. R. (2010). Pathways to homogamy in marital and cohabiting unions. Demography, 47(3), 735753.

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The Economist. (2012). Higher education: Not what it used to be. December 01. http://www.economist.com/ news/united-states/21567373-american-universities-represent-declining-valuemoney-thcir-studcnts-notwhat-it. Accessed 12 August 2014.

(1) Wc used delinquency rates provided by the Federal Reserve Bank of New York (FRBNY 2013).

(2) There are also potentially significant non-pecuniary returns to higher education. For example, Oreopoulos and Salvanes (2011) show that more schooling reduces the likelihood of getting divorced, having mental diseases, or teenage birth. Similarly, Hout (2012) shows that on average college graduates experience greater economic success, better health outcomes and family stability. Furthermore, Oreopoulos and Petronijevic (2013) stress that more education helps individuals to secure jobs that bring a greater sense of success, and allows more individual independence and creativity.

(3) A good summary of the previous research can be found in Katz and Autor (1999).

(4) All three price indexes were adjusted to 100 in 1987. The period started in 1987, since it was the first available year for the Case-Shiller home price index.

(5) The delinquency rates are the percentage of all loans that are 90+ days delinquent

(6) To be precise Avery and Turner (2012) considered just tuition (no room and board); we include full costs: tuition; room and board and fees.

(7) We have data for tuition costs only for the period 1964-2010, hence we restricted our sample to 1965-2011, since survey year corresponds to the previous calendar year. In other words, the 2011 survey year corresponds to the 2010 calendar year.

(8) We did this exercise for all available calendar years from 1964 to 2010. These results are available upon request. We show the results for only the first and last available calendar years due to the length limitations.

(9) Avery and Turner (2012) use only tuition, they did not include room and board, and other fees.

(10) We construct the distribution of opportunity costs. It is possible that the first percentile of this distribution is much smaller than the second percentile. In other words, it does not pay to go to college for an individual located at the second and third percentile, but it is worthwhile for the individual located at the first percentile.

(11) Tuition costs are present discounted values of the full cost of getting a degree (tuition, room and board, and other fees) accumulated over four years. For 1964 we use tuition costs for the academic year 1964-1965. For 2010 we use tuition costs for the 2010-2011 academic year. Data: U.S. Department of Education: National Center for Education Statistics.

(12) To be precise public tuition is below the 23rd percentile, while private is below the 87th. Table 1 shows just select percentiles. The fall table (all percentiles for all survey years) is available upon request.

Vitaliy Strohush vstrohush@elon. edu

[1] Elon University, 2075 Campus Box, Eton, NC 27244, USA

Vitaliy Strohush [1], Justin Wanner [1]

Published online: 29 May 2015 [C] International Atlantic Economic Society 2015

Table 1 Select percentiles of lost wages while in college, and tuition
costs

Statistics         1964     2010     1964-2010
                                     (% increase)

2nd percentile     4671     25370    543.1
5th percentile     9233     29679    321.4
10th percentile    19578    43961    224.5
25th percentile    42720    61768    144.6
50th percentile    67007    80333    119.9
75th percentile    91652    102261   111.6
90th percentile    115995   139864   120.6
95th percentile    131697   172677   131.1
98th percentile    145619   208465   143.2
Public tuition     19765    59990    303.5
Private tuition    39675    122921   309.8

For 2010, only four-year institutions were included. For 1964, both
two and four year institutions are included, (we do not have separate
data for only four year institutions). We use full tuition set to
[[summation].sup.4.i=1] Tuition / [beta].sup.i=1], where Tuition is
per year real tuition at a four-year institution.
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