Research Division
Federal Reserve Bank of St. LouisWorking Paper Series

Student Loans and Repayment: Theory, Evidence and Policy

Lance J LochnerandAlexander Monge-Naranjo

Working Paper 2014-040B
http://research.stlouisfed.org/wp/2014/2014-040.pdf

November 2014
Revised November 2014

FEDERAL RESERVE BANK OF ST. LOUIS
Research Division
P.O. Box 442
St. Louis, MO 63166______________________________________________________________________________________The views expressed are those of the individual authors and do not necessarily reflect official positions of
the Federal Reserve Bank of St. Louis, the Federal Reserve System, or the Board of Governors.
Federal Reserve Bank of St. Louis Working Papers are preliminary materials circulated to stimulate
discussion and critical comment. References in publications to Federal Reserve Bank of St. Louis Working
Papers (other than an acknowledgment that the writer has had access to unpublished material) should becleared with the author or authors.

Student Loans and Repayment: Theory, Evidence andPolicyLance J Lochner∗

Alexander Monge-Naranjo† ‡November 12, 2014

Abstract
Rising costs of and returns to college have led to sizeable increases in the demand forstudent loans in many countries. In the U.S., student loan default rates have also risen
for recent cohorts as labor market uncertainty and debt levels have increased. We discussthese trends as well as recent evidence on the extent to which students are able to obtainenough credit for college and the extent to which they are able to repay their student debts
after. We then discuss optimal student credit arrangements that balance three important
objectives: (i) providing credit for students to access college and finance consumption whilein school, (ii) providing insurance against uncertain adverse schooling or post-school labormarket outcomes in the form of income-contingent repayments, and (iii) providing incentives
for student borrowers to honor their loan obligations (in expectation) when informationand commitment frictions are present. Specifically, we develop a two-period educational
investment model with uncertainty and show how student loan contracts can be designed to
optimally address incentive problems related to moral hazard, costly income verification, andlimited commitment by the borrower. We also survey other research related to the optimal
design of student loan contracts in imperfect markets. Finally, we provide practical policy
guidance for re-designing student loan programs to more efficiently provide insurance while
addressing information and commitment frictions in the market.

Keywords: Human Capital, Borrowing, Student Loans, Default, Repayment, IncomeContingent, Credit Constraint.
JEL Codes: D14, D82, H21, H52, I22, I24, J24∗

CIBC Centre for Human Capital & Productivity, Department of Economics, University of Western Ontario;
CESifo; and NBER.
†
Federal Reserve Bank of St. Louis and Washington University in St. Louis.
‡
The views expressed are those of the individual authors and do not necessarily reflect official positions of theFederal Reserve Bank of St. Louis, the Federal Reserve System, or the Board of Governors.

1

Contents
1 Introduction

4

2 Trends
2.1 Three Important Economic Trends . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 U.S. Trends in Student Borrowing and Debt . . . . . . . . . . . . . . . . . . . . .
2.3 U.S. Trends in Student Loan Delinquency and Default . . . . . . . . . . . . . . .
2.4 Summary of Major Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5
5
8
15
16

3 Current Student Loan Environment
3.1 Federal Student Lending Programs in the U.S. . . . . . . . . . . . . . . . . . . . .
3.2 Private Student Loan Programs in the U.S. . . . . . . . . . . . . . . . . . . . . . .
3.3 The International Experience . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Comparing Income-Contingent Repayment Amounts . . . . . . . . . . . . . . . .

18
18
23
24
27

4 Can College Students Borrow Enough?

27

5 Do Some Students Borrow Too Much?
5.1 Student Loan Repayment/Nonpayment 10 Years after Graduation . . . . . . . . .
5.2 Default and Non-Payment at Two-Year Institutions . . . . . . . . . . . . . . . . .
5.3 Evidence from Canada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32
34
39
41

6 Designing the Optimal Credit Program
6.1 Basic Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Unrestricted Allocations (First Best) . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Limited Commitment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1 Complete Contracts with Limited Enforcement . . . . . . . . . . . . . . .
6.3.2 Incomplete Contracts with Limited Enforcement . . . . . . . . . . . . . . .
6.4 Costly State Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Moral Hazard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6 Multiple Incentive Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.1 Costly State Verification and Moral Hazard . . . . . . . . . . . . . . . . .
6.6.2 Limited Commitment: Default or Additional Constraints? . . . . . . . . .
6.7 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43
44
46
48
48
51
55
58
62
62
65
70

7 Key Principles and Policy Guidance
7.1 Three Key Principles in the Design of Student Loan Programs . . . . . . . . . . .
7.2 The Optimal Structure of Loan Repayments . . . . . . . . . . . . . . . . . . . . .
7.3 Reducing the Costs of Income Verification . . . . . . . . . . . . . . . . . . . . . .
7.4 Enforcing Repayment and the Potential for Default . . . . . . . . . . . . . . . . .
7.5 Setting Borrowing Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.6 Other Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77
77
79
80
81
82
83

2

8 Conclusions

84

3

1

Introduction
Three recent economic trends have important implications for financing higher education: (i)rising costs of post-secondary education, (ii) rising average returns to schooling in the labor market,
and (iii) increasing labor market risk. These trends have been underway in the U.S. for decades;
however, similar trends are also apparent in many other developed countries. Governments aroundthe world are struggling to adapt tuition and financial aid policies in response to these changes. Inan era of tight budgets, post-secondary students are being asked to pay more for their education,
often with the help of government-provided student loans.
While some countries have only recently introduced student loan programs, many American
students have relied on student loans to finance college for decades. Still, the rising returns andcosts of education, coupled with increased labor market uncertainty, have generated new interestin the efficient design of government student loan programs. In this chapter, we consider boththeoretical and empirical issues relevant to the design of student loan programs with a particularfocus on the U.S. context.
The rising returns and costs of college have dramatically increased the demand for creditby American students. Since the mid-1990s, more and more students have exhausted resources
available to them from government student loan programs, with many turning to private lenders
for additional credit. Despite an increase in private student lending, there is concern that a
growing fraction of youth from low- and even middle-income backgrounds are unable to access theresources they need to attend college (Lochner and Monge-Naranjo, 2011, 2012).
At the same time, new concerns have arisen that many recent students may be taking on too
much debt while in school. Growing levels of debt, coupled with rising labor market uncertainty,
make it increasingly likely that some students are unable to repay their debts. These problems
became strikingly evident during the Great Recession, when many recent college graduates (anddropouts) had difficulties finding their first job (Elsby et al., 2010; Hoynes et al., 2012). For the
first time in more than a decade, default rates on government student loans began to rise in the
U.S.
Altogether, these trends raise two seemingly contradictory concerns: Can today’s college students borrow enough? Or, are they borrowing too much? Growing evidence suggests that bothconcerns are justified and that there is room to improve upon the current structure of student

4

loan programs. This had led to recent interest in income-contingent student loans in the U.S. andmany other countries.
We, therefore, devote considerable attention to the design of optimal student lending programsin an environment with uncertainty and various market imperfections that limit the extent ofcredit and insurance that can be provided. In a two-period environment, we derive optimal student credit contracts that are limited by borrower commitment (repayment enforcement) concerns,
incomplete contracts, moral hazard (hidden effort), and costly income verification. We show how
these incentive and contractual problems distort consumption allocations across post-school earnings realizations, intertemporal consumption smoothing via limits on borrowing, and educational
investment decisions. We also summarize other related research on these issues and related concerns about adverse selection in higher education, as well as dynamic contracting issues in richer
environments with many years of post-school repayment. Based on results from our theoreticalanalysis and the literature more generally, we discuss important policy lessons that can help guidein the design of optimal government student loan programs.
This rest of this chapter proceeds as follows. Section 2 documents several recent trends in thelabor market and education sector relevant to our analysis of student loans. We then describe
current student loan markets (especially in the U.S.) in Section 3 before summarizing literatures
on borrowing constraints in higher education (Section 4) and student loan repayment (Section 5).
Our analysis of optimal student credit contracts under uncertainty and various information andcontractual frictions appears in Section 6, followed by a discussion of important policy lessons in
Section 7. Concluding remarks and suggestions for future research are reserved for Section 8.

2

Trends2.1

Three Important Economic Trends

Three important economic trends have substantially altered the landscape of higher educationin recent decades, affecting college attendance patterns, as well as borrowing and repayment
behavior. These trends are all well-established in the U.S., but some are also apparent to varying
degrees in other developed countries. We focus primarily on the U.S. but also comment on a few
other notable examples.
First, the costs of college have increased markedly in recent decades, even after accounting

5

for inflation. Figure 1 reports average tuition, fees, room and board (TFRB) in the U.S. (inconstant year 2013 dollars) from 1990-91 to 2012-13 for private non-profit four-year institutions aswell as public four-year and two-year institutions. Since 1990-91, average posted TFRB doubled
at four-year public schools, while it increased by 65% at private four-year institutions. Average
published costs rose less (39%) at two-year public schools. The dashed lines in Figure 1 report
net TFRB each year after subtracting off grants and tax benefits, which also increased over thisperiod. Accounting for expansions in student aid, the average net cost of attendance at public
and private four-year colleges increased by ‘only’ 64% and 21%, respectively, while net TFRB
declined slightly (6%) at public two-year schools. Driving some of these changes are increases
in the underlying costs of higher education. Current fund expenditures per student at all public
institutions in the U.S. rose by 28% between 1990-91 and 2000-01 reflecting an annual growth rateof 2.5% (Snyder, Dillow and Hoffman, 2009, Table 360).1 Expenditures per pupil have also risen
in many other developed countries (OECD, 2013). In some of these countries, governments haveshouldered much of the increase, while tuition fees have risen substantially in others like Australia,
Canada, Netherlands, New Zealand, and the UK.2
Second, average returns to college have increased sharply in many developed countries, including Australia, Canada, Germany, the U.K., and the U.S.3 In the U.S., Autor et al. (2008)
document a nearly 25% increase in weekly earnings for college graduates between 1979 and 2005,
compared with a 4% decline among workers with only a high school diploma. Even after accounting for rising tuition levels, Avery and Turner (2012) calculate that the difference in discounted
lifetime earnings (net of tuition payments) between college and high school graduates rose by morethan $300,000 for men and $200,000 for women between 1980 and 2008.4 Heckman et al. (2008)
estimate that internal rates of return to college vs. high school rose by 45% for black men and1
Jones and Yang (2014) argue that much of the increase in the costs of higher education can be traced to therising costs of high skilled labor due to skill-biased technological change.
2
Tuition and fees rose by a factor of 2.5 in Canada between 1990-91 and 2012-13. Australia, Netherlands andthe UK all moved from fully government-financed higher education in the late 1980s to charging modest tuition
fees by the end of the 1990s. Current statutory tuition fees in the Netherlands stand at roughly US$5,000, while
tuition in Australia now averages more than US$6,500. Most dramatically, tuition and fees nearly tripled from justover £3,000 to £9,000 (nearly US$5,000 to over US$14,500) at most UK schools in 2012. Tuition fees have also
increased substantially in New Zealand since fee deregulation in 1991.
3
See, e.g., Card and Lemieux (2001) for evidence on Canada, the U.K., and U.S.; Boudarbat et al. (2010) on
Canada; Dustmann et al. (2009) on Germany; and Wei (2010) on Australia. Pereira and Martins (2000) estimate
increasing returns to education more generally in Denmark, Italy, and Spain, as well.
4
These calculations are based on a 3% discount rate.

6Figure 1: Evolution of Average Tuition, Fees, Room & Board in the U.S. (2013 $)$45,000$40,000

Private 4-yr TFRB

Public 4-yr In-state TFRB

Public 2-yr In-state TFRB

Private 4-yr Net TFRB

Public 4-yr In-state Net TFRB

Public 2-yr In-State Net TFRB

$35,000$30,000$25,000$20,000$15,000$10,000$5,000$0

Source: College Board (Online Tables 7 and 8), Trends in College Pricing, 2013.

60% for white men between 1980 and 2000.
Third, labor market uncertainty has increased considerably in the U.S. Numerous studies
document increases in the variance of both transitory and persistent shocks to earnings beginningin the early 1970s.5 Lochner and Shin (2014) estimate that the variance in permanent shocks toearnings increased by more than 15 percentage points for American men over the 1980s and 1990s,
while the variance of transitory shocks rose by 5-10 percentage points over that period. A numberof recent studies also document increases in the variances of permanent and transitory shocks
to earnings in Europe since the 1980s.6 The considerable uncertainty faced by recent schoolleavers has been highlighted throughout the Great Recession with unemployment rates rising for
5

See Gottschalk and Moffitt (2009) for a recent survey of this literature. More recent work includes Heathcote,
Perri, and Violante (2010); Heathcote, Storesletten, and Violante (2010); Moffitt and Gottschalk (2012), andLochner and Shin (2014).
6
Fuchs-Schundeln et al. (2010) document an increase in the variance of permanent shocks in Germany, while
Jappelli and Pistaferri (2010) estimate increases in the variance of transitory shocks in Italy. Domeij and Floden(2010) document increases in the variance of both transitory and permanent shocks in Sweden over this period.
In Britain, Blundell et al. (2013) find that increases in the variance of permanent and transitory shocks has been
concentrated in recessions.

7young workers regardless of their educational background.7 While very persistent shocks early inborrowers’ careers clearly threaten their ability to repay their debts in full, even severe negativetransitory shocks can make maintaining payments difficult for a few years without some form ofassistance or income-contingency.

2.2

U.S. Trends in Student Borrowing and Debt

Despite rising costs of college and labor market uncertainty, the steady rise in labor market
returns to college has driven American college attendance rates steadily upward over the pastfew decades. The fraction of Americans that had enrolled in college by age 19 increased by 25
percentage points between cohorts born in 1961 and 1988, while college completion rates rose by
about 7 percentage points over this time period (Bailey and Dynarski, 2011).
The rising costs and returns to college have also led to a considerable increase in the demand forstudent loans in the U.S. Figure 2 demonstrates the dramatic increase in annual student borrowing
between 2000-01 and 2010-11 as reported by College Board (2011).8 Not surprisingly, debt levels
from student loans have also exploded, surpassing total credit card debt in the U.S. Analyzing data
drawn from a random sample of personal credit reports (FRBNY Consumer Credit Panel/Equifax,
henceforth CCP), Bleemer et al. (2014) report that combined government and private student debt
levels in the U.S. quadrupled (in nominal terms) from $250 billion in 2003 to $1.1 trillion in 2013.
The dramatic increases in aggregate student borrowing and debt levels reflect not only the risein college enrolment in the U.S. over the past few decades, but also an increase in the share of
students taking out loans and greater borrowing among those choosing to borrow. Based on the
CCP, Bleemer et al. (2014) show that the fraction of 25 year-olds with government and/or private
student debt rose from 25% in 2003 to 45% in 2013. Over that same decade, average student
debt levels among 22-25 year-olds with positive debt nearly doubled from $10,600 to $20,900 (in2013 $). Akers and Chingos (2014) use the Survey of Consumer Finances (SCF) to study theevolution of household education debt (including both private and government student loans) overtwo decades for respondents ages 20-40. As shown in Figure 3, the fraction of these householdswith education debt nearly doubled from 14% in 1989 to 36% in 2010, while the average amount of7

See Elsby et al. (2010) and Hoynes et al. (2012) for evidence on unemployment rates during the Great Recession
by age and education in the U.S. Bell and Blanchflower (2011) document sizeable increases in unemployment
throughout Europe for young workers with and without post-secondary education.
8
Total Stafford loan disbursements also more than doubled in the previous decade (College Board, 2001).

8

Figure 2: Growth in Student Loan Disbursements in the U.S. (in 2013 $)$110$102.9Loans in Constant 2013 Dollars (in Billions)

$100

$90.1

$90

$79.1

$80

$74.7
$67.1

$70
$58.1

$60
$50
$40

$46.7
13%
3%
9%

$50.3
14%
3%
9%

16%
3%
9%

18%
3%
10%

75%

25%
23%

21%

2%
11%

3%
11%

7%
1%

$91.3

8%
1%

12%

13%

15%

35%

35%

1%
12%

26%
2%
2%

12%

12%

75%

$30
$20

$82.7

$104.7

73%

71%

69%

63%

66%

60%

61%

$10
$0

2000-01 2001-02 2002-03 2003-04 2004-05 2005-06 2006-07 2007-08 2008-09 2009-10 2010-11
Academic Year
Stafford Loans

PLUS Loans

Perkins and Other Federal Loans

Source: College Board (2011).

9

Nonfederal LoansFigure 3: Incidence and Amount (in 2013 $) of Household Education Debt for 20-40 Year-Olds in
the U.S.

40$20,000

35$18,000

Perecent with debt

$14,000

25$12,000

20$10,000$8,00015$6,00010$4,000

5
0

Average debt (2013 $)$16,000

30$2,000
$0
1989

1992

1995

1998

Percent with education debt

2001

2004

2007

2010

Average debt (among those with debt)

Source: Table 1, Akers and Chingos (2014).

debt (among families with debt) more than tripled.9 Altogether, these figures imply an eight-foldincrease in average debt levels (per person) among all 20-40 year-old households (borrowers andnon-borrowers alike) between 1989 and 2010.10
With the CCP and SCF, it is difficult to determine debt levels at the time students leaveschool, so figures from these sources reflect both borrowing and early repayment behavior. By
contrast, the National Postsecondary Student Aid Study (NPSAS) allows researchers to study
the evolution of education-related debt accumulated during college. Using the NPSAS, Hershbein
and Hollenbeck (2014a,b) consider total student debt (government and private) accumulated bybaccalaureate degree recipients who graduated in various years back to 1989-90. See Table 1. They
9

Brown et al. (2014) compare household debt levels in the CCP and SCF for the years 2004, 2007 and 2010.
Their findings suggest that student loan debts appear to be under-reported by 24% (2004) to 34% (2010) in the
SCF relative to credit report records in the CCP.
10
Here and below, we refer to 20-40 year-old households as households in which the SCF respondent was between
the ages of 20 and 40.

10report that the fraction of baccalaureate recipients graduating with education debt increased bynearly one-third from 55% in 1992-93 to 71% in 2011-12, while average total student debt per
graduating borrower nearly tripled. Together, total student debt per graduate more than doubled
between the 1989-90 and 2011-12 cohorts.
Table 1: Education Debt for Baccalaureate Degree Recipients in NPSAS (2013 $)Year Graduating
1989-1990
1995-1996
1999-2000
2003-2004
2007-20082011-2012

Percent witheducation debt
55%
53%
64%
66%
68%
71%

Average cumulative
student loan debt
(per borrower)
7,300
9,300
14,60015,10017,60021,200

Average cumulative
student loan debt
(per graduate)
13,50017,80022,90023,00025,80029,700Source: Hershbein and Hollenbeck (2014a,b).

Figure 4 documents the changing distribution of cumulative loan amounts among baccalaureate recipients over time in the NPSAS (Hershbein and Hollenbeck, 2014a,b). The figure reveals
different trends at the low and high ends of the debt distribution. The fraction of college graduatesborrowing less than $10,000 (including non-borrowers) declined sharply in the 1990s but remained
quite stable thereafter until the financial crisis in 2008. By contrast, undergraduate student debts
of at least $30,000 increased more consistently over time, with the exception of the early 2000s
when the entire distribution of debt was relatively stable. Since 1989-90, the fraction of college
graduates that borrowed more than $30,000 increased from 4% to 30%. Though not shown in the
figure, less than 1% of all graduates had accumulated more than $50,000 in student debt before
1999-2000, while 10% had by 2011-12 (Hershbein and Hollenbeck, 2014a,b).
Figure 5, from Steele and Baum (2009), reports the distribution of accumulated student loan
debt separately for associate and baccalaureate degree recipients in the 2007-08 NPSAS. Students
earning their associate degree borrowed considerably less, on average, than did those earning abaccalaureate degree. Roughly one-half of associate degree earners did not borrow anything, while
only 5% borrowed $30,000 or more.
11Figure 4: Distribution of Cumulative Undergraduate Debt for Baccalaureate Recipients over Time(NPSAS)

100%
90%
80%
70%

percent

60%
50%
40%
30%
20%
10%
0%
1989-1990
No borrowing

1995-1996$1 - $10,000

1999-2000$10,001 - $20,000

2003-2004
Year$20,001 - $30,000

Source: Hershbein and Hollenbeck (2014).

12

2007-20082011-2012$30,001 - $40,000>$40,000

Figure 5: Distribution of Cumulative Student Loan Debt By Undergraduate Degree (NPSAS
2007-08)

Associate Degree52%

Baccalaureate Degree

23%

34%

0%

No borrowing

10%

20%

$1 - $9,999

14%

30%

19%

15%

40%
50%
60%
percent with specified debt levels$10,000 - $19,999

14%$20,000 - $29,999

70%

6%

9%

80%

$30,000 - $39,999

3%2%

10%

90%

100%

$40,000 or more

Source: Steele and Baum (2009).
Note: Data from 2007-08 NPSAS and includes U.S. citizens and residents. Excludes PLUS loans, loans from family/friends, and credit cards.

13

The steady rise in total student borrowing over the late 1990s and 2000s belies the fact thatgovernment student loan limits remained unchanged (in nominal dollars) between 1993 and 2008.
Adjusting for inflation, this reflects a nearly 50% decline in value. In 2008, aggregate Stafford
student loan limits for dependent undergraduate students jumped from $23,000 to $31,000, although this value was still more than 10% below the 1993 limit after accounting for inflation.
Not surprisingly, a rising number of students have exhausted available government student loansources over this period. For example, the share of full-time/full-year undergraduates that ‘maxedout’ Stafford loans increased nearly six-fold from 5.5% in 1989-90 to 32.1% in 2003-04 (Berkner,
2000; Wei and Berkner, 2008).
Undergraduates turned more and more to private lenders to help finance their education prior
to the 2008 increase in federal student loan limits and contemporaneous collapse in private credit
markets. Between 1999-2000 and 2007-08, average debt from federal student loan programs declined by a few thousand dollars among baccalaureate degree recipients, but this was more thancompensated for by a sizeable jump in private student loan debt (Woo, 2014). The top parts ofeach bar in Figure 2 reveal the aggregate shift in undergraduate borrowing toward non-federal
sources (mostly private lenders), which peaked at 25% of all student loan dollars in 2007-08 before
dropping below 10%.11 Finally, data from the NPSAS shows that the fraction of undergraduatesusing private student loans rose from 5% in 2003-04 to 14% in 2007-08 before dropping back to
6% in 2011-12 (Arvidson et al., 2013).
Akers and Chingos (2014) discuss three important reasons that these increases in student
borrowing do not necessarily imply greater monthly repayment burdens on today’s borrowers:(i) earnings have increased significantly for college students, especially those graduating with abaccalaureate degree or higher, (ii) nominal interest rates on federal student loans have fallen,and (iii) amortization periods for federal student loans have been extended.12 Indeed, Akers andChingos (2014) report that among 20-40 year-old households with positive education debt andwage income of at least $1,000, median student loan payment-to-income ratios remained relatively
constant at 3-4% between 1992 and 2010, while average monthly payment-to-income ratios actually
11

These figures do not include student credit card borrowing, which has also risen over this period. In 2008, 85%of undergraduates had at least one credit card and carried an average balance of $3,173 (Sallie Mae, 2008).
12
Nominal interest rates on federal student loans fell from 8.3% in 1992 to 5.5% in 2010; average amortization
periods on federal student loans increased from 7.5 to 13.4 years among 20-40 year-old households with debt (Akers
and Chingos, 2014). Together, these imply a reduction in annual repayments of 42%.

14

fell by half over the 1990s and have remained fairly stable thereafter. High payment-to-income
ratios (e.g. at least 20%) also fell over this period. It is important to note, however, that thesestatistics (in all years) likely understate the financial burden of student loan payments on recent
school-leavers, since they do not consider very low income households (wage income less than
$1,000/month) and since earnings levels are typically lowest in the first few years out of school.13

2.3

U.S. Trends in Student Loan Delinquency and Default

Student loan delinquency and default rates provide another useful picture of borrowers’ capacity
and willingness to repay their student loan obligations. Figure 6 reports official two- and threeyear cohort default rates from 1987 to 2011. These default measures reflect the fraction of students
entering repayment in a given year that default on their federal student loans within the next twoor three years, respectively.14 Despite increases in student debt levels over the 1990s, default rates
declined considerably over this period. While largely unstudied, this decline likely reflects theincrease in earnings associated with post-secondary schooling over that period as well as increased
enforcement and collection efforts by the federal government.15 After remaining relatively stable
over the early 2000s, default rates on federal student loans began to increase sharply with thefinancial crisis of 2007-08 and the onset of the Great Recession. Two-year cohort default rates
more than doubled from 4.6% in 2005 to 10% in 2011.
Figure 7 reveals that the decline in default rates over the 1990s was most pronounced among
two-year schools and four-year for-profit institutions, which all had much higher initial default rates
than four-year public and private non-profit schools.16 Since 2005, default rates have increased
most at for-profit institutions and public two-year schools, which now stand at 13-15%. Default
rates at these institutions are at least five percentage points higher than at other school types.
Default is only one very extreme form of non-payment. Using CCP data, Brown et al. (2014)
show high and increasing rates of delinquency (90 or more days late) on student loan payments
13

The downward trend in payment-to-income ratios may also be driven, at least partially, by more severe underreporting of student debt in the SCF as suggested by Brown et al. (2014). See footnote 9.
14
Borrowers that are 270 days or more late on their Stafford student loan payments are considered to be in
default.
15
Throughout the 1990s, the federal government expanded default collection efforts to garnish wages and seize
income tax refunds from borrowers that default. The Department of Education began to exclude postsecondary
institutions with high default rates (currently 30% or higher for 3 consecutive years) from participating in federal
student aid (including Pell Grant) programs in the early 1990s.
16
These figures are calculated from official default rates by institution as maintained by Department of Education.

15

Figure 6: Trends in Federal Student Loan Cohort Default Rates
25

20

Percent

15

10

52-year CDR

3-year CDR

0(including government and private student loans) over the past decade. Among borrowers underage 30 still in repayment, the fraction delinquent on student loans increased sharply from 20%
in 2004 to 35% in 2012. Using student loan records from five major loan guarantee agencies,
Cunningham and Kienzl (2014) report that among students entering repayment in 2005, 26% had
become delinquent and 15% had defaulted at some point over the next five years; another 16%
had received a forbearance or deferment for economic hardship. Altogether, 57% had experienced
a period where they did not make their expected payments.

2.4

Summary of Major Trends

Summarizing these trends for the U.S., both the costs of and returns to college have risen
dramatically in recent decades. On balance, the net returns to college have risen, which has led
to important increases in college attendance rates. Student borrowing has also risen at both theextensive and intensive margins. While borrowing from government student loan programs has
increased over this period, students have turned increasingly more to private lenders since theearly 1990s to help fill the gap between sharply growing demand for credit and relatively stable or16

Figure 7: Trends in Federal Student Loan Two-Year Cohort Default Rates by Institution Type
0.25
Public 4-year

Private Non-Profit 4-year

For-Profit 4-year

Public 2-year

Private Non-Profit 2-year

For-Profit 2-year

0.2

Default Rate

0.15

0.1

0.05

0
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Year

17

declining supply from government sources. Rising debt levels, coupled with an increase in labormarket uncertainty, have given rise to higher delinquency and default rates on government andprivate student loans.
After discussing the current student loan environment in the U.S. and a few other countries, wereturn to some of these issues below in Sections 4 and 5 where we summarize evidence on borrowing
constraints in higher education and the determinants of student loan repayment/default.

3

Current Student Loan Environment
In this section, we describe the current student loan environment with an emphasis on the

U.S. However, we also provide a brief international context for student loan programs, devoting
considerable attention to income-contingent loan repayment schemes.

3.1

Federal Student Lending Programs in the U.S.

Most federal loans are provided through the Stafford Loan program, which awarded about $90
billion in the 2011-12 academic year, compared to $19 billion awarded through Federal Parent
Loans (PLUS) and Grad PLUS Loans combined, and just under $1 billion through the Perkins
Loan program. For some perspective, total Pell Grant awards amounted to about $34 billion.
See College Board (2013) for these and related statistics. Important features of the main federal
student loan programs are summarized in Table 2. We briefly discuss these programs in thefollowing subsections.
Stafford Loans
The federal government offers Stafford loans to undergraduate and graduate students throughthe William D. Ford Federal Direct Student Loan (FDSL) program.17 Students are not charged
interest on subsidized loans as long as they are enrolled in school, while interest accrues on unsubsidized loans. Only undergraduates are eligible for unsubsidized loans. In order to qualify
for subsidized loans, undergraduate students must demonstrate financial need, which depends on
17

In the past, private lenders provided loans to students under the Federal Family Education Loan Program(FFEL), and the federal government guaranteed those loans with a promise to cover unpaid amounts. Regardlessof the source of funds, the rules governing FDSL and FFEL programs were essentially the same. Prior to theintroduction of unsubsidized Stafford Loans in the early 1990s, Supplemental Loans to Students (SLS) were analternative source of unsubsidized federal loans for independent students.

18

Table 2: Summary of Current Federal Student Loan Programs

Perkins

PLUS&
GradPLUS

Students

PLUS: Parents
GradPLUS: Grad. Students

Financial NeedNo Adverse Credit History
or cosigner required$5,500$5,500$5,500$27,500

All Need
All Need
All Need
All Need$20,500$138,500$8,000$60,000

All Need
All Need

Undergrad.: Variable, ≤8.25%
Grad.: Variable, ≤9.5%

5%

Variable, 10.5% Limit

1.07%

None

4.3%

6 Months

9 Months

up to 6 Months

Dependent
Students

Stafford
Independent
Students∗

RecipientStudents

Eligibility

Subsidized: Undergrad., Financial Need∗∗
Unsubsidized: All Students

Undergrad. Limits:
Year 1
Year 2Years 3+
Cum. Total
Graduate Limits:
AnnualCum. Total∗∗∗Interest Rate

Fees
Grace Period$5,500$6,500$7,500$31,000

Students$9,500$10,500$12,500$57,500

Notes:∗ Students whose parents do not qualify for PLUS loans can borrow up to independent student
limits from Stafford program.
∗∗ Subsidized Stafford loan amounts cannot exceed $3,500 in year 1, $4,500 in year 2, $5,500 in years 3+,
and $23,000 cumulative.
∗∗∗ Cumulative graduate loan limits include loans from undergraduate loans.

19family income, dependency status, and the cost of institution attended. Unsubsidized loans areavailable to both undergraduate and graduate students and can be obtained without demonstrating need. In general, students under age 24 are assumed to be “dependent”, in which case theirparents’ income is an important determinant of their financial need.
Dependency status and class level determine the total amount of Stafford loans a student iseligible for as seen in Table 2. Dependent students can borrow as much as $31,000 over theirundergraduate years, while independent students can borrow twice that amount.18 Annual limits
are lowest for the first year of college, increasing in the following two years.
Interest rates on Stafford loans are variable subject to upper limits of 8.25% for undergraduates
and 9.5% for graduate students.19 Fees are levied on borrowers of about 1%, which is proportionallysubtracted from each disbursement. Students need not re-pay their loans while enrolled at least
half-time, though interest does accrue on unsubsidized loans. After leaving school, borrowers are
given a 6 month grace period before they are required to begin re-paying their Stafford loans.
PLUS and GradPLUS Loans
The PLUS program allows parents who do not have an adverse credit rating to borrow for
their dependent children’s education. The GradPlus program offers the same opportunities forgraduate and professional students. Generally, parents and graduate students can borrow up to
the total cost of schooling less any other financial aid given to the student. For this purpose, thecost of schooling is determined by the school of attendance and includes such expenses as tuition
and fees, reasonable room and board allowances, expenses for books, supplies, and equipment.
Interest rates are variable (10-year Treasury note plus 4.6%) subject to a 10.5% limit, and fees of
4.3% of loan amounts are charged on origination. Graduate students enrolled at least half-time
can defer all GradPLUS loan payments until six months after leaving school. Parents borrowing
from the PLUS program can also request such a deferment.
18

Dependent students whose parents do not qualify for the PLUS program can borrow up to the independent
student Stafford loan limits.
19
Interest rates for undergraduate and graduate students are equal to the 10-year Treasury note plus 2.05% and3.6%, respectively, subject to the upper limits. For the 2013-14 academic year, the rates equal 3.86% and 5.41%
for undergraduates and graduates, respectively.

20

Perkins Loans
The Perkins Loan program targets students in need, distributing funds provided by the government and participating post-secondary institutions. Loan amounts depend on the student’s
level of need and funding by the school attended, but they are subject to an upper limit of $5,500
per year for undergraduates and $8,000 per year for graduate students. By far the most financiallyattractive loan alternative for students, Perkins loans entail no fees and a fixed low interest rate of
5%. (See Table 2.) Students are also given a 9 month grace period after finishing (leaving) school
before they must begin re-payment of a Perkins loan.
Federal Student Loan Repayment and Default
Re-payment of student loans begins six (Stafford) or nine (Perkins) months after finishingschool with collection managed by the Department of Education. To simplify repayment, borrowers
can consolidate most of their federal loans into a single Direct Consolidation Loan. Borrowers with
Stafford or Direct Consolidation Loans have a number of repayment plans available to them.20
Under the Standard Repayment Plan and Extended Repayment Plan, borrowers make a standard fixed monthly payment based on their loan amount amortized over 10-30 years. For example,
repayment periods are limited to 10 years for borrowers owing less than $7,500, 20 years for borrowers owing less than $40,000, and 30 years for those owing $60,000 or more.21 Borrowers may
also choose the Graduated Repayment Plan, which starts payments at low monthly amounts, increasing payment amounts every two years over the 10-30 year repayment period. Final payments
may be as much as three times initial payments under this plan. While the reduced starting
payments of the Graduated Repayment Plan can be helpful for borrowers with modest initial earnings after leaving school, payments are not automatically adjusted based on income levels. Thus,
payments under all of these debt-based repayment plans may be difficult for those who experience
periods of unemployment or unusually low earnings. If these borrowers can demonstrate financial
hardship, they may qualify for either a forbearance or deferment, which temporarily reduces ordelays payments.22
20

Payments for non-consolidated Perkins Loans are fixed based on a 10-year amortization period.
These repayment periods apply to borrowers who hold consolidated loans. For those with other non-consolidated
federal loans, the Extended Repayment Plan allows for repayment periods of up to 25 years for those with loans
exceeding $30,000.
22
Borrowers can request a deferment during periods of unemployment or when working full time but earning lessthan the federal minimum wage or 1.5 times the poverty level. Borrowers are entitled to deferments of up to three21

21

Alternatively, borrowers may choose from a variety of income-based plans that directly link
payment amounts to current income. The newest (and most attractive) of these plans is known as
the Pay As You Earn Plan (PAYE). Under this plan, monthly payments are the lesser of the fixed
payment under the 10-year Standard Repayment Plan and 10% of discretionary family income.23
Borrowers on PAYE never pay more than the standard payment amount, and those with income
less than 150% of the poverty level are not required to make any payment. Interest continues toaccumulate even when payments are reduced or zero; however, any remaining balance after 20
years is forgiven.
Loans covered by the federal system cannot generally be expunged through bankruptcy except
in very special circumstances. Thus, the only way a borrower can ‘avoid’ making required payments is to simply stop making them, or default. A borrower is considered to be in default once
he becomes 270 days late in making a payment. If the loan is not fully re-paid immediately, or if asuitable re-payment plan is not agreed upon with the lender, the default status will be reported tocredit bureaus, and collection costs may be added to the amount outstanding. Up to 15% of theborrower’s disposable earnings can be garnished (without a court order), and federal tax refunds
or Social Security payments can be seized and applied toward the balance.24 In practice, thesesanctions are sometimes limited by the inability of collectors to locate those who have defaulted.
Wage garnishments are ineffective against defaulters that are self-employed. Furthermore, individuals can object to the wage garnishment if it would leave them with a weekly-take home payof less than 30 times the federal minimum wage, or if the garnishment would otherwise result inan extreme financial hardship.
years due to unemployment or economic hardship. Borrowers can request a forbearance (usually up to 12 months
at a time) due to economic hardship (e.g. monthly payments exceed 20% of gross income).
23
Discretionary income is the amount over 150 percent of the poverty guideline (based on family size and stateof residence). In 2014, the federal poverty guideline for a single- (two-) person family was $11,670 ($15,730) in the48 contiguous states, so the income-based payment amount for a single- (two-) person family is 10% of any income
over $17,505 ($23,595).
24
Other sanctions against borrowers who default include a possible hold on college transcripts, ineligibility forfurther federal student loans, and ineligibility for a deferment or forbearance. Since the early 1990s, the government
has also punished educational institutions with high student default rates by making their students ineligible toborrow from federal lending programs.

22

3.2

Private Student Loan Programs in the U.S.

As noted earlier, 14% of all undergraduates in 2007-08 turned to private student loan programs
to help finance their education. Due to tightening private credit markets and expansions in the
Stafford Loan Program, the fraction of undergraduates borrowing from private lenders dropped bymore than half over the next few years (Arvidson et al., 2013). However, private student loans arestill an important source of funding for some students, especially those attending more expensive
private non-profit and proprietary schools.
Private loans are not need-based. Instead, students or their families must demonstrate their
creditworthiness to lenders whose aim is to earn a competitive return. Private student loans
are generally capped by the total costs of college less any other financial aid; however, lenders
sometimes impose tighter constraints. Eligibility, loan limits, and terms generally depend on the
borrower’s credit score and sometimes depend on other factors that may affect repayment, such as
the institution of attendance and degree pursued. In most cases, lenders require a cosigner (withan eligible credit score) to commit to repaying the loan if students themselves do not; a cosigner
may also improve the terms of the loan. Among student loans distributed by some of the top
private lenders in recent years, more than 90% (60%) of all undergraduate (graduate) borrowers
had a cosigner (Arvidson et al., 2013). Interest rates charged on private loans are typically higher
than those offered by federal student loan programs, especially for borrowers with poor credit
records. Rates may be fixed or variable and are usually pegged to either the prime rate or the
London Interbank Offer Rate (LIBOR).
Repayment terms typically range between 10 and 25 years, almost universally with fixed debtbased payments. Some programs require borrowers to begin repaying their loan shortly after
taking it out, while others provide students with deferments during enrolment periods. Some evenoffer up to a six month grace period after students leave school. In some cases, lenders may offer
opportunities for deferment/forbearance due to economic hardship. All of these attributes are at
the discretion of the lender.
Since 2005, private student loans (like federal student loans) cannot be expunged throughbankruptcy except in exceptional circumstances.25 However, private lenders do not have the same
powers as the federal government to enforce repayment. Most notably, lenders must receive a
25

These limits on bankruptcy do not extend to other sources of financing like credit cards or home mortgages,
which are also sometimes used to finance higher education.

23

court judgment in order to garnish wages or seize a delinquent borrower’s assets.

3.3

The International Experience

Many countries offer government student loans for higher education (OECD, 2013). In mostcases, the general structure for these programs is similar to that of the U.S. in that students
can borrow to help cover tuition/fees and living expenses, payments can be deferred until after
leaving school, and repayment terms are debt-based.26 Contingencies like deferment/forbearance
for borrowers experiencing financial hardship are common; however, most countries do not offer
explicit income-contingent repayment schemes. Exceptions include Australia, Canada, Chile, New
Zealand, the United Kingdom, and South Africa who all offer explicit income-contingent repayment
schemes. Chapman (2006) provides a comprehensive discussion of income-contingent programsaround the world. We document key aspects of these repayment plans in a few of these countries(as well as the U.S.) in Table 3.
Like the U.S., Canada offers student loans under debt-based repayment contracts along with
an option for income-contingent repayment for borrowers with low income levels.27 Standard
repayment terms (fixed payments based on 10- or 15-year amortization periods) are similar to
those in the U.S. and include a 6 month grace period after school before repayment begins. Interest
accrues at either a fixed (prime+5%) or floating (prime+2.5%) rate. Introduced in 2009, CSLP’s
Repayment Assistance Program (RAP) offers reduced income-based payments for borrowers withlow post-school incomes. Like PAYE in the U.S., RAP payments are given by the lesser of thestandard debt-based payment and an income-based amount ranging from zero to 20% of income
above a minimum threshold. Borrowers earning less than a minimum income threshold need not
make any payments under RAP.28 For low payment levels, interest payments are covered by thegovernment. After 15 years, any debt still outstanding is forgiven. As in the U.S., student loan
debts cannot typically be expunged through bankruptcy. The official three-year cohort default
rate of 14.3% for loans with repayment periods beginning in 2008-09 was very similar to the26

Even in nordic countries like Denmark, Norway and Sweden that charge zero or negligible tuition and fees,
government loans are an important source of funding for student living expenses.
27
In 2010-11, the Canada Student Loans Program (CSLP) provided $2.2 billion in loans to approximately 425,000
full-time students in all provinces/territories except Quebec, which maintains its own student financial aid system(Human Resources and Skills Development Canada, 2012).
28
The minimum income threshold increases with family size beginning at CA$20,208 (in annual terms) for
childless single borrowers.

24

Table 3: Summary of Income-Contingent Repayment Plans

Australia

New
ZealandUnitedKingdom

CanadaUnitedStates

Maintenance andTuition Fee Loans

RAP∗

PAYE∗

Program Name

HECS-HELP

Year Adopted

1989

1992

1998

2009

2012

Collected with Taxes?

Yes

Yes

Yes

No

No

Covers Living Expenses?

No

Yes

Yes

Yes

Yes

Interest Rate∗∗

CPI

0%

RPI + 0-3%

Prime +
2.5 or 5%

10-yr T-Note+ 2.05%Fees

10%∗∗∗$60 initial,$40 annual

No

No

No

Minimum income
threshold for payment?

Yes

Yes

Yes

Varies byfamily size

Varies byfamily size

Repayment
beginsIncome >thresholdIncome >threshold

April after
school ends

After school+ 6 months

After school+ 6 months

Repayment rate(% of income)4-8%

12% (overthreshold)9% (overthreshold)

0-20% (overthreshold)10% (overthreshold)

Repayment rate increase
with income?

Yes

No

No

Yes

No

Prepayment discount?

5%

No

No

No

No

Loan foregiveness?

No

No

After 30
years

After 15
years

After 20years∗

Eligibility for both RAP in Canada and PAYE in the U.S. requires financial hardship.
In Australia, debt levels increase with inflation as determined by the consumer price index (CPI).
In the UK, interest rates are linked to the Retail Price Index (RPI) and increase with borrower
income levels. In New Zealand, an interest rate of 5.9% is charged for borrowers who move overseas.
In Canada, the variable rate is prime + 2.5% and the fixed rate is prime + 5%.
∗∗∗
Australian borrowers who make up-front fee payments (rather than borrow) receive a 10% discount.
25∗∗

corresponding rate of 13.4% for the U.S.
While the details of student loan programs in Australia, New Zealand and the UK have changed
over the years, repayment schemes have been fully income-contingent for many years. Students
choose how much they wish to borrow each schooling period – Australian students can borrow
up to tuition/fees, while New Zealand and UK students can also borrow to cover living expenses– and do not need to make any payments until after leaving school.29 In all cases, repayment
amounts depend on borrower income levels and are collected through the tax system. Borrowers
with income below specified minimum thresholds need not make any payments, while payments
increase with income above the thresholds. Annual income thresholds range from a low of 19,800
NZ dollars (roughly US$15,500) in New Zealand to £21,000 (roughly US$35,000) in the UK to ahigh of 51,300 Australian dollars (roughly US$45,000) in Australia. Borrowers in New Zealandand the UK pay 12% and 9%, respectively, of their income above this threshold towards their loanbalance once they leave school. In Australia, those with incomes above the threshold must makepayments of 4-8% of their total income with the repayment rate increasing in their income level.30
Australian borrowers receive a 5% discount on any additional prepayments they make above therequired amount.
In Australia and New Zealand, borrowers are expected to make payments until their student
debt is paid off; although, student debts can be cancelled through bankruptcy in New Zealand(not Australia). Fees and interest rates charged on the loans will determine the number of years
borrowers must make payments, even if they do not affect annual payment amounts. In Australia,
students who attend Commonwealth-supported (i.e. public) institutions do not face any explicit
fees on HECS-HELP loans; however, a discount of 10% is granted for any amount over $500 paid
up front for tuition. This effectively implies a 10% initiation fee on student loans.31 Other thanthese fees, Australian students do not pay any real interest on their loans; although, the valueof student debts is adjusted with the Consumer Price Index (CPI) to account for inflation. By
contrast, New Zealand charges modest fees of $60 at the time a loan is established and $40 eachyear thereafter; however, it charges zero interest and does not adjust loan amounts for inflation.
29

In most cases, New Zealand students can borrow for up to 7 full-time equivalent school years.
Students in Australia and New Zealand must make payments while enrolled in school if they earn above theincome thresholds when they are enrolled.
31
Under the FEE-HELP program in Australia, which provides loans to students at institutions that are notsubsidized by the government, an explicit 25% initiation fee is charged on all loans, but there is no discount on
up-front payments.
30

26

The UK does not charge any initial fees on loans, but it charges interest based on the Retail
Price Index (RPI). While in school, interest accrues at a rate equal to the RPI + 3%. After
school, students with income below the income threshold of £21,000 face an interest rate equal to
the RPI. Above the threshold, the rate linearly increases in income until £41,000 when it reaches
a maximum of RPI + 3%. Any outstanding debt is cancelled 30 years after repayment begins;
however, debts cannot be cancelled through bankruptcy.

3.4

Comparing Income-Contingent Repayment Amounts

Figure 8 shows annual required payment amounts as a function of post-school income in Australia, New Zealand and the UK, along with income-based payments on RAP in Canada and
PAYE in the U.S. All amounts have been translated into U.S. dollars to ease comparison.32 The
figure clearly shows that repayments are lowest in the UK and, to a lesser extent, Australia.
Canada appears to be the least generous (especially as incomes rise above $30,000); however, it
is important to remember that actual RAP payment amounts never exceed standard debt-based
payments. So, a student borrowing $20,000 at an interest rate of 5.5% (the current CSLP floatingrate) would never be required to pay more than $2,650 per year. Repayments in the U.S. aresimilarly capped; although, the current interest rate (3.96%) and corresponding annual payment($2,450) are slightly lower. Thus, for low student debt levels, Canada and the U.S. repayments are
similar to those in New Zealand at low- to middle-income levels and lower at higher incomes. Of
course, debt-based payments in Canada and the U.S. are increasing with student debt levels. So,for example, debt-based payments for students borrowing $40,000 at current interest rates would
be roughly $5,300 in Canada and $4,900 in the U.S. In this case, payments are relatively high in
Canada for borrowers with incomes between $30,000 and $60,000.

4Can College Students Borrow Enough?
As noted in Section 2.2, an increasing number of undergraduates exhaust their government

student loan options, turning to private lenders for additional credit. The 2008 increase in Stafford
Loan limits effectively shifted the balance of student loan portfolios back toward government
sources (see Figure 2), but it is less clear whether this policy expanded total (government plus
32

Based on September, 2014, exchange rates.

27

Figure 8: Income-Contingent Loan Repayment Functions for Selected Countries

20,000Australia

NZ

UK

Canada (RAP)

US (PAYE)

18,000

Repayment Amount (US Dollars)

16,00014,00012,00010,000
8,000
6,000
4,000
2,000
0
10,00020,00030,00040,00050,00060,000
Income (US Dollars)

70,00080,00090,000Notes: All currencies translated to US dollars using Sept, 2014, exchange rates. Repayments for Canada and U.S. are for single
childless persons and only reflect the income-contingent repayment amount which may exceed the debt-based payment.

28

100,000

private) student credit. Regardless, without more regular increases in federal student loan limits,
it is likely that continued increases in net tuition costs and returns to college will raise demands
for credit beyond supply for many students.
While it is straightforward to measure the number of students who exhaust their government
student loans – one-third of all full-time/full-year undergraduates in 2003-04 (Wei and Berkner,
2008) – the rise of private student lending over the past 20 years makes it is much more difficult
to determine how many potential students may be unable to borrow what they want and theextent to which constraints on borrowing distort behavior. Lochner and Monge-Naranjo (2011,2012) argue that the increased supply of student credit offered by private lenders over the late
1990s and early 2000s likely did not meet the growing demands of many potential students.33
However, there is little consensus regarding the extent and overall impact of credit constraints inthe market for higher education.34 We offer a brief review of evidence on borrowing constraints in
the U.S. education sector but refer the reader to Lochner and Monge-Naranjo (2012) for a morecomprehensive recent review.35
A few studies directly or indirectly estimate the fraction of youth that are borrowing constrained. In their analysis of college dropout behavior, Stinebrickner and Stinebrickner (2008)
directly ask students enrolled at Berea College in Kentucky whether they would like to borrow
more than they are currently able to. Based on their answers to this question, about 20% of recent
Berea students appear to be borrowing constrained. Given the unique schooling environment at
Berea – the school enrolls a primarily low-income population but there is no tuition – it is difficult to draw strong conclusions about the extent of constraints in the broader U.S. population,
including those who never enroll in college. Based on an innovative model of intergenerationaltransfers and schooling, Brown et al. (2011) estimate the fraction of youth that are constrained
based on whether they receive post-school transfers from their parents. Their estimates suggestthat roughly half of all American youth making their college-going decisions in the 1970s, 1980s
and 1990s were borrowing constrained. Finally, Keane and Wolpin (2001) and Johnson (2013)use different cohorts of the National Longitudinal Survey of Youth (NLSY) to estimate simi33

For example, private lenders almost always require a cosigner for undergraduate borrowers (Arvidson et al.,2013), so students whose parents have very low income or who have a poor credit record are unlikely to obtain
private student loans.
34
Caucutt and Lochner (2012) argue that credit constraints appear to distort human capital investments in young
children more than at college-going ages.
35
See Carneiro and Heckman (2002) for an earlier review of this literature.

29

lar dynamic behavioral models of schooling, work and consumption that incorporate borrowing
constraints and parental transfers. Using the 1979 Cohort of the NLSY (NLSY79), Keane andWolpin (2001) estimate that most American youth were borrowing constrained in the early 1980s,
whereas Johnson (2013) finds that few youth were constrained in the early 2000s based on the1997 Cohort of the NLSY (NLSY97). In the latter analysis, students are reluctant to take onmuch debt due to future labor market uncertainty.36 Unfortunately, the contrasting empiricalapproaches and sample populations used in these four studies make it difficult to reconcile theirvery different findings. There is little consensus regarding the share of American youth that facebinding borrowing constraints at college-going ages.
There is slightly more agreement about the extent to which binding constraints distort schoolingchoices. Most studies analyzing the NLSY79 find little evidence that borrowing constraints affectedcollege attendance in the early 1980s. Cameron and Heckman (1998, 1999), Carneiro and Heckman(2002), and Belley and Lochner (2007) all estimate a weak relationship between family income
and college-going after controlling for differences in cognitive achievement and family background.
Cameron and Taber (2004) find no evidence to suggest that rates of return to schooling vary withdirect and indirect costs of college in ways that are consistent with borrowing constraints. Even
Keane and Wolpin (2001), who estimate that many NLSY79 youth are borrowing constrained,find that those constraints primarily affect consumption and labor supply behavior rather thanschooling choices.
The rising costs of and returns to college, coupled with stable real government student loan limits, make it likely that constraints have become more salient in recent years (Belley and Lochner,
2007; Lochner and Monge-Naranjo, 2011). One-in-three full-time/full-year undergraduates in
2003-04 had exhausted their Stafford loan options, a six-fold increase over their 1989-90 counterparts (Berkner, 2000; Wei and Berkner, 2008). Despite an expansion of private student loan
opportunities, family income has become an increasingly important determinant of who attends
college. Youth from high-income families in the NLSY97 are 16 percentage points more likely
to attend college than are youth from low-income families, conditional on adolescent cognitive
achievement and family background; this is roughly twice the gap observed in the NLSY79 (Belley and Lochner, 2007). Bailey and Dynarski (2011) show that gaps in college completion rates
36
By contrast, Keane and Wolpin (2001) estimate very weak risk aversion among students. While the implieddemands for credit are high, the costs associated with limited borrowing opportunities are low based on theirestimates.

30

by family income also increased across these two cohorts; although, they do not account for differences in family background or achievement levels. Altogether, these findings are consistent with animportant increase in the extent to which credit constraints discourage post-secondary attendancein the U.S.37
Although Johnson (2013) estimates that fewer youth are borrowing constrained in the NLSY97
compared to estimates in Keane and Wolpin (2001) based on the NLSY79, Johnson (2013) findsthat increasing borrowing limits would have a greater, though still modest, impact on college
completion rates. His estimates suggest that allowing students to borrow up to the total costsof schooling would increase college completion rates by 8%.38 Unfortunately, neither of thesestudies help explain the rising importance of family income as a determinant of college attendance
observed over the past few decades.
Credit constraints may also affect the quality of institutions youth choose to attend. Belleyand Lochner (2007) estimate that family income has become a more important determinant ofattendance at four-year colleges (relative to two-year schools) in recent years. However, this is
not the case for income – attendance patterns at highly selective (mostly private) schools versus
less-selective institutions. Kinsler and Pavan (2011) estimate that attendance at very selective institutions has become relatively more accessible for youth from low-income families due to sizeable
increases in need-based aid that accompanied skyrocketing tuition levels. There is little evidence
that youth significantly delay college due to borrowing constraints (Belley and Lochner, 2007).
Borrowing constraints affect more than schooling decisions. Evidence from Keane and Wolpin(2001), Stinebrickner and Stinebrickner (2008), and Johnson (2013) suggests that consumption
can be quite low while in school for constrained youth. Constrained students also appear to work
more than those that are not constrained (Keane and Wolpin, 2001; Belley and Lochner, 2007).
Evidence from Belley and Lochner (2007) suggests that this distortion has become more importantfor high ability youth in recent years. Unfortunately, little attention has been paid to the welfare
impacts of these distortions on youth; however, the fact that schooling decisions are not affected
37

Belley and Lochner (2007) show that the rising importance of family income cannot be explained by a modelwith a time-invariant ‘consumption value’ of schooling.
38
Based on a calibrated dynamic equilibrium model of schooling and work with intergenerational transfers andborrowing constraints, Abbott et al. (2013) show that long-term general equilibrium effects of increased student
loan limits are likely to be smaller than the short-term effects (like those estimated by Keane and Wolpin (2001)
and Johnson (2013)) due to skill price equilibrium responses and to changes in the distribution of family assets
over time.

31

in Keane and Wolpin (2001) suggests that the welfare impacts of the consumption and leisuredistortions are probably quite small in their analysis.
As we discuss further in Section 6, uninsured labor market risk can discourage college attendance in much the same way as credit constraints might. Youth from low-income families may be
unwilling to take on large debts of their own to cover the costs of college when there is a possibility
that they will not find a (good) job after leaving school. Indeed, standard assumptions about risk
aversion coupled with estimated unemployment probabilities and a lack of insurance opportunities(i.e. repayment assistance or income-contingent repayments) imply very little demand for credit
in Johnson’s (2013) analysis. Navarro (2010) also explores the importance of heterogeneity, uncertainty, and borrowing constraints as determinants of college attendance in a life-cycle model. His
estimates suggest that eliminating uncertainty would substantially change who attends college;
although, it would have little impact on the aggregate attendance rate. Most interestingly, hefinds that simultaneously removing uncertainty and borrowing constraints would lead to sizeable
increases in college attendance, highlighting an important interaction between borrowing limits
and risk/uncertainty. The demand for credit can be much higher with explicit insurance mechanisms or implicit ones such as bankruptcy, default, or other options (e.g. deferment and forgivenessin government student loans). Despite their importance, the empirical literature on schooling has
generally paid little attention to the roles of risk and insurance. We examine these issues further
in the remaining sections of this paper.

5

Do Some Students Borrow Too Much?
Even if a growing number of American youth are finding it more difficult to finance the risingcosts of higher education, increases in student borrowing and default rates raise concerns that somestudents may be borrowing too much. In an uncertain economy, some students will inevitably failto repay their loans. Indeed, an optimal lending scheme will not fully recover the same amountfrom all borrowers.
In designing and evaluating student loan programs, it is important to know which borrowers
do not make their expected payments and under which conditions. Both government and private lenders are particularly interested in the expected returns on the loans they disburse. Whiledefault is a key factor affecting expected returns on student loans, other factors can also be im-32

portant. For example, government student loans offer opportunities for deferment or forbearance,
which temporarily suspend payments (without interest accrual in some cases). Expected returns
on income-contingent lending programs like ‘Pay As You Earn’ can lead to full or partial loan forgiveness for borrowers experiencing low income levels for extended periods, which clearly reduces
expected returns on the loans. The timing of income-based payments can also influence expected
returns if lenders have different discount rates from the nominal interest rates charged on theloans. Finally, the timing of default also impacts returns to lenders. It matters if a borrower
defaults (without re-entering repayment) immediately after leaving school or after five years of
payments, since the discounted value of payments is higher in the latter case. Put another way,
the creditworthiness of different borrowers (based on their background or their schooling choices)
depends on their expected payment streams and not simply whether they ever enter default.
Despite the recent attention paid to rising student debt levels and default, surprisingly little
is known about the determinants of student loan repayment behavior. Much of the literature
is based on studies of default from more than 30 years ago. For example, Dynarski (1994),
Flint (1997), and Volkwein et al. (1998) study the determinants of student loan default using
nationally representative data from the 1987 NPSAS that surveyed borrowers leaving school in
the late 1970s and 1980s.39 Gross et al. (2009) provide a recent review of this literature. Amongthe demographic characteristics that have been examined, most studies find that default rates arehighest for minorities and students from low-income families. The length and type of schooling also
matter, with college dropouts and students attending two-year and for-profit private institutions
defaulting at higher rates. Finally, as one might expect, default rates are typically increasing instudent debt levels and decreasing in post-school earnings.
Three very recent studies analyze student loan repayment/non-payment among cohorts that
attended college in the 1990s or later.40 Given the important changes in the education sector andlabor market over the past few decades, we focus attention on these studies; although, conclusions
regarding the importance of demographic characteristics, educational attainment, debt levels, andpost-school earnings for default are largely consistent with the earlier literature. In addition to39

Other U.S.-based studies analyze default behavior at specific institutions or in individual states. Schwartz and
Finnie (2002) study repayment problems for 1990 baccalaureate recipients in Canada.
40
In addition to the studies discussed in detail, Cunningham and Kienzl (2014) examine default and delinquency
rates by institution type and educational attainment for students entering repayment in 2005. Their findings are
consistent with results surveyed in Gross et al. (2009).

33

studying more recent cohorts, these analyses extend previous work by exploring a number of otherdimensions of student loan repayment/non-payment. First, using data on American students
graduating from college in 1992-93, Lochner and Monge-Naranjo (2014a) consider multiple measures of student loan repayment and non-payment (including the standard measure, default) ten
years after graduation in order to better understand how different factors affect expected returns on
student loans. Second, Gervais, Kochar, and Lochner (2014) analyze student loan default and nonpayment among American students attending two-year colleges in the late 1990s and early 2000s.
This analysis focuses on understanding important differences in default/non-payment across institution types as highlighted in Figure 7. Third, Lochner, Stinebrickner, and Suleymanoglu (2013)combine administrative and survey data to study the impacts of a broad array of available financial
resources (income, savings, and family support) on student loan repayment in Canada over the
past few years. We discuss key findings from each of these studies.

5.1

Student Loan Repayment/Nonpayment 10 Years after Graduation

Lochner and Monge-Naranjo (2014a) use data from the 1993-2003 Baccalaureate and Beyond
Longitudinal Study (B&B) to analyze different repayment and nonpayment measures to learn
more about the expected returns on student loans to different borrowers. The B&B follows arandom sample of 1992-93 American college graduates for 10 years and contains rich information
about the individual and family background of respondents, as well as their schooling choices,borrowing and repayment behavior.
Table 4 reports repayment status five and ten years after graduation in B&B. In both years, 8%of all borrowers were not making any payments on their loans. In addition to default, deferment
and forbearance are important forms of non-payment, especially in the earlier period. Table 5 documents varying degrees of persistence for different repayment states. Among borrowers making
loan payments (or fully repaid) five years after graduating, 94% remained in that state five years
later while only 4% had entered default. Roughly half of all borrowers in default five years after
school had returned to making payments (or fully repaid) after another five years, while 42% werestill in default. Not surprisingly, deferment/forbearance is the least persistent state, since it is designed to provide temporary aid to borrowers in need. Among borrowers in deferment/forbearance
five years after school, three-in-four were making payments (or had fully repaid), while 8.5% werein default five years later. The dynamic nature of student loan repayment status suggests that34

standard measures of default at any fixed date, especially in the first few years of repayment,
provide a limited picture of lifetime payments and expected returns to lenders. One would expect
greater persistence in non-payment as time elapses; however, the literature is surprisingly silent
on this issue.
Table 4: Repayment Status for 1992-93 Baccalaureate Recipients Five and Ten Years after Graduation (B&B)

StatusFully repaid
Repaying or fully paid
Deferment or forbearance
Default

Years Since Graduation
Five Years
Ten Years
0.269
0.639
(0.013)(0.013)0.920
0.917(0.008)(0.007)0.038
0.025(0.006)(0.004)0.042
0.058(0.006)(0.005)

Note: The table reports means (standard errors) for repayment
status indicators based on the B&B sample of borrowers.
Source: Lochner and Monge-Naranjo (2014a).

Using student loan records, Lochner and Monge-Naranjo (2014a) compute five different measures of repayment and nonpayment of student loans 10 years after graduation: the fraction of
initial student debt still outstanding, an indicator for default status, an indicator for nonpayment
status (includes default, deferment and forbearance), the fraction of initial debt that is in default,
and the fraction of initial debt that is in nonpayment. Analyzing the determinants of these repayment/nonpayment measures, they focus on the roles of individual and family background factors,
college major, postsecondary institution characteristics, student debt levels, and post-school earnings. Table 6 reports estimates for all five repayment/nonpayment outcomes based on their mostgeneral specification that simultaneously controls for all of these potential determinants. Only
variables that are statistically significant for at least one outcome are included.41
Among the individual and family background characteristics, only race is consistently important for all measures of repayment/nonpayment. Ten years after graduation, black borrowers owe
41

The table notes detail all other variables included in the analysis.

35

Table 5: Repayment Status Transition Probabilities for 1992-93 Baccalaureate Recipients (B&B)
Repayment Status Five
Years after Graduation
Repaying or fully paid
Deferment or forbearance
Default

Repayment Status Ten Years after Graduation
Repaying/Fully Paid Deferment/Forbearance
Default
0.939
0.020
0.040
(0.006)(0.004)(0.005)
0.749
0.165
0.085
(0.063)(0.057)(0.032)
0.544
0.038
0.418
(0.070)(0.020)(0.068)

Note: The table shows the probability of each status in 2003 conditional on the status in 1998. Estimates
based on the B&B sample of borrowers. Standard errors are listed in parentheses.
Source: Lochner and Monge-Naranjo (2014a).

22% more on their loans, are 6 (9) percentage points more likely to be in default (nonpayment),
have defaulted on 11% more loans, and are in nonpayment on roughly 16% more of their undergraduate debt compared with white borrowers. These striking differences are largely unaffectedby controls for choice of college major, institution, or even student debt levels and post-school
earnings. By contrast, the repayment and nonpayment patterns of Hispanics are very similar to
those of whites. Asians show high default/nonpayment rates (similar to blacks) but their sharesof debt still owed or debt in default/nonpayment are not significantly different from those ofwhites. This suggests that many Asians who enter default/nonpayment do so after repaying muchof their student loan debt. Maternal college attendance is associated with a greater share of debt
repaid after 10 years, while dependency status and parental income are largely unimportant for
repayment/nonpayment after controlling for other factors.
The B&B data reveal modest variation in repayment/nonpayment across college major choices;
however, which majors are most successful in terms of repayment depends on the measure. Engineering majors owe a significantly smaller share of their debts (than ‘other’ majors) after 10 years,
while social science and humanities majors owe a larger share. Humanities majors are also in
nonpayment on the greatest share of debt. Default rates are lowest for business majors, whereas
health majors default on the lowest fraction of their debts (these are the only significantly different coefficients). In most cases, differences in these repayment measures across majors are modest
compared with differences between blacks and whites. The increasing importance of college ma-36

Table 6: Effects of Significant Factors on Student Loan Repayment/Non-Payment Outcomes Ten
Years after Graduation
Share ofUG Debt
Variable
Still Owed
Black
0.216∗(0.040)Asian
0.107(0.062)
SAT/ACT Quartile 4
0.029(0.028)Mother some college-0.047∗(0.021)
Mother BA+-0.062∗(0.021)Business-0.020(0.032)Engineering-0.090∗(0.038)
Health-0.007(0.038)Social science
0.078∗(0.035)
Humanities
0.083∗(0.035)HBCU
0.041(0.069)1997 earnings-0.011∗($10,000s)(0.005)
2003 earnings-0.004($10,000s)(0.003)
UG loan amount
0.133∗($10,000s)(0.012)Fractionin
Default
0.055∗(0.022)0.072∗(0.033)0.006(0.018)0.023(0.014)0.003(0.015)-0.081∗(0.031)-0.018(0.029)-0.048(0.027)-0.022(0.024)0.001(0.023)-0.005(0.038)-0.001(0.004)-0.008∗(0.003)0.028∗(0.008)Fraction
Not
Paying0.085∗(0.025)0.089∗(0.038)0.006(0.020)0.008(0.016)-0.007(0.017)-0.051(0.029)-0.021(0.035)-0.020(0.029)-0.014(0.027)0.023(0.025)-0.040(0.044)-0.003(0.005)-0.012∗(0.003)0.039∗(0.008)

Default ×
Share of Debt
Still Owed
0.108∗(0.021)
0.003(0.033)0.022(0.015)0.001(0.011)-0.019(0.011)-0.024(0.017)-0.016(0.020)-0.042∗(0.020)-0.008(0.019)0.031(0.019)-0.060(0.037)-0.005(0.003)-0.001(0.001)0.029∗(0.007)

Not Paying ×
Share of Debt
Still Owed
0.158∗(0.029)0.008(0.045)0.041∗(0.020)-0.014(0.015)-0.013(0.016)-0.010(0.024)-0.008(0.028)-0.027(0.028)0.008(0.026)0.081∗(0.026)-0.117∗(0.050)-0.004(0.004)-0.004∗(0.002)0.034∗(0.009)The table reports estimated coefficients/average marginal effects on reported repayment/non-paymentoutcomes based on a sample of baccalaureate recipients in 1992-93. Outcomes are measured 10 years
after graduation, and regressors are only included in this table if the estimated coefficient on that variable
is statistically significant for at least one repayment/non-payment outcome. In addition to regressors
above, specifications also control for the following: gender; Hispanic; SAT/ACT quartiles 1-3; dependent
status; parental income (for dependents); major indicators for public affairs, biology, math/science,
history and psychology; institutional control indicators for private for-profit and private non-profit;
Barron’s Admissions Competitiveness Index indicators for most competitive, competitive, and noncompetitive; and state or region fixed effects. Standard errors in parentheses. ∗ p < 0.05.
Source: Lochner and Monge-Naranjo (2014a).

37

jor as a determinant of earnings (Gemici and Wiswall, 2011) suggests that greater differences inrepayment across majors for more recent students might be expected, but this is far from certain
given the modest role of earnings differences in explaining variation in repayment/nonpayment bycollege major.
Despite large differences in national cohort rates between four-year public and non-profit
schools on the one hand and for-profit schools on the other (see Figure 7), the multivariate analysis of Lochner and Monge-Naranjo (2014a) suggests little difference in repayment patterns acrossthese institution types after controlling for borrower characteristics.42 Thus, much of the difference
in default rates across institutions can be traced to differences in student composition. It is also
important to note that these results apply to students who graduate from college. As noted by
Deming et al. (2012), dropout rates are much higher at for-profit institutions. Since default rates
are typically higher for dropouts than graduates (Gross et al., 2009), at least some of the default
problem at four-year for-profit schools may simply reflect an underlying dropout problem.
Not surprisingly, borrowers are less likely to experience repayment problems when they have
low debt levels or high post-school earnings. As a ballpark figure for all repayment/nonpayment
measures, an additional $1,000 in debt can be roughly offset by an additional $10,000 in income.
For example, an additional $1,000 in student debt increases the share of debt in nonpayment by
0.3 percentage points, while an extra $10,000 in earnings nine years after graduation reduces thisshare by 0.4 percentage points.
Given the importance of post-school earnings for repayment, one might expect that differencesin average earnings levels across demographic groups or college majors would translate into corresponding differences in repayment/nonpayment rates — but this is not always the case. Despite
substantial differences in post-school earnings by race, gender, and academic aptitude, differencesin student loan repayment/nonpayment across these demographic characteristics are, at best,modest for all except race. And, while blacks have significantly higher nonpayment rates thanwhites, the gaps are not explained by differences in post-school earnings — nor are they explainedby choice of major, type of institution, or student debt levels. Differences in post-school earnings(and debt) also explain less than half of the variation in repayment/nonpayment across college
majors.
42

Lochner and Monge-Naranjo (2014a) include indicators for institutional control (public vs. private non-profit vs.
for-profit) and college selectivity as measured by Barron’s Admissions Competitiveness Index. Because coefficientestimates for all of these variables are insignificant in all specifications, they do not appear in Table 6.

38

An important general lesson of Lochner and Monge-Naranjo (2014a) is that differences between
default rates and other measures of nonpayment can be sizeable. For example, modest black-white
differences in default understate much larger differences in expected losses when measured by thefraction of initial debt still owed or in default after 10 years. The opposite is true comparing
Asians and whites.

5.2

Default and Non-Payment at Two-Year Institutions

As Figure 7 highlights, default rates have been highest at two-year institutions over most of thepast two decades. Gervais, Kochar, and Lochner (2014) use data from Beginning Postsecondary
Studies (BPS) to analyze the determinants of student loan default and non-payment for students
entering two-year colleges in 1995-96 and 2003-04. They measure default and non-payment (default, deferment or forbearance) six years after first entering college.
Estimating specifications similar to those of Lochner and Monge-Naranjo (2014a), Gervais,
Kochar, and Lochner (2014) also find significant default/non-payment differences by race after
controlling for other demographic factors, course of study, college grades, and highest degree.
Black students enrolling in two-year schools in 2003-04 were more than 10 percentage points more
likely to have non-payment problems and 5-10 percentage points more likely to be in default six
years after entering college. These differences were even larger for the earlier cohort. Family
income was also a significant factor for dependent students, reducing default and non-payment
rates. Differences in non-payment rates across course of study are mostly insignificant; although,education majors tended to have relatively high non-payment rates in the earlier cohort. The
highest degree obtained by students was very strongly (and statistically significantly) related to
non-payment. For example, 2003-04 students (initially enrolled in two-year schools) that obtained
an associate degree were roughly 10 percentage points less likely to be in non-payment, while those
who went on to finish a four-year baccalaureate degree were even less likely to experience payment
problems.
Gervais, Kochar, and Lochner (2014) devote considerable attention to the role of institution
control, examining differences in default and non-payment between public, non-profit, and forprofit institutions. Table 7 reveals qualitatively different patterns and time trends for default
and non-payment rates by type of two-year institution. Default rates were significantly higher
among students initially enrolling in for-profit two-year schools (21% vs. 9% for public school
39

Table 7: Default and Non-Payment Rates Six Years After Entering a Two-Year College (BPS)
1995-96 Cohort
Institution TypeDefault Non-Payment
Public9%25%
Private Non-Profit
14%30%
Private For-Profit
21%
29%

2003-04 Cohort
Default Non-Payment
8%
27%
15%
35%
24%
43%

The table reports default and non-payment (default, deferment or forbearance)
rates by institution type and BPS cohort.
Source: Gervais et al. (2014).

students) with a modest increase in the gap over time. By contrast, non-payment rates were quite
similar across school types for the earlier cohort (25-30%); however, the non-payment gap between
students attending public and for-profit schools grew considerably. For the 2003-04 cohort, forprofit students were 16 percentage points more likely to be in non-payment than were students
attending public schools. Put another way, rates of default and of forbearance/deferment havebeen relatively stable over time for students attending two-year public schools. While default
rates have only increased a few percentage points at for-profit schools, the fraction of students indeferment or forbearance has dramatically increased.
Focusing on the most recent cohort, estimates from Gervais, Kochar, and Lochner (2014)
suggest that differences in borrower characteristics (e.g., age, race, parental income and parental
education) account for 30-40% of the gaps in non-payment and default rates between public andfor-profit students; differences in post-school income explain about 40% of the remaining gap for
non-payment but none of the gap in default rates. Overall, roughly one-third of the gaps in nonpayment and default rates between two-year public and non-profit institutions can be attributed
to the types of students that enrol in these institutions. For-profit schools enroll students frombackgrounds that make them more likely to experience difficulties in student loan repayment. The
fact that students attending for-profit institutions tend to earn less after school also helps explain
why they are more likely to be in deferment/forbearance than students from public schools.

40

5.3

Evidence from Canada

As we discuss further below, an efficient lending program should provide some form of insurance
against uncertain labor market outcomes with payments depending on available resources. Whilelenders can expect some losses from impoverished borrowers, they should collect from those withadequate resources. Yet, measuring the full array of resources available to borrowers after theyleave school can be challenging. Although labor market income is an important financial resource,
access to other resources like personal savings, loans/gifts from families, or other in-kind assistancefrom families (e.g., the opportunity to live at home) may be readily available.
Combining administrative data on student loan amounts and repayment with data from the
CSLP’s 2011-12 Client Satisfaction Surveys (CSS), Lochner, Stinebrickner, and Suleymanoglu(2013) provide evidence on the link between a broad array of available resources (i.e., income,savings, and family support) and student loan repayment in Canada. Because their data also
contain questions soliciting borrowers views on the importance of repaying student loans and thepotential consequences of not doing so, they are able to account for heterogeneity in these factors
when assessing the importance of income and other resources.
For perspective, the official three-year cohort default rate of 14.3% for CSLP loans with repayment periods beginning in 2008-09 was very similar to the corresponding rate of 13.4% for the U.S.
More than one-in-four CSLP borrowers in their first two years of repayment were experiencing
some form of repayment problem at the time of the CSS.
Lochner, Stinebrickner, and Suleymanoglu (2013) estimate that post-school income has strong
effects on student loan repayment for recent Canadian students. Borrowers earning more than
$40,000 per year have non-payment rates of 2-3 percent, while borrowers with annual income ofless than $20,000 are more than ten times as likely to experience some form of repayment problem.
These sizeable gaps remain even after controlling for differences in other demographic characteristics, educational attainment, views on the consequences of non-payment, and student debt. On the
one hand, the very low non-payment rates among borrowers with high earnings suggest that student loan repayment is well-enforced in Canada. On the other hand, high delinquency and default
rates among low-income borrowers signal important gaps in more formal insurance mechanisms
like the CSLP’s Repayment Assistance Program (RAP).43
43
RAP is an income-contingent repayment scheme that reduces CSLP loan payments for eligible borrowers to’affordable’ amounts no greater than 20% of gross family income. See Section 3.3 for further details on RAP.

41

Despite relatively high non-payment rates for low-income borrowers, more than half of theseborrowers continue to make their standard student loan payments. Other financial resources in
the form of personal savings and family support are crucial to understanding this. Low-income
borrowers with negligible savings and little or no family support are more likely than not (59%) toexperience some form of repayment problem, while fewer than 5% of low-income borrowers withboth savings and family support do. Consistent with larger literatures in economics emphasizing the roles of savings and family transfers as important insurance mechanisms (Becker, 1991),
Lochner, Stinebrickner, and Suleymanoglu (2013) estimate that borrower income has small andstatistically insignificant effects on the likelihood of repayment problems for those with modest
savings and access to family assistance. By contrast, among borrowers with negligible savings andlittle or no family assistance, the effects of income on repayment are extremely strong. Measuresof parental income when students first borrow are a relatively poor proxy for these other forms
of self- and family-insurance, suggesting that efforts to accurately measure savings and potential
family transfers offer tangible benefits.
Interestingly, these findings may offer an explanation for the poor repayment performance ofAmerican black students conditional on their post-school income, debt and other characteristics as
discussed earlier. Given relatively low wealth levels among American blacks (Shapiro and Oliver,
1997; Barsky et al., 2002), it is likely that weaker financial support from parents at least partiallyexplains their high nonpayment rates.
These findings also have important implications for the design of income-contingent repayment
schemes. Lochner, Stinebrickner, and Suleymanoglu (2013) estimate that expanding RAP to automatically cover all borrowers would reduce program revenues by roughly half for borrowers earlyin their repayment period.44 This is because a more universal income-based repayment scheme
would significantly reduce repayment levels for many low-income borrowers who currently maketheir standard payments. At the same time, little revenue would be raised from inducing borrowers currently in delinquency/default to make income-based payments, since the vast majority ofthese borrowers have very low income levels.
Lochner, Stinebrickner, and Suleymanoglu (2013) find that slightly more than half of all lowincome borrowers have little self- or family-insurance. These borrowers currently have high delin44

RAP currently requires borrowers to re-apply every six months with eligibility restricted to borrowers with low
family income relative to their standard debt-based loan repayment amount. Any debt remaining after 15 years is
forgiven. See Section 3.3 for further details on RAP.

42

quency/default rates and would surely benefit from greater government insurance as discussed in
the next section. Yet, their results also suggest considerable caution is warranted before broadly
expanding current income-contingent repayment schemes. Many low-income borrowers have access to savings and family support that enables them to make standard payments. Lowering
payments for these borrowers based on their incomes alone (without raising payment levels forothers) could significantly reduce student loan program revenues. These results present significant
challenges regarding the appropriate measurement of borrower resources and the extent to whichloan repayments should depend on broader family resources and transfers (to the extent possible).

6

Designing the Optimal Credit Program
In this section, we use standard economic models to provide benchmarks on how credit andrepayment for higher education should be designed in order to maximize efficiency and welfare.
Using the same simple environment, we derive the optimal credit contracts under a variety of
incentive problems and contractual limitations. Starting from the “first best” – when investments
maximize expected net income and all idiosyncratic risk is fully insured – we sequentially consider
the impact on both investments and insurance of introducing limited commitment, incomplete
contracts, moral hazard (hidden action) and costly state verification. These incentive problems
are standard in the theoretical literature of optimal contracts and are the staple in some appliedfields (e.g. corporate finance); however, only recently have they been used in studies of humancapital investment. We go beyond the usual approach of analyzing one incentive at at time, andconsider models in which two or three incentive problems are present. While the analysis in thissection is largely normative, the implications of different models also provide useful insights about
the observed patterns of repayment and default.
We first consider a two-period environment in which we analytically characterize the natureof distortions introduced to investment and insurance by the different incentive problems. At theend of the section, we discuss richer environments in which other forms of dynamic incentives andcontractual issues may arise.

43

6.1

Basic Environment

Consider individuals that live for two periods, youth and maturity. Individuals are heterogenous in two broad characteristics: their ability, a > 0, and their initial wealth, W ≥ 0. Ability
encompasses all personal traits relevant to a person’s capacity to learn (when in school) and to
produce (when working). Initial wealth, which can be used for consumption and/or investment includes not only resources available from family transfers but also potential earnings during youth.
We take both a and W as given to focus on college education decisions. However, our analysis
could be included in richer settings in which families invest in early schooling for children (shapinga) and deciding on bequest and inter vivos transfers (determining W ).
A young person can invest in schooling, h, which augments his labor earnings in the next period.
We assume that investment is in terms of consumption goods, but more general specifications inwhich the cost of investment is also in terms of time can be easily added without changing thesubstance of our results.45 Post-school labor market earnings are given by
y = zaf (h) ,where f (·) is a positive, increasing, continuous and strictly concave function that satisfies the
Inada conditions. These assumptions ensure that investment in human capital is always positive.
Ability a and the function f (·) are assumed to be known by everyone at the time of investing h.
Labor market earnings and, therefore, the returns to human capital investment are also shiftedby labor market risk z, a continuous random variable with support Z = R+ . The distribution ofrisk z is endogenous to the exertion of effort, e, by the individual. However, we assume that it
is independent of (a, W ) and human capital investments h. At this point, one can interpret e as
either effort during school or during labor markets. What is essential is that a higher effort e leads
to a higher (first order increase in the) distribution of risk z.46
Our baseline model assumes that z has continuous conditional densities φ (· |e). Also, for mostof our analysis, we assume two levels of effort e ∈ {eL , eH }, where eL ≤ eH ; however, we briefly
discuss settings with more effort options below.
Throughout this section, we assume that financial markets are competitive. Lenders, or more
45

In the context of college, it is useful to think of h as reflecting a combination of both years of schooling andquality of the institution. We clearly abstract from issues related to the tradeoff between quality and quantity ofschooling to focus on the general nature of optimal loan contracts.
46
That is, for any function p (·) increasing in z, the conditional expectation E [p (z) |e] is increasing in e.

44

broadly, financial intermediaries, are assumed to be risk neutral. They evaluate streams of resources by their expected net present value, discounting future resources with a discount factorq ∈ (0, 1), the inverse of the risk-free rate (1 + r). We also assume that the lender is free fromincentive problems and can commit to undertake actions and deliver on contracts that ex-post
entail a negative net payoff. Finally, we assume equal discounting between the borrower and thelender (i.e. q = β) to simplify the exposition.47
We assume that borrowers evaluate consumption/effort allocations (as of the time they decide
their schooling) according toZu (ct ) − v (e) + βu (ct+1 ) φ (z|e) dz,(1)Z

where u (·) is the utility of consumption (an increasing and concave function) and v (·) is thedisutility of effort (an increasing function).
We use this environment to study the optimal design of student loans. In this environment,a student loan contract is an amount of credit d given by the lender to the student in the youth
period (while in school) in exchange for a repayment D (z) after school from the student to thelender. The repayment D (z) may depend on the realization of labor market risk z, as well as
all observed student characteristics and his investments in human capital. Along with the pair{d, D (z)}, an allocation of consumption, effort and human capital investment {ct , ct+1 , e, h} ischosen subject to the participation constraint of the lender,Z
D (z) φ (z|e) dz.
d≤β

(2)

Z

Once discounted, the expected value (conditional on e) of the repayments cover the cost of thecredit provided to the borrower. As for the borrower, initial consumption is given by
ct = W + d − h.

(3)

As students, individuals consume from their initial wealth W , plus resources borrowed from thelender (or deposited if d < 0) less resources invested in human capital. Second period consumption
may be risky and is given by
ct+1 (z) = zaf (h) − D (z) ,(4)47
Differences in discounting between the lender and the borrower lead to trends between ct and ct+1 (z). Suchtrends could be easily added, but they would complicate the algebra without providing any additional insights.

45

labor earnings less repayments (or plus insurance transfers from the lender if D (z) < 0).
In this environment, we consider a number of different incentive and contractual problems
that restrict the design of {d, D (z) ; ct , ct+1 , e, h}. We assume that initial wealth W , abilitya, first period consumption ct , and schooling investment h are always observable by creditors.
However, we will consider environments in which there may be limits on repayment enforcement(limited commitment), labor market outcomes y = zaf (h) might be costly to observe (costly
state verification), and effort e is not observable (moral hazard). In the first case, we also consider
the possibility of incomplete contracts, in which repayments cannot be made contingent on labormarket outcomes. We explore the optimal provision of credit and repayment design under each ofthese incentive problems.

6.2

Unrestricted Allocations (First Best)The natural starting point is the case in which neither incentive problems nor contractual
limitations distort investment and consumption allocations. In this case, the choice of {d, D(z);ct , ct+1 , e, h} maximizes the value of the borrower’s lifetime utility (1) subject to the break-evenor participation condition for the lender (2). The program reduces to choosing {d, D (z) ; e, h},because expressions (3) and (4) pin down consumption levels in both periods.
We first derive the allocations conditional on effort and then discuss the determination of
optimal effort. Consider the determination of {d, D (z) ; h} conditional on e = ei for i = L, H
(leaving the conditioning implicit for now). From the conditions for d and D (z), the optimal
allocation of consumption over time satisfies
u0 (ct ) = u0 (ct+1 (z)) .

(5)

Regardless of investment decisions, the optimal contract provides perfect insurance, i.e. full smoothing of consumption over labor market risk. Since utility u (·) is strictly concave, the equality of
marginal utilities also implies equality of consumption levels, i.e. ct+1 (z) = ct for all z. This
simple result highlights the fact that insurance is a crucial aspect of the ideal contract. When
repayments can be arbitrarily contingent on the realization of risk, the optimal allocation pushes
the lender to absorb all the risk. Full insurance could mean that the lender must make a positivetransfer to the borrower (D (z) < 0) after school, even if the lender provided the financing for
education and early consumption. Similarly, full insurance could mean that lucky borrowers end46

up paying the lender several times what they borrowed, which, as discussed below, may require
an unreasonable level of commitment on behalf of borrowers.
With respect to optimal investment in human capital, combining the first order conditions ford and h yields the condition
E [z|ei ] af 0 [h] = β −1 .

(6)

In the first best, the expected marginal return on human capital investment equals the risk freerate, i.e. the opportunity cost for the lender to provide credit. This result holds, because theborrower is fully insured by the lender and the lender is risk-neutral. Under these circumstances, it
is natural for investment in human capital to maximize the expected return on available resources,
regardless of the dispersion and other higher moments of labor market risk z.
Consider the stark predictions of this environment. Conditional on the level of effort, neither
the implication of consumption smoothing in (5) nor the choice of investment in (6) depend on
the individual’s wealth W . First, the full insurance condition indicates that lifetime consumption
profiles should be flat for all students: rich and poor, high and low ability alike. The values of W
and a only determine the level of consumption, not its response to income shocks z or evolution
over the lifecycle. Second, condition (6) indicates that all individuals invest at the efficient level,
regardless of whether they need to borrow a lot or nothing at all. Conditional on effort, only
ability a and the technology of human capital production determine investment levels. All otherindividual factors, including available resources W and preferences for the timing of consumption,
should not influence educational investments given effort; these factors only affect the financing ofinvestments. These sharp implications of the frictionless, complete markets model have provided
the basis for various tests of the presence and importance of credit constraints.48
We now compare the utilities and allocations conditional on the two effort levels and determine
which is optimal. Let hF (a, ei ) denote the first best level of human capital conditional on ei (i.e.
the solution to (6) conditional on both levels of effort, i = L, H). Notice first that investments will
be higher for high levels of effort, since E[z|eH ] > E(z|eL ). For each effort level, the present value
of resources for the borrower would be given by W − hF (a, ei ) + βE [z|ei ] af hF (a, ei ) . Since theagent is fully insured, consumption in both periods would equal
W − hF (a, ei ) + βE [z|ei ] af hF (a, ei )c (W, a; ei ) =
.
1+β
F

48

See Lochner and Monge-Naranjo (2012) for an overview of this literature.

47

Consumption levels are strictly increasing in wealth W and ability a, as well as the expected
realization E [z |ei ]. Since the latter is increasing in e, higher effort is also associated with higher
consumption. Conditional on effort levels, the level of utilities, as of the time when investments
are decided equal
U F (W, a; ei ) = (1 + β) u cF (W, a; ei ) − v (ei ) .
Whether high effort is optimal in the first best (i.e. whether U F (W, a; eH ) > U F (W, a; eL ))depends on the counterbalance of wealth effects in the demand for consumption cF (W, a; ei ) vs. thedemand for leisure or utility cost of higher effort. When utility is separable between consumption
and effort as assumed here, leisure is a superior good. Given ability a, a sufficiently high wealth W
implies that the marginal value of consumption is low, as is optimal effort (and investment). Given
wealth W , individuals with higher ability would find it more desirable to exert higher effort. Thus,
more able individuals would exhibit more investment due to both the direct impact of ability on
earnings and the indirect impact of ability on effort.
We now study how different incentive problems distort investment in and insurance for humancapital by reshaping the allocation of credit and the structure of repayments. To focus our discussion on these issues, we abstract from effort decisions until we introduce moral hazard in Section
6.5.

6.3

Limited Commitment

A crucial, yet often implicit, assumption in the solution of optimal credit arrangements is thatboth parties can fully commit to deliver their payments as contracted. In practice, borrowers
sometimes default on the repayments, or at least face the temptation to do so. A rational lendershould foresee these temptations and determine conditions under which default will take place.
Formally, the lender can foresee the borrower’s participation constraints necessary to preclude
default. In this section, we consider the implications of borrower commitment problems. We first
assume that repayment functions D (z) can be made fully contingent on the actual realization oflabor market risk z. Then, we examine the case in which these contingencies are ruled out.
6.3.1

Complete Contracts with Limited Enforcement

Limited commitment problems are often invoked for investments in education, because humancapital is a notably poor collateral (Becker, 1975; Friedman and Kuznets, 1945). While human48

capital cannot be repossessed, the cost of defaulting on a loan might depend directly on the
education of the individual as it determines his earnings. Then, the amount of credit a person
could obtain would be endogenously linked to his investments in education, as these investments
determine the amount of credit that the borrower can credibly commit to repay (Lochner andMonge-Naranjo 2011, 2012).49
To formalize this argument, assume that once a borrower leaves school, he can always opt
to default on a repayment D (z) contracted earlier. But, default is not without its costs. For
simplicity, assume that a defaulting borrower loses a fraction κ ∈ (0, 1) of his labor earnings, so
his post-school consumption is cD
t+1 (z) = (1 − κ) zaf (h). These losses could reflect punishments
imposed by lenders themselves (e.g. wage garnishments) or by others (e.g. landlords refusing torent or employers refusing to hire). Alternatively, the borrower could repay D (z) yielding postschool consumption cR
t+1 (z) = zaf (h) − D (z). The borrower’s decision is straightforward: repay
if the cost of defaulting exceeds the cost of repaying:
D (z) ≤ κzaf (h) .

(7)

Obviously, if reneging on the debt were costless (κ = 0), then no student loan market could besustained, since no borrower would ever repay. Similarly, if κ is high enough, the temptation todefault could be eliminated, and we would be back to the first best.
The restrictions (7) can be seen as participation constraints on the borrower. As long as they
are satisfied, the credit contract ensures that the borrower remains in the contractual arrangement.
Any contract in which default occurs can be replicated by a contract without default by setting
D (z) = κzaf (h). Since default is costly for the borrower and the lender does not necessarily
recover all of those losses, optimal contracts in this setting would always prevent default. The
optimal lending contract is similar to the first best problem only restricted so that condition (7)holds for all z ∈ Z.
Let λ (z) be the Lagrange multipliers associated with the inequality (7) for any realized z.50 The
optimal program maximizes the value of the borrower’s lifetime utility (1) subject to the breakeven or participation condition for the lender (2), the expressions (3) and (4) for consumption
during and after school, and inequality (7) for all z ∈ Z.
49

We only consider one-sided limited commitment problems where the lender can fully commit. This is naturalwhen considering the optimal design of government credit arrangements.
50
The multipliers are discounted and weighted by probabilities, i.e. the term βφ (z) λ (z) multiplies the condition(7) for each z.

49

The first order optimality conditions for this problem are straightforward. The optimal repayment value D (z) conditional on the realization z implies the following relationship between
ct+1 (z) and ct :u0 (ct ) = [1 + λ (z)] u0 [ct+1 (z)] .
For states of the world in which the participation constraint is not binding (i.e. D (z) < κzaf (h)),λ (z) = 0 and there is full consumption smoothing: ct+1 (z) = ct . However, when the participation
constraint is binding, λ (z) > 0 and ct+1 (z) > ct . The participation constraint restricts therepayment that can be asked of the borrower for high labor market realizations. In turn, those
restrictions limit the capacity of the student to borrow resources while in school, resulting in low
school-age consumption relative to post-school consumption in high-earnings states.
From the first order conditions for d and h, one can show that optimal human capital investment
satisfies 

1 + κλ (z)af [h] E z= β −1 .
1 + λ (z)
0

(8)

i
h 
< E [z] as long as κ < 1 and participation constraints bind (i.e.
Notice that E z 1+κλ(z)1+λ(z)
λ (z) > 0) for some realizations of z. Comparing (8) to (6), it is clear that, given concavity inf (·), the inability to fully commit to repayment reduces human capital investment below the first
best level. The presence of limited commitment effectively reduces the expected return on humancapital due to the inability to effectively borrow against returns in the highest earnings states orto spread the resources from those states to other states with fewer resources.
In contrast to the unrestricted environment above, family resources W are a determinant ofinvestment levels under limited commitment. Individuals with low wealth levels will want toborrow more while in school. This raises desired repayment amounts D(z) in all future states,
causing participation constraints to bind more often and more severely. Thus, poorer students
face greater distortions in their consumption and investment allocations than wealthier students.
It is important to understand the nature of credit constraints that arise endogenously fromthe participation constraints associated with commitment problems. As with any other model ofcredit constraints, this environment predicts inefficiently low early consumption levels for thosethat are constrained (i.e. a first order gain could be attained by increasing early consumption andreducing post-school consumption for some labor market realizations). A more unusual aspectof constraints in this environment is that they arise due to an inability to extend insurance to50

fully cover high earnings realizations. The participation constraints do not restrict the ability tosmooth consumption across adverse labor market outcomes, since the contract allows for negative
repayments for low enough realizations of z. Rather, the limits arise due to the incentives ofborrowers to default on high payments associated with strong positive earnings outcomes. The
lender must reduce requested repayments in those states to drive the borrower to indifference
between repaying and defaulting. This reduction in repayments must be met with less credit
up front.51 Finally, it is important to note that default never formally happens in equilibrium,
because repayments D (z) are designed to provide as much insurance as possible while avoiding
default.
The ability to write fully contingent contracts is important for many of these results. As weshow next, contracts and borrower behavior differ substantially if the repayment function D (z)cannot be made contingent on labor market realizations.
6.3.2

Incomplete Contracts with Limited Enforcement

Now, consider the same contracting environment, only add the restriction that repayments
cannot be made contingent on labor market realizations z. Instead, assume that any lending
amount d is provided in exchange for a “promise” to repay a constant amount D. However, as in
the previous subsection, the borrower retains the option to default, which will be exercised if it isin his best interest ex post. Of course, lenders are aware of this and incorporate this possibility
into the contracts they write. For simplicity, we assume that lenders do not recover any payments
when borrowers default.52
With incomplete contracts, just two amounts (d, D) must balance multiple trade-offs. On
the one hand, the fact that contracts cannot provide explicit insurance against downside risks
leaves the option of default to take on that role, at least partially. On the other hand, borrowers
no longer have an incentive to default when they experience high earnings realizations, since
the repayment amount does not increase with earnings. As a result, limited commitment with
51

An interesting illustration of limited commitment is the failure of Yale’s Tuition Postponement Option, which was implemented in the 1970s and finally rolled back in 1999. The most successful participants ‘bought out’ of their commitment to pay 4% of their income as specified by the plan. See
http://yaledailynews.com/blog/2001/03/27/70s-debt-program-finally-ending/.
52
Assuming that the lender recovers a fraction of the defaulting costs simply adds an additional term in the
break-even condition for the lender. See Lochner and Monge-Naranjo (2012) and the discussion in Section 6.6.2
below.

51

incomplete contracts may generate default from borrowers with low earnings as an implicit – andimperfect – form of insurance against downside labor market risks. This insurance is implicitly
priced by lenders as they incorporate the probability of default in the amount of credit d that they
offer in exchange for a defaultable promise to repay a given amount D.
To develop the optimal contract, consider a person with ability a who enters the labor market
with human capital investment h and student debt D. The decision of whether to honor the debt
or default on it depends on the labor market realization z. If the borrower repays, his post-school
consumption is ct+1 (z) = zaf (h) − D, while it is ct+1 (z) = (1 − κ) zaf (h) if he defaults. The
borrower is better off repaying when the realization z equals or exceeds the threshold
z̃ ≡

D
;
κaf (h)otherwise, he would be better off defaulting. Prior to learning z, the probability of default is given
R z̃
by Φ (z̃) = 0 φ (z) dz. At the time schooling and borrowing/lending decisions are made, default
is a stochastic event with the probability increasing in the amount of debt and decreasing in the
borrower’s ability and investment. Both ability and investment determine the borrower’s earnings
potential and are important factors for the credit contract.
Contemplating the probability of being defaulted upon, the participation constraint for thelender becomesd ≤ βD [1 − Φ (z̃)] .

(9)

The right hand side is the discounted expected net repayment, where we have assumed thatthe lender receives zero in case of default. Borrowers pay an implicit interest rate of D/d =β −1 [1 − Φ(z̃)]−1 , which is increasing in the probability of default.53
The expected utility for a student with wealth W and ability a who invests h in his humancapital, borrows d, and “promises” to repay D is
Z z̃

Z ∞
u [W + d − h] + βu [ (1 − κ) zaf (h)] φ (z) dz +u [ zaf (h) − D] φ (z) dz .
0

(10)

z̃

The first term reflects utility while in school, and the rest reflects expected post-school utility overboth repayment and default states. Maximizing the borrowers utility (10) subject to the lender’sparticipation constraint (9), the first order conditions for d and D (after some basic simplifications
53

Students with high enough wealth W may choose to save (d < 0) receiving payment −d/β after school.

52

and use of the expression for z̃) produce the following condition:u0 (ct ) =E [u0 (ct+1 (z)) | z > z̃],
1 − η (z̃) Dz̃φ(z̃)
where η (z̃) ≡ 1−Φ(z̃)> 0 is the hazard function for labor market risk z.54 In this model, borrowing

or lending does not lead to the standard Euler equation for the permanent income model (i.e.
u0 (ct ) = E [u0 (ct+1 )]), because here each additional unit of borrowing increases the probability ofdefault and raises implicit interest rates. Even if early consumption is low relative to expected
future consumption, borrowers may not want to take on more debt because of worsening interest
rates on inframarginal dollars borrowed.
The first order condition for investment h can be re-written as00
E [zu (ct+1 (z))] − κΦ (z̃) E [zu (ct+1 (z)) |z < z̃] hiE [z] af 0 (h) = β −1 .
f 0 (h)0E [z] u (ct ) 1 − βDφ (z̃) z̃ f (h)Limited commitment with incomplete contracting produces a wedge (the term in brackets) between
the expected marginal return to human capital and its marginal cost.
The human capital investment wedge consists of four distinct economic forces. The first two
derive from the nature of constraints that arise when defaulters are disciplined via losses that
depend on their earnings. First, human capital returns are reduced by a fraction κ in states thattrigger default. This implicit tax on earnings unambiguously discourages investment. Second,
human capital investments improve credit terms by reducing the likelihood of default. This force0(h)< 1 in the denominator. This ‘credit expanis captured by the expression 1 − βDφ (z̃|eH ) z̃ ff (h)sion’ effect encourages human capital investment. The third force derives directly from market
incompleteness, which limits consumption smoothing. Imperfect insurance leads to a negative covariation between labor market realizations z and their valuation u0 (ct+1 ), since ct+1 is increasing
in z. Hence, E [z · u0 (ct+1 )] < E [z] · E [u0 (ct+1 )]. This reduces the marginal value of investment
54

The first order conditions are as follows:[d]: u0 (ct ) = λ
(
)
Z z̃
Z ∞
∂ z̃
0
0
0
[h]: u (ct ) + λβDφ (z̃|eH )= βaf (h) (1 − κ̃)zu [(1 − κ̃) zaf (h)] φ (z|eH ) dz +zu [zaf (h) − D] φ (z|eH ) dz
∂h
0
z̃


Z ∞

∂ z̃
0
[D]: λ β (1 − Φ (z̃|eH )) − βφ (z̃|eH )=βu [zaf (h) − D] φ (z|eH ) dz
∂Dz̃0

where λ is the Lagrange multiplier on the lender’s participation constraint.

53

relative to the case with full insurance, since individuals are unable to optimally allocate the uncertain returns on their investments across labor market states. The fourth force comes from thefact that u0 (ct ) > E [u0 (ct+1 (z)) | z > z̃], i.e. that school-age consumption is too low relative tosome post-school states when the returns of human capital arrive. Unless the credit expansion
effect is particularly strong, it seems likely that this environment would yield under-investment in
human capital and a positive relationship between family wealth W and human capital.
Combined with limited commitment, the absence of repayment contingencies has a numberof important empirical and policy implications. First, as indicated already, default can occur
in equilibrium. Second, if default occurs, it is for low realizations of z when both earnings andconsumption are low. Third, the option of default serves a useful insurance role, since by defaulting,the borrower can maintain a higher level of consumption when his labor market outcomes are poor.
Thus, eliminating default may be inefficient and could even reduce investment in human capital.
Fourth, the probability of default is explicitly linked to the ability and educational investment
decisions of borrowers. More able borrowers who invest more in their human capital, all else
equal, should have lower default rates. Fifth, the model also shows how student loan terms
and repayments need to be adjusted for the probability of default. The implicit interest ratehi−1
is β −1 1 − Φ κafD(h), an equilibrium object that depends on ability a and human capital
investment h, as well as the distribution of labor market shocks z, because of their impacts on thedefault rate.
Despite the many simplicity and attractive features of this framework, it is difficult to justify
the lack of any explicit contingencies on either theoretical or empirical grounds. Theoretically,such an assumption requires prohibitively high costs of writing contracts or an inability of lenders
to observe anything about the labor market success of borrowers. Empirically, we observe explicit(albeit limited) income contingencies in repayment in both government and private student loan
markets as described in Section 3.
The model also abstracts from other important incentive problems that can distort humancapital accumulation and its financing. We discuss several of these problems in the next few
subsections.
Finally, this framework is a weak normative guide, since it abstracts from a primal component
on the design of student loan programs, namely, the design of repayment of loans D (z), even whenincorporating contingencies on repayment is a costly endeavor.
54

6.4

Costly State Verification

Instead of arbitrarily ruling out contingent repayments, we now consider an environment inwhich lenders must pay a cost ϑ ≥ 0 to observe/verify the borrower’s post-school earnings. Contingencies become costly, because the repayment D (z) cannot be made contingent on z unlessthere is verification. If there is no verification, then the repayment is a fixed amount D̄, which
implicitly depends on the amount borrowed. To explore this friction in isolation, we abstract fromother incentive problems until Section 6.6 below. The environment in this subsection is, therefore,
a straight adaptation of Townsend’s (1979) costly state verification model to the study of humancapital and student loans.
As in Townsend (1979), we can solve for the optimal contract by considering truthful revelation
mechanisms that specify a contingent repayment D (z) in cases of verification, and a constant
repayment D̄ in all others.55 It can be shown that, since contingencies in D (z) are driven by
insurance motives, verification will only occur for low realizations of z < z̄, where the optimalvalue of threshold z̄ must trade-off the provision of insurance against the cost of verification.
Recognizing this, the participation condition for the lender can be written asZ z̄D (z) φ (z) dz − ϑΦ (z̄) + D̄ [1 − Φ (z̄)] .
d≤β

(11)

0

The first term in brackets reflects expected payments received (or paid if D (z) < 0) from the borrower if there is verification, while the second term reflects the expected costs of verification. The
third term reflects expected repayments when there is no verification. Given any d, D (z) , D̄, h ,a borrower’s expected utility is

Z z̄
Z z̄


u [zaf (h) − D (z)] φ (z) dz +u zaf (h) − D̄ φ (z) dz .
u [W + d − h] + β
0

(12)

0

55

More formally, as the borrower uncovers his realization z in the labor market, he makes an announcement ẑ
to the lender. Upon this announcement, the lender can either: (i) verify the announcement (χ (ẑ) = 1) at costϑ to learn the true outcome and execute a payment Dv (z, ẑ) that depends on the realized and announced labormarket outcomes; or (ii) not verify the borrower’s announcement (χ (ẑ) = 0), avoiding the cost ϑ, and request a
repayment Da (ẑ) based only on the announced ẑ. We assume that the lender can commit to carry out pre-specified
verification policies χ : Z → {0, 1} that map announcements to verification decisions. The borrower knows thispolicy and therefore, knows the set of announcements that trigger verification and those that do not.
It is easy to see that the lender would not be able to tell apart different announcements for which χ = 0.
Borrowers that avoid being verified would announce the ẑ associated with the lowest repayment. Therefore, for allstates of the world in which there is no verification, the borrower repays D̄ = inf {z:χ(z)=0} {Da (z)}. It is also thecase that, upon verification, the lender can provide as much insurance as needed. The optimal contract would alsorule out detectable deviations, e.g. by setting zero consumption for borrowers they catch in a lie (i.e. z 6= ẑ).

55

The optimal student loan contract in this setting maximizes (12) subject to (11). Combining
the first order conditions for d and D (z) yields
u0 (ct ) = u0 (ct+1 (z)) for z < z̄.
The optimal contract provides full consumption smoothing (ct+1 (z) = ct ) across school and postschool periods for “bad” states of the world in which verification occurs. Once z is truthfully
learned by both parties, it is optimal for the risk neutral lender to absorb all residual risk. Whileleft implicit above, borrower’s characteristics such as ability a and wealth W , as well as aspects ofthe environment like verification costs ϑ and the distribution of labor market risk φ(z), determine
the set [0, z̄] for which this takes place. These factors also affect the level of consumption ct for
the early period and for the states of verification.
The previous result is useful to derive the optimal region for verification. Consumption ct+1 (z)does not exhibit a jump at the threshold z̄, because the borrower could deviate and attain a firstorder gain. The condition ct+1 (z̄) = ct imposes a direct link between z̄, D̄, and ct in the form
ct +D̄z̄ = af. Since increases in the level of consumption under verification ct or in the required(h)payment in the absence of verification D̄ both increase the value of verification for the borrower,
the region of verification must also increase to satisfy the lender’s participation constraint. The
verification region decreases with investment, because h improves the distribution of consumption
under non-verification ct+1 (z), which discourages verification.
With these conditions, the optimal loan program can be solved entirely in terms of ct , D̄, h .
Let ψ denote the Lagrange multiplier on the lender’s participation constraint (11).56 The firstorder conditions for this problem imply that ct (consumption during school and after when there
is verification) is set so that




1
βϑφ (z̄).
u (ct ) = ψ 1 +
1 + βΦ (z̄) af (h)056The concentrated Lagrangian in terms of ct , D̄, h is


Z z̄


L = u (ct ) + β u [ct ] Φ (z̄|eH ) +u zaf (h) − D̄ φ (z|eH ) dz
0




Z z̄
+ ψ W + β af (h)zφ (z|eH ) dz − (ϑ + ct ) Φ (z̄|eH ) + D̄ [1 − Φ (z̄|eH )] − h − ct ,0

ct +D̄
where z̄ = af
(h) .

56

(13)

The second term in braces represents the increased verification costs associated with a higher ct .
Aiming to save on costs of verification, the optimal contract reduces the level of ct and, therefore,
student loan amounts. Similarly, after some simplification, the optimal level of D̄ leads to thefollowing conditionE [u (ct+1 (z)) | z > z̄] = ψ 1 − η (z̄)
0ϑaf (h)

,(14)

where η (·) is the hazard rate as defined above. As with ct , the fixed level of debt repayment D̄ isreduced also with the aim of reducing verification costs.
From expressions (13) and (14), it is clear that u0 (ct ) > E [u0 [ct+1 (z)] | z > z̄], and the implied
behavior of consumption is consistent with the usual notion of credit constraints. This is also thecase when we look at implications for optimal investment in human capital. From the first ordercondition for h, we can show that investment in human capital satisfiesE [min {z, z̄}]0
E [z] af (h) Γ + (1 − Γ) ×
≥ β −1 ,E [z]0(ct+1 (z))|z>z̃]< 1 and the human capital investment wedge in braces iswhere 0 < Γ ≡ (1+β)E[uu0 (ct )+βE[u0 (ct+1 (z))]

less than one. The lack of consumption insurance for higher earnings realizations due to costly
verification reduces the marginal value of human capital and discourages investment.
Costly verification of income yields an endogenous form of market incompleteness in which
lenders require the same payment from all borrowers who receive “good” labor market shocks.
In this respect, the model is similar to the limited commitment framework above in which we
exogenously ruled out all explicit income contingencies (subsection 6.3.2). However, the distinction
between endogenous partial market incompleteness due to costly verification and exogenous fullmarket incompleteness with limited commitment is quite important, since these two models yieldvery different implications for borrowers who receive adverse labor market outcomes. In theincomplete markets model with limited commitment, these unlucky borrowers enter default, which
entails additional losses or penalties and reduces consumption levels below income levels. By
contrast, under costly state verification, unlucky borrowers are audited and receive full insurance.
Empirically, we certainly observe default in countries without fully income-contingent loan
programs like the U.S. and Canada. However, many borrowers with low post-school earnings also
receive significant reductions in their payments through forbearance or deferment. Others also
take advantage of more explicit income-contingent plans for low earners. Still, even low income

57borrowers do not appear to receive full insurance from student loan programs.57 As we see next,
introducing other forms of asymmetric information can help in understanding when this imperfect
insurance might be desirable.

6.5

Moral Hazard

A college education not only requires readily observable investment expenditures like tuition,
fees, and materials (h in our setting), but it also requires other student-specific inputs that may
be more difficult to measure and control, like effort and the choice of school and courses appropriate for a student’s talents and potential.58 While these actions may be crucial for a successful
college experience, they may also be “hidden” or difficult to control and monitor by lenders. We
incorporate these hidden actions by explicitly modeling a costly effort e. When the lender does
not observe this effort, a “moral hazard” problem can arise, as the costs of effort fall entirely on
the borrower while the ensuing returns can be shared between the student and the creditor.
To examine the design of student loan contracts to deal with these incentives, we re-consider
the determination of effort. Recall our assumption: High effort is costly, v (eH ) > v (eL ), but also
productive in that it improves the distribution of labor market shocks z. That is, the distributionof labor market risk under high effort dominates (in the first order sense) the distribution under
low effort. Even stronger, we assume a monotone likelihood ratio, i.e. l (z) ≡ φ (z|eL ) /φ (z|eH ) isstrictly decreasing. We also assume that the support of z is the same under both levels of effort
so there are no perfectly detectable deviations (realizations of z that can happen under one but
not the other effort level). We restrict l (z) to be bounded from below and from above.
The moral hazard problem arises, because the level of effort e cannot be directly controlled
by the lender. Therefore, the level of investment h, the amount of credit d, and repayments D(z)must be designed so that the borrower finds it in his own best interest to exert the effort expectedby the creditor. For now, we consider a model in which moral hazard is the sole incentive problem.
We defer to Section 6.6 cases in which moral hazard interacts with previously discussed contractual
frictions.
57
It is important to note that other forms of social insurance (e.g. unemployment insurance, welfare) may effectively deliver a fixed minimal consumption level for a range of low post-school income levels.
58
While we emphasize effort in school, our analysis applies equally to unobservable effort in the labor market(e.g. job search effort) or to the tradeoff between higher paying jobs and those that may be more appealing onother grounds (Rothstein and Rouse, 2011).

58

Consider first a student with ability a and wealth W that faces a contract {d, h, D (·)} offered
by a lender that expects he will exert the high level of effort, eH . If the student conforms, he obtains
an expected utility level equal to UH = u (ct ) − v (eH ) + βE [u [zaf (h) − D (z)] | eH ]. If he instead
deviates and shirks, his expected utility is UL = u (ct ) − v (eL ) + βE [u [zaf (h) − D (z)] | eL ]. If
the high effort eH is to be implemented, the contract {d, D (z) , h} must satisfy the following
incentive compatibility constraint (ICC) UH ≥ UL :Z ∞u [zaf (h) − D (z)] [φ (z|eH ) − φ (z|eL )] dz ≥ 0.
[v (eL ) − v (eH )] + β

(15)

0

The optimal student loan contract is found by choosing {d, D (z) ; e, h} to maximize theexpected utility of the borrower (1) subject the break-even or participation condition for thelender (2) and the accounting expressions for consumption in both periods, (3) and (4). If the
optimal contract requires high effort from the student, then condition (15) must also be satisfied.
Relative to the first best, the provision of insurance must give way, at least partially, to rewards
for the student’s success.
Let µ ≥ 0 denote the Lagrange multiplier associated with condition (15). Combining the firstorder conditions for d and D (z), it is straightforward to obtain the relationshipu0 [ct+1 (z)] [1 + µ (1 − l (z))] = u0 (ct )(16)between current and future consumption for any labor market outcome z. Since the likelihood
ratio l (z) is monotonically decreasing, when the ICC (15) is binding, µ > 0 and post-school
consumption ct+1 (z) is strictly increasing in z. The economics underlying this result are clear:since effort is unobservable, the only way for the contract to induce high effort is to reward higher
earnings with higher consumption. This is effective, because high realizations of z are more likely
with high effort while low realizations of z are more likely with low effort. The lender must adhere
to this rule in order to induce high effort even if he knows that the contract always induces higheffort. The downside of these contracts is that unlucky students must bear low consumption evenwhen they have exerted high effort. Finally, notice that if high effort is not optimal so the contract
need not induce it, then e = eL , µ = 0, and full insurance can be provided: ct+1 (z) = ct .
The first order condition for human capital investment h can be written as
βaf 0 (h) {(1 + µ) E [zu0 (ct+1 (z)) |eH ] − µE [{zu0 [ct+1 (z)] |eL }]} = u0 (ct ) .
59

(17)

On the left-hand side, the first term inside braces denotes the value of earnings from additional
human capital. A term weighted by µ is added, because investments help relax the ICC. In thesame vein, the negative term multiplied by µ reflects the negative impact on the ICC that arises
from a higher value on the option to shirk. The right hand side is simply the marginal cost of one
unit of investment.
Interestingly, using the consumption optimality condition (16), we can replace the values foru0 [ct+1 (z)] in terms of u0 (ct ) and the ratio l (z). After simplifying, the condition (17) reduces tothe first best condition
af 0 (h) E [z|eH ] = β −1 .
As long as the contract induces the first best level of effort e = eH , it also yields the first bestlevel of investment h. More generally, it is optimal to design the contract so that the first best
investment amount is chosen for whatever effort is exerted. Importantly, this implies that if
the repayment schedule D (z) is well-designed and can induce appropriate effort, the education
prospects of students that need to borrow are the same as those coming from richer families thatcan self-finance their education. The “cost” of borrowing for economically disadvantaged students
comes in the form of imperfect insurance.
The key with moral hazard is in the design of D (z), which can be a difficult task. It is useful1−σ

to illustrate this point using the well-known CRRA utility function u (c) = c1−σ with σ > 0. The
post-school consumption schedule (16) becomes1

ct+1 (z) = ct [1 + µ (1 − l (z))] σ ,which is delivered by setting the repayment to1

D (z) = zaf (h) − ct [1 + µ (1 − l (z))] σ .
Given the condition that l (0) > 1, the contract yields ct+1 (z) < ct for low values of z. That is,unsuccessful students experience a fall in their consumption after school. However, notice thatsome insurance is still being provided, as D (z) may be negative. On the contrary, for high valuesof z, the likelihood ratio l (z) < 1, so successful students are rewarded with an increase in theirconsumption.
Even with this specific functional form, it is not possible to say much about the shape of
ct+1 (z) except that it is increasing. Likewise, except for the fact that D (z) might be negative at60

low values of z, little more can be said regarding its shape unless more information is available on
the distribution of labor market outcomes and the risk preferences of borrowers. In fact, not eventhe monotonicity of D (z) can be established. In any event, a reliable empirical characterization ofrisks and preferences is necessary to characterize even the most general features of optimal student
loan programs.
Thus far, we have emphasized the case in which high effort is optimal. This need not be thecase if, for example, either a or W is so low that most of the resources generated by investment
need to be repaid to the lender, leaving little for the borrower to consume. Low effort might also be
efficient for very high wealth individuals, who place more value on leisure (i.e. low effort) than theextra consumption that comes from exerting higher effort. If low effort is optimal, then investment
for those exerting low effort is set to the first best under low effort: af 0 (h) E [z|eL ] = β −1 ; since
the ICC is not binding, µ = 0 and full insurance is provided, i.e. ct+1 (z) = ct for all z. The
problem of moral hazard only distorts investment choices for those who are discouraged fromputting forth high effort when it would otherwise be optimal. Since utility associated with higheffort is distorted due to imperfect insurance while utility associated with low effort is not, there
will be a set of (W, a) values for which effort and investment choices are distorted by moral hazard.
The sharp result that conditional on effort investment is not distorted (relative to the firstbest) generalizes to any number of potential effort choices. Additionally, if any two individuals
with the same ability end up exerting the same effort, then they will make the same educational
investment and attain the same prospects for labor earnings, regardless of their family wealth.59
However, the finding that either consumption or effort and investment are distorted, but not
all simultaneously, is special to two effort levels. With more effort levels, all three (consumption,
effort, and investment) may be distorted. This will generally be the case when there is a continuumof effort levels.
Rather than exploring a richer structure for moral hazard, we now direct our discussion to theless explored environments in which moral hazard co-exists with other primal incentive problems,
costly state verification and limited commitment.
59

Similarly, suppose two individuals possess the same ability level but one lives in an environment with moral
hazard and the other does not. If their wealth levels are such that they both end up exerting the same effort level,
they will both make the same investment.

61

6.6

Multiple Incentive Problems

In this section, we examine the optimal design of student loan programs in environments inwhich multiple incentive problems coexist.
6.6.1

Costly State Verification and Moral Hazard

Consider now the case in which both the effort e of the student cannot be observed by thelender and the actual labor market outcome can only be verified by the lender at a cost ϑ > 0. The
loan contract must be designed to address both of these information frictions to provide as muchinsurance as possible to the borrower while making sure the creditor is repaid in expectation.
Because of the cost ϑ, the optimal verification policy will preserve the threshold property ofSection 6.4: If the borrower realizes a labor market outcome z below a threshold z̄, the lender
will verify the outcome at cost ϑ and request repayment D (z) (which can be negative) that iscontingent on z. Otherwise, if z ≥ z̄, the lender will not bother to verify and the borrower repays
a fixed amount D̄. In both cases, the repayment can be set as a function of previously determined
and known variables such as d, a and h; however, we leave this conditioning implicit. Expressions
for the lender’s participation constraint (11) and borrower’s expected utility (12) are the same as
for the costly state verification (CSV) model above.
The contract must also induce the optimal level of effort. If low effort eL is optimal, then there
is no moral hazard problem and the optimal contracts are of the pure CSV case studied in Section
6.4. However, if high effort eH is to be induced, then the contract must satisfy an ICC modified
by the threshold property of the verification policy. That is, the expected discounted gains frombetter labor market outcomes should more than compensate the student for the cost of effort:

Z z̄
Z ∞


β
u [zaf (h) − D (z)] [φH (z) − φL (z)] dz +u zaf (h) − D̄ [φH (z) − φL (z)] dz
0z̄≥ v (eH ) − v (eL ) ,(18)

where we defined φi (z) = φ (z|ei ) for i = H, L to shorten the expression.
Given a student’s ability a and wealth W , the optimal loan contract sets d, h, z̄, D̄ and D (z)for z < z̄ aiming to maximize (12) subject to the break-even constraint (11) and the ICC (18).
As argued in the pure CSV case, consumption should not jump at the threshold of verification,
so ct+1 (z̄) = z̄af (h) − D̄. Therefore, we can write D̄ = z̄af (h) − ct+1 (z̄), and solve for it as afunction of the threshold z̄.
62

The first order conditions for the amount of credit d and repayments D(z) in a state of verification imply
u0 [ct+1 (z)] [1 + µ (1 − l (z))] = u0 (ct )for all z < z̄,(19)where µ is the Lagrange multiplier on (18). When verification occurs, we recover exactly the same
relationship between marginal utilities of consumption (and, therefore, consumption distortions)as in the pure moral hazard case (given µ).60 Here, verification does not generally yield fullconsumption smoothing (as in the CSV model) due to the need to incentivize effort. However, if
the conditional distributions of low-income realizations (i.e. z < z̄) are quite similar across effort
levels, then l(z) will be relatively flat in the relevant region and considerable consumption insurance
can be provided at the low end of the income distribution. Moral hazard is less of a concern at highincome realizations, since verification does not take place and payments are independent of income
for z ≥ z̄. For high z, consumption allocations are such that u0 [ct+1 (z)] [1 + µ (1 − l (z))] < u0 (ct ).
The first order condition for z̄ implies that the threshold is set according to the condition∂ D̄
u0 (ct )= ϑη (z̄|eH ) 0
,
(20)
∂ z̄
u (ct ) − E [u0 (ct+1 (z)) (1 + µ [1 − l (z)]) | z ≥ z̄; eH ]where η (·|eH ) is again the hazard function as defined above (evaluated at z̄ here) conditional onhigh effort. The left-hand side represents the increased fixed payment D̄ needed when setting ahigher verification threshold; the right hand side compounds the increased expected cost of verification with a measure of the distance between the consumption schedule outside the verification
region and the ideal schedule used to provide incentives and insurance as in (19). For ϑ > 0, thelatter (in brackets) is greater than zero but less than one.
Finally, with respect to the optimal investment in human capital, the first order condition forh can be written as
E [min{z, z̄}|eH ] E {[z − z̄] u0 [ct+1 (z)] [1 + µ (1 − l (z))] |z ≥ z̄; eH }0
E [z|eH ] af (h)+= β −1 ,E [z|eH ]E [z|eH ] u0 (ct )(21)
which is derived using condition (19) for z < z̄. Verification costs leave upside risk uninsured, so
the term inside brackets is strictly less than one, and investments in this environment are lower
than the first best.
60

However, note that the values of µ, ct and the range of z for which (19) holds now depend on the verification
cost ϑ.

63

The combination of costly state verification and moral hazard produces a very useful benchmark
for the design of optimal student loan arrangements. On the one hand, this framework incorporates
the desire to save on verification and other administrative costs. When income verification iscostly, it should only occur when labor market outcomes are particularly low. In these cases,
the commitment of lenders to verify some of the lower reports by the borrower provides themwith the right incentives to truthfully report those states to reduce their payments. Doing so,
the program can provide at least some insurance for the worst labor market realizations, precisely
when borrower’s are most in need of it. On the other hand, moral hazard implies that even forthese unlucky borrowers the optimal arrangements must sacrifice some insurance and consumption
smoothing in order to incentivize effort. Moral hazard also reduces the value of verification itself,sice the ability to provide insurance is limited.
While the optimality conditions can be algebraically cumbersome, the general structure of the
optimal contract is quite simple. To illustrate this point, consider the CRRA specification usedearlier. For some positive values µ, ct , and z̄ (which should depend on a borrower’s ability andwealth), the loan repayment is1α
D (z) = zaf (h) − (1 + µ [1 − l (z)]) × ct − ϑ if z < z̄D̄
if z ≥ z̄
yielding post-school consumption
ct+1 (z) =1(1 + µ [1 − l (z)]) α × ct if z < z̄zaf (h) − D̄
if z ≥ z̄.

Above a certain threshold, the borrower absorbs all upside risk, paying a constant amount independent of z; however, downside risk is shared between the borrower and the lender. Absent
moral hazard concerns, risk neutral lenders would absorb all downside risk; however, with moral
hazard, it is optimal to make borrowers bear some of the downside risk to help incentivize effort.
If low realizations are the smoking gun of low effort, then little insurance must be provided.
Finally, it is important to recognize that even if the contract is optimally designed, insurance
may be quite limited and human capital will be lower than under full insurance in the first best.
This naturally implies that human capital investments will be responsive to family wealth W
among borrowers. Yet, such a relationship does not necessarily imply an inefficiency in existing
credit arrangements, but instead it may signal that information or commitment frictions areimportant in the student loan market.
646.6.2

Limited Commitment: Default or Additional Constraints?

The previous arrangement was derived under the assumption that both the borrower and thelender could fully commit to any post-school payments. As we saw in the pure limited commitment
model above, relaxing this assumption can have important implications for the optimal student
loan arrangement. We now explore the interactions between limited commitment, moral hazard,
and costly state verification – the three main credit market frictions we have considered. As
above, assume that the borrower can always default on the repayment to the lender, but thatdoing so entails a cost that is proportional to his income. In addition to the lender’s break-even or
participation constraint and the incentive compatibility constraint, the contract must also respect
the no-default restrictions D (z) ≤ κzaf (h) for all z if default is to be avoided. As discussed
below, however, default may sometimes be an optimal feature of contracts with costly verification.
Consider first the case with costless income verification (ϑ = 0), but when both moral hazard
and limited commitment constrain contracts. The optimal contract maximizes (1) subject to theparticipation condition for the lender (2), the ICC condition (15), and the no-default constraints(7). As above, let µ be the Lagrange multiplier associated with the ICC and λ (z) the multiplierassociated with (7) for each z.
Following the same steps as in the previous models, the optimal allocation of consumption
must satisfy
u0 [ct+1 (z)] [1 + µ (1 − l (z)) + λ (z)] = u0 (ct ) .
For those states in which (7) does not bind, λ (z) = 0 and consumption smoothing is distorted
only to induce high effort as in the pure moral hazard case. On the contrary, if the no-default
constraint (7) does bind, then ct+1 (z) = (1 − κ) zaf (h) and the impact of λ (z) > 0 and µ > 0
must be accommodated via lower borrowing d (and school-age consumption ct ) and lower humancapital investment h, which must now satisfy the condition
1 + µ (1 − l (z)) + κλ (z)E z×eH af 0 (h) = β −1 ,1 + µ (1 − l (z)) + λ (z)where the term in brackets is less than E [z|eH ] if the no-default constraint binds for any z. Thus,
incorporating limits on contract enforceability produces under-investment in human capital when
there is moral hazard even if the efficient amount of ability is induced. As in the case without
moral hazard (see Section 6.3.1), individuals under-invest, because they cannot spread the rewards
65

from investment in very high-income states to other states nor can they fully borrow against thesestates. Moral hazard can further reduce investment relative to the pure limited commitment case,especially for individuals who are not induced to provide the efficient amount of effort.
Importantly, when ϑ = 0, the ability to set D (z) fully contingent on the realization z rules out
default in equilibrium. Any contract that involves default in some states can always be replicatedby a contract in which the borrower repays κzaf (h) in those states, which would make the lenderstrictly better off and the borrower no worse off. The fact that the lender can be made better off
implies that he can also offer a better contract to the borrower that eliminates default.
This is not necessarily true when verification is costly (i.e. ϑ > 0). With costly verification,
there will be some z for which the lender verifies the borrower’s announced outcome (denoted by
the indicator function χ (z) = 1) and others for which he does not (χ (z) = 0). In the latter case,the repayment is a constant amount D̄ independent of z. For the set of all other realizations, thelender verifies and requests a payment of D(z). Altogether, the borrower has three options once
he observes z: (i) repay D̄ without asking for verification; (ii) request verification and pay/receive
an amount D (z) that depends on z; or (iii) default and forfeit a fraction κzaf (h) of his income.
In case (iii), the lender receives nothing.
Given repayment contract D (z) , D̄ , the borrower will choose to default whenever κzaf (h) <D (z) in verification states and κzaf (h) < D̄ in non-verification states. Yet, lenders know thisand will take it into account when designing contracts. On the one hand, it is possible that the
optimal contract would set both D̄ and D(z) below κzaf (h) for all relevant values of z, thereby
precluding default as when ϑ = 0. On the other hand, with non-negligible verification costs, it ispossible that default is preferred by both borrower and lender alike for some realizations of z.
Under what conditions might default arise under optimal contacts? To answer this question,
it is useful to think about default as just another repayment state or as part of a contract. For
default to happen in equilibrium, it has to be that both borrowers and lenders would be better
off if the borrower opts to default. For borrowers to prefer defaulting, repayment must be morecostly than default, D (z) > κzaf (h). For lenders to prefer default, the cost of verification ϑ must
exceed payments under verification. Taken together, default is only possible (though not assured)
when ϑ > κzaf (h).
Default becomes more attractive to lenders if they can capture some of the defaulting borrowers
losses. To explore this possibility, suppose the borrower still loses a fraction κ of his income upon66

default, but assume that the lender can recover a fraction κ0 ≤ κ of those losses. That is, lenders
recover κ0 zaf (h) from defaulted loans as would be the case under wage garnishments. If thelender chooses to verify, at most he would receive a payoff of κzaf (h) − ϑ once verification costs
are subtracted. Ex post, the lender would prefer to be defaulted upon if z falls below a thresholdz A defined by
zA =

ϑ
.
(κ − κ0 ) af (h)Among other things, this threshold reiterates the fact that default should not occur if verificationis costless, since this implies z A = 0. An alternative extreme arises when ϑ > 0 and the lender
captures all default losses, κ0 = κ. If so, z A → ∞, and ex post a lender would always prefer toabandon the lending contract rather than verify it. However, this does not mean that verification
never occurs. Ex ante, the lender may want to offer and commit to deliver on a contract in which
D (z) is low, or even negative for some z, in order to provide valuable insurance.
Default should be seen as an option for the lender in his design of the repayment function
D (z). The lender can always set the value of D (z) below the cost of default and preclude that
action by the borrower. The option of setting the repayment D (z) above the default cost κzaf (h)for some z, allows the lender to avoid having to pay the verification cost. This option can be used
to save on verification costs and ultimately, allow lenders to offer better contracts to borrowers.
Altogether, the design of the optimal repayment function {D̄, D(z)} must meet a number of
constraints and objectives: it must ensure that the expected repayment less any verification costs(plus any amounts received in the case of default) cover the lender’s cost of funds; it must balance
the provision of insurance with incentives to encourage effort by the student; and it must properly
weigh the costs of verification with losses associated with default. Like verification, default is one

67possible tool or option for the lender.61
We now discuss repayment patterns in terms of verification (V), default (D), and full repayment(R). We consider the most tractable case in which κ0 → κ, and ϑ > 0, so z A = ∞. The shapeof the likelihood function l (z) can give rise to a number of possibilities as illustrated in Figure 9.
In all four cases, the horizontal axis represents labor income realized after school, zaf (h). The
vertical axis reflects the level of consumption for alternative responses of the borrower: fully repay(blue, dashed line), default (red, dash-dot line) or partial payment D(z) < D̄ based on verification(green, dashed line) as given by condition (19). The continuous black line in each graph represents
the upper envelope of these different responses, i.e. the equilibrium post-school consumption level
for the borrower.
Panel (a) reflects the case without moral hazard. In this case, the borrower asks for verification when earnings are low, triggering a repayment/transfer designed to yield him the same
consumption as during school. For high earnings, he would rather just repay the constant amountD̄. If default occurs, it is only for intermediate labor market outcomes. A similar pattern canarise when moral hazard is present, as shown in panel (b). Because higher effort is associatedwith better outcomes in the labor market, consumption under verification is strictly increasing in
61

Recall χ : Z → {0, 1} is an indicator function if there is verification (χ = 1) or not (χ = 0). Similarly, letξ : Z → {0, 1} be the indicator function of whether the participation condition of the borrower is binding (ξ = 1)
or not (ξ = 0). Then, the break-even condition of the lender becomes
Z



d≤β
(1 − ξ) χ (D (z) − ϑ) + (1 − χ) D̄ + ξκ0 zaf (h) φ (z|eH ) dz.
(22)
Z

It can be shown that full repayment must occur for an upper interval [z̄, ∞). Hence, the expected discounted utilityof the borrower is given by
Z z̄

Z ∞
  D





u (ct ) + β
ξu c (z) + χu cV (z) φ (z|eH ) dz +u zaf (h) − D̄ φ (z|eH ) dz ,
(23)
0

z̄

where cD (z) = (1 − κ) zaf (h) and cV (z) = zaf (h) − D (z), are the consumption levels in the cases of default andverification, respectively. Finally, using (23), we can derive the relevant ICC for the optimal contracting problem,
which is also subject to the participation constraints (7).
The optimal contract maximizes initial utility (23) subject to the break-even constraint (22) of the financial
intermediary, and subject to the relevant ICC (not derived here). The participation constraints (7), must also besatisfied. However, more than a no default condition, in this case, default occurs whenever the constraints (7) bind,because the borrower is indifferent between requesting verification or defaulting and the lender is strictly betteroff not having to verify. In those cases, D (z) = κzaf (h). On the other hand, when (7) are slack and there isverification, then D (z) is set according to the condition (19) as in the model when limited commitment is not abinding constraint. The threshold z̄ for full repayment and the human capital investment level are set according
to similar expressions as (20) and (21) but with corrections for the regions of default.

68Figure 9: Consumption Patterns and Verification (V), Default (D), and Repayment (R) Behavior
in a Model with Costly State Verification, Moral Hazard, and Limited Commitment
7

7

Default

Verify6

Repay
6

Default
Verify5consumption, ct+1(z)consumption, ct+1(z)

5

4

3

2

Repay
4

3

2

1

1

cons. if repays
cons. if defaults
cons.if verify

cons. if verify or repay
cons. if default
0

0

1

2

3

4

5

6

7

8

9

0

10

0

1

2

3

4

income, y=zaf(h)(a) No Moral Hazard: V, D, R
7

6

6

VerifyDefault(z)

t+1

consumption, c

4

Repay
3

cons. if repays
cons. if defaults
cons.if verify

2

Verify Default

Verify

1

2

3

4

5

6

9

10

Repay

Default

4

3

1

0

8

2

1

0

7

5

consumption, ct+1(z)Verify6(b) Moral Hazard: V, D, R

7

5

5

income, y=zaf(h)

7

8

9

0

10

income, y=zaf(h)cons. if repays
cons. if defaults
cons. if verify
0

1

2

3

4

5

6

7

8

income, y=zaf(h)(c) Moral Hazard: V, D, V, R(d) Moral Hazard: V, D, V, D, R

69

9

realized income, as required by the ICC on effort.
Panel (c) of Figure 9, shows that a very different pattern can also emerge. If the function l (z) isrelatively flat at the low end of outcomes but particularly steep in the intermediate range (i.e. effort
has weak effects on the likelihood of low-income realizations but strong effects on the likelihoodof intermediate realizations), then there can be two separate verification regions separated by aregion of default. In this case, the region of default includes low to intermediate outcomes. Finally,as shown by panel (d), multiple regions of verification and default can alternate before reaching
the full repayment region. This could happen when the function l (z) switches multiple times
from convex to concave and multiple steep regions of consumption under partial repayment leadto multiple crossings of this function with consumption under default.
Notice that for all possibilities, verification occurs at the low end of income realizations. Thishighlights two crucial aspects of the optimal contract. First, providing insurance for the worst
income realizations is quite valuable. Second, default can be a useful but imperfect insurance
tool, that is always dominated by partial insurance at the very low end. Also, notice that full
repayment is always the preferred option for high labor market outcomes. When labor market
outcomes are very high, the marginal value of insurance is quite low. Given the desire to save on
verification costs, a constant repayment amount is preferred to providing additional insurance andpaying those costs. Furthermore, the losses associated with default grow with income, making a
constant payment preferable to both borrower and lender.

6.7

Related Literature

Our basic two-period model generates a number of lessons on how to design student loansthat are self-financed, provide insurance, and optimally address a number of incentive problems,
including limited commitment, moral hazard, and costly state verification. This framework notonly generates endogenously restricted borrowing, but it also produces interesting patterns interms of repayment and default. Some of these aspects deserve further exploration. Our analysis
also omits a number of important incentive problems and the potential interactions of student
loans with other public and private institutions. In particular, we have abstracted from issues ofadverse selection (prior private information of borrowers about their potential returns on humancapital or their willingness to repay), taxes, subsidies and other government interventions in credit
markets, as well as social welfare programs like unemployment insurance. Rather than trying to70

tackle all of these issues within our framework above, we review recent and ongoing work in eachof these areas.62 For reasons of space, we only discuss the research most closely related to our
objectives in this monograph.
A series of papers by Ionescu (Ionescu, 2008, 2009, 2011), analyzes models with contractual frictions and incentive problems. Her primary objective in these papers is to study college enrollment,
borrowing, and default decisions when credit is subject to limited commitment and moral hazard.
Her analysis is directed specifically to existing government student loan programs and suggeststhat default rates are not generally higher among individuals that are most financially constrained.
Instead, those that are constrained appear to be more restricted in terms of investment and borrowing. Most interestingly, she considers the impact of various forms of repayment flexibility (e.g.,
lock-in low interest rates, switching to income-contingent repayments, or alternative bankruptcy
discharges) in calibrated versions of her models. Consistent with our analysis above, she findsthat the degree to which contingencies (repayment flexibilities) can be incorporated into student
loan repayment schemes can have significant effects on schooling and welfare. More than hardborrowing constraints, the lack of insurance can be the limiting factor for schooling decisions.
Chatterjee and Ionescu (2012) consider student loans that offer insurance against the risk offailing college, a non-trivial risk for recent U.S. college cohorts. Their model considers adverse selection and moral hazard. Their findings suggest that offering loan forgiveness when a student fails
college can lead to significant welfare gains without adverse impacts on enrollment or graduation
rates. If forgiveness is also provided to students that choose to leave college without necessarily
failing, the welfare gains are still positive but lower than under conditional forgiveness. Unconditional forgiveness raises enrollment and graduation, but is less efficient because of the adverse
incentives it produces.
Related and complementary work by Eckwert and Zilcha (2012) and Hanushek, Leung, andYilmaz (2014) studies different impacts of alternative repayment arrangements and government
interventions in the market for student loans. Eckwert and Zilcha (2012) consider different repayment alternatives in a model where individuals’ abilities are heterogeneous and publicly known,
but there is also exogenous labor market risk.63 They abstract from borrowing for consumption
62

Friedman and Kuznets (1945) first raise the issue of income-contingent loans to deal with uncertainty andlimited commitment problems, while Nerlove (1975) offers an early analysis of ex ante adverse selection and ex post
moral hazard in reference to such loans.
63
Alternatively, we can think of initial ability as a signal of true ability realized upon labor market entry.

71purposes and from family transfers, further requiring that all investment expenditures must be
borrowed. Using a three-period-lived overlapping generations (OLG) model, they contrast the resulting human capital, welfare and growth outcomes from three different student loan repayment
schemes: (i) standard loan with fixed interest rate (i.e. no insurance); (ii) insurance with poolingacross abilities (i.e. payments are a function of realized income but not initial ability), so there
is cross-subsidization from high to low ability types; and (iii) insurance within ability groups, so
there is no ex ante cross-subsidization. Their analysis produces two important conclusions. First,
providing insurance conditional on ability (regime iii) is better for human capital investment,
growth and welfare relative to a standard loan scheme (regime i). Second, risk-pooling conditionalon ability (regime iii), relative to unconditional pooling (regime ii), improves educational outcomes
and also improves welfare as long as individuals are not too risk averse. Both of these conclusions
highlight the importance of insurance and its counterbalance with proper incentives.
Hanushek, Leung, and Yilmaz (2014) use a three-period-lived OLG environment with heterogeneity in ability, exogenous borrowing constraints, and intergenerational bequests to evaluate
the implications of different stylized education policies for economic efficiency, inequality, and intergenerational mobility. In their framework, interventions can be welfare improving due to theborrowing constraint and the lack of insurance against uncertain labor market outcomes. They
consider uniform education subsidies, merit-based subsidies, need-based subsidies, and loans withincome-contingent repayment. Regarding the latter, students are restricted to borrow the full costof college (or not at all) and must repay a constant fraction of their post-school income. While thisstructure, like that of government student loan programs in many countries, provides a limited
form of insurance, it can also generate an adverse selection problem by encouraging lower ability
students to attend (and borrow) for college even if their labor market returns are low. Their calibrated model produces a number of interesting results. First, merit aid performs poorly in termsof both equity and efficiency, because parental income and ability are highly correlated. Second,an income-contingent loan may end up subsidizing low ability children from well-off parents at thecost of high ability children from poor parents, because the latter repay more than the former. Thishighlights the problems with loan programs that effectively pool individuals of different abilities
with ex ante cross-subsidization. Third, while income-contingent loans can perform quite well inproviding insurance and reducing inequality, a sizeable need-based aid program can perform betterin terms of equity and efficiency. Finally, they demonstrate that general equilibrium responses to72policy through changing skill prices are nontrivial.
Abbott et al. (2013) also study education subsidies and standard student loan programs (withdebt-based repayments and no default) in a richer OLG general equilibrium environment withfull lifecycles, incomplete markets, post-school labor market uncertainty, and inter vivos transfers.
Based on their calibrated model, they conclude that current student loan programs in the U.S.
improve welfare over the alternative of no government lending. However, further expansions of
traditional student loans (without any income-contingencies) would have very minor effects on
education choices and welfare.64 Contrary to Hanushek, Leung, and Yilmaz (2014), Abbott et al.
(2013) do not consider different student loan repayment schemes; however, they do find thatgeneral equilibrium responses are important in evaluating policies.
Adverse selection is the central focus of Del Rey and Verheyden (2013). They consider anumber of policy interventions in an economy with competitive credit contracts under limited
commitment, adverse selection (due to heterogeneous unobserved ability), and labor market risk.
Different equilibria may arise depending on the degree of contract enforcement, e.g. separating
equilibria with some insurance if enforcement is high; pooling equilibria with no insurance (but withex-post default) with moderate punishments. The student loan market collapses if enforcement is
too weak.
Del Rey and Verheyden (2013) highlight a number of policy insights. For example, a government subsidy to banks can lead to some credit in equilibrium even when enforcement is so weakthat student credit markets would not survive in laissez faire. Also, by requiring universal participation and limiting private competition, the government might be able to enforce pooling acrossindividuals of different ability/risk and provide partial insurance. However, as in Eckwert andZilcha (2012), this would entail taxing high ability students to subsidize those of low ability. One
concern is the extremely stylized nature of their model, binary choices and outcomes for nearly
every dimension (e.g., invest/not invest, successful/failure in school, high/low ability, borrow fullschooling costs vs. no investment/borrowing) and the extent to which their main results would
hold in more realistic environments.
The papers mentioned thus far consider specific policy interventions without necessarily deriving optimal policies. Related to this, it is relevant to recall that the traditional problem of64

Keane and Wolpin (2001) and Johnson (2013) also find modest effects of expanding current loan limits (without
income contingencies), while Navarro (2010) finds that expanding both loan limits and extending full insurance
could have very large effects on enrollment decisions.

73

optimally designing taxes and other government transfer programs has been revisited over the lastfifteen years by the ’New Dynamic Public Finance’ literature, which has moved away from theRamsey tradition (taking a set of taxes as given) toward the Mirrleesian tradition (deriving optimal taxes from an incentive-constrained contracting problem).65 A few papers in this tradition(Bovenberg and Jacobs, 2011; Bohacek and Kapicka, 2008; Kapicka, 2014; Kapicka and Neira,2014; Stantcheva, 2014) have included endogenous human capital formation in their analyses of
optimal taxation, considering education subsidies as instruments to cope with tax distortions.
Most papers within the Mirrleesian paradigm derive optimal non-linear taxes in environments
in which labor income is observed but the underlying combination of ability, effort and humancapital is not observed. Therefore, taxes must be set entirely as a function of observed earnings
even if it would have been desirable to tax effort, ability and human capital separately (the lattermay or may not be observed). Taxes are set to maximize a welfare function, typically utilitarian,subject to an incentive compatibility constraint on each individual, to ensure that high ability(and/or human capital if unobserved) types do not exert low effort and impersonate a low ability(and/or human capital) type.
For the study of human capital accumulation, the state-of-the-art in this tradition is Stantcheva(2014). In her model, human capital can be accumulated with both, real resources (e.g. tuition)and training time (e.g. on-the-job training). Labor market earnings are determined not only byhuman capital and labor effort, but also a stochastic yet persistent ability term. Her model allows
for fairly general wage functions, which can change over time. Stantcheva (2014) assumes that the
government does not observe ability (neither its initial realization nor its lifetime evolution).
In Stantcheva’s framework, it is optimal for the government to subsidize human capital expenses, counterbalancing distortions on the taxation of wage and capital income, encouraging
labor supply, and providing insurance against adverse draws of productivity in the labor market.
Whether full deductibility of education expenses is optimal depends on whether the ability elasticity of wages is increasing in education. Similarly, whether training time must be deducted fromtaxes depends on whether labor effort increases (learning-by-doing) or reduces (on-the-job training) future earnings. While the optimal taxation program is quite complex, Stantcheva (2014)
reports numerical results which suggest that simple linear age-dependent policies can come fairly
close to the second best and that full deductibility of expenses might be close to optimal.
65

See Golosov, Tsyvinski, and Werning (2007) for an overview of this literature.

74

The public finance literature with optimal education subsidies and progressive taxes tackles
the same basic economic problem as our optimal contracting formulation, namely, transferring resources across time (post-school to the schooling period) and across different post-school earnings
realizations. Despite sharing similar objectives, the two formulations have notable differences intheir emphases. First, the Mirrleesian problem assumes a utilitarian objective, such that redistribution across ex ante heterogeneous but unobserved abilities is an important aspect of the optimal
policy. In our optimal contract formulation above, ability and wealth are observable and each loan
must be paid in expectation. Therefore, the resulting allocations can be easily implemented byprivate markets or by the government. Moreover, it is straightforward to handle observed wealthheterogeneity in the optimal contracting formulation.66 Some of the optimal allocations in the Mirrleesian framework may require the authority to tax or to regulate participation in markets, since
as illustrated by the failure of the “Yale Plan” discussed above, students with the best earnings
prospects may simply not join or find a way to drop out. Second, the public finance literature uses
as instruments grants or deductions and progressive taxes, while the optimal contract formulation
specifies loan amounts and their implied repayments. The bridge between the two formulations
is illustrated by recent work by Findeisen and Sachs (2013, 2014) and Gary-Bobo and Trannoy(2014). They use a Mirrleesian problem to derive the optimal repayment for different loans froma menu available to borrowers. The menu of loans must be designed to deal with adverse selection
and moral hazard (ex ante and ex post heterogeneity) including unobserved effort exertion whilein the labor market.
The work by these two sets of authors is highly complementary. Gary-Bobo and Trannoy (2014)
consider a more stylized environment (two ability types) and are able to prove that the optimalarrangement entails incomplete insurance (because of moral hazard as in our model) and typicallyinvolves cross-subsidization across students of ex ante different ability levels. More interestingly,
loan repayments cannot be decomposed as the sum of an income tax (depending only on ex-postschool earnings) and a loan repayment (depending only on student debt). Therefore, optimal loan
repayments must be income-contingent, or equivalently, income tax must comprise a student loantax.67 Findeisen and Sachs (2013) consider a richer environment with a continuum of types.68
66

In this respect, see the work of Mestieri (2012) that considers unobserved heterogeneity in both wealth andability, giving rise to a role for entry exams.
67
Unfortunately, their analysis does not include differences in family wealth.
68
Findeisen and Sachs (2014) enrich this setting further to deal with multiple dimensions of heterogeneity.

75

Their numerical results also point to income-contingent repayment of loans. Most interestingly,
they find that optimal repayment schemes for college loans can be well-approximated by a schedulethat is linearly increasing in income up to a threshold and constant afterwards. This is somewhat
similar to our model of moral hazard with CSV, but it is driven by the provision of ex ante
incentives as opposed to saving on verification costs. The results of Findeisen and Sachs (2013)
support our main conclusion that the welfare gains from optimally designed income-contingent
repayment can be significant.
The work of Findeisen and Sachs (2013, 2014) and Gary-Bobo and Trannoy (2014) complementsthat of Hanushek, Leung, and Yilmaz (2014) by characterizing the optimal repayment of loans
given the specified economic environment. However, these papers abstract from risk and other lifecycle aspects that modern quantitative macro models consider essential. In this respect, Krueger
and Ludwig (2013a, 2013b) restrict attention to a class of parameterized taxes (constant marginaltaxes with non-zero deductions) and uniform subsidies in order to find the best tax scheme withina richer life-cycle environment. Specifically, Krueger and Ludwig (2013a, 2013b) use a modelthat allows for endogenous human capital formation, borrowing constraints and income risks with(exogenously) incomplete financial markets and no default.69 Krueger and Ludwig find that thedegree of tax progressivity and the education subsidy that would maximize a utilitarian welfare
function are larger than in the current U.S. status quo.
In addition to income taxes, there are a number of other government and private institutions
that may also interact with student loan programs. In ongoing work (Lochner and Monge-Naranjo,
2014b), we study the design of optimal student loan programs with and without the integration ofunemployment insurance. This work considers a framework with an initial schooling investment
choice and an infinite horizon labor market with search frictions. Students face labor market riskin terms of unemployment duration after leaving school. We follow Hopenhayn and Nicolini (1997)
by considering moral hazard in job search. We further consider the possibility that school successcan be distorted by hidden effort.
As in the models analyzed above, borrowing and investment are increasing in ability and optimal borrowing helps finance consumption during school. A number of interesting considerations
and results arise from the optimal contract. First, borrowing and investments are set trying tominimize the possibility of “debt overhang”, i.e. situations in which debt is so high relative to
69

They abstract from parents inter vivos transfers and from wealth effects in labor supply.

76

potential income that it hinders incentives of the borrower to seek (and maintain employment)
to the point that reduces expected payoffs for both the borrower and lender. Second, insurance
is provided not only in the form of positive transfers to the unemployed but also in the formof time-varying repayment as a function of unemployment duration. The repayment must increase (in present value) with the duration of unemployment to encourage job seeking by theborrower. Third, the optimal contract delivers higher investments and (potentially greatly) higher
welfare than other suboptimal arrangements, such as autarky, unemployment insurance alone,or the case in which unemployment insurance is not integrated with student loan repayment.70
Finally, the optimal arrangement that arises from this environment highlights the importance ofproperly handling inter-temporal incentives. In particular, it suggests that as formulated, thedebt-forgiveness component of current and newly proposed income-contingent repayments, e.g.
Dynarski and Kreisman (2013), can unravel the incentives of young indebted workers early on.
If so, arbitrary time-dependent debt forgiveness can reduce the capacity for optimally designed
student loan contracts to provide incentives and insurance, and ultimately, credit.

7

Key Principles and Policy Guidance
Our characterization and overview of optimal student loan arrangements under both informa-tion and commitment frictions provide us with a number of broad lessons. We begin with threebasic principles that should form the foundation of any efficient student loan program. We thendiscuss a number of specific lessons regarding the optimal structure of loan repayments, the costs
of income verification, repayment enforcement and default, and borrowing limits.

7.1

Three Key Principles in the Design of Student Loan Programs

Three key principles are central to any well-designed student loan program, public or private.
First, borrowers should fully repay the lender in expectation. This does not mean that every
borrower always repays in full. Borrowers will sometimes make only partial payments or may
default entirely on the loan, while others end up paying more than the present value of the debt
evaluated at the risk free rate. While there may be considerable uncertainty at the time borrowers
70

Earlier work by Moen (1998) shows that reducing interest payments during unemployment can help achieve
efficient investment in human capital. His results derive from very different economic reasons related to a hold-up
problem on the side of firms for the investment in human capital of the worker.

77

take out their loans, the contract should be designed such that the borrower expects to repay it
in full when averaging across all possible outcomes and associated repayment amounts. While
the government can certainly fund losses for a student loan program through tax revenue, thosesubsidies can be better offered more directly in the form of grants, scholarships or lower tuitionlevels. Grants and reduced tuition can be better targeted (across need and merit groups) andmore transparent, and they may entail lower administrative costs. For similar reasons, efforts toredistribute gains and losses across different types of students can also be better done throughdirect transfers rather than via student loan programs. Additionally, efforts by government student
loan programs to extract higher returns from some borrowers to subsidize losses on others (basedon ex ante known information) are likely to be undermined by competitive private creditors who
would aim to poach students with better prospects.
Second, insurance is a central aspect in the design of student loans. School itself may be risky
as many students fail to complete their desired course of study. Even successful graduates, as
highlighted by the recent recession, can struggle to find a well-paying job, or any job at all, after
leaving college. An efficient lending contract ought to provide as much insurance as feasible throughincome-contingent repayments. Even if the provision of contingencies involves non-trivial costs, it
is always efficient to provide considerable insurance in terms of reduced payments or even transfers
to borrowers experiencing the worst labor market outcomes. In the extreme, when contracts cannot
be made contingent on income (i.e. limited commitment with incomplete contracts), default serves
as an implicit and imperfect form of insurance at the bottom of the income distribution. Inasmuch
as lenders can pool loans across many borrowers or can engage in other forms of hedging, theyshould act as risk-fee entities, providing insurance to students against idiosyncratic risk in theireducational investments but pricing the cost of that insurance in the terms of the loan.
Third, incentive problems must be recognized and properly addressed. Due to private information and repayment problems associated with limited enforcement mechanisms, the amount andnature of consumption insurance is limited. An optimal contract must address many often conflicting goals, such as providing the student with the appropriate incentives to study hard, search
for a job, report their income, and repay their loans. Incentive problems are not only relevant
for low earnings states, but they can also limit the income-contingency of repayments at the highend. Because of moral hazard and limited commitment, lenders rely on charging high repayments
for lucky students. Moreover, incentive problems can vary over different stages of the loan, with78

adverse selection concerns prominent at the time of signing, hidden action problems and moral
hazard concerns during school and in the labor market, and income verification and commitment
problems during repayment. A central challenge in practice is to properly assess the nature andseverity of these incentive problems in order to provide the right incentives to align the interestsof the student and creditor.
In short, an optimal student lending arrangement must strike the right balance between providing insurance and incentives to borrowers, while ensuring the lender is repaid in expectation.

7.2

The Optimal Structure of Loan Repayments

The optimal student loan arrangement must exhibit a flexible income-based repayment schedule
to provide the maximal amount of insurance while ensuring proper incentives for borrowers to exert
effort and honestly report their income. In practice, the income-contingent repayment schemes
observed in the U.S. and other countries (see Section 3) offer some insurance to borrowers. Yet,
optimal contracts are likely to look quite different. Students of different abilities, making different
investments, and borrowing different amounts should generally face different repayment schedules.
The optimal contract is unlikely to be characterized by a single income threshold below which
payments are zero for all borrowers or by a single constant repayment rate as a fraction of income
above the threshold. Indeed, the optimal contract may allow for additional transfers to borrowers
experiencing the worst post-school outcomes.71
An important lesson from our analysis is that the optimal contract aims to provide the greatest insurance at the bottom of the outcome distribution where it is most valuable. Absent moral
hazard problems, consumption and not payments would be constant across all low income levels.
At the same time, repayments may be considerably higher than the amount borrowed plus interest(with a modest risk premium) for the luckiest borrowers who experience very high earnings realizations; however, when income is costly to verify, repayments should be constant across all highincome realizations, a feature that is typically observed in practice for student loans and otherforms of debt. Relative to standard repayment schemes, the optimal design of repayments canlead to important gains in welfare and efficiency by providing additional consumption smoothing,71

As we discuss further below, other forms of social insurance (e.g. welfare, unemployment insurance, disability
insurance) may provide for minimal consumption levels, eliminating the need for student loan repayment plans toprovide additional transfers to borrowers earning very little after school. However, as we also discussed above, theoptimal student loan should integrate in its design the presence of such programs.

79

by properly encouraging effort and income reporting, and by yielding efficient investments in education. We demonstrate that default can arise even under the optimal contract, an interesting
feature not well-established in the literature. However, we argue that default should occur infrequently and not among those with the worst labor market outcomes, because insurance is better
provided with verification and income-contingent repayment.
The optimal structure of repayments can be summarized as follows. In the absence of hidden
effort, consumption would be smooth and repayments increasing one-for-one in income acrossstates of the world for which income is observed (i.e. verified) by the lender. The presence of moral
hazard limits the amount of insurance that can be provided, because effort must be incentivized bylinking payments and consumption to income levels. The more difficult it is to encourage proper
effort, the less insurance can be provided and the less payments should increase with earnings.72
When income is costly for the lender to observe, it is inefficient to write contracts fully contingent
on high earnings levels. Instead, borrowers with sufficiently high earnings should be asked to pay
a fixed amount and avoid going through the verification process. In this case, moral hazard isprimarily a a concern for low income realizations. Finally, imperfect enforcement mechanisms meanthat lenders cannot always enforce high payments from lucky borrowers. This can be especiallylimiting when verification is quite costly and moral hazard problems are modest, because contracts
would ideally specify high payments from those with high labor incomes. The combination of costly
verification and limited commitment can also lead to default in equilibrium for low- to middleincome borrowers, though not the most unfortunate. It is important to note that these market
frictions not only limit consumption smoothing across post-school earnings realizations, but theyalso limit the amount students can borrow for college and discourage educational investments.
Credible evidence on the extent of these information and enforcement frictions is crucial if they
are to be addressed appropriately.

7.3

Reducing the Costs of Income Verification

Income verification costs change the nature of the contract by limiting the contingency of
repayments on income for high earnings states. With high enough costs, it may become too
costly to link repayments to income over a broad range of income realizations. This can severely72

As a corollary, lenders should absorb all risk beyond the borrower’s control (e.g. aggregate unemployment risk
due to business cycle fluctuations).

80

limit insurance and increase the likelihood of default. Together, these lead to reductions in credit
and can discourage educational investments. Consequently, institutional reforms that lower thecosts of verifying income and that facilitate the linking of payments to income can improve theflexibility of contracts to enhance consumption insurance, allow for greater borrowing, and increase
investments. If verification costs can be reduced enough, default can be eliminated entirely.
These lessons favor integrating the monitoring of income and payment collection efforts with,for example, the collection of social security taxes, unemployment insurance contributions, orincome taxes as suggested in the recent proposal by Dynarski and Kreisman (2013). Indeed, thisis a key feature of income-contingent lending schemes in countries like Australia, New Zealand,
and the United Kingdom (Chapman, 2006). By eliminating the duplication of costs, better terms
can be offered to students. This also highlights one key advantage governments have over private
lenders and educational institutions in the provision of student loans. As stressed above, theintegration of student loan programs with other social insurance institutions such as unemployment
insurance, can go well beyond the reduction of verification costs, and can include additional
mechanisms to provide insurance and incentives.

7.4

Enforcing Repayment and the Potential for Default

When student loan contracts are designed optimally, default is just one of many “repayment”
states. Although the potential for default can severely limit the amount of credit students receive,
it can also provide a valuable source of insurance and collection when it is costly to incorporate
contingencies into repayment contracts.
For extremely high verification costs, default may be the least expensive way to effectively
provide insurance against some subpar labor market outcomes. At the other extreme, if income
verification costs are low and contracts can efficiently be made contingent on all, or at least
most, income levels, then flexible repayment schedules that link payments to income will always
dominate default. As long as verification costs do not preclude any form of income-contingency,
default should never occur in the very best or very worst states. Contracts should always bedesigned to ensure repayment from the highest earners, and they can better provide insurance
than default at the low end with explicit contingencies.73
73

Default may be the efficient response for the lowest set of income realizations if other forms of social insurance
provide a high enough consumption floor.

81

Default becomes a more attractive feature of loan contracts when lenders can capture some of
the losses from defaulters (e.g. wage garnishments). Indeed, better collection efforts that increase
the amount creditors can seize in the event of default can theoretically lead to more not less default
in equilibrium, as contracts would optimally adjust to take advantage of lower default losses.
Finally, it is important to recognize that the existence (or extent) of default need not imply any
inefficiencies, especially if verification costs are high relative to the losses associated with default.
Different labor market risks and their dependence on the exertion of effort by the student canlead to complex patterns in the incidence of default, verification and full repayment of loans in
the optimal contract. In practice, of course, default is also more likely when contracts are notproperly designed, especially in accounting for imperfect enforcement. If so, unusually high levelsof default associated with poor ex post labor market outcomes would signal inefficiencies in theway that student credit is allocated and/or repayments are structured.

7.5

Setting Borrowing Limits

The different credit contracts derived in Section 6 specify repayment functions, borrowing
amounts, and investment levels as functions of all observable borrower characteristics (especially
their family wealth and ability) and other factors that might affect the returns on their investments(e.g. post-secondary institution, course of study). In those contracts, it was not necessary to impose
a maximum credit amount, since the financial feasibility constraint was always imposed. Then,the amount of credit would also adjust to the initial characteristics of the individual and proposed
investment and consumption decisions, and the lender was always repaid in expectation.
In practice, student loan programs specify repayment schedules as functions of the amountborrowed, the amount invested, and other relevant characteristics. In this case, we can think
about the borrowing levels d specified by our contracts as limits lenders might place on different
borrowers. Higher credit levels could be made available, but as long as the conditions for expected
repayment are imposed, well-informed students should not over-borrow.
Given substantial heterogeneity in post-secondary institutions and college majors in termsof costs and post-school earnings distributions, the efficient loan scheme would link maximum
loan amounts to college and major choices, as well as other relevant observed characteristics ofthe borrower (e.g. student ability as measured by grades or aptitude tests). With asymmetric
information, it might also be optimal to condition the amount of lending on the own contribution82

of the student and his family towards the cost of college. Section 5 documents the extent towhich many of these factors affect default rates and expected repayment amounts under current
government student loan programs. The considerable variation in default rates across many exante observable factors suggests that either loan limits or repayment rates need to be adjusted tobetter equalize expected returns across borrowers and to improve the efficiency of these programs.

7.6

Other Considerations

Our discussion has largely assumed that student loan programs themselves are the only sourceof insurance against adverse labor market outcomes. Yet, most countries have a broad social safety
net, including welfare, unemployment insurance, and disability insurance in developed countries
and informal family arrangements in both developed and developing countries. The optimal student loan contract should be designed with these in mind. For example, if other social programs
provide a modest consumption floor for all workers, then it is unlikely that any post-school transfers from the lender to unlucky borrowers would be needed. Default may also be optimal for themost unlucky of borrowers when verification costs are non-negligible, since there is no need for
insurance through the loan contract. More generally, student loan contracts should take into consideration the provision of insurance and incentive effects of other social insurance mechanisms.
Given dramatic differences across countries and even states within the U.S., we might expect very
different contracts to arise optimally in different locations.
The general environments and contracts we have discussed apply equally to public and private
lenders. Yet, governments have some advantages over private creditors in terms of income verification, collection, and sometimes enforcement penalties; although, some of these advantages are
not necessarily inherent. Private lenders can be given similar enforcement powers as in the 2005
changes to U.S. bankruptcy regulations, and they may also be quite efficient at collection in somemarkets. Additionally, private credit markets may be more nimble and responsive to economic
and technological changes. Adverse selection problems pose a particular concern with competitive
lending markets, since they may prevent the market from forming for some types of students.
Governments may be able to enforce participation in student loan markets to minimize adverse
selection concerns or to form pooling equilibria where one would not arise in a competitive market.
In these cases, it may be desirable to reduce competitive pressures, which might otherwise unravel
markets. Of course, it can be very difficult to ‘enforce’ full participation, unless governments are83

prepared to eliminate self-financing by requiring that all students borrow the same amount.
In the U.S. and Canada, both government and private student loan programs coexist. In
these cases, it is important for governments to account for the response of private lenders. For
example, government programs that attempt to (or inadvertently) pool borrowers of different ex
ante risk levels may be undercut by private creditors, leaving government loan programs with
only the unprofitable ones.74 A different form of adverse selection problem can also arise for
specific schools or even states that try to provide flexible income-contingent loan programs fortheir students or residents: even if all students are forced to participate in the program, better
students (or those enrolling in more financially lucrative programs) may choose to enrol elsewhere.
For these reasons, federal student loan programs are likely to be more successful.

8

Conclusions
The rising costs of and returns to college have increased the demand for student loans in the

U.S., as well as many other countries. While borrowing and debt levels have risen for recent students, more and more appear to be constrained by government student loan limits that have not
kept pace with rising credit needs. At the same time, rising labor market instability/uncertainty,
even for highly educated workers, has made the repayment of higher student debt levels more
precarious for a growing number of students. These trends have led to a peculiar situation where,
ex ante, some students appear to receive too little credit, while ex post, others appear to haveaccumulated too much relative to their ability to repay. Together, these patterns suggest inefficiencies in the current student lending environment, making it more important than ever to carefullyreconsider its design.
Optimal student credit arrangements must perform a difficult balancing act. They must provide
students with access to credit while in school and help insure them against adverse labor market
outcomes after school; however, they must also provide incentives for students to accurately reporttheir income, exert efficient levels of effort during and after school, and generally honor their debts.
They must also ensure that creditors are repaid in expectation.
We have shown how student loan programs can most efficiently address these objectives. When74

As documented in Section 5, expected loan losses and default rates vary considerably based on ex ante observablefactors. This suggests that government student loan programs do pool risk groups, which leaves them open to theseconcerns.

84

post-school incomes are costly to verify, optimal repayment plans will specify a fixed debt-based
payment for high income realizations and income-based payments for all others. Absent moral
hazard concerns, all but the luckiest borrowers should receive full insurance, i.e. their payments
should adjust one-for-one with income to maintain a fixed consumption level. More realistically,
when moral hazard concerns are important such that borrowers must be provided with incentives
to work hard in school and in the labor market, payments should increase (less than one-for-one)in income among those experiencing all but the best income realizations. The more difficult it
is to encourage effort, the more repayments should increase with income. The fact that loan
contracts cannot always be fully enforced means that some borrowers may wish to default on their
obligations, which further limits the contracts that can be written. When income verification
costs are negligible, contracts should be written to avoid default, since the provision of explicit
insurance would always be better. By contrast, high verification costs leave room for default as
an efficient outcome for some income realizations, since it may be a relatively inexpensive way toprovide partial insurance that does not require outlays to verify income. Importantly, we showthat default is generally inefficient for borrowers experiencing the worst income realizations, since
explicit insurance that can be provided with income verification always dominates in these cases.
Yet, an important conclusion from our analysis is that the existence of default for some borrowers
is not prima facia evidence of any inefficiency in student lending arrangements. We have also
shown that optimal student loan programs will generally lead to lower educational investments forborrowers (relative to non-borrowers) when information and commitment concerns limit the loan
contracts. The inability to fully insure all risk discourages investment, more so for students withfewer family resources to draw on.
We have also summarized a small but growing literature that examines the determinants ofstudent loan default and other forms of non-payment. While the existence of default itself does notnecessarily imply inefficiencies in the system, the fact that expected losses associated with nonpayment appear to be quite high among some borrowers is inconsistent with the basic principle that
lenders should be repaid in expectation. Fairly high default rates for some types of borrowers alsosuggests inefficiencies in terms of either inappropriately high loan limits (for them) or inadequate
insurance for borrowers who experience very poor labor market outcomes. At the other extreme(and given current repayment plans), it is possible that loan limits are too low for some student
types that rarely default.
85

Finally, we have provided practical guidance for re-designing student loan programs to more
efficiently provide insurance while addressing information and commitment frictions in the market. While some recommendations are relatively easy to make (e.g. lowering verification costs bylinking student loan collection/repayment to social security, tax, or unemployment collections),
others require better empirical evidence on important features of the economic environment. In
particular, the optimal design of income-based repayment amounts depends critically on the extent of moral hazard in the market, yet we know very little about how student effort responds toincentives. The literature on optimal unemployment insurance and labor supply can be helpful for
determining the value of incentives in the labor market. Additional information on ex ante uncertainty, repayment enforcement technologies, and the costs of verification are also needed to design
optimal student loan programs. Here, new data sources on education and borrowing behavior,labour market outcomes, and student loan repayment/default can be useful; however, these data
will need to be analyzed with these objectives in mind.

References
Abbott, B., G. Gallipoli, C. Meghir, and G. L. Violante (2013). Education policy and intergenerational transfers in equilibrium. NBER Working Paper No. 18782.
Akers, B. and M. M. Chingos (2014). Is a student loan crisis on the horizon? In B. J. Hershbein
and K. Hollenbeck (Eds.), Student Loans and the Dynamics of Debt. Kalamazoo, MI: W.E.
Upjohn Institute for Employment Research.
Arvidson, D., D. Feshbach, R. Parikh, and J. Weinstein (2013). The MeasureOne private student
loan report 2013. http://www.measureone.com/reports.
Autor, D. H., L. F. Katz, and M. S. Kearney (2008). Trends in u.s. wage inequality: Revising therevisionists. The Review of Economics and Statistics 90 (2), 300–323.
Avery, C. and S. Turner (2012). Student loans: Do college students borrow too much–or notenough? Journal of Economic Perspectives 26 (1), 165–192.
Bailey, M. J. and S. M. Dynarski (2011). Inequality in postsecondary education. In G. J. Duncan

86and R. J. Murnane (Eds.), Whither Opportunity? Rising Inequality, Schools, and Children’sLife Chances, Chapter 6, pp. 117–131. New York: Russell Sage Foundation.
Barsky, R., J. Bound, K. Charles, and J. Lupton (2002). Accounting for the black-white wealthgap: A nonparametric approach. Journal of the American Statistical Association 97 (459),
663–673.
Becker, G. S. (1975). Human Capital, 2nd ed. New York, NY: Columbia University Press.
Becker, G. S. (1991). A Treatise on the Family, Enlarged Edition. Cambridge, MA: Harvard
University Press.
Bell, D. N. and D. G. Blanchflower (2011). Young people and the great recession. Oxford Review
of Economic Policy 27 (2), 241–267.
Belley, P. and L. Lochner (2007). The changing role of family income and ability in determining
educational achievement. Journal of Human Capital 1 (1), 37–89.
Berkner, L. (2000). Trends in Undergraduate Borrowing: Federal Student Loans in 1989-90,
1992-93, and 1995-96. Washington D.C.: U.S. Department of Education, National Center for
Education Statistics, NCES 2000-151.
Bleemer, Z., M. Brown, D. Lee, and W. van der Klaauw (2014). Debt, jobs, or housing: what’s
keeping millenials at home? Working Paper, Federal Reserve Bank of New York.
Blundell, R., H. Low, and I. Preston (2013). Decomposing changes in income risk using consumption data. Quantitative Economics 4 (1), 1–37.
Bohacek, R. and M. Kapicka (2008). Optimal human capital policies. Journal of Monetary
Economics 55 (1), 1–16.
Boudarbat, B., T. Lemieux, and W. C. Riddell (2010). The evolution of the returns to humancapital in canada, 19802005. Canadian Public Policy 36 (1), 63–89.
Bovenberg, L. and B. Jacobs (2011). Optimal taxation of human capital and the earnings function.
Journal of Public Economic Theoryl 13 (6), 957–971.

87

Brown, M., A. Haughwoutt, D. Lee, J. Scally, and W. van der Klaauw (2014). Measuring student
debt and its performance. In B. J. Hershbein and K. Hollenbeck (Eds.), Student Loans and the
Dynamics of Debt. Kalamazoo, MI: W.E. Upjohn Institute for Employment Research.
Brown, M., A. Haughwoutt, D. Lee, and W. van der Klaauw (2014). Do we know what we owe? acomparison of borrower- and lender-reported consumer debt. Working Paper, Federal Reserve
Bank of New York.
Brown, M., J. K. Scholz, and A. Seshadri (2011). A new test of borrowing constraints for education.
University of Wisconsin, Working paper.
Cameron, S. and J. J. Heckman (1998, April). Life cycle schooling and dynamic selection bias:
Models and evidence for five cohorts of American males. Journal of Political Economy 106 (2),262–333.
Cameron, S. and J. J. Heckman (1999). Can tuition policy combat rising wage inequality? In M. H.
Kosters (Ed.), Financing College Tuition: Government Policies and Educational Priorities, pp.
76–124. Washington D.C.: American Enterprise Institute Press.
Cameron, S. and C. Taber (2004). Estimation of educational borrowing constraints using returns
to schooling. Journal of Political Economy 112 (1), 132–82.
Card, D. and T. Lemieux (2001). Can falling supply explain the rising return to college for younger
men? a cohort-based analysis? Quarterly Journal of Economics 116 (2), 705–746.
Carneiro, P. and J. J. Heckman (2002). The evidence on credit constraints in post-secondary
schooling. Economic Journal 112 (482), 705–734.
Caucutt, E. and L. Lochner (2012). Early and late human capital investments, borrowing constraints, and the family. NBER Working Paper No. 18493.
Chapman, B. (2006). Income contingent loans for higher education: International reforms. In
E. Hanushek and F. Welch (Eds.), Handbook of the Economics of Education, Volume 2, Chapter 25, pp. 1435–1503. Amsterdam: Elsevier.
Chatterjee, S. and F. Ionescu (2012, November). Insuring student loans against the risk of college
failure. Quantitative Economics 3 (3), 393–420.
88College Board (2001). Trends in Student Aid. New York, NY: College Board Publications.
College Board (2011). Trends in Student Aid. New York, NY: College Board Publications.
College Board (2013). Trends in Student Aid. New York, NY: College Board Publications.
Cunningham, A. F. and G. S. Kienzl (2014). Delinquency: The Untold Story of Student Loan
Borrowing. Washington, DC: Insititute for Higher Education Policy.
Del Rey, E. and B. Verheyden (2013). Loans, insurance and failures in the credit market for
students. Working Paper.
Deming, D., C. Goldin, and L. Katz (2012). The for-profit postsecondary school sector: Nimble
critters or agile predators? Journal of Economic Perspectives 26 (1), 139–164.
Domeij, D. and M. Floden (2010). Inequality trends in sweden 1978-2004. Review of Economic
Dynamics 13 (1), 179–208.
Dustmann, C., J. Ludsteck, and U. Schoneberg (2009). Revisiting the german wage structure.
Quarterly Journal of Economics 124 (2), 843–881.
Dynarski, M. (1994). Who defaults on student loans? Findings from the National Postsecondary
Student Aid Study. Economics of Education Review 13 (1), 55–68.
Dynarski, S. and D. Kreisman (2013). Loans for educational opportunity: Making borrowing workfor today’s students. The Hamilton Project Discussion Paper.
Eckwert, B. and I. Zilcha (2012). Private investment in higher education: Comparing alternative
funding schemes. Economica 79 (313), 76–96.
Elsby, M. W., B. Hobijn, and A. Sahin (2010). The labor market in the great recession. NBER
Working Paper No. 15979.
Findeisen, S. and D. Sachs (2013). Education and optimal dynamic taxation: The role of incomecontingent student loans. Working Paper.
Findeisen, S. and D. Sachs (2014). Designing efficient college and tax policies. Working Paper.

89

Flint, T. (1997). Predicting student loan defaults. Journal of Higher Education 68 (3), 322–54.
Friedman, M. and S. Kuznets (1945). Income from Independent Professional Practice. NBER
Books.
Fuchs-Schundeln, N., D. Krueger, and M. Sommer (2010). Inequality trends for Germany in thelast two decades: A tale of two countries. Review of Economic Dynamics 13 (1), 103–132.
Gary-Bobo, R. and A. Trannoy (2014). Optimal student loans and graduate tax under moral
hazard and adverse selection. CESIfo Discussion Paper no. 4279.
Gemici, A. and M. Wiswall (2011). Evolution of gender differences in post-secondary humancapital investments: College majors. IESP Working Paper No. 03-11.
Gervais, M., C. S. Kochar, and L. Lochner (2014). Profits for whom? the unprofitability of lending
to for-profit students. Working Paper.
Golosov, M., A. Tsyvinski, and I. Werning (2007). New dynamic public finance: A user’s guide.
In D. Acemoglu, K. Rogoff, and M. Woodford (Eds.), NBER Macroeconomics Annual 2006,
Volume 21, pp. 317–388. MIT Press.
Gottschalk, P. and R. Moffitt (2009). The rising instability of u.s. earnings. Journal of Economic
Perspectives 23 (4), 3–24.
Gross, J., O. Cekic, D. Hossler, and N. Hillman (2009). What matters in student loan default: A
review of the research literature. Journal of Student Financial Aid 39 (1), 19–29.
Hanushek, E. A., C. K. Y. Leung, and K. Yilmaz (2014). Borrowing constraints, college aid, andintergenerational mobility. Journal of Human Capital 8 (1), 1–41.
Heathcote, J., F. Perri, and G. L. Violante (2010). Unequal we stand: An empirical analysis
of economic inequality in the united states: 1967-2006. Review of Economic Dynamics 13 (1),
15–51.
Heathcote, J., K. Storesletten, and G. L. Violante (2010). The macroeconomic implications ofrising wage inequality in the united states. Journal of Political Economy 118 (4), 681–722.

90

Heckman, J. J., L. J. Lochner, and P. E. Todd (2008). Earnings functions and rates of return.
Journal of Human Capital 2 (1), 1–31.
Hershbein, B. J. and K. Hollenbeck (2014a). The distribution of college graduate debt, 1990 to
2008: A decomposition approach. In B. J. Hershbein and K. Hollenbeck (Eds.), Student Loans
and the Dynamics of Debt. Kalamazoo, MI: W.E. Upjohn Institute for Employment Research.
Hershbein, B. J. and K. Hollenbeck (2014b). The distribution of college graduate debt, 1990
to 2008: A decomposition approach –updated web tables and figures. W.E. Upjohn InstituteWorking Paper.
Hopenhayn, H. A. and J. P. Nicolini (1997). Optimal unemployment insurance. Journal of Political
Economy 105 (2), 412–438.
Hoynes, H., D. L. Miller, and J. Schaller (2012). Who suffers during recessions?

Journal of

Economic Perspectives 26 (3), 27–48.
Human Resources and Skills Development Canada (2012). Canada Student Loans Program: Annual Report 2010-2011. Ottawa.
Ionescu, F. (2008). Consolidation of student loan repayments and default incentives. The B.E.
Journal of Macroeconomics 8 (1), 1682–1682.
Ionescu, F. (2009). The federal student loan program: Quantitative implications for college enrollment and default rates. Review of Economic Dynamics 12 (1), 205 – 231.
Ionescu, F. (2011). Risky human capital and alternative bankruptcy regimes for student loans.
Journal of Human Capital 5 (2), 153–206.
Jappelli, T. and L. Pistaferri (2010). Does consumption inequality track income inequality initaly? Review of Economic Dynamics 13 (1), 133–153.
Johnson, M. (2013). Borrowing constraints, college enrollment, and delayed entry. Journal ofLabor Economics 31 (4), 669–725.
Jones, J. B. and F. Yang (2014). Skill-biased technical change and the cost of higher education.
State University of New York – Albany, Working Paper.
91

Kapicka, M. (2014). Optimal mirrleesean taxation with unobservable human capital formation.
Working Paper.
Kapicka, M. and J. Neira (2014). Optimal taxation in a life-cycle economy with endogenous humancapital formation. Working Paper.
Keane, M. and K. I. Wolpin (2001). The effect of parental transfers and borrowing constraints on
educational attainment. International Economic Review 42 (4), 1051–1103.
Kinsler, J. and R. Pavan (2011). Family income and higher education choices: The importance ofaccounting for college quality. Journal of Human Capital 5 (4), 453–477.
Lochner, L. and A. Monge-Naranjo (2011). The nature of credit constraints and human capital.
American Economic Review 101 (6), 2487–2529.
Lochner, L. and A. Monge-Naranjo (2012). Credit constraints in education. Annual Review of
Economics 4, 225–56.
Lochner, L. and A. Monge-Naranjo (2014a). Default and repayment among baccalaureate degree
earners. In B. J. Hershbein and K. Hollenbeck (Eds.), Student Loans and the Dynamics of Debt.
Kalamazoo, MI: W.E. Upjohn Institute for Employment Research.
Lochner, L. and A. Monge-Naranjo (2014b). Student loans with unemployment and moral hazard.
Working Paper, Federal Reserve Bank of St. Louis.
Lochner, L. and Y. Shin (2014). Understanding earnings dynamics: Identifying and estimating thechanging roles of unobserved ability, permanent and transitory shocks. NBER Working Paper
No. 20068.
Lochner, L., T. Stinebrickner, and U. Suleymanoglu (2013). The importance of financial resources
for student loan repayment. CIBC Working Paper No. 2013-7.
Mestieri, M. (2012). Wealth distribution and human capital: How borrowing constraints shapeeducational systems. Working Paper.
Moen, E. R. (1998). Efficient ways to finance human capital investments. Economica 65 (260),
491–505.
92

Moffitt, R. A. and P. Gottschalk (2012). Trends in the transitory variance of male earnings:
Methods and evidence. Journal of Human Resources 47 (1), 204–236.
Navarro, S. (2010). Using observed choices to infer agent’s information: Reconsidering the importance of borrowing constraints, uncertainty and preferences in college attendance. University of
Wisconsin, Working Paper.
Nerlove, M. (1975). Some problems in the use of income-contingent loans for the finance of higher
education. Journal of Political Economy 83 (1), 157–183.
OECD (2013). Education at a Glance 2013: OECD Indicators. OECD Publishing.
Pereira, P. and P. Martins (2000). Does education reduce wage inequality? quantile regressions
evidence from fifteen european countries. IZA Discussion Paper No. 120.
Rothstein, J. and C. E. Rouse (2011). Constrained after college: Student loans and early-career
occupational choices. Journal of Public Economics 95 (1-2), 149–163.
Sallie Mae (2008). How undergraduate students use credit cards.
Schwartz, S. and R. Finnie (2002). Student loans in canada: An analysis of borrowing andrepayment. Economics of Education Review 21 (5), 497–512.
Shapiro, T. and M. Oliver (1997). Black Wealth/White Wealth: A New Perspective on Racial
Inequality. New York, NY: Routeledge.
Snyder, T., S. Dillow, and C. Hoffman (2009). Digest of Education Statistics 2008. Washington,
DC: National Center for Education Statistics, Institute of Education Sciences, U.S. Departmentof Education.
Stantcheva, S. (2014). Optimal taxation and human capital policies over the life cycle. Working
Paper.
Steele, P. and S. Baum (2009). How Much are College Students Borrowing?
College Board Publications.

93

New York, NY:Stinebrickner, T. and R. Stinebrickner (2008). The effect of credit constraints on the college dropout decision: A direct approach using a new panel study. American Economic Review 98 (5),2163–84.
Volkwein, F., B. Szelest, A. Cabrera, and M. Napierski-Prancl (1998). Factors associated with student loan default among different racial and ethnic groups. Journal of Higher Education 69 (2),
206–37.
Wei, C. C. and L. Berkner (2008). Trends in Undergraduate Borrowing II: Federal Student Loans in
1995-96, 1999-2000, and 2003-04. Washington D.C.: National Center for Education Statistics,
U.S. Department of Education.
Wei, H. (2010). Measuring economic returns to post-school education in australia. Australian
Bureau of Statistics Research Paper.
Woo, J. H. (2014). Degrees of Debt – Student Borrowing and Loan Repayment of Bachelro’s Degree
Recipients 1 Year After Graduating: 1994, 2001, and 2009. Washington, DC: National Center
for Education Statistics, Institute of Education Sciences, U.S. Department of Education.

94