Consolidation of Student Loan Repayments and Default Incentives

Abstract

I study repayment behavior for college graduates who borrow under the U.S. Federal Student Loan Program to finance higher education. I develop a dynamic model with uninsurable shocks to earnings and student loan rates that explains the repayment pattern in U.S. data: college graduates with lower debt will lock-in interest rates, while those with higher debt will switch to an income-contingent plan. Default does not occur among the most financially constrained group of college graduates. I use the model to quantify the effects of a reform introduced in 2006 that eliminates the possibility to lock-in interest rates for student loans. The reform induces a significant increase in default rates, which is largely accounted for by low-income borrowers.

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The B.E. Journal of Macroeconomics
Topics
Volume 8, Issue 1 2008 Article 22
Consolidation of Student Loan Repayments
and Default Incentives
Felicia A. Ionescu∗
∗Colgate University, fionescu@colgate.edu
Recommended Citation
Felicia A. Ionescu (2008) “Consolidation of Student Loan Repayments and Default Incentives,”
The B.E. Journal of Macroeconomics:Vo l . 8: Iss. 1 (Topics), Article 22.
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Consolidation of Student Loan Repayments
and Default Incentives∗
Felicia A. Ionescu
Abstract
I study repayment behavior for college graduates who borrow under the U.S. Federal Student
Loan Program to finance higher education. I develop a dynamic model with uninsurable shocks to
earnings and student loan rates that explains the repayment pattern in U.S. data: college graduates
with lower debt will lock-in interest rates, while those with higher debt will switch to an income-
contingent plan. Default does not occur among the most financially constrained group of college
graduates. I use the model to quantify the effects of a reform introduced in 2006 that eliminates
the possibility to lock-in interest rates for student loans. The reform induces a significant increase
in default rates, which is largely accounted for by low-income borrowers.
KEYWORDS: student loans, consolidation, default
∗A special thanks to B. Ravikumar, Nicole Simpson, and Chris Sleet for their valuable advice. I
would also like to thank seminar participants at the University of Iowa, Iowa Alumni Workshop,
and Macro Midwest Meetings for useful comments, especially Kartik Athreya, Marina Azzimonti,
Beth Ingram, Fernando Leiva, Linnea Polgreen, Pedro Silos, and Galina Vereshchagina.
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1Introduction
Borrowing and repaying student loans have become an important issue to
policy makers. The role of the F e d e r a l Student Loan Program (FSLP) in
financing college education has significantly increased since its introduction in
1965, in part as aresult of v a r i o u s policyc h a n g e s that have ma d e it more
generous. Currently more than 7million peopleborrowunder the program for
atotal of $54 billion compared to $10 billion in the early 1970s (College Board
(2003)).1Approximately 5percentof these borrowersdefault on student loan
payments, and the total amount of outstanding debt reached $25 billion in
2001. This paper studies the repayment patterns of college graduates who
borrowedunder the FSLP to finance their undergraduate education.
Student loans in the U.S. are based on financial need, and require no credit
history. Students are eligible to borrowup to the college cost minus an ex-
pectedfamily contribution. Student loans are made through aprivate creditor
and are guaranteed b y the U.S. federal government or are directly lent from
the U.S. government. The interest rate c h a r g e d b y creditors is set b y the go-
v e r n m e n t based on the 91-day T r e a s u r y bill rate; as aresult, it fluctuates with
the market. F o r most of these loans, the U.S. government fully subsidizes the
interest rate while students are in college. Students start repaying their loans
six months after graduation. Borrowers face amenu of repayment schedules
and have the opportunity to default on their loans.
High default rates in the late 1980s led legislators to introduce aseries of
policyc h a n g e s , including aconsolidation program that allows for more flexibi-
lity in repayment. As aresult, borrowerscan c h o o s e to set payments based on
their income (income consolidation) or they can lock-in interest rates for the
remainder of the loan (standard consolidation). This helps borrowershedge
against either income or interest rate risk, thus affecting incentives to default.
Seemingly these policies w o r k e d : the default rate declined from ahigh of
22.4 percentin 1990 to 5.4 percentin 2001 (a t w o - y e a r basis c o h o r t default
rate).2The drawback of locking-in interest rates, however, is that subsidizing
1
Amounts are reported in real terms (2001 constant dollars). In 2001 the unsecured
consumer debt amounted to $692 billion (Chatterjee et al. (2007)).
2
Other policiesthat w e r e introduced and might have contributed to the decline in default
rates include c h a n g e s to the consequences of default such as more severe w a g e garnishment
and dischargeability rules (two important limitations on di s char g eabili ty w e r e introduced in
1990 and 1998). Schools are also subject to sanctions if their cohort default rate exceeds
25 percent for three consecutive y e a r s , or 40 percent in one y e a r (ED (2004, 2001a)). In
addition, the economic expansion in the 1990s might have caused fewer college graduates
to default. This paper fo cuses on the effect of the consolidation program for repayment
incentives.
1
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the consolidation option is costly to the government. According to the GAO
(2003), the cost of this program rose to $2.1 billion in the 2003 fiscal y e a r
from $650 million the previous fiscal y e a r . In 2004 college graduates could
consolidate to lock-in interest rates as low as 3.5 percent. But when market
rates rise above that fixed rate, the government is obliged to make up the
difference, guaranteeing lenders acertain profit. As more students c h o o s e to
lock-in interest rates, the program becomes more expensive for the federal
government when interest rates rise.
Concerned that the cost w o u l d continue to rise, legislators adopted are-
form in 2006 that discontinues the opportunity to lock-in interest rates.3This
reform eliminates the fixed rates for students and replaces them with v a r i a b l e
rates that fluctuate with the market (91-day T r e a s u r y bill rate). Critics of the
reform emphasize that eliminating the option to lock-in interest rates will force
students to pay more, which will mostly affect low- and middle-income stu-
dents. F u r t h e r m o r e , they claim that higher interest rates and higher monthly
payments make graduates less likely to repay, leading to higher default rates
and more federal resources devoted to bailing out private lenders.
In this paper, Istudy the repayment behaviorof college graduates and the
consequences of this policyreform across different groups of college graduates
in aframework that mimics many features of the FSLP. Iuse the Baccalaureate
and Beyond (B&B) 1993-1997 data set to look at the repayment behavior
of 1992/1993 college graduates who borrowedunder the program. Idevelop
adynamic stochastic model calibrated to the U.S. economy to explain the
k e y features of repayment behaviorarising from this data set. Central to the
model is the decision of the college graduate to repay his loan under alternative
loan policies. Both the data and the model suggest that the program allows
borrowersto risk-share and smooth consumption across states and o v e r time.
Ifocus on the outcomes of individuals from low- and middle-income groups
who benefitmost from the consolidation program.
The model qualitatively and quantitatively replicates the observed c h o i c e
of repayment plans across different groups of college graduates who do not
default on their loans. It explains the sorting evidence b y e a rnings and debt
in the B&B 93/97 data set: payers under the income-contingent plan have
higher debt levels and lower earnings on a v e r a g e relative to those under the
standard plan. In addition, the model accounts for the observed c h a r a c t e r i s t i c s
of defaulters v e r s u s non-defaulters: defaulters have lower earnings and higher
levels of debt relative to non-defaulters. F u r t h e r m o r e , the model predicts that
default does not occuramong the most financially constrained group of college
3
HR 4283 to amend the Higher Education Act 1965, section 425.
2
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graduates. Instead, default is more common among college graduates with
intermediate debt levels (around $10,000 in 1992 dollars). When the debt
level is low, agents prefer the standard consolidation that allows them to hedge
against interest rate risk. Those with larger student loans enter default since
they are constrained in their ability to repay. But if the loan amount is too
high, default becomesv e r y costly, so income consolidation is optimal. This is
becausedefault punishments are increasing in bothearnings and debt levels,
whereas income consolidation is less sensitive to debt levels.
Iuse the model to test the implications of the reform introduced in 2006.
Results of the policyexperiment show that when college graduates cannot lock-
in interest rates, the default rate increases significantly (from 5.1 percentto 27
percent). Given non-dischargeability of student loans, however, the cost from
additional default is not aconcern, contrary to what some of the opponents
of the reform have stated. Amore interesting result is that the additional
default is accounted for b y low-income borrowers. Given severe consequences
to default, low-income college graduates end up paying more for their education
loans compared to the case where they can lock-in interest rates. The model
predicts redistribution effects across income groups: college graduates from
low- and middle-income groups are most affected b y the reform, as critics of
the reform have feared. High-income groups benefitfrom the reform. The
interest rate risk is not significant enough for the high-income borrowersto
w a r r a n t the higher taxes they have to pay to supp ort this option, whereas for
low-income borrowers,the converse is true.
The absence of the possibility to hedge against interest rate fluctuations
might deter students from entering the program, which therefore has implica-
tions for college enrollment. Iconsider these issues in separate research that
endogenizes college enrollment and borrowing(Ionescu (2008)). That paper
focuses on college enrollment and default rates induced b y alternative loan
policiesin the early 1990s, whereas the current paper focuses on repayment
patterns for college graduates and analyzes the impact of the 2006 consolida-
tion reform. Ionescu (2008) abstracts, however, from modeling income uncer-
tainty, an essential feature of the current paper.
The risk of failure at college might affect the w e l f a r e analysis and default
rates. Currently, Iabstract from modeling the decisions for college dropouts,
in part given the focus on behaviorof college graduates, and in part becauseof
data limitations (B&B 93/97 does not include college dropouts). Accounting
for this risk might reveal significant predictions about how v a r i o u s loan policies
affect different groups of students. The risk of college failure appears to be
highest currently for individuals from low- and middle-income groups, based
on Akyol &A t h r e y a (2005), Caucutt &Kumar (2003), Chatterjee &Ionescu
3
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(2008), Manski &Wise (1983), and Restuccia &Urrutia (2004).
The college financing literature is v e r y rich, with significant contributions
b y Carneiro &Heckman (2002), Dynarski (2003), Heckman et al. (1998), Hoxby
(2004), and Keane &W o l p i n (2001). Not until recently, however, has the fo-
cus turned toward student loans. Earlier w o r k has abstracted from analyzing
repayment incentives under the student loan program. An important contribu-
tion b y Lochner &Monge (2008) looks at the interaction betweenborrowing
constraints, default, and investment in h u m a n capital in an environment based
on the U.S. Guaranteed Student Loan Program (GSL). My study d iffers from
theirs in several important w a y s . First, Iincorporate the a v a i l a b l e repayment
schedules, including the opportunity to lock-in interest rates and to switch to
an income plan. Second, Ifocus on the FSLP, whereas they focus on the GSL
program (the former FSLP) with adifferent set of rules upon default. Conse-
quently, default penaltiesare modeled differently. Third, Iexplain repayment
patterns for 1992/1993 college graduates, while their paper explains empiri-
cal findings regarding c h a r a c t e r i s t i c s of defaulters before1987 as presented in
Dynarsky (1994). F o u r t h , Ipropose an analysis of the consolidation program
on repayment behavior,whereas their research focuses on the severity of pu-
nishments upon default and government subsidies. Lucas &Moore (2007) also
address the consolidation of student loans in apaper that develops an option
pricing model. The focus of their paper is on the estimation of the cost of
consolidation and its sensitivity to program rules rather than on repayment
behavioror the effects of the 2006 reform, the focus of the current paper.
T o m y knowledge, this is the first study to develop atheoretical frame-
w o r k that quantifies the implications of the recent consolidation reform for
default incentives. The paper sheds light on the current policydebate regar-
ding consolidation. More important, it explains boththe repayment patterns
and default incentives under the FSLP, k e y results for policymakers as they
w o r k to redesign it. The rest of the paper is organized as follows: Section
2provides institutional details, Section 3presents the model, and Section 4
describes the parameterization. Results for the benchmarkeconomy are given
in Section 5and results for the policyreform are in Section 6. Section 7pro-
vides robustness results, and Section 8concludes. The details of the data are
provided in the Appendix.
4
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2Institutional Details on the Student Loan
Program
The F e d e r a l Student Loan Program (FSLP) consists of av a r i e t y of t y p e s of
loans, the majority of which are government-backed loans provided through the
Stafford loan program: the F e d e r a l F a m i l y Education Loan Program (FFELP)
and the F e d e r a l William D. F o r d Direct Loan Program (FFDLP) (ED (2007)).
Loans made through the FFELP are from aprivate creditor and guaranteed
b y the government for any amount that is not paid. Loans can be either
subsidized (the U.S. Department of Education pays for the interest until the
borrowerenters repayment after graduation) or unsubsidized (the borroweris
responsible for interest payments). In 1994 the U.S. government started the
FFDLP, which lets students borrowmoney directly from the government. In
addition there are F e d e r a l Plus loans and F e d e r a l P e r k i n s loans. Plus loans
allow parents to borrowfor their c h i l d r e n ’ s education, while P e r k i n s loans
are offered b y participating schools and need to berepaid to the scho ol, but
the federal government subsidizes the interest payments during the time in
college. This study focuses on college graduates who borrowfor undergraduate
education under the FFELP and FFDLP.4
2.1 Repayment Options and Consolidation
The design of the FSLP is such that students start repaying their loans six
months after graduation under astandard plan that lasts for 10 y e a r s . P a y -
ments fluctuate based on the 91-day T r e a s u r y bill interest rate. Any time after
graduation, borrowerscan c h o o s e , upon consolidation, to opt-out of this initial
repayment plan. They face amenu of repayment options: standard, extended,
graduated, and the income-contingent plan (see Berkner &Bobbitt (2000)).
The extended plan is similar to the standard plan in the sense that it
consists of fluctuating payments based on the 91-day T r e a s u r y bill interest
rate, but o v e r alarger period(25 y e a r s ) . Borrowers have the c h o i c e to make
extra payments. The total amount of interest paid, however, is significantly
higher o v e r the life of the loan.
The graduated and income-contingent plans bothgive the borrowerpay-
ment relief when his income is lowest after graduation. The graduated plan
starts with low payments immediately after graduation, but payments incre-
mentally increase thereafter. This is accomplished b y requiring only the in-
4
Both Plus and P e r k i n s loans are not included in the computation of the national cohort
default rate.
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terest to bepaid for an initial fixed period(usually t w o or four y e a r s depending
on the size of the loan), followed b y principal and interest payments o v e r the
remainder of the term. The payment amount increases in several steps, and
payments last for up to 10, 15, or 25 y e a r s , depending on the size of the loan.
In contrast, the income-contingent plan provides aw a y to hedge against
income shocks. This schedule is av a r i a t i o n of the graduated plan. P a y m e n t s
are computed as apercentageof the borrower’sadjusted gross income. Hence,
payments increase only if income increases. The fraction of income that goes
toward repayment is computed according to the federal statute, and it is based
on the principal, the interest rate, and the income level at consoli d ation time.
It is higher if the debt level is higher, the income level is lower, or the in-
terest rate is higher. In practice, payments range from 3to 10 percentof
the borrower’sincome. P a y m e n t s are generally capped at an amount slightly
less than the required payment under astandard schedule and cannot beless
than $5. As with the graduated plan, lower initial payments are balanced b y
inflated payments later. P a y m e n t s last for up to 25 y e a r s from the time of
consolidation.
Most college graduates consolidate their student loans and c h o o s e to opt-
out from the initial standard plan and switch to one of the other a v a i l a b l e
repayment options. Upon consolidation, the existing loan is paid with anew
loan. Important features of the consolidation program include: 1) The oppor-
tunity to consolidate several t y p e s of federal student loans with v a r i o u s repay-
ment schedules into one loan;52) The eligibility to consolidate anytime after
they graduate, leave school, or drop belowhalf-time enrollment;63) Borrowers
can consolidate their student loans one time. Once made, federal consolidation
loans cannot beundone becausethe loans that w e r e consolidated have been
paid off and no longer exist. The line of credit of the new loan is transferred to
the government; 4) Repayment of consolidation loans beginswithin 60 days of
the disbursement of the loan. The payback term ranges from 10 to 25 y e a r s ,
depending on the amount of education debt beingrepaid and the repayment
option selected; 5) Regardless of the repayment option borrowersc h o o s e , after
25 y e a r s , borrowersare exempt from repaying the outstanding debt; 6) There
are no application fees or prepayment penaltiesfor consolidation. Also, no
credit c h e c k s are required.
When the consolidation program w a s introduced in 1988, it also allowed
student borrowersto hedge against interest rate risk b y locking-in the interest
5
Borrowers can consolidate either fully or partially on their loans. Data show that when
they c h o o s e to consolidate, however, they do so for all of their loans.
6
Borrowers who are delinquent (30 days or more late in making aloan payment) or in
default m u s t meet certain requirements beforethey may consolidate their loans.
6
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rate for the remainder of the loan. When borrowerslocked-in interest rates,
they automatically prolonged the life of the loan b y another 10 y e a r s . P a y -
ments w e r e similar to those under the standard repayment option, with the
main difference beingfixed rates instead of v a r i a b l e rates. Th e fixed interest
rates are set according to aformula established b y afederal statute. The rate
is based on the w e i g h t e d a v e r a g e of the interest rates on the loans at the time
of consolidation, rounded up to the nearest one-eighth of apercent. The in-
terest rate cannot exceed 8.25 percent.The consolidation rate is fixed for the
life of the loan, which protects the borrowerfrom future increases in v a r i a b l e
rate loans but prevents him from benefitingfrom future decreases in v a r i a b l e
rates. Data show that most college graduates in 1992-1993 c h o s e this repay-
ment option (96 percent). While the consolidation program s t i l l exists under
the current FSLP, the option to lock-in interest rates is not a v a i l a b l e anymore.
This w a s discontinued in June 2006.
2.2 Default
P e o p l e have the option of defaulting on their student loans. However, default
does not have the traditional meaning. It is merely adelay in repayment that
comes with acost on the part of the defaulter. Default can occurat any time
during the repayment phase of the loan, regardless of whether the debtor has
consolidated his loan. In practice, anegligible fraction of those who consolidate
c h o o s e to default post-consolidation,even though the data show no indication
that the consequences of default after consolidation are different. If borrowers
do not make any payments within 270 days, they are generally c o ns i d e r e d in
default, unless an agreement with the lender is reached. In default, the line of
credit is shut down and is transferred to student loan guarantee government
agencies. The guarantee agency holding the defaulter’s loan reports the default
status to the credit bureaus and designs arepayment plan that is immediately
implemented together with aseries of penaltieson the defaulter.
The consequences to default are n u m e r o u s . First, the defaulter enters re-
payment at ahigher debt level, up to 25 percentof the principal. This higher
debt recovers some of the collection costs of the defaulted loan. The defaulter
also loses his right to consolidate after default. P a r t of the borrower’sw a g e is
garnished in the y e a r default occurs,which may constitute up to 10 percent
of annual w a g e s . This punishment is stopp ed once the defaulter starts repay-
ment.7Finally, credit bureaus may benotified. Bad credit reports are erased,
7
The Debt Collection Improvement Act of 1996 raised the garnishment limit to 15 percent
of the defaulter’s pay.
7
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however, and credit market participation is not restricted once the borrower
starts repaying. In addition, federal tax refunds are seized, apossible hold
may beplaced on undergraduate transcripts, and borrowersm a y beineligible
for future student loans.8The IRS can intercept any income tax refund the
defaulter may beentitled to until student loans are paid in full. This punish-
ment can bea v o i d e d , however, if the borrowerhas repaid the loan or is making
payments under anegotiated repayment agreement.
Dischargeability of defaulted student loans is v e r y limited. They can be
discharged only in case of death or permanentdisability. Student loans can be
discharged in Chapter 13 bankruptcy, but this is v e r y rare. Cha p t e r 13 of the
Bankruptcy Co de requires the debtor to reorganize and restructure his assets
and liabilities b y reducing consumption to finance at least partial repayment of
his obligations. Dischargeability of student loans is not allowed unless ” u n d u e
hardship” is placed on the debtor.9
3Model
3.1 Environment
The economy consists of heterogeneous agents who are infinitely lived. Time is
discrete and indexed b y t.Central to the model is the decision of college gra-
duates to repay their student loans. Agents start with debt they encountered
in college, do,and some initial level of assets, ao
.There are t w o sources of un-
certainty in this economy, earnings and interest rates on student loans, which
bothfollow stochastic processes. There is no labor decision in the model; the
income process is exogenously given. Agents have access to asavings tech-
nology at the riskless interest rate Rs
.They face three payment options for
their student loans: not to consolidate and remain in the standard plan with
fluctuating payments (no consolidation), to consolidate b y locking-in the in-
terest rate without c h a n g i n g the standard plan (standard consolidation), or to
consolidate and switch to the income-contingent plan (income consolidation).
In addition, they can default on their student loans.
Agents start repaying their student loans with fluctuating payments for
Tperiods(T=10 y e a r s under the FSLP). Borrowers can hedge against both
income and interest rate risks. There are t w o other repayment plans a v a i -
lable upon consolidation: (1) standard consolidation sets payments to befixed
8
Institutions with high default rates are also penalized (see ED (2001b).
9
As apractical matter, it is v e r y difficult to demonstrate undue hardship unless the
defaulter is physically unable to w o r k .
8
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payments until the loan is paid in full, while (2) the income-contingent con-
solidation assumes that payments are contingent on income realizations. I
abstract from considering extended and graduated plans since bothgive the
borrowerrelief when his income is lowest. Mo deling the income plan alone is
sufficient to capture the income risk hedging behavior. Agents who have not
consolidated in the past can c h o o s e among the standard plan and the income
plan. They cannot switch betweenthe t w o consolidation plans. Consolidation
can happen only once and it does not involve any resource cost. Agents cannot
partially consolidate. Once they consolidate, they extend the life of the loan
to another Tperiodsunder standard consolidation and up to T′periodsunder
income consolidation (T′=25 y e a r s under the FSLP).
Corresponding to the agents’ three payment options, there are three t y p e s
of payments, pt∈P={pnc,psc,pic},given b y :
pnct=dt
Eh1 + PT
k=t+1
1
Qk
i=t+1 Rii,no consolidation
psct=dt
PT−1
k=0
1
Rk j
,standard consolidation (1)
pict=γ(yj
,dj
,Rj
)E[yt
], income consolidation
where dtrepresents the debt level in periodtand Rithe interest rate at period
i.P a y m e n t s are computed to make the present v a l u e equal to the face v a l u e
of debt dt
.F o r standard consolidation, Trepresents the n u m b e r of payment
periodsafter consolidation. The interest rate is fixed for the remainder of
the loan, Rj
,the rate at time of consolidation. F o r income consolidation,
payments are given b y afraction γ(yj
,dj
,Rj
)of the agent’s perperiodearnings
yt
.This fraction depends on income, debt level, and interest rate at time of
consolidation, γyj<0, γdj>0, and γRj>0. In case the loan is not fully paid
after an u m b e r of periods,T′
,the remaining debt is discharged. P a y m e n t s
under no consolidation and income consolidation are expressed in exp ected
v a l u e terms, since there is interest rate risk and income risk. Debt evolves
according to the equation d′= (d−p)Rwhere p∈Pis the payment made in
the previous period.
In addition to the repayment schemes already described, agents have the
option to default. As under the FSLP, this option does not represent default
in the traditional sense, since it is adelay in repayment that comes with a
series of consequences on the part of the defaulter. In the model, the agent
does not make any payment during the periodin which default occurs, and
he starts repaying his loan the following period. The agent loses his right to
9
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consolidate after default. Under the program, if the defaulter delivers several
regular payments, he regains his right to consolidate. F o r tractability pur-
poses,however, Iabstract from modeling this particular feature. There are
consequences of default modeled to mimic those in the data: agarnishment
of apart of the defaulter’s earnings (ρ)and an increase in his debt (α). The
defaulter is not excluded from the risk-free market. Ido not mo del the IRS tax
withholdings punishment given immediate repayment in m y set-up. Iabstract
from modeling ineligibility for further student loans, since Irestrict attention
to those students who c h o o s e not to go back to school.10 Also, as Ifocus on the
individual’s c h o i c e ; Ido not model penaltiesimposed on institutions. Default
in the model is possibleas long as the agent has not consolidated. Iassume
default does not occurpost-consolidation.While it is true that some borrowers
who use the consolidation option may find it optimal to default later on, in
practice, anegligible fraction of borrowersdo so. Irelax this assumption in
Section 7and discuss its implications.
The debt evolution is given b y d′=d(1 +α)Rfor the periodduring which
default occursand b y d′= (d−pd nc )Rfor the following periods,where pd nc
is similar to the payment under no consolidation, with the difference that
payments are o v e r T′periods(T′=25 y e a r s under the FSLP), not T=10.
Constraints for each case are given b y
no consolidation: c+pnc +a′
≤y+Rs
a,
standard consolidation: c+psc +a′
≤y+Rs
a,(2)
income consolidation: c+pic +a′
≤y+Rs
a,
after default :c+pd
nc +a′
≤y+Rs
a,
where cis consumption, yis earnings, Rs
aare assets from the previous period,
and a′is current savings with a′
≥0. F o r the periodin which default occurs,
the constraint is c+a′
≤y(1 −ρ) + Rs
a.
The preferences in the economy are standard with the lifetime utility:
(1 −β)
∞
X
t=0
β
tc(1−σ)
t
(1 −σ)
,(3)
where β∈(0,1) is the discount factor. The per period utility function is
CRRA with σbeingthe coefficient of risk a v e r s i o n .
10
Ido not observe the repayment status of borrowerswho decide to continue their edu-
cation, since they are eligible for loan deferments.
10
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3.2 Agent’s Problem
The agent maximizes his lifetime utility (Equation 3) b y c h o o s i n g the opti-
mal time to consolidate or to default (j), the consolidation t y p e (standard
or income), and the savings and consumption paths for the first Tperiods,
and savings and consumption every periodthereafter. Given the debt level,
income, and the interest rate he learns at the beginningof each period, as
long as the agent has not y e t consolidated, he c h o o s e s one of the four options
he faces. Once he consolidates and switches to the standard plan or to the
income plan, he cannot undo the process, remaining in that state until the
loan is paid in full. Hence, for every periodbeforeT, the agent can bein one
of the following states:
Case 1: A l r e a d y c o n s o l i d a t e d under the standard plan
The interest rate is determined at the time of consolidation and fixed for
the life of the loan. The v a l u e function is given b y :
VSC
(z,d, a, y,R) = max
a′{u(c) + Ey′β[VSC
(z
′
,d′
,a′
,y
′
,R)]}
s.t. c+psc +a′
≤y+Rs
a(4)
d′= (d−psc)R, a′
≥0
z
′=z−1, z > 0
The state v e c t o r includes the n u m b e r of periodsuntil full payment (z), debt
(d), assets (a), earnings (y), and interest rate (R). V a r i a b l e zk e e p s track of
the time remaining until full payment. In case z=0, the agent is in the last
periodof payment. F o r instance, if standard consolidation occurredat time
j < T ,z= 0 at time k=j+T.The expectation is o v e r earnings, since the
next period’srate is irrelevant after standard consolidation occurs.
Case 2: A l r e a d y c o n s o l i d a t e d under the income plan
The v a l u e function is similar to case 1with the difference that the payment
represents afraction γ(.)of earnings and the expectation is o v e r bothinterest
rates and earnings. Under this repayment schedule the interest rate is v a r i a b l e .
As in the previous case, the function is v a l i d as long as the agent has not
finished repaying the loan. When d′=0,there is no debt left for the next
period,so z=0,the last payment beingmade in the current period. If after
alimit of T′periodsd′is still positive, the time counter zis set to 0. F o r
instance, if income consolidation occurredat time j < T ,zcan become0at
any time kwith j+ 1 <k≤j+T′
.Time kis different across agents, since it
depends on their debt level at time of consolidation and income process they
face in periodsafter that. F o r example, an agent with aseries of low income
sho cks and high debt needs alonger time to pay relative to an agent with a
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higher income stream and alower debt level. If the time in which the agent
pays-off his debt, td′
=0,is less than T′then kis set to k=td′
=0 ,otherwise
k=T′
.A t T′periodsafter consolidation occurred,any outstanding debt is
discharged. That is, k=min{td′
=0, T ′
}.
VIC
(z,d, a, y,R) = max
a′{u(c) + Ey′
,R′
β[VIC
(z
′
,d′
,a′
,y
′
,R′
)]}
s.t. c+pic +a′
≤y+Rs
a(5)
d′= (d−pic)R, d′>0,a′
≥0
z
′
(d) = z(d)−1,z(d)>0
Case 3: Default
The v a l u e function for the periodin which default occursis given b y :
VD
(z,d, a, y,R) = max
a′{u(c) + Ey′
,R′
βV
D
NC
(z
′
,d′
,a′
,y
′
,R′
)]}
s.t. c+a′
≤y(1 −ρ) + Rs
a(6)
d′=d(1 +α)R, a′
≥0
z
′=z−1,z
′>0
Next periodafter default, the only a v a i l a b l e option is paying at fluctuating
interest rates. In the benchmarkeconomy Ido not allow for the possibilityto
repeat default. Irelax this assumption in Section 7and study its implications.
The v a l u e function VD
NCrepresents the path with fluctuating payments after
default occurred.This is given belowb y :
VD
NC
(z,d, a, y,R) = max
a′{u(c) + Ey′
,R′
β[VD
NC
(z
′
,d′
,a′
,y
′
,R′
)]}(7)
s.t. c+pnc +a′
≤y+Rs
a
d′=d(1 −pd
nc)R, a′
≥0
z
′=z−1, z > 0
In the case default occursat time j,z= 0 at time k=j+T′
.
Case 4: Not yet c o n s o l i d a t e d or in default
Under this case, the agent maximizes o v e r all four possiblec h o i c e s : entering
the next periodbeingconsolidated under the standard or the income plan, or
not consolidated, or as adefaulter.
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VNC
(z,d, a, y,R) = max
a′
,d′{u(c) + Ey′
,R′
βmax[VNC
(z
′
,d′
,a′
,y
′
,R′
),
VSC
(z
′
,d′
,a′
,y
′
,R′
),VIC
(z
′
,d′
,a′
,y
′
,R′
),VD
(z
′
,d′
,a′
,y
′
,R′
)]}
s.t. c+p+a′
≤y+Rs
a, a′
≥0,(8)
d′=λ(d−p)R+(1 −λ )d(1 +α)R, p∈P,
z
′=z−1,z
′>0,
where λ= 0 if default occursand λ= 1 otherwise. Additionally, for compu-
tational purposes, Iconsider ano consolidation path. This coincides with the
v a l u e function in Equation 8, in which VNCgives the highest v a l u e for every
periodt=1,2...T −1. In this case, z= 0 at time k=T.
WNC
(z,d, a, y,R) = max
a′{u(c) + Ey′
,R′
β[WNC
(z
′
,d′
,a′
,y
′
,R′
)]}(9)
s.t. c+pnc +a′
≤y+Rs
a
d′=d(1 −pnc)R, a′
≥0
z
′=z−1, z > 0
With the appropriate parameters and the estimated Markov processes for
loan rates and earnings, Isolve for optimal c h o i c e s within ea ch repayment
path and dynamically pick the optimal repayment t y p e and time. First, I
solve the problem after full payment is delivered. F o r every periodafter the
loan term is o v e r , the agent’s problem becomesastandard consumption and
savings problem, given b y
V(a, y) = max
a′{u(c) + Ey′βV(a′
,y
′
)}(10)
s.t. c+a′
≤y+Rs
a, a′
≥0
Then, the solution to this simple consumption/savings problem, V(a, y), pins
down the v a l u e function for the last periodin the life of the loan. This last
perioddepends on the time and t y p e of consolidation or the time of default.
The v a r i a b l e zin the v a l u e function k e e p s track of the n u m b e r of periodsuntil
full payment is delivered under the alternative c h o i c e s , VSC
,VIC
,and VD
.
When z=0, the agent is in the last periodof payment. He will c h o o s e only
consumption and savings for the remaining periods.F o r standard consolidation
that occursat time j < T ,zbecomes 0at time k=j+T.F o r income
consolidation that occursat time j < T ,zcan become0at any time kwith
k=min{td′
=0, T ′
}and j+ 1 <k≤j+T′
.F o r default that occursat time
j < T , z becomes0at time k=j+T′
.
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Thus, there is aterminal node for each path and consolidation/default time
jgiven b y :
Vj
SC
(0,d, a, y) = max
a′
≥0{u(y+Rs
a−a′−d)+βV(a′
,y
′
)}
Vj
IC
(0,d, a, y) = max
a′
≥0{u(y+Rs
a−a′−d)+βV(a′
,y
′
)}(11)
Vj
D
(0,d, a, y) = max
a′
≥0{u(y+Rs
a−a′−d)+βV(a′
,y
′
)}(12)
If consolidation/default has not occurredTperiodsafter borrowersenter re-
payment, the path is given b y Equation 9where z= 0 at k=T.The terminal
node is simply given b y ,
VNC
(0,d, a, y) = WNC
(0,d, a, y) = max
a′
≥0{u(y+Rs
a−a′
−d)+βV(a′
,y
′
)}.(13)
Iuse these terminal nodes to solve for the consumption/savings decisions
within each repayment path for all possibleswitches to that particular path.
Finally, Idynamically pick the optimal payment option and time (Equation 8).
This implies maximizing o v e r the four v a l u e functions at each pointin time.
This takes into account the possibilityto consolidate or default at alater date
and the possibilityto discharge one’s debt after income consolidation with the
corresponding terminal nodes.
3.3 P o l i c y Reform
T o simulate the policyreform that discontinues the option of locking-in interest
rates, Ieliminate the standard consolidation option, case 2, in the benchmark
economy. Keeping everything else the same, case 4, not y e t consolidated or in
default state, becomes:
VNC
(z,d, a, y,R) = max
a′
,d′{u(c) + Eβmax[VNC
(z
′
,d′
,a′
,y
′
,R′
),
VIC
(z
′
,d′
,a′
,y
′
,R′
),VD
(z
′
,d′
,a′
,y
′
,R′
)]}(14)
s.t. c+p+a′
≤y+Rs
a, a′
≥0
z
′=z−1, z > 0
3.4 Government Budget Constraint
In m y framework, the only role of the government is to subsidize the student
loan program. In the context of the model, this supp oses financing three t y p e s
of costs: 1) the cost of discharged loans under income consolidation computed
14
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as the difference betweenthe loan amount and the present v a l u e of payment;
2) the cost from defaulted loans computed as the loan amount minus the
present v a l u e of the part recouped through repayment and punishments; and
3) the cost associated with standard consolidation that comes from subsidizing
the difference between the fixed consolidated rate and the v a r i a b l e market
interest rate. Icompute the total cost to the government in pr esent v a l u e
terms under boththe benchmarkeconomy and the policyreform environment.
Iassume that this cost is financed through lump-sum transfers, τB
,and τPol,
respectively, equally collected from agents. With Nthe total n u m b e r of agents
in the economy, the government budget constraints under the t w o alternative
environments are given belowb y :
Nτ
B=
X
i∈IC
Bhdi
0−PVpi ic i+X
i∈DEF
Bhdi
0−PVpi
def i+X
i∈SC
Bdi
0−PVpi sc 
Nτ
Pol =
X
i∈IC
Pol hdi
0−PVpi ic i+X
i∈DEF
Pol hdi
0−PVpi
def i,(15)
with the first equation for the benchmarkeconomy and the second one for the
policyreform. The first term is the cost associated with income consolidation,
with IC
B(IC
Pol)the set of agents who c h o o s e this option. The second term
represents the cost associated with default, with DEF
B(DEF
Pol)the set
of agents who c h o o s e default. The third term (not present in the budget
constraint for the policyreform) represents the cost associated with standard
consolidation, with SC
Bthe set of agents who c h o o s e this option. In the
model, the tax that the government collects each periodis computed as the
fixed payment for aconsole with the discounted present v a l u e that equals the
face v a l u e of the tax τBand τPol,respectively.
3.5 W e l f a r e
In order to study the benefitsand losses of eliminating the consolidation loan
program across different groups of college graduates, Icompare the policyenvi-
ronment (without standard consolidation) to the benchmarkcase. As aw e l f a r e
measurement, Iuse aggregate total w e l f a r e with agents equally w e i g h t e d . De-
note WPol as total w e l f a r e in the case where consolidation is discontinued, and
WBas total w e l f a r e under the benchmarkcase. Iquantify µ=WPol−WB
|WB
|.This
measure is given in utility terms and represents the utility that makes agents
indifferent betweenhaving the option to lock-in interest rates and not having
that option. Thus µ > 0implies aw e l f a r e gain if the program is discontinued;
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otherwise, the reverse is true. The total w e l f a r e measures are calculated b y
aggregating the v a l u e functions at time 0across all agents in the economy.
Given that m y analysis is apartial equilibrium framework economy, w e l f a r e
calculations do not take into account price effects. There are no labor or capital
markets. My analysis of redistributional effects, however, gives asense of the
direction of c h a n g e s in w e l f a r e across different groups of college graduates and
can beused to study which income groups are mostly affected b y the policy
reform, one of the k e y issues raised in the debate.
4P a r a m e t e r i z a t i o n
The model is calibrated to the U.S. economy. The procedure involves standard
parameters (discount factor, risk a v e r s i o n coefficient) and policyparameters
(loan duration, penaltiesfor default, fraction of income that is paid under the
income plan), the calibration of the distributions of post-collegedebt and a-
ssets, and the calibration of the sto chastic processes for loan rates and earnings.
The model periodequals one y e a r . F o r policyparameters, Iuse Department of
Education data. F o r the loan rate process Iuse the time series for the 91-day
T r e a s u r y bill rate. F o r the earnings process, as w e l l as the distribution of debt
and assets post-college,Iuse the National P o s t s e c o n d a r y Student Aid Survey
(NPSAS) data set, specifically the Baccalaureate and Beyond surveys (B&B
93/97). The B&B 93/97 data set is nationally representative, and it is com-
prised of students, parents, and institutions. The survey has followed through
1997 arandom sample of 11,000 individuals who received their baccalaureate
degree during the 1992-1993 academic y e a r . There w a s an initial survey at
graduation and t w o follow-up interviews in 1994 and 1997. Ido not take into
account students who w e n t to graduate scho ol, since those continuing educa-
tion are eligible for deferments on their loans. The sample in 1997 includes
808 college graduates. Details on background c h a r a c t e r i s t i c s of borrowersare
provided in the Appendix.
4.1 P a r a m e t e r s
P a r a m e t e r v a l u e s are given in T a b l e 1. The discount factor is 1/1.04 to match
the risk-free interest rate of 4percentand the coefficient of risk a v e r s i o n of
2is standard in the literature. The savings rate is 4percentto match the
a v e r a g e rate in 1994. The initial duration of the loan, T,is set according to
the ED. These 10 y e a r s represent the initial duration of the loan payment that
can bec h a n g e d upon default or consolidation. Iset the w a g e garnishment,
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T a b l e 1: P a r a m e t e r V a l u e s
P a r a m e t e r V a l u e T a r g e t / S o u r c e
β0.96 real a v g rate=4%
σ2Aiyagari (1994)
Rs1.04 a v g rate in 1994
T10 ED
ρ0.0265 4y e a r s default rate=5.14%
α0.1 ED
ρ,upon default to match the default rates for 92/93 college graduates in m y
sample. In practice, this punishment v a r i e s across agents and can beas high
as 10 percent. Iestimate ρ=2.65 percentto match the 5.14 percentdefault
rate four y e a r s after entering repayment. Within the model, the default rate
is computed as the percentageof agents who defaulted within four periods.
11
Iset the increase in debt level upon default, α=10 percent. In practice,
the increase in the debt level v a r i e s across agents depending on collection fees,
and attorney fees and can beas high as 25 percentof the amount of the loan
when default occurs.The guideline for defaulting borrowersdoes not provide
an explicit rule. My robustness c h e c k s in Section 7show that the results are
not sensitive to reasonable v a r i a t i o n s of this parameter.
Under the FSLP, the fraction of income, γ(y,d, R), used as payment under
the income-contingent plan is based on the income level, y,the principal, d,
and the interest rate, R,at consolidation time. There is aschedule of fractions
paid under the actual program that increase with the level of debt, decrease
with the level of income, and increase with the interest rate. P a y m e n t s are
generally capped at an amount slightly less than the required payment under
astandard schedule and cannot beless than $5. T o estimate these fractions
Iuse the payment calculator provided b y the Department of Education. I
computed the v a l u e s of fractions of income that go toward repayment for the
mean, median, and maximum level of debt, taking into account the interest
rate and income levels in m y model. The computed v a l u e s for the low interest
rate are given in T a b l e 2. F o r example, an agent with the highest income level,
11
The U.S. Department of Education uses at w o - y e a r basis cohort default rate (CDR) as
aprimary measure. This represents the percentage of borrowerswho default b y the end of
the next fiscal y e a r after entering repayment. The CDR understates the default problem
and other measures such as longer period a v e r a g e default rates are desirable. The CDR
takes into account all borrowerswho enter repayment in aparticular fiscal y e a r , including
dropouts. Given the purpose of the current study, the data set used, and m y model, Iuse
the default rates for college graduates four y e a r s after entering repayment.
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T a b l e 2: γ(y,d, R)
Earnings Median debt Mean debt Maximum debt
9400 0.0378 0.0446 0.0734
13740 0.0378 0.0446 0.0734
22555 0.0373 0.0441 0.0732
27192 0.0373 0.0441 0.0732
35567 0.0368 0.0436 0.0727
54843 0.0368 0.0436 0.0727
$54,843, that accumulated amedian college debt and faces alow interest rate
at consolidation time will pay 3.68 percentof his income each perioduntil the
loan is paid in full.12 Iextrapolate this schedule for the entire range of debt
using linear approximations for each of the six income levels in m y model. The
fraction increases in debt and decreases in income. V a l u e s range from 0.035 to
0.073 in the case of the low interest rate and from 0.03 to 0.105 in the case of
the high interest rate.
T o calibrate debt and asset distributions Iuse the B&B data set and the
SCF 1983, respectively. F o r debt levels Iuse the amount borrowedfor un-
dergraduate education. The mean is $10,270 and the standard deviation is
$5158 in 1992 constant dollars. The maximum allowed is $17,250 for federal
student loans (College Board (2003)). F o r assets Iinclude pap er assets, which
are given b y the sum of financial assets, cash v a l u e of life insurance, loans out-
standing, gas leases, v a l u e of land contracts, and thrift accounts. F o r y o u n g
college graduates in the SCF, Iget amean of $1526 and astandard deviation
of $1806 in 1992 constant dollars.
4.2 Loan Rates Process
The interest rate on education loans is set according to the procedur e used
b y the government in 1994. It is based on the 91-day T r e a s u r y bill rate plus
athreshold of 2.3 percent(U.S. Department of Education). T he rate follows
asto chastic process, given b y a2b y 2transition matrix Π(R′
,R)on {R,R},
calibrated to match the T-bill rate in the 1990s.13 T o estimate the sto chastic
process for loan rates, Iuse the time series for 91-day T-bill rates for 1980-1996
adjusted for inflation. Ifit the real rate time series with the AR(1) process
12
The v a l u e s are given in 1992 constant dollars.
13
While aprocess with alarger n u m b e r of states is desirable, this increases the computa-
tional burden.
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Rt=µ(1 −ρ) + ρRt −1+ε, ε∼N(0,σ
2
). The estimates of the t w o moments
are given b y ρ=0.9038 and σ=0.7788. Iaggregate this to annual data and
the autocorrelation is given b y 0.297 and the unconditional standard deviation
b y 1.817. Ihave approximated this process as at w o - s t a t e Markov c h a i n . The
support is R∈{1.038,1.075}.The transition matrix is 0.65 0.35
0.35 0.65 .
4.3 Earnings Process
T o calibrate the earnings process Iuse earnings as of April 1994 and 1997
from the B&B 93/97 samples and PSID earnings for college graduates in 1994.
Earnings follow asto chastic process given b y a 6 b y 6transition matrix Q(e′
,e)
on the supp ort {b, e1,e2,e3,e4,e5}.The support consists of the a v e r a g e s for
the earnings quantiles in the B&B 1997 sample, e1...e5, and the benefitwhen
unemployed, b.The unemployment benefitis estimated from the CPS data set
for college graduates, since the B&B survey does not provide any information
on it. My estimate from the CPS is $9400 based on w e e k l y w a g e s of $717.
T a b l e 3presents the estimates given in 1992 constant dollars.
T a b l e 3: Earnings
b9400
e1 13740
e2 22555
e3 27192
e4 35567
e5 54843
Icalibrate the transition matrix using the PSID individual income and
employment status data for college graduates in 1992 and 1993 and estimate
an annual frequency transition matrix for the income. This is given belowb y :





0.30 0.47 0.07 0.07 0.045 0.045
0.03 0.69 0.17 0.05 0.03 0.03
0.04 0.15 0.61 0.12 0.05 0.03
0.03 0.05 0.18 0.55 0.14 0.05
0.02 0.02 0.04 0.19 0.64 0.09
0.02 0.01 0.01 0.03 0.20 0.73





.
Using the B&B samples, Ican obtain only athree-year calibrated earnings
process that cannot be transformed to aone-year frequency. Ic h o o s e the
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support for earnings, however, from m y B&B sample, to beconsistent with
other dimensions of heterogeneity in m y set-up.14
5Results for Benchmark Economy
In the benchmarkeconomy agents c h o o s e betweenstandard consolidation, in-
come consolidation, no consolidation, and default. Ifirst present the pre-
dictions of the benchmarkeconomy regarding the repayment pat t erns among
non-defaulters who constitute 95 percentof borrowers. Then, Ianalyze the
behaviorof defaulters in the model.
5.1 Repayment P a t t e r n s for Non-defaulters
This section focuses on the repayment behaviorof those borrowerswho c h o o s e
not to default on their student loans. The model replicates the consolidation
pattern as delivered b y the 1997 B&B survey. According to the data, four
y e a r s after graduation all borrowerswho do not default on their debt c h o o s e
to consolidate, with 96 percentof them remaining under the st an da r d plan.
My model shows that 93 percent of non-defaulters will lock-in the interest
rate under standard consolidation, 6percent of them will switch to income
consolidation, and the remaining 1percentwill c h o o s e not to consolidate at
all.
The model simulations show that borrowersc h o o s e to lock-in interest rates
early after graduation.15 This is becausem y simulations mimic market con-
ditions since 1992/1993 when interest rates on student loans w e r e low. Given
interest rate uncertainty, borrowerswill take advantage of the low interest rates
earlier in the repayment phase of the loan. F e a r i n g higher interest rates in the
near future, the majority of borrowers switch to the standard consolidation
program immediately after entering repayment.
The model explains the observed c h o i c e of repayment plans across different
groups of college graduates. The data suggest that borrowerssort themselves
into c h o o s i n g the repayment option on their education loans: the mean ear-
nings of payers in the income-contingent plan are about 65 percentof those
14
The procedure implies computing the third root of the three-year matrix from m y B&B
samples. Since the eigenvalues are too small, the decomposition does not w o r k , so instead I
use the transition matrix obtained from PSID. When Iraise the PSID matrix to the third
powerand compare it against the matrix estimated from the B&B, differences are small, so
Ic h o o s e to use the PSID matrix.
15
Isimulate 100 economies with apopulation of 10,000 agents. All results are a v e r a g e s
o v e r these 100 economies.
20
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of payers in the standard plan (see figure A-1). Also, the mean debt of pay-
ers in income consolidation is higher than that under standard consolidation.
Income consolidation allows y o u n g agents, more likely constrained in their abil-
ity to borrow,to redirect a v a i l a b l e funds toward other purchases. Once they
accumulate income later on in their lives, they can deliver higher payments
toward their education loans. Fluctuating payments contingent on income re-
alizations give the debtor the possibilityto smooth consumption across states
and periods. While income consolidation allows borrowersto hedge against
income risk, standard consolidation allows borrowersto hedge against interest
rate risk. T a b l e s 4a and 4b show data and model counterparts for a v e r a g e s
of earnings, debt levels, and debt to earnings ratios (debt burden) for payers
under bothconsolidation options.16
T a b l e 4a: Data
Consolidation Earnings Debt Debt/Earnings
Income 20539 10955 0.66
Standard 30965 7538 0.46
T a b l e 4b: Model
Consolidation Earnings Debt Debt/Earnings
Income 22695 13813 0.78
Standard 29563 7322 0.31
The model quantitatively and qualitatively explains the repayment pa-
tterns with respect to debt levels. Agents with higher debt levels are betteroff
in the income-contingent plan than under the standard plan. F o r any income
and interest rate process, as debt increases, agents are less likely to complete
loan payments in 25 periods.The model mimics the data in that the borrower
is exempt from repaying any outstanding debt 25 periodsafter entering income
consolidation. In addition, payments perperiodare m u c h lower under income
consolidation than under standard consolidation, especially for higher debt
levels.
16
Debt is measured as the amount still o w e d in 1997 and earnings as the annual job income
for the y e a r before the interview date. Icompute the model counterparts of these measures
b y calculating debt and income levels four periods after entering repayment. The debt
burden is computed (both in the model and in the data) as the group a v e r a g e of individual
ratios of debt to earnings four periodsafter entering repayment.
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The model also accounts for the fact that agents with lower income levels
c h o o s e income consolidation. Given low income levels, payments under the
income plan are low relative to payments a v a i l a b l e under other options in the
model. Agents with low income streams are less likely to complete payments
in 25 periods. The model quantitatively accounts for the income differences
in 1997 betweenthose who c h o o s e consolidation under standard and income-
contingent plans. It predicts that only agents among those that are initially
unemployed or in the first earnings quantile c h o o s e the income plan. The fact
that unemployment induces peopleto c h o o s e income consolidation is consistent
with data. In the B&B sample, the duration of unemployment for payers
in income consolidation is longer relative to that for payers under standard
consolidation (2.71 v e r s u s 2.27 months).17 It is possible,however, that not
only does unemployment induce peopleto c h o o s e income consolidation, but
also the income plan itself may encourage peopleto stay unemployed longer.
This framework cannot capture this aspect of reality, since employment is
exogenous. Y e t the effect of student loan policieson labor effort represents an
interesting topic for future research.
Overall, the model predicts that higher debt-earnings ratios correspond to
ahigher coincidence of income consolidation. This result is driven b y the t w o
main tensions in the model: 1) interest rate uncertainty and 2) income uncer-
tainty. The main trade-off between standard and income consolidation options
is hedging against interest rate risk while paying the full amount v e r s u s hed-
ging against income risk with lower payments perperiodand the possibility
to partially pay the loan amount. Interest rate uncertainty makes standard
consolidation more attractive, whereas income uncertainty makes income con-
solidation more attractive. There is no interest rate risk hedging on the income
plan, since the interest rate fluctuates with the market.
Hence agents in lower income groups opt for income consolidation in the
case of high debt levels, while those with low debt levels will opt for standard
consolidation. Even though the income level is low, the debt accumulated in
college is not large enough to benefitfrom the possibilityto partially repay
the loan. They are betteroff paying at afixed rate with higher paym e nts per
period,rather than paying sub ject to astochastic interest rate and contingent
on stochastic income realizations. The same intuition applies to agents in other
income groups. Consequently, agents in higher income quantiles that can afford
higher payments perperiodwill c h o o s e standard consolidation regardless of
their debt levels. F o r them, hedging against interest rate risk is more attractive
17
Unemployment spells represent continuous n u m b e r of months unemployed since gradu-
ation.
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than hedging against income risk. If there is no interest rate uncertainty,
standard consolidation in the model coincides with the no consolidation path.
Under this scenario, more peopleswitch to the income-contingent plan.
T o summarize, acombination of debt and income levels will affect the
c h o i c e betweenincome and standard consolidation for borrowerswho do not
default. Inow analyze those agents who c h o o s e to default on their student
loans.
5.2 Who Defaults on Student Loans?
Data show that defaulters have lower income levels and higher debt levels on
a v e r a g e relative to borrowerswho do not default. The model q u a l i t a t i v e l y
replicates these facts as T a b l e s 5a and 5b show. The mo del o v e r e s t i m a t e s ,
however, the magnitude of the difference betweenmean earnings for the t w o
groups of borrowers.
T a b l e 5a: Default v e r s u s Non-default
Model
P e r c e n t a g e Earnings Debt Debt/Earnings
Defaulters 5.14% 22897 10042 0.55
Non-defaulters 94.86% 29466 7797 0.34
T a b l e 5b: Default v e r s u s Non-default
Data
P e r c e n t a g e Earnings Debt Debt/Earnings
Default 5.14% 29748 9430 0.59
Nondefault 94.86% 30481 7899 0.47
Given income, assets, and interest rates, the model delivers debt thresholds
d(a, y,R)and d(a, y,R)that induce different repayment c h o i c e s . T a b l e 6sums
up of the thresholds b y income and debt levels. F o r peoplewith low income
levels, for every debt level, d(a, y,R)>d(a, y,R), income consolidation is
c h o s e n and for d(a, y,R)<d(a, y,R), standard consolidation is c h o s e n . As
argued in the previous section, agents with higher debt levels are more likely
to switch to income consolidation, whereas agents with lower debt levels are
more likely to switch to standard consolidation.
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T a b l e 6: Repayment behaviorbased on income and debt
Low debt (<d)Intermediary debt (d,d)High debt (>d)
Low income Standard consolidation Default Income consolidation
High income Standard consolidation Standard consolidation Standard consolidation
When comparing the option to default relative to the t w o consolidation
options, default is optimal in the intermediate range, (d(a, y,R),d (a, y,R)).
This result requires at w o f o l d explanation: First, why is standard consolida-
tion preferred o v e r default for agents with low debt levels? Given aparticular
level of income and assets, when the debt level is low, (<d)the agent prefers to
pay under standard consolidation, which allows him to lock-in interest rates.
F o r ahigher loan amount, however, he enters default, given that he is con-
strained in his ability to repay. The intuition behindthis result is that the
default option lowers payments perperiod,since the defaulter can extend the
life of the loan to 25 y e a r s . F o r some, this option might bemore attractive
even after accounting for the debt increase after default. Th e main trade-
off between standard consolidation and default is higher payments perperiod
with no interest rate risk v e r s u s lower payments perperiodwit h interest rate
fluctuations. Hence the threshold that makes default preferable to standard
consolidation, d(a, y,R), declines in interest rates as standard consolidation
becomesless attractive. Second, why is income consolidation preferred o v e r
default for agents with high debt levels? Both options allow for lower pay-
ments, since the life of the loan is extended to 25 y e a r s . If the loan amount
is too high (>d), default becomesv e r y costly. After default, the debt level
increases b y 10 percentof the principal at the time default occurs.While both
default punishments and payments in the income-contingent plan are increa-
sing in earnings and debt levels, the main difference betweenthe t w o options
is that default is more sensitive to debt levels and less sensitive to income le-
v e l s , whereas the converse is true for income consolidation. The debt increase
is sizable, while the w a g e garnishment upon default happens only once and
it represents only 2.65 percentof income. Under the income-contingent plan,
the borrowerpays 3to 10 percentof his income (depending on the debt level
and interest rate) every perioduntil full payment is delivered or 25 y e a r s have
passed, whichever comes first.
Both thresholds (that separate default from standard consolidation, d,and
default from income consolidation, d)are increasing functions of earnings.
This is becauseas the agent becomesless constrained financially, more debt is
needed to trigger default. Consequently, the model delivers no thresholds for
higher earnings levels. The agent c h o o s e s standard consolidation regardless
24
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of his debt level. When the exogenous parameters of the model are c h a n g e d ,
the thresholds c h a n g e accordingly. F o r instance, d(.)increases in γ.The debt
level that makes income consolidation preferable to default increases with the
fraction of income paid under the income plan as income consolidation becomes
less attractive.
Quantitatively, the model matches the data regarding the mean debt for
defaulters v e r s u s that for non-defaulters, as T a b l e 7shows.
T a b l e 7: Repayment behaviorb y debt levels
Standard consolidation Default Income consolidation
Model $7,322 $10,042 13,813
Data $7,538 $9,430 $10,955
6P o l i c y Reform
Prior to 2006, peoplew e r e able to lock-in interest rates on their student loans.
This section considers the implications of the policyreform implemented in
2006, where the U.S. government discontinued the opportunity to lock-in in-
terest rates for student loans. Thus, the options peoplehave are: no consolida-
tion, income consolidation, and default (i.e., no standard consolidation plan).
Section 6.1 considers c h a n g e s in repayment patterns induced b y the reform
and Section 6.2 analyzes the w e l f a r e effects of the reform.
6.1 Effects on Repayment Behavior
The findings of the model are presented in T a b l e s 9a and 9b. The model
delivers adefault rate of 27.5 percent, an increase of 22 percentagepoints
from the benchmarkmodel. Even though this represents afivefold increase
in the default rate, given the rules for default under the FSLP, it should not
w o r r y either policymakers or borrowers.The government collects most of the
loan amount. In addition, interest rates for student loans do not take into
account the risk of default as interest rates for unsecured c r e d i t do. Under
the student loan program, more peopledefaulting does not necessarily imply
higher interest rates for these loans.
Regarding repayment patterns for non-defaulters, the model predicts that
borrowerswith lower earnings and higher debt levels still c h o o s e income con-
solidation. Y e t , when standard consolidation is not allowed, 93.5 percentof
borrowersc h o o s e not to consolidate.
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T a b l e 8: Repayment behaviorbased on income and debt -reform
Low debt (< dp
)Intermediary debt (dp
,dp
)High debt (>dp
)
Low income No consolidation Default Income consolidation
High income No consolidation No consolidation No consolidation
T o understand who switches and who stays under the standard plan with
fluctuating payments, consider debt thresholds that induce different repayment
plans, as illustrated in T a b l e 8. Under the reform, these thresholds are such
that given earnings and assets, agents with high debt levels c h o o s e income
consolidation (>dp
), those with intermediate debt levels default (dp
,dp
), and
those with low debt levels do not consolidate (<d
p
). The option to lock-in
interest rates is not a v a i l a b l e ; thus, most borrowers who previously locked-
in interest rates will c h o o s e to stay under the standard plan, paying at a
v a r i a b l e rate. Borrowers at the margin will enter the default range given a
slight increase in the debt burden relative to earnings under v a r i a b l e rates
(d
p<d). F o r higher debt levels, however, default is too costly, so income
consolidation is preferred. Similar to the benchmarkeconomy, these thresholds
exist for lower income levels. F o r higher income levels, there are no such
thresholds; hence, the elimination of standard consolidation will not induce
extra default. Borrowers will c h o o s e to stay under the standard plan with
fluctuating payments. Between default and not consolidating, the main trade-
off is lower payments per period at acost v e r s u s ashorter time to repay.
Overall, the model delivers that 70 percentof those who previously locked-
in interest rates will remain on the standard plan with fluctuating payments,
25 percent of them will default, and only 5percent will switch to income
consolidation.
Consequently, defaulters have lower earnings on a v e r a g e relative to non-
defaulters. Note, however, that the difference in earnings between the t w o
groups is larger compared to the benchmarkcase, and the difference in debt
levels is reversed: non-defaulters have more debt on a v e r a g e . The explanation
is that from the poolof peoplewho have not y e t defaulted, those with lower
earnings but relatively lower debt levels will c h o o s e to default. Those with
higher debt levels in the low-income groups will opt for income consolidation.
T o conclude, the model predicts that eliminating the ability to lock-in
interest rates lowers the incentives to repay student loans. The additional
default comes from borrowersin low-income groups and with relatively low
debt levels. If debt levels are high, default w o u l d betoo costly, given the debt
increase upon default. Borrowers with high income levels are still betteroff
paying at the fluctuating interest rate than defaulting, given the high cost of
26
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T a b l e 9a: P o l i c y reform
P e r c e n t a g e Earnings Debt Debt Burden
Default 27.5% 19824 8121 0.48
Non-default 72.5% 32667 9473 0.34
T a b l e 9b: P o l i c y reform
P e r c e n t a g e Earnings Debt Debt Burden
Income Consolidation 6.5% 11243 13169 1.2
No Consolidation 93.5% 32035 7099 0.25
default as aresult of w a g e garnishment.
6.2 W e l f a r e Analysis
My results suggest that the additional cost from income consolidation induced
b y the 2006 reform is negligible, whereas the cost of subsidizing standard
consolidation is sizable.18 Note there is no cost from default, since everything
is paid back under this option.19 Thus default rates do not affect w e l f a r e .
The reform improves w e l f a r e for the aggregate economy b y 0.19 percent
relative to the benchmarkcase. Higher taxes are needed when borrowersare
allowed to lock-in interest rates, since the student loan program is more costly
to the government. In the case of the reform, taxes are less, sin c e less is sub-
sidized. Thus, borrowersare h u r t b y higher taxes in the benchmarkeconomy.
They benefit, however, from the opportunity to remove interest rate uncer-
tainty. Overall taxes are high enough to more than offset the positive effect
of standard consolidation. As aresult, when borrowerscannot consolidate to
lock-in interest rates, they are betteroff on a v e r a g e .
T a b l e 10: W e l f a r e c h a n g e s b y groups of borrowers
Quartile 1Quartile 2Quartile 3Quartile 4
Earnings -0.024 +0.327 +0.415 +0.469
Debt to Earnings +0.412 +0.136 +0.261 +0.188
More interesting results emerge when comparing w e l f a r e effects across in-
18
F o r an economy of 10,000 agents, the estimated total cost from additional income con-
solidation is $39,380. The total cost of subsidizing standard consolidation is $3.7 million.
19
In the benchmarkcase Ido not allow for the possibilityof repeated default. In section
7 I relax this assumption and discuss its implications for the cost of default.
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come groups. T a b l e 10 shows w e l f a r e c h a n g e s b y quartiles of earnin g s and
debt-to-earnings ratios. Borrowers from the top income quartile benefitthe
most from the reform. Their w e l f a r e improves b y almost 0.5 percent,while
borrowersfrom the second quartile gain 0.33 percent.Borrowers from the low-
est income quartile experience aslight w e l f a r e loss from the reform (-0.02%).
Thus, w e l f a r e gains increase with income. With the reform, peoplefrom higher
income groups will c h o o s e not to consolidate, accepting the fluctuating inter-
est rate, whereas those from lower income groups might not beable to sustain
higher payments and might be forced to default or switch to the income-
contingent plan. Hence, low-income borrowerspay more than the initial loan
amount, with the reform, despite lower taxes.
Redistributional effects can also becompared across debt to earnings quar-
tiles. W e l f a r e gains are larger for borrowerswith relatively little debt, under
the reform. Those with high debt-to-earnings ratios consider the income-
contingent plan before the reform. F o r them, income uncertainty is more
significant. Under the reform, they do not switch to another option, but they
pay lower taxes. Thus, they are benefitingmore relative to other groups. Bo-
rrowers with low debt to earnings ratios will benefitthe most from the reform.
They c h o o s e standard consolidation with fixed payments under the benchmark
economy, and under the reform, they switch to fluctuating payments. Given
low debt levels, the negative effect of this switch is not large enough to offset
the benefit of paying lower taxes. Borrowers in the second quartile of debt
to earnings will benefitrelatively less. This is precisely the group that w a s
under standard consolidation beforethe reform and switched to default after
the reform w a s introduced.
T o conclude, the reform will induce redistributional effects across income
groups: most peoplegain from the reform except for the poorestborrowers,
as opponents of the reform have feared. These are the peoplefor whom the
interest rate risk seems to besignificant enough to w a r r a n t the higher taxes
they have to pay when standard consolidation is a v a i l a b l e . Once hedging
against the interest rate risk becomesunavailable, they will not consolidate
or they will default. Those with lower debt to earnings ratios can afford
the fluctuating payments under no consolidation, but those wit h intermediate
debt-to-earnings ratios will enter default. The cost of doing so more than
outweighs the benefitof paying lower taxes. F o r borrowerswith higher debt to
earnings ratios, on the other hand, the income risk is more significant, so they
will k e e p paying under the income plan. F o r them, as w e l l as for peoplewith
higher income levels, the interest rate risk is not significant enough to w a r r a n t
the higher taxes they have to pay to support standard consolidation.
My results suggest that an additional cost to the government from extra
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default w a s an unfounded w o r r y of the opponents of the reform. As the w e l f a r e
analysis shows, however, their concerns regarding redistributional effects are
more w e l l - g r o u n d e d .
7Robustness
This section presents robustness c h e c k s on v a r i o u s parameters of this model. I
first consider c h a n g e s in parameters that represent penaltiesupon default for
student loans: α,the increase in debt, and ρ,the fraction of income that is
garnished. Then Irelax t w o assumptions in the benchmarkeconomy, no default
post-consolidationand no repeated default, and discuss their implications.
In the calibrated economy, α=0.10. When Iv a r y around this v a l u e , the
model predicts adefault rate of 4.8 percentfor α=0.09 and adefault rate of
5.9 percentfor α=0.11. While these c h a n g e s affect the quantitative results
of the model, they do not affect the qualitative results, i.e. options c h o s e n
across v a r i o u s groups of borrowers. The model is more sensitive to the w a g e
garnishment penalty,ρ.In the benchmarkeconomy, Iestimate this parameter
to match the default rate of 5.14 percent. Iset the w a g e garnishment, ρ=
0.0265. When Ic h a n g e it to 0.0215, the default rate is 6.7 percentand for a
v a l u e of 0.0315, the default rate is 4percent.The higher sensitivity of default
behaviorto the w a g e garnishment relative to the debt increase is due to the fact
that an increase in debt affects agents differently across debt groups, while the
increase in w a g e garnishment affects agents similarly regardless of their debt
levels. Hence an increase in αinduces previous defaulters with higher debt
levels to reconsider their c h o i c e , but not necessarily those with lower debt
levels. Those who switch will opt for income consolidation. An increase in ρ,
on the other hand, induces previous defaulters with bothhigher and lower debt
levels to reconsider their c h o i c e . They will switch to standard consolidation
and income consolidation, respectively.
When Iallow for default post-consolidation,the additional default rate is
negligible (less than 1percent). This is becauseonce borrowerslock-in low
interest rates, they are betteroff paying at this low interest rate for 10 periods
rather than defaulting and paying at afluctuating rate for 25 periods. The
extra default comes from borrowers who c h o s e not to consolidate before(1
percentin the benchmarkeconomy). In the case of high interest rates, they
are better off paying at fluctuating interest rates rather than consolidating
under the standard plan and paying at that high interest rate for 10 periods.
With the opportunity of defaulting after consolidation, however, they will find
it optimal to consolidate, deliver ahigh payment perperiod,and then default
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to pay for the rest of the loan (adjusted for the debt increase punishment)
for 25 periods. T o gain intuition behindthis result, consider individuals with
high levels of income that face astream of high interest rates. Given high
income levels, income consolidation is not attractive. Given the sequence of
high interest rates, standard consolidation is not attractive either. Between
no consolidation and default post-consolidation, they may prefer the latter,
since they can lower payments perperiod. Why do they prefer default after
consolidation to regular default (even if that can occurin aprevious period)?
They are not constrained in their ability to repay, so they can afford to deliver
high payments for awhile. Under standard consolidation at ahigh rate, they
will deliver higher payments than under no consolidation. Hence, they lower
their loan amount enough to make the 10 percentincrease of the debt at the
time default occursw o r t h the benefitof enjoying subsequent lower payments.20
When Iallow for repeated default, the cost from default is positive, but
negligible. This positivecost comes from the possibilitythat the borrowersmay
beexempt from repaying the outstanding debt 25 y e a r s after def ault occurred
for the first time. This path is similar in nature to the income plan in that
the federal government will continue to garnish part of the de f aulter’ s w a g e ,
partially collecting the loan amount in this manner. In practice, more severe
punishments are imposed on borrowerswho c h o o s e to repeatedly default, such
as having the IRS tax withhold tax refunds and beingexcluded from credit
markets. No defaulter ends up in that stage for along periodof time. In
m y model relaxing this assumption means allowing borrowersto default t w i c e .
Given that the additional cost is negligible, w e l f a r e predictions do not c h a n g e .
8Conclusion
Ihave developed adynamic stochastic economy that replicates the repayment
behaviorfor college graduates who borrowedfor their undergraduate education
under the FSLP. The model accounts for repayment patterns in the data.
Most borrowersc h o o s e to consolidate after graduation, with the ma jority of
them locking-in interest rates on student loans. The model qua l it a ti ve ly and
quantitatively explains c h a r a c t e r i s t i c s of borrowersamong different groups of
20
In practice, extending payments o v e r alarger period is a v a i l a b l e without any additional
penalty (the extended plan). This might explain why the fraction of those who default
post-consolidation is negligible. The extended plan is absent in the B&B data, the reason
being low interest rates that followed aperiod of v e r y low levels with aslight upward trend.
Hence, most of borrowers found standard consolidation optimal. Some opted for income
consolidation, but none c h o s e the extended plan.
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payers. It replicates the repayment plan c h o i c e for non-defaulters. My model
explains the sorting evidence b y earnings and debt in 1997: payers under
the income plan have higher debt levels and lower earnings levels on a v e r a g e
relative to those under the standard plan. Default is optimal for intermediate
levels of debt.
Iuse the model to test the implications of the 2006 reform that elimi-
nates the possibilityto lock-in interest rates. Results show that the reform
will induce an increase in the default rate b y 22 percent, primarily b y low-
income borrowers. The cost to the government from the extra def a ult w a s
an unfounded w o r r y of the opponents of the reform, given that student loans
are not dischargeable. The model predicts, however, that borrowersfrom the
lowest income group experience aw e l f a r e loss.
The absence of the possibility to hedge against interest rate fluctuations
might deter students from using the program, with implications for borrowing
behaviorand college enrollment. Iconsider these issues in separate research
that endogenizes enrollment and borrowingdecisions and ties policyanalysis
to life-cycle earnings and h u m a n capital accumulation. In addition, the current
framework is silent with respect to the behaviorfor college dropouts. F u r t h e r
research on this might provide useful insights into understanding default and
w e l f a r e effects of the loan program. College education is arisky investment:
currently 50 percentof students who enroll do not graduate. Alternative poli-
cies under the student loan program might affect the risk of failing at college
differently, with important consequences for income profiles and w e l f a r e across
different groups of students.
AAppendix
F o r repayment patterns under the FSLP, Iuse the Baccalaureate and Beyond
surveys (B&B 93/97) for college graduates in 1992-1993. T a b l e A-1 reports
background c h a r a c t e r i s t i c s for m y sample for the follow-up survey in 1997. V a -
lues are given in 1992 constant dollars. The second table presents percentages
of particular c h a r a c t e r i s t i c s . Subjects in the sample graduated from college
between July 1992 and June 1993 and entered repayment six months after
graduation. The debt v a r i a b l e in 1997 represents the amount still o w e d at the
interview date out of the amount borrowed.Annual earnings in the sample are
given as of the interview dates in April 1994 and April 1997. Unem p loyme nt
sp ells represent continuous n u m b e r of months unemployed since graduation.
This v a r i a b l e is based on the matrix of v a l u e s with unemployment status for all
months since graduation until the interview date. Job income and total income
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are annual measures for 1993 and 1996, respectively. Repayment decisions in
1994 are given for the first loan only. Iused this v a r i a b l e , since 52 percentof
the sample had only one loan, and for the rest of the sample, most of them had
the same repayment plan as for the first one. In 1997 they combined all loans
into asingle one through consolidation. Earnings include unem p loyment be-
nefits for those who declared they w e r e unemployed at the t w o interview dates:
7.9 percentin 1994 and 6.97 percentin 1997. Iestimate the unemployment
benefitfor the t w o y e a r s using CPS data set for college graduates, since there
is no information on that in the B&B surveys. My estimates from the CPS are
$6330 and $9400 for the t w o y e a r s , based on w e e k l y w a g e s of $487 and $717,
respectively.
T a b l e A-1: Sample Background Characteristics
V a r i a b l e Mean Standard Error
Amount borrowed 10763 6402
Debt still o w e d in 1997 8442 7082
Job income 1993 15402 10013
T o t a l income 1993 16275 10539
Earnings in 1994 21892 9894
Job income 1996 30002 16074
T o t a l income 1996 30827.8 16345
Earnings in 1997 31873 21867
Unemployment spell until 1994 1.46 2.95
Unemployment spell until 1997 2.32 4.18
Number of dependents 0.58 0.94
T a b l e A-2 reports information about students’ repayment behavior ex-
tended to include the graduated plan. Earnings and income a v e r a g e s v a r y
across the three plans. The job income levels in the y e a r s beforethe interview
dates are the most relevant v a r i a b l e s for the repayment decision borrowers
made b y April 1994 and 1997. Note that in 1997, the differences across repay-
ment plans are sizable compared to those in 1994. All borrowersin the sample
have consolidated b y 1997. They self-select in c h o o s i n g the right repayment
plan given their income. The unemployment spell differences are larger in the
1997 interview, when most borrowersconsolidated and updated their plans.
There are more dependents on a v e r a g e for payers under the income plan. Those
with more than one dependent usually opt for income consolidation. The in-
come sorting evidence is robust when conditioned on loan amount quantiles
with the exception of the third quantile. Sorting evidence is robust when
32
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T a b l e A-2: Characteristics of Borrowers b y Repayment Choice
Average Standard Plan Graduated Plan Income Plan
College debt 10167 10945 12209
Debt still o w e d in 1997 7538 10512 10955
Job income -1993 15453 15040 14152
Job income -1996 30965 27426 20539
T o t a l income -1993 16315 16277 14765
T o t a l income -1996 31369 27982 25920
Earnings -1994 21922 21476 21546
Earnings -1997 32013 32184 28334
Unemployment spell until 1994 1.46 1.71 1.15
Unemployment spell until 1997 2.27 2.66 2.71
Debt/Earnings 0.46 0.59 0.66
Figure A-1: Repayment Plans By Income and Debt
0 10,000 20,000 30,000
Income Contingent Standard
Average Income By Repayment Plans
Earnings Total income
0 5,000 10,000 15,000
Income Contingent Standard
Average Debt By Repayment Plans
conditioned on college ma jor and access to different savings technologies. Fi-
gure A-1 illustrates the sorting evidence restricted to the t w o repayment plans
modeled in the paper. T a b l e A-3 shows details on c h a r a c t e r i s t i c s of defaulters
v e r s u s non-defaulters. Defaulters have higher debt on a v e r a g e , both at the
time they graduate and four y e a r s after graduation. They have lower income
on a v e r a g e relative to non-defaulters, but differences are not sizable.
33
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T a b l e A-3: Characteristics of Defaulters v e r s u s Non-defaulters
Default Nondefault
V a r i a b l e Mean Standard Error Mean Standard Error
Debt from college 11942 8610 10379 6046
Debt still o w e d 9430 7437 7899 6686
Job annual income 1996 29748 19256 30481 15747
T o t a l income 1996 30564 18963 30995 16055
Earnings April 1997 33110 21160 33595 21500
Household income 1996 35091 23141 46204 28223
Debt burden 0.59 0.50 0.47 0.43
Unemployment spell 3.34 5.16 2.25 4.07
Savings 0.47 0.51 0.7 0.49
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