Working Paper Series 

Congressional Budget Office 

Washington, D.C. 

GUARANTEED VERSUS DIRECT LENDING: 

THE CASE OF STUDENT LOANS 

Deborah Lucas 

Northwestern University and National Bureau of Economic Research 

E-mail: d-lucas@kellogg.northwestern.edu 

Damien Moore 

Congressional Budget Office 

E-mail: damien.moore@cbo.gov 

June 2007 

Working Paper 2007-09 

This paper was prepared for the NBER/Zell Center conference “Measuring and 

Managing Federal Financial Risk” at the Kellogg School of Management, 

Northwestern University. The authors thank Janice Eberly and Marvin Phaup for 

helpful comments on an earlier draft. Working papers in this series are preliminary 

and are circulated to stimulate discussion and critical comment. They are not 

subject to CBO’s formal review and editing processes. The analysis and conclusions 

expressed in them are those of the authors and should not be interpreted as those of 

the Congressional Budget Office. References in publications should be cleared with 

the authors. Papers in this series can be obtained at www.cbo.gov/publications.
 2

Abstract 

The federal government makes low-cost financing for higher education widely available 

through its fast-growing direct and guaranteed student loan programs. Both programs 

offer borrowers similar loan products and terms. From the perspective of other key 

stakeholders, including educational institutions, commercial lenders, and state guaranty 

agencies, the programs differ significantly. The programs also report widely divergent 

budgetary costs. In this study, we propose and implement a methodology to estimate the 

cost of the two programs in market-value terms. In doing so, we address the question of 

how much of the difference in reported subsidy rates can be attributed to real cost 

differences and how much is due to idiosyncrasies in the rules that govern the budgeting 

of federal credit. We find that budgetary costs for both programs are well below their 

market value. This is mostly attributable to budget rules requiring that expected net cash 

flows be discounted at Treasury rates. Understatement of the market cost of capital also is 

the reason that some direct loans appear to make money for the government, despite the 

favorable terms offered to borrowers. Administrative costs are accounted for 

inconsistently across programs, complicating cost comparisons. Nevertheless, it appears 

that the guaranteed program is fundamentally more expensive than the direct program. 

Guaranteed lenders are paid more than is required to induce them to lend at statutory 

terms. The excess funds are largely absorbed in competition for borrowers, which occurs 

through various discounts, marketing activities, and higher service levels and subsidies to 

educational institutions. 
 3

1. Introduction 

The federal government makes low-cost financing for higher education widely available 

to borrowers through its fast-growing student loan programs. The existence of two 

competing government programs provides a unique opportunity to compare the cost to 

the government of direct federal lending versus loan guarantees. 

The direct and guaranteed student loan programs offer borrowers similar loan products 

and terms. From the perspective of other key stakeholders, including educational 

institutions, commercial lenders, and state guaranty agencies, the programs differ 

significantly. The programs also report widely divergent budgetary costs: The FY2007 

budget records a 2 percent subsidy rate on direct loans, versus a subsidy rate of 10 

percent for loans provided through the guaranteed program. The subsidy rate captures the 

expected present value of the lifetime shortfall of net federal cash flows for each dollar of 

credit extended. 

In this study, we propose and implement a methodology to estimate the cost of the two 

programs in market-value terms. In doing so, we address the question of how much of the 

difference in reported subsidy rates can be attributed to measurable cost differences and 

how much is due to idiosyncrasies in the rules for budgeting for federal credit. A 

potential source of a real cost differential is in the cost of capital. Data from the 

secondary market for guaranteed student loans provide some interesting evidence on the 

size of this effect. 

To preview the main results, we find that budgetary costs for both programs are well 

below costs measured at their market value. This is mostly attributable to budget rules 

that require the discounting of expected net cash flows at Treasury rates. Understatement 

of the market cost of capital also is the reason that some direct loans appear to make 

money for the government, despite the favorable terms offered to borrowers. 

Administrative costs are accounted for inconsistently across programs, complicating cost 

comparisons. Nevertheless, it appears that the guaranteed program is fundamentally more 

expensive than the direct program. Guaranteed lenders are paid more than is required to 

induce them to lend at statutory terms. The excess funds are largely absorbed in 

competition for borrowers, which occurs through various discounts, marketing activities, 

and higher service levels and subsidies to educational institutions. To the extent that the 

market is not perfectly competitive, guaranteed lenders presumably retain some of the 

surplus as above normal profit. This suggests that reductions in government payments to 

guaranteed lenders could result in reduced benefits to borrowers and schools, as well as 

affect profitability. 

The rest of the paper is organized as follows: Section 2 provides an overview of federal 

student loan programs—their size, their product offerings, the roles of various 

stakeholders, and their market structure. Section 3 describes how the government budgets 

for student loans and guarantees, how these rules have influenced structural changes in 

the programs over time, and the decomposition of costs in the budget. In Section 4, we 
 4

discuss the private market for student loans and the information it provides on the market 

cost of capital and administrative costs. 

In Section 5, we turn to the central problem of estimating the market value of federal 

student loans and loan guarantees. The exercise requires modeling loan cash flows, which 

under the direct loan program are affected by defaults, deferrals, forbearance, 

prepayments, and other embedded options. For the guaranteed program, government cash 

flows are also affected by payments to and fees from private lenders. Identifying 

financing versus administrative costs is important both for assessing total cost and for 

understanding the cost differential between programs. Rates on private student loans are 

used as a starting point for risk adjustment. The resulting market-value estimates are 

presented and subjected to sensitivity analysis. Section 6 concludes with a discussion of 

some of the broader policy questions that the analysis raises. 

2. Overview 

The Department of Education (ED) oversees two competing student loan programs: the 

Federal Family Education Loan (FFEL), or guaranteed, program; and the William D. 

Ford Federal Direct Loan, or direct loan, program. In the guaranteed program, which 

dates back to the mid-1960s, the government guarantees loans originated by private 

lenders against losses from default and makes supplemental payments to lenders. In the 

direct program, which began operation much more recently, in 1994, the government 

directly lends to qualifying students. 

2.1 Program Size 

The federal student loan program is one of the largest credit programs operated by the 

U.S. government. Table 1 shows the rapid growth in the value of outstanding federally 

backed student loans, which in 2005 totaled over $380 billion. Statistics compiled by the 

ED indicate that, in the same year, about 6.8 million students, and 750,000 parents of 

students, borrowed $56 billion in new federally backed loans (and that an additional 

$69.6 billion in old loans was consolidated). The guaranteed program was responsible for 

77 percent of this new-loan volume. Another 2.5 million borrowers took advantage of the 

option to convert their outstanding Stafford loans into more favorable consolidation 

loans. 

2.2 Product Offerings 

Both programs offer three basic types of loans, with loan terms set by statute under the 

Higher Education Act: 

Stafford. These 10- to 30-year loans are available to students enrolled in eligible 

educational institutions, which includes most U.S. colleges and universities, trade 

schools, and for-profit schools. Between 1998 and July 2006, these loans carried a 

floating rate that reset annually, based on the three-month Treasury rate plus a fixed 

spread. Since July 2006, Stafford loans have carried a fixed 6.8 percent per annum 

interest rate, with flexible repayment plans that begin when a student completes or drops 
 5

out of a course of study. Stafford loans may be “subsidized” or “unsubsidized”; the 

difference is that the federal government pays all of the accrued interest on subsidized 

Stafford loans while a borrower is in school, grace or deferment, whereas the interest 

accrues on unsubsidized loans. Both types carry a below-market interest rate. Eligibility 

for subsidized loans is based on income. Borrowers are assessed a one-time 3 percent 

origination fee, although this may be paid by the lender in the guaranteed program or 

reduced in the direct program. Recent legislation gradually phases out the origination fee. 

Parent Loan for Undergraduate Students (PLUS). Traditionally, these were loans made 

to parents of students attending eligible institutions. In July 2006, borrowers began 

paying a fixed 8.5 percent per annum rate for PLUS loans, and students attending 

graduate schools became eligible to take out PLUS loans.1 For parent borrowers, loan 

repayment begins immediately. Student borrowers begin repayment upon completion of 

their studies or if their course load drops below 50 percent of full-time status. All PLUS 

loans are unsubsidized but still carry interest rates that are generally below those 

available in private credit markets. 

Consolidation. Borrowers with one or more Stafford or PLUS loans may replace them 

with a single consolidation loan anytime after completing their course of study. 

Consolidation loans offer a new repayment plan and an interest rate equal to the weighted 

average of interest rates on the underlying Stafford or PLUS loans rounded up to the 

nearest eighth of a percentage point. Thus, the portion of post–July 2006 Stafford loans 

that are consolidated will carry a rate slightly above 6.8 percent. Consolidation loans 

offer a similar set of flexible repayment terms as Stafford loans, including forbearance 

and in-school deferment. 

Although guaranteed lenders receive lower compensation from the government for 

Consolidation loans than they do for Stafford loans, the returns are still positive, and 

competition to offer these loans is brisk. An exception is that guaranteed lenders often 

avoid consolidating distressed loans, which are more expensive to administer and have a 

lower expected income stream. As a result, a disproportionate share of distressed loans is 

consolidated into the direct loan program. 

2.3 Stakeholders 

Students and parents of students pursuing postsecondary degrees clearly benefit from 

these programs, which lower the cost and increase the availability of funding for higher 

education. From an economic perspective, such assistance can be welfare improving 

when imperfections in private credit markets limit access to education or when education 

has significant positive externalities.2

 However, some students may borrow excessively to 

 

1

 Because of an administrative oversight, Direct PLUS loans began carrying a 7.9 percent rate as of 

June 2006. 

2

 Several studies question the effectiveness of such policies, for example, De Fraja (2002), Dynarski 

(2002), Edlin (1993), Hanushek (1989), and Keane (2002). Gale (1991) points out that many federal credit 

programs probably have a small real effect on the allocation of credit, in many cases simply crowding out 

private borrowing and lending. 
 6

pay for degrees that add little to their earning potential. Unsubsidized Stafford loans are 

not means-tested, and borrowing limits are tied to years of educational attainment. 

Educational institutions also depend on federal student loan programs for financial 

support. Without assistance, many students would be unable or unwilling to pay the high 

tuition charges at many schools.3 To a lesser extent, schools benefit directly if they elect 

to participate in the guaranteed loan program. Guaranteed lenders offer schools various 

types of support in exchange for featuring their loans, including educational grants and 

administrative, educational, and systems support to financial aid offices. In “school as 

lender” programs, where the educational institution itself takes on the origination role, the 

school retains the excess of government payments over its cost of extending credit. 

Providing financing for guaranteed student loans has been a profitable line of business for 

private lenders, even as competition in the industry has intensified over time and with the 

liberalization of interstate banking. Although over 3,500 lenders originate, service, and 

finance federally guaranteed loans, the market is dominated by a few large lenders, 

including the leading commercial banks and Sallie Mae. Sallie Mae, by far the largest 

guaranteed lender, began as a government-sponsored enterprise but now is fully 

privatized. 

State and private nonprofit guaranty agencies are another constituency that benefits 

financially from the guaranteed loan program. These entities administer the federal 

guarantee and provide services to schools and lenders. As of 2006, there were 35 active 

guaranty agencies, some operating in multiple states. Each guarantee agency maintains an 

account in federal trust, which is used to pay out claims from lenders. Those funds are 

replenished by the federal government. Guaranty agencies also receive federal funds for 

performing collection activities, currently 22 percent of the recovered amounts or 8 

percent if the recovery is achieved via a consolidation loan. The agencies may use their 

share of collections to fund scholarships and educational outreach programs and for 

default-aversion activities. 

2.4 Market Structure 

Schools have a choice of whether to participate in the direct or guaranteed loan program. 

Simultaneous participation in both programs is not permitted, but a school can elect to 

switch programs, and some choose to do so.4

 Competition for volume between the two 

programs therefore centers on school administrators, particularly financial aid officers. 

Recall that both programs offer students nearly identical loan terms, so differentiation 

occurs along other dimensions. The direct program offers greater administrative 

simplicity, which initially attracted many schools to the program. Guaranteed lenders 

responded by offering schools and borrowers improved service and other inducements, 

 

3

 Some analysts have argued that the generous borrowing limits in the federal student loan program 

have accommodated the growth in college tuition, which has exceeded the growth of the overall economy. 

(Add citation) 

4

 A single university may have some schools participating in the direct program and others using the 

guaranteed program. 
 7

and since the late 1990s the guaranteed program has slowly regained market share (see 

Figure 1). 

Competition also takes place at each FFEL school between guaranteed lenders. Although 

there are thousands of lenders potentially competing for borrowers’ business, at the 

school level, competition is much more limited. The financial aid office serves as a 

gatekeeper, counseling students who seek advice and including only a limited number of 

lenders on its “preferred lender list.” Most students have little financial experience and 

rely on the advice of the school, although direct-to-student marketing of loan products is 

becoming more common and some students venture beyond the preferred lender list. 

Northwestern University provides a fairly typical example close to home. It includes five 

major lenders on its preferred list for undergraduate students. It does not officially rank 

them, but Citibank holds the coveted first position on the (nonalphabetical) list. The 

preferred lender lists for Northwestern’s various graduate and professional schools are 

shorter. The business, law, and medical schools offer just three options, with the first one 

being Northwestern University itself. Only two lenders are recommended to students 

pursuing part-time MBAs. 

Understanding the competitive structure of guaranteed lending is important for 

identifying the likely disposition of rents that arise from federal payments to lenders in 

excess of production costs. Although we do not model these interactions formally, it is a 

reasonable first approximation to assume that competition among the large players for 

access to borrowers leaves guaranteed lenders with only very low levels of above normal 

profit. The gatekeeper role of schools suggests that they capture a large portion of rents, 

but those may be passed on to students through scholarships, expanded program 

offerings, or other means. The common practice of lenders paying the origination fee for 

students is evidence that some of the rent goes directly to students. Some rents are also 

absorbed by marketing costs and inducements to schools and financial aid officers that 

are unlikely to provide much benefit to students. 

3. Budget Estimates 

Most analyses of the cost difference between the direct and guaranteed loan programs 

rely on budget estimates prepared by the Congressional Budget Office (CBO) and the 

Office of Management and Budget (OMB). Budget estimates are systematically lower 

than the market-based costs described in Section 4. An interpretation of a market-based 

cost estimate for a program is the up-front price a competitive private entity would charge 

to assume the federal government’s role in the program. Such prices reflect the market’s 

valuation of risk, whereas current budget estimates assume that the cost of risk to the 

government is zero. Because budget measures call for the use of risk-free discount rates 

for government credit programs, programs structured so that the government instead of 

private entities bears risk will always report a lower budget cost.5

 

5

 Lucas and Phaup (2007) discuss the pros and cons of using market-based estimates in federal 

budgeting. 
 8

The current budget treatment provides a useful starting point for evaluating the cost of the 

student loan program. In this section we describe the rules governing budgeting for 

credit, how changes in budget rules over time have affected the federal student loan 

program, and what budget estimates reveal about the breakdown of costs for the two 

programs. 

3.1 Budgeting for Federal Credit Programs 

Before fiscal year 1992, credit programs, like most other government programs, were 

accounted for on a cash basis. For a new direct loan program, this implied a large upfront cost equal to the principal borrowed, with no offset for expected future repayments. 

An economically equivalent credit guarantee program had a much lower, or even 

negative, up-front budget cost. For credit guarantees, few defaults occur in the first year, 

and guarantee fees are collected up front. This accounting favored new guaranteed loan 

programs over almost all alternative policies, including direct loan programs. 

The Federal Credit Reform Act of 1990 (FCRA) effectively put credit on an accrual 

basis, with cost measured as the net present value of current and future cash flows 

associated with the current-year commitment. Although FCRA moved the budget toward 

making credit and other forms of assistance comparable, the subsidy estimates do not 

measure cost in terms completely equivalent to cash spending. The biggest discrepancy 

arises from the mandated use of interest rates on maturity-matched U.S. Treasury 

securities for discounting, rather than a market-based cost of capital that includes the cost 

of market risk. It also treats administrative costs inconsistently across programs, with 

some costs included in subsidy rates and others recorded elsewhere on a cash basis. 

3.2 Effects of Budget Rules on Student Loans 

Accounting conventions have had a significant effect on the structure and evolution of 

the federal student loan programs. Most notably, the direct student loan program appears 

to have been made feasible from a budgetary perspective by FCRA. Although such a 

program was proposed on several occasions in the late 1980s, its high initial cash cost 

was a decisive obstacle. The direct loan program was enacted in 1993 shortly after the 

FCRA went into effect. 

As for other credit programs, the mandated use of maturity-matched Treasury rates 

without risk adjustment and the inconsistent treatment of administrative costs drive a 

wedge between budget estimates and the market-value estimates of program cost. The 

inconsistent treatment of costs across programs is particularly pronounced for student 

loans. Unlike with many credit programs, administrative costs are included in the subsidy 

rate reported for guaranteed loans. This occurs because the federal government makes 

supplementary allowance payments to private lenders to cover the lender’s administrative 

and other expenses in excess of the amounts collected from borrowers. Inasmuch as those 

payments continue for the life of the guaranteed student loan, they are capitalized and 

included in subsidy costs. By contrast, administrative costs in the direct program are 

accounted for separately on a cash basis and are not included in subsidy estimates. The 
 9

extent to which this inconsistency affects the difference in subsidy rates has been 

estimated to be no more than 1.5 percentage points (CBO, 2005). 

A discrepancy between budget and market-value cost also arises from the budgetary 

treatment of floating-rate loans. Through June 2006, the only large federal direct lending 

program with floating rates was the direct student loan program. The FCRA is interpreted 

as requiring the use of long-term Treasury rates for discounting, whereas market values 

reflect the shorter effective maturity of floating-rate loans. Because of the term premium 

in long-term rates, this tends to bias down federal estimates of direct loan value. This 

undervaluation has potential real effects. For instance, it prompted the Department of 

Education to propose a sale of direct loans in 2003. The plan was to sell the loans, apply 

some of the proceeds to paying off Treasury debt, and use the net gain to provide 

additional assistance to students. In fact, the sale would have entailed additional 

administrative costs without generating any real savings. Although switching to fixed 

rates for new student loans after June 2006 mitigated this effect, the payments to 

guaranteed lenders still depend on short-term interest rates and will continue to be 

misvalued. 

3.3 Budget Cost Decomposition 

The Credit Supplement to the Budget, prepared by OMB, provides a breakdown of 

subsidy cost across four cost components (defaults, interest, fees, and “other”) for four 

loan categories (Stafford Subsidized, Stafford Unsubsidized, PLUS, and Consolidated). 

Table 2 reproduces this data from the 2007 Credit Supplement in terms of subsidy rates. 

The subsidy rate is the present value of net losses divided by the underlying loan 

principal at origination. 

Both programs report a similar, but small, subsidy cost component for defaults. As 

discussed below, this component of cost appears inexplicably low for both programs. For 

the remaining components, the breakdown of subsidy costs is markedly different across 

the two programs. 

First, the direct program reports large interest income, whereas the guaranteed program 

reports large interest costs. In the direct program, the government reports interest income 

as the present value of any interest paid by borrowers in excess of the cost of financing, 

which is taken to be a Treasury rate. Because the borrower interest rate on most loans 

typically exceeds the Treasury rate, this item reduces the subsidy cost. In contrast, the 

interest component in the guaranteed program represents the present value of the net 

payments paid to private guaranteed lenders (the difference between the lenders’ rate, 

which is indexed to the 3-month commercial paper rate, and the borrowers’ rate), which 

is positive on average. Although classified as interest, these payments are more 

accurately described as covering administrative costs because the borrower rate typically 

exceeds lenders’ cost of funds. Administrative costs in the direct program that are paid 

directly by the federal government, however, are excluded from subsidy estimates. Direct 

lending administrative costs that entail payments to third parties for tasks such as 

collecting on loans appear in the category “other.” 
 10

Fees levied on borrowers, guaranteed lenders, and guaranty agencies reduce subsidy 

costs. These fees include the up-front application fee on Stafford and PLUS loans in both 

programs, as well as the 1.05 percent per annum consolidation fee paid by private lenders 

to the federal government in the guaranteed program. The remaining category, other, 

largely includes the subsidy cost contribution associated with collecting loans and 

payments to third parties for performing administrative tasks. 

The last two columns of Table 2 show expected cumulative lifetime default and recovery 

rates (the latter is the expected cash flow recovered as a percentage of defaulted 

principal).6 Default rates are similar in the two programs, reflecting the similar borrower 

populations. The exception is for consolidation loans, which experience much higher 

default rates in the direct program. As noted earlier, the higher default rate can be 

explained by the reluctance of guaranteed lenders to consolidate loans on the brink of 

default, while the direct program accepts those loans for consolidation. 

4. Inferences from the Private Loan Market 

A systematic way of identifying the market value of the federal government’s credit 

commitments is to use the prices of comparable securities offered in private markets. For 

student loans, we propose to use rates quoted to borrowers in the private market for 

student loans. 

Limits on federal borrowing and increasing educational expenses have contributed to the 

development and rapid growth of a competitive private market for student loans. The 

market primarily serves students who have exceeded federal lending limits, which 

currently are set at a cumulative amount of $23,000 for undergraduates and at a combined 

limit of $65,500 for undergraduate and graduate study.7

 

The main players in the private loan market are the largest guaranteed lenders—Sallie 

Mae and major national and regional commercial banks. Economies of scale in 

marketing, systems administration, and funding, and the experience gained from 

guaranteed lending, give these institutions a competitive advantage over other potential 

entrants. Although students can obtain private loans on their own, as with guaranteed 

lending, students often rely on the financial aid office for recommendations, which tends 

to limit direct competition between lenders. 

 

6

 The surprisingly high reported recovery rates arise from two idiosyncrasies in budget reporting: 

The recovery amounts are not discounted, and not all collection costs are deducted. As shown in the next 

section, adjusting for these factors yields recovery rates that are in line with experience in the private 

student loan market. 

7

 There are also various annual limits on federal borrowing. For independent students and those 

whose parents have been denied a PLUS loan, the current cumulative limits are $46,000 and $138,500, 

respectively. Some medical school students may be able to borrow up to $40,500 a year (up from $38,500) 

and $189,125 total. 
 11

4.1 Federal-Private Differences 

Although the private loan market provides data that are useful in estimating the market 

value of government loans and loan guarantees, various differences make direct cost 

comparisons problematic. Here we describe the main differences between private and 

government-backed loans and propose some adjustments to account for the resulting cost 

differentials. 

Borrowers: Federal programs serve a much broader population of students than do 

private lenders. Because private loans appeal to students who have hit federal borrowing 

limits, they tend to be used by students at high-cost undergraduate institutions and by 

students preparing to enter such professions as medicine, law, and business. Several 

factors suggest that federal borrowers are likely poorer credit risks. The eligibility of 

borrowers for federal loans or subsidies does not depend on a credit score, whereas 

private lenders use credit scores to assess borrowers’ creditworthiness, refusing credit 

entirely below a certain cutoff. Private lenders also can avoid originating loans at schools 

whose graduates’ employment prospects are weak. Conversely, private lenders extend 

credit to students who already have high federal loan balances and who start work with 

much higher levels of total indebtedness. 

Default Losses: Federal and private lenders report quite similar losses from default (net of 

recoveries and collection costs) of approximately 1 percent per annum, but the 

composition of default losses is starkly different. Default rates in the federal programs are 

approximately 2 percent of outstanding principal per annum, whereas they are only 1 

percent per annum for typical private loans. The lower default rates in the private 

program are offset by lower recovery rates because private lenders do not have access to 

federal collection remedies, such as the Treasury offset program and administrative wage 

garnishment. The recovery rate is computed by discounting the cash flow stream of loans 

in default over their remaining life. Because many defaulted federal loans are only 

partially recovered and recovery is an expensive process, federal recovery rates are about 

50 percent of the defaulted sum (this estimate is discussed in more detail in the next 

section). 

Loan Terms and Fees: Apart from carrying higher interest rates, private loan terms are 

less favorable than those for Stafford loans along a number of dimensions. Private loans 

lack the valuable consolidation option, repayment options are more limited, and lenders 

may be less generous with forbearance. There are no grace or deferment periods, and in 

contrast with federal loans, death or disability does not trigger forgiveness. Private loans 

do offer long loan maturities of up to 20 years, and the mechanisms to collect on 

defaulted loans are weaker (see Section 5.1.2). As on guaranteed loans (but not with 

direct loans), lenders often offer incentives for on-time and electronic payments, etc. 

Among these nonrate differences, the consolidation option is likely to be the biggest 

advantage of the federal programs. In Lucas and Moore (2006), we estimate that in every 

year since 2001 the consolidation option has added more than 2 percent to the marketvalue subsidy rate on new loans. (With the switch to fixed rates, the consolidation option 

will have less value going forward, but borrowers with fixed rates will have the valuable 
 12

option to speed up repayment when rates are low or to slow down repayment when rates 

are high.) 

Competitive pressures have reduced or eliminated origination fees on private loans, hence 

administrative costs are covered by higher rate spreads. Similarly, most guaranteed 

lenders pay the federal origination fee on behalf of borrowers. On direct loans, however, 

borrowers still are required to pay 1.5 percent up front and the entire fee if they fail to 

make a timely first payment. 

Administrative Costs: The task of identifying administrative costs and allocating them 

across activities is complicated by the lack of either government or private data. Common 

administrative functions include origination, servicing, collection, and general overhead. 

Origination costs are probably somewhat higher for private loans because of fees paid to 

obtain credit scores (including those paid for students who ultimately borrow elsewhere 

or don’t qualify). Private loans also involve higher contracting costs (legal expenses, for 

instance) than do direct loans. Loan servicing is a competitive industry, and it is safe to 

assume that servicing costs are similar for all lenders. Loan collection services can also 

be obtained at competitive prices, although guaranty agencies are paid a statutory amount 

that appears to exceed their cost of providing services. We assume similar collection 

costs for private and direct loans, and adjust for the subsidy component of payments to 

guarantee agencies in the guaranteed program. 

Additional administrative cost arises for guaranteed and private loans because of higher 

service levels and marketing expenses. Such expenses include information systems, 

marketing personnel, phone center staff, conference sponsorship, travel to schools, and so 

on. 

The financial statements of private and guaranteed lenders provide some data on 

administrative costs. Noninterest expense, broken into various categories, is reported on 

an annual basis. Some costs, such as servicing, apply to the portion of the outstanding 

loan portfolio in repayment, while other costs are incurred for origination activity, but 

financial reports do not allocate costs by activity. Data from one lender for 2006 are used 

to make some rough imputations.8

 We attribute 80 percent of personnel, consulting, and 

occupancy expenses to origination, 100 percent of promotional expenses to origination, 

and 50 percent of computer and other expenses to origination. Total origination expenses, 

divided by total volume of Stafford and private originations, is 0.95 percent. 

Representing this as an annual rate spread on a 10-year amortizing loan implies an 

origination cost of 22 basis points (bps). The remaining noninterest expenses, divided by 

the portfolio of loans in repayment, gives an annual cost of 45 bps. Thus, private lenders 

bear an amortized cost of 67 bps, excluding collection costs, which we account for 

separately in default losses. 

 

8

 Simply dividing total noninterest expense over the loan portfolio would be misleading because a 

large portion of the total is current originations. 
 13

Administrative per-dollar costs for outstanding loans in the direct program appear to be 

lower than per-dollar costs for private loans. An annual appropriation to the Department 

of Education covers the administrative costs of the direct program, although some of 

these costs are attributable to administering both the direct and guaranteed programs. 

That appropriation was approximately $600 million in 2006. At that time, the outstanding 

direct program portfolio was approximately $100 billion and the guaranteed portfolio 

approximately $300 billion. In disclosures to CBO, the department reported allocating 

approximately $200 million of the appropriation to direct program servicing contracts, 

$30 million to direct program origination contracts, and $200 million to direct and 

guaranteed program recovery contracts. We assume the remaining unallocated $170 

million is attributable to servicing and origination functions of the direct and guaranteed 

programs in proportion to the size of each program. The amounts attributable to the direct 

program divided by the $100 billion outstanding yield an estimate of amortized direct 

program origination and servicing cost of 30 bps.9

4.2 Estimating the Cost of Capital from Private Market Rates 

In a competitive private lending market, the rate charged by private lenders should 

recover all costs associated with making the loan, including administrative costs, losses 

from default, and the cost of capital. A broad measure of the market cost of federal credit 

includes all of these components because that is what the government would have to pay 

private lenders to provide this service to students. 

Although we can infer loans’ losses and administrative costs directly from Department of 

Education records, we have no way of directly estimating the loans’ cost of capital 

because federal loans are not traded without their guarantee. Thus, we estimate the cost of 

capital for federal student loans from the cost of capital for private student loans. That 

cost of capital includes a charge for the systematic risk in student loans losses, the risk 

premium for student loans. 

Private lenders charge students floating rates tied to the London Interbank Offered Rate 

(LIBOR). Quoted rates range from LIBOR+2 percent to LIBOR+7 percent. The rate 

offered varies by credit score and educational institution, but LIBOR+4 percent is typical. 

Assuming a 30 basis-point spread between one-year LIBOR and one-year Treasury, the 

interest rate spread over Treasury is 4.3 percent. 

The risk premium on student loans—the difference between the loan cost of capital and 

the Treasury rate—can be estimated by starting with this 4.3 percent spread and 

subtracting estimates of other cost components. As discussed above, administrative costs 

are on the order of 72 bps,10 and the annual default loss rate from federal student loan 

data is approximately 1 percent per annum. This leaves 2.58 percent attributable to a 

 

9

 We assume that the federal program is close to a steady state, so dividing total costs by total loans 

is a reasonable approximation of annual costs. 

10 Private administrative costs for collections of 5 bps are added to the 67 bps for the servicing, 

origination, and general administration of loans. 
 14

market-risk premium, an estimate we use in the cost analysis in the next section. Because 

of the many reasons the private and federal risk premiums differ, in our sensitivity 

analysis, we consider lower and higher levels of the risk premium. 

The special allowance payments to lenders have significantly lower risk than do the 

student loans. The payments are based on commercial paper rates, which typically are 

about 30 bps over Treasury rates. Hence, these payments are discounted at Treasury rates 

plus a spread of 30 bps. 

An alternative approach would be to approximate private lenders’ cost of capital by 

looking at the weighted average cost of debt and equity capital for public firms in this 

business. This turns out to be impractical because there are few publicly traded 

companies whose primary business is making and self-funding private student loans. 

Further, the few publicly traded companies that specialize in private loans have a short 

history. They also tend to repackage the risk, for instance through securitization 

structures. Hence, the cost of capital for private student loans cannot be accurately 

inferred from traded debt and equity returns. 

5. Estimating Federal Program Costs 

The main cost analysis involves projecting the distribution of future cash flows to and 

from the government over the life of a loan or guarantee obligation and discounting at 

risk-adjusted rates. We start by modeling the cash flows associated with the underlying 

loans, taking into account program rules, borrower behavior, and the various options 

affecting payment patterns. These cash flows, in combination with rules for payments 

between guaranteed lenders and the government, also determine the cash flows associated 

with guaranteed loans. 

A subsample of student records from the Department of Education’s National Student 

Loan Database System (NSLDS) provides information on historical borrower payment 

patterns, which is used to parameterize the model. In particular, we derive new estimates 

of default and recovery, which are critical inputs into the subsidy rate. We use a sample 

from the database drawn in January 2006, which contains historical information on loans 

and borrowers dating back to 1980, although we used the older data only where 

absolutely necessary. The sample consists of over 10 million loan records and 1 million 

borrowers. We use Monte Carlo simulation to project future cash flows that depend on 

stochastic interest rates and borrower behavior. Discounting projected cash flows at the 

risk-adjusted rates (derived as described above) yields cost estimates for both programs. 

In addition, we present alternative estimates based on a simple comparison of private and 

government student loan rates. 

5.1 Cash flows 

On direct loans, a net outflow of principal occurs when the borrower takes a new loan 

(less the 1.5 percent origination fee paid by the borrower). Subsequently, net inflows of 

repaid principal and outstanding interest flow to the government over time, including 
 15

amounts recovered from default less any recovery costs. The government also incurs 

ongoing administrative costs, which we allocate to individual loans on a per annum basis 

in proportion to their outstanding amount. 

In the guaranteed program, government cash flows include net transfers to and from 

lenders (indirectly via guaranty agencies) on each outstanding loan, equal to the 

difference between the borrower’s interest payment (if any) and the three-month 

commercial paper rate plus a spread. This is referred to as a Special Allowance Payment, 

or SAP. Currently the spread is equal to 1.74 percent per annum for Stafford loans when 

the borrower is in school, 2.34 percent for Stafford loans when the borrower is in 

repayment, and 2.64 percent (less the 1.05 percent per annum lender consolidation fee) 

for consolidation loans. The government also makes guarantee payments to lenders for 

claims on defaulted loans and pays “retention” fees to guaranty agencies in proportion to 

their recoveries on defaulted loans. 

5.1.1 Effective Maturity and Repayment Status 

The repayment horizon for federally backed loans varies from less than a year to over 30 

years. Borrowers may prepay their federal loans, which can significantly shorten loan 

terms, without penalty. For example, approximately 8 percent of originated loans close in 

fewer than five years, and approximately 60 percent close within 15 years.11 Historical 

data may understate the future distribution of loan lifetimes because closure rates at long 

horizons are estimated from loans originated when the federal loan program offered less 

favorable terms to borrowers. 

While they are in school and for a few months after graduating, borrowers do not need to 

make payments on federally backed student loans. During this grace period, the federal 

government pays the interest for subsidized loans, whereas interest accrues on 

unsubsidized loans. Periods of grace necessarily raise the market-based subsidy cost even 

for unsubsidized loans because the interest rate is typically lower than the rate a private 

lender would charge. Over 95 percent of loans by originated value are in an in-school or 

grace period in the year of origination, but fewer than 10 percent of loans were in a grace 

period four years after origination. The average time in school is approximately 2.5 years 

(excluding time in loan deferral for subsequent schooling, which is discussed next). 

Borrowers are entitled to lengthy payment deferral in times of financial hardship or, in 

the case of Stafford loans, when borrowers want to pursue further studies. Stafford loans 

are also forgiven in the event of the death or disability of the borrower (parent loans are 

forgiven upon the death, but not disability, of the student). An effect of these provisions 

is that they may lower reported default rates. Periods of in-school deferment last as long 

as the borrower remains in school, whereas a borrower who experiences financial 

hardship may elect a three-year payment deferment or a payment forbearance period (the 

former is available only under more restrictive conditions). Analysis of loans in the 

NSLDS suggests that borrowers with outstanding loans in repayment enter deferment or 

 

11 These estimates treat loan consolidations as an extension of the original loan rather than as a new 

loan. Stafford loan lifetimes would otherwise appear to be much shorter than this. 
 16

forbearance at a rate of approximately 6 percent per annum for a typical term of three 

years. 

The effect of these repayment options is shown in Figure 3, which illustrates the 

breakdown of outstanding loan principal by loan status in January 2006 for both the 

direct and guaranteed program. Overall, only about half of the loans are in repayment, 

while grace, deferral, forbearance, and default account for the remainder. 

Borrowers have standard options to extend Stafford loans beyond the basic 10-year 

maturity even without consolidation. Stafford borrowers with a balance of $30,000 or 

more from a single lender (whether a single guaranteed lender or a loan from the direct 

program) may choose an extended repayment plan of up to 25 years. Income-contingent 

and graduated repayment plans are also available. The right to consolidate Stafford loans 

also allows borrowers to extend the term of their original loans, as well as to convert 

floating-rate loans to a fixed rate. For some borrowers, consolidation allows them to 

extend for up to 30 years. Eligibility for term extension depends on the size of the 

consolidated loan, as shown in Table 3. 

The OMB treats consolidation loans as new loans rather than as extensions of existing 

loans. This paper treats consolidation as an extension of existing loans. Treating a 

consolidation loan as an extension of an original loan avoids double counting of loan 

volumes and default rates. This approach also ensures that the subsidy cost includes the 

value of the option to consolidate. 

5.1.2 Default and Recovery 

Borrower default is an ongoing source of costs in both the direct and guaranteed lending 

programs, despite the strong loan enforcement mechanisms that the government has at its 

disposal.12 Before direct lending, the guaranteed lending program reported very high 

default rates. In response, the Congress made a number of changes to the Higher 

Education Act. Chief among them was the use of cohort default rates as a performance 

measure and as a criterion for schools to retain access to federal student loans and grant 

funding. Since the adoption of these measures, new default claims in both the direct and 

guaranteed lending programs have more than halved. 

The strength of the U.S. economy and the increased use of deferment, forbearance, and 

consolidation have also contributed to the lowering of default rates. Offering more 

generous terms to students is costly, however, since it may delay an inevitable default and 

make recovery more difficult. Table 4 below reports default claims as a percentage of 

outstanding balance for 1990, 1996, and 2005. 

Figure 4 shows the average annual default rate of loans by the number of years that have 

elapsed since the loans entered repayment for the four classes of loans (guaranteed 

Stafford, guaranteed Consolidated, direct Stafford, and direct Consolidated). Average 

 

12 Student loans are not dismissed in bankruptcy. The government can collect through the Treasury 

Offset Program. 
 17

default rates are about 2 percent per annum. Stafford loans experience higher levels 

shortly after entering repayment, which may in part reflect the cumulative effect of inschool grace periods (since a borrower cannot default while he or she remains in school 

even though adverse circumstances may arise that impair a borrower’s current and future 

ability to repay his or her loan). Consolidated direct loans report strongly higher default 

rates than consolidated Stafford loans because the Education Department frequently 

consolidates loans for borrowers that guaranteed lenders consider too risky. Even though 

guaranteed lenders bear virtually no credit risk, the administrative expense of 

consolidating a borrower’s loans and resolving default is a sufficient disincentive to 

consolidate risky borrowers. Data confirm that borrowers who consolidate defaulted 

loans are more likely to default on their consolidation loans than are other borrowers. We 

attribute the cost of these defaults to the program in which the original loans were 

originated rather than to the program that consolidated them. 

OMB reports recovery rates on student loans that far exceed those on other forms of 

unsecured consumer credit, but as discussed in Section 3.3, that agency’s measure 

neglects collection costs and time value. Relying instead on NSLDS data, we find that 

individual loans exhibit significant variability in recoveries, with some defaulted loans 

resolved quickly and others remaining uncollected for more than 10 years. The typical 

pattern suggests that collection rates diminish over time. Applying a risk-adjusted 

discount rate (equal to the average interest rate over the data period plus our assumed 

2.58 percent risk premium) and subtracting a 16 percent recovery cost suggests a 

recovery rate of about 50 percent of the defaulted principal. Combining this with the 

annual default rate of 2 percent per annum implies losses from default equal to 1 percent 

of principal outstanding per annum. 

5.2 Simulating Cash Flows 

Cash flows for both programs depend on the stochastic path of future interest rates, 

program rules, and borrower behavior. These are modeled using Monte Carlo simulation. 

Each month, a random draw from a normal distribution determines the innovation in the 

short-term interest rate, and the corresponding term structure is derived from the Cox 

Ingersoll Ross (CIR) model (see Appendix 2 for a complete description of the interest 

rate model and the parameters used in estimation). Variation in interest rates affects the 

discount rate and guaranteed lender payments. 

Monthly loan repayment cash flows depend on various borrower behaviors: whether the 

student is in-school; the borrower’s repayment plan; consolidation; default, recovery, 

prepayment; and an administrative charge. Appendix 2 contains a description of how we 

simulate the cash flows that depend on stochastic borrower behavior. It also describes the 

aggregation of cash flows across representative loan groupings. 

The cash flow model is calibrated under the following base-case assumptions: 

Borrower Interest Rates: As of June 2006, borrowers began paying a fixed rate of 6.8 

percent per annum on all new Stafford loans. The interest rate on consolidation loans is a 
 18

weighted average of the interest rates prevailing on the loans consolidated rounded up to 

the nearest 1/16th of a percentage point. For a student whose original loans all have a 6.8 

percent rate, the consolidation loan interest rate will be 6.875 percent per annum. 

Repayment Horizons: A typical loan repays over a 20-year term, but any individual loan 

can be repaid over shorter or longer horizons. The probability of longer repayment is 

positively correlated with the borrower’s balance. For borrowers entering repayment, 

approximately one-third of all loan value is in each of three balance categories, and 

respectively 15 percent, 40 percent, and 60 percent of borrowers in each category take up 

the maximum extension options. 

Default Losses: The value of default losses each year is equal to 1 percent of outstanding 

balances in both the direct program and guaranteed program. Although there are reasons 

that default losses for the two programs differ,13 the available historical data did not 

contain information on direct program recoveries to estimate the direction or magnitude 

of the difference. 

Noncollection-Related Federal Administrative Expenses: The federal government incurs 

direct administrative expenses for both programs. These costs are not included in official 

budget subsidy estimates, but they are included in the more comprehensive estimates 

here. We assume that, each year, the department directly spends 0.3 percent of 

outstanding principal administering the direct program and 0.1 percent administering the 

guaranteed program. The administrative costs borne by guaranteed lenders in the 

guaranteed program do not directly affect subsidy rates. 

Guaranteed Lender Payments: The federal government pays guaranteed lenders a spread 

above the quarterly reset three-month commercial paper rate. That spread varies with the 

type of loan and its payment status as described earlier and terminates upon default. 

Loan Origination Fee Receipts: The government charges borrowers a 3 percent 

origination fee in both programs, which reduces the subsidy cost by a corresponding 

amount. In the guaranteed program, guaranteed lenders often pay this fee for the 

borrower. In the direct program, the Department of Education charges half of the 3 

percent fee up front and levies the remaining 1.5 percent only if borrowers fail to enter 

repayment on time. For simplicity, we assume one-half of borrowers enter repayment on 

time, reducing the total fee (in present value) to 2.25 percent. 

Adjustments for Federal Revenue Effects: The companies that serve the direct and 

guaranteed programs pay federal corporate income taxes. Ideally, the corporate income 

taxes paid should be taken into account in calculating the net federal outlay. However, 

current budget practice does not recognize income tax receipts in subsidy estimates. A 

recent study by Price Waterhouse Coopers (2005) estimated that the guaranteed lending 

program generates corporate income tax with a present value of 1.5 cents per dollar of 

loans originated, which translates to an approximate per annum tax receipt of 20 basis 

 

13 For example, the direct program reports slightly higher default rates, and the guaranty agencies in 

the guaranteed program are paid a higher collection fee than are contract collectors in the direct program. 
 19

points per dollar outstanding. The direct program also generates corporate income taxes 

from information technology, servicing and collections contracts with private companies. 

We assume this generates no more than 5 basis points of tax revenue, leaving a 15 basispoint per annum tax differential between the direct and guaranteed programs. In our basecase subsidy estimates, we ignore this differential. 

5.3 Discounting Risky Cash Flows 

Under current budgetary treatment of credit programs, expected net federal outlays are 

forecast using a simulation model. Those expected cash flows are then discounted using 

maturity matched zero-coupon Treasury bond yields to produce subsidy estimates.14 In a 

market-based valuation of the federal exposure, we adopt a similar simulation approach, 

but we additionally categorize cash flows by their exposure to market risk and discount 

them using risk-adjusted rates. 

To incorporate the effect of interest rate and credit risks on the value of direct and 

guaranteed loans, we overlay a simple two-state model of default on a model of interest 

rates to provide state-dependent discount rates (or state prices). Each state of the model 

corresponds to an interest rate and a borrower default state (in other words, whether 

default has occurred or not) allowing us to specify cash flows in each of those states and 

discount them accordingly. The appropriate discount rates for default and nondefault 

states is inferred from the credit-risk premium derived in Section 4 (and justified by a noarbitrage argument). Interest rates are calibrated to prices of long- and short-term 

Treasury securities.15 Appendix 2 explains the model in detail. 

Despite the apparent differences between the cash flows of the two programs (as 

described in Section 5.1), using market-based discount rates ensures that program subsidy 

rates are consistent whether programs are publicly or privately financed. In particular, a 

direct program whose administration is competitively outsourced to a private lender will 

have a market-based subsidy identical to that of a guaranteed loan program with a 100 

percent credit guarantee and a competitively determined private lender yield. That is, in a 

market-based approach, it is irrelevant whether public or private entities raise capital for 

the program because the cost of capital is determined by the underlying assets. In 

contrast, current budget practice will not produce equal direct and guaranteed subsidy 

rates in this case because lender yields in the guaranteed program include compensation 

for the credit-risk premium (required to ensure the participation of lenders), which is 

implicitly excluded from the subsidy rate of the direct program due to the use of Treasury 

discount rates for all cash flows. 

 

14 Using a full schedule of Treasury maturities captures the interest rate term premium inherent in 

longer-term cash flows. 

15 For simplicity, we assume that the risk factors driving interest rates are independent of the risk 

factors driving credit spreads. We also ignore the well-documented term premium in credit spreads and 

assume that a constant credit-risk premium applies to the underlying loans irrespective of their term. 
 20

5.4 Base-Case Subsidy Estimates 

Table 5 presents subsidy estimates for newly originated loans in academic year 2006–

2007 (July 1, 2006, to June 30, 2007) under the base-case assumptions outlined above. 

The overall subsidy estimate for each program is computed by averaging over 

representative groupings of loans by subsidized status and maximum available repayment 

horizon. The difference between subsidized and unsubsidized loans is the present value 

of in-grace and in-deferment interest paid by borrowers with unsubsidized loans that is 

not paid by borrowers with subsidized loans. Considering that a typical subsidized 

borrower will spend about three years in grace and in deferment, the 6.8 percent per 

annum forgone interest adds up to a subsidy of about 12 percent of the loan amount. 

Subsidy rates vary with the term of loan repayment. Allowing borrowers to extend a 10-

year Stafford loan to 20-years raises the subsidy cost for that loan by about $3 per $100 

originated. This increase would be even higher, but many borrowers fail to take 

advantage of term-extension options and frequently pay off their loans early. 

Guaranteed loans have a consistently higher subsidy rate than do direct loans. Subsidies 

for both programs are computed under the assumption that actual administrative and 

capital costs are similar across both programs. But the net income payments to 

guaranteed lenders and guaranty agency collection fees are significantly more than is 

required to cover those costs in the guaranteed program. 

Looking to the future, subsidy rates for new loans may be considerably different from the 

estimates for 2006 reported in Table 5. The most obvious cause of future variation in 

new-loan subsidy rates is changes in interest rate conditions. This is because borrower 

interest rates are fixed at 6.8 percent per annum for all new Stafford loans, whereas the 

government’s opportunity cost moves with prevailing interest rates. Thus, if interest rates 

go up next year, subsidy rates will rise; if interest rates decline, so will subsidy rates. 

Figure 5 shows average, 10th and 90th percentiles of subsidy estimates for each of the 

next 10 years. To make these forecasts, we use the interest rate model combined with 

current yield curve information to provide simulated paths of future interest rates to 

determine starting conditions for each year. We assume loan cash flow performance is 

consistent with the assumptions of the base case (but appropriate to interest rate 

conditions). As the horizon lengthens, the course of future interest rates becomes more 

uncertain, so the band of subsidy values widens in both programs. 

5.5 Sensitivity Analysis 

Aggregate subsidy estimates under alternative assumptions are shown in Table 6. Subsidy 

estimates are quite sensitive to the assumed risk premium. A one-percent higher (lower) 

risk premium than that assumed in the base case raises (lowers) subsidy rates by $7 per 

$100. For the direct program, this is most easily understood as the higher discount rate 

reducing the value of future repayments. On the guaranteed loans, the effect of market 

risk is to raise the present value of guarantee payments made on defaulted loans. The 

credit-risk premium has a small effect on the present value of net income payments to 
 21

guaranteed lenders, as discussed in Section 5.3. The effective duration of the loans also 

affects value, with loan extension generally increasing cost. Table 6 also reports subsidy 

costs with 25 percent faster and slower loan repayment rates, which serves to lengthen or 

shorten the average loan term by approximately four years. The increase (decrease) raises 

(lowers) subsidy costs by about $2 per $100. 

To compare the cost of the two programs, it is useful to break subsidy costs into their 

component parts. Table 7 reports a breakdown into market risk, default losses, up-front 

fees, and other administrative expenses. The cost attributable to each component is found 

by sequentially removing each cost element from cash flows or discount rates, computing 

the new subsidy cost and then reporting the difference.16 Any residual subsidy cost is 

driven by the difference between the student interest rate and risk-free rate of return. 

Market risk and default losses are the most important elements of the direct loan subsidy. 

The guaranteed lender payments add significantly to the guaranteed program’s subsidy 

cost. 

Finally, Table 8 reports subsidy costs for the direct and guaranteed programs for a variety 

of policy alternatives. One option is to lower the guaranteed lender payments to bring the 

guaranteed subsidy closer to the direct loan subsidy rate. The first two rows of Table 7 

report the predicted subsidy estimates after lowering lenders payments by 0.5 percent and 

1.0 percent per annum, respectively. The effect of the 1.0 percent reduction is to bring the 

subsidy in the guaranteed program to within 3 percent of the direct program. Another set 

of alternatives relates to the interest rate paid by borrowers. Switching from variable to 

fixed interest rates on Stafford loans has increased the subsidy cost for 2006 by 

approximately $2 per $100, in part because fixed rate loans should have a premium above 

variable-rate loans and in part because our long-term interest rate projections imply that 

the variable-rate loan will be above 6.8 percent. If market interest rates continue to 

increase, subsidy costs on loans originated after 2006 could be significantly higher than 

they would be under the variable-rate policy. Several proposals to lower borrower rates 

are being discussed by members of the Congress. One proposal would cut the borrower 

rate in half over the entire life of the loan, which would increase the subsidy cost by 

approximately $15 per $100. (In fact, the subsidy cost could increase by even more than 

this if the lower rates caused borrowers to lower their rate of prepayment and switch to 

longer-term repayment plans). 

5.6 Alternative Estimates 

A ballpark market-value estimate of the cost to the government of direct lending is 

obtained by comparing the rate charged to students on private loans with the rate charged 

by the government and discounting the annual savings. Although such an estimate does 

not control for the differences between private and direct loans and greatly oversimplifies 

the pattern of cash flows, it provides a useful comparison point and confirms that the low 

 

16 The order that different cost elements are removed has a modest impact on the cost attribution to 

different components. 
 22

subsidy cost for direct loans in the budget is probably well below the true cost to 

taxpayers. 

Like the earlier calculation of the cost of capital, the estimate is based on typical terms 

for floating-rate Stafford loans and private loans made in recent years, where LIBOR+4 

percent approximates the average rate. Stafford loans carry a rate based on a three-month 

Treasury rate that resets annually, plus a spread. The spread equals 1.7 percent when the 

student is in school, in grace, or in deferment, and 2.3 percent otherwise. Approximating 

the difference between LIBOR and three-month Treasury at 30 bps, and assuming a 2 

percent average spread on federal loans, students typically pay 2.3 percent more per 

annum on private loans than on federal loans. We assume further that both types of loans 

amortize over 10 years, abstract from the effects of prepayment and default, set LIBOR to 

5 percent, and discount at LIBOR + 4 percent. This yields an estimated present value 

interest savings to students of $10,463 per $100,000 borrowed, or a 9.8 percent subsidy 

rate. The higher subsidy rate in the more complete analysis can be attributed to the value 

of the various extension and deferral options. 

6. Discussion and Conclusions 

This paper presents two main findings: First, the market-value estimates developed here 

indicate that the cost to taxpayers of both programs is significantly understated in the 

budget. Second, even under a market-based valuation methodology, the guaranteed 

program reports a significantly higher subsidy rate than does the direct program. We 

conclude with further discussion of the government’s apparent cost advantage over the 

private sector in funding fully guaranteed student loans. 

Guaranteed lenders routinely obtain funding by securitizing parcels of previously 

originated federal loans and selling these asset-backed securities to investors at a 

weighted average rate slightly over LIBOR. This suggests that private investors do not 

view guaranteed loans as perfect substitutes for Treasury securities, despite the 97 

percent to 99 percent credit guarantee.17 In addition, lenders bear underwriting, SEC 

filing, and other administrative fees that add to the total cost of capital. In comparison 

with the cost of Treasury funding for direct loans, it appears that guaranteed lenders pay 

25 to 35 basis points more to borrow. What accounts for the higher cost? One factor is 

that a guaranteed loan is not completely risk-free—lenders who fail to administer loans 

according to ED policy and regulations may have the guarantee voided for those loans. 

The exemption of Treasury interest from state and local taxes also lowers Treasury rates 

relative to LIBOR. Further, securitized student loans are less liquid than Treasury 

securities. The prepayment and extension options add uncertainty about maturity, also 

increasing funding cost (as evidenced by higher spreads on the tranches of securitizations 

that absorb the maturity risk). However, these options also increase the cost of funding 

direct loans and, as with the risk premium, should be included in a market-value cost 

estimate for either program. 

 

17 This discussion is based on securitizations of floating-rate loans and prospectus data from Sallie 

Mae on recent issues. 
 23

Prior to the mid-1970s, individual federal agencies raised funds separately, but 

recognition of the cost advantage of centralized borrowing led to a policy of 

consolidating federal borrowing through the Treasury, via the Federal Financing Bank. 

Since that time, growth in federally guaranteed loan programs has reduced some of this 

advantage. There may be instances when private intermediation adds value, for instance 

through better screening or monitoring of borrowers. However, in the case of student 

loans, which have categorical entitlement and an almost full credit guarantee, it is not 

clear that the value added by private intermediation justifies the significantly higher cost. 
 24

Table 1: Federal Student Loans Outstanding, 1998-2005

(Millions of dollars)

 1998 1999 2000 2001 2002 2003 2004 2005

Family Federal 

Education Loan 

Program 

Unconsolidated 

(Stafford & PLUS) 

74,727 92,760 106,220 122,423 129,757 130,455 142,405 148,391

Consolidated 9,675 20,008 27,891 32,384 49,434 79,017 100,176 138,457

Subtotal 84,402 112,768 134,111 154,807 179,191 209,472 242,581 286,848

Ford Federal Direct 

Loan Program 

Unconsolidated 

(Stafford & PLUS) 

26,937 33,763 43,091 47,958 50,264 51,013 52,090 47,679

Consolidated 4,733 12,067 14,622 22,526 29,807 33,507 37,155 47,027

Subtotal 31,670 45,830 57,713 70,484 80,071 84,520 89,245 94,706

Total 116,072 158,598 191,824 225,291 259,262 293,992 331,826 381,554

Source: Office of Management and Budget, as reported in the budget appendix. 
 25

Table 2: Composition of Subsidy Costs 

(Percent) 

 Subsidy 

Rate 

Composition 

of Subsidy

Default 

Rate 

Recovery 

Rate 

 Defaults 

(net of 

recovery) 

Interest Fees All 

other 

 

Ford Direct Loan 

Program 

 

Weighted Average of 

Total Obligations 

2.05 1.31 -2.66 -1.67 5.07 14.00 118.29

Subsidized Stafford 9.83 0.67 6.44 -3.00 5.72 12.04 118.93

Unsubsidized Stafford -8.28 0.82 -12.59 -3.00 6.49 12.09 116.57

PLUS -6.37 0.89 -11.97 -4.00 8.71 5.50 101.51

Consolidation 4.37 1.92 -0.99 n/a 3.44 17.20 119.56

Family Federal 

Education Loan 

Program 

Weighted Average of 

Total Obligations 

9.87 0.89 11.12 -5.54 3.40 12.04 117.65

Subsidized Stafford 17.78 0.86 17.62 -3.25 2.55 12.04 118.99

Unsubsidized Stafford 1.12 0.96 0.79 -3.25 2.62 11.15 116.27

PLUS -0.01 0.88 -1.73 -3.25 4.09 5.38 101.08

Consolidated 12.20 0.88 15.46 -8.26 4.12 13.27 118.64

Source: Federal Credit Supplement 2006.

Table 3: Allowable Term by Balance 

Term (years) Balance Must Be at 

Least: 

10 -

12 $7,500

15 $10,000

20 $20,000

25 $40,000

30 $60,000

Note: Allowable term for extended and graduated repayment plans in the direct program 

and for newly consolidated loans in both programs. Balance refers to total balance of 

loans in the direct program for direct program extensions and total balance of loans 

consolidated for consolidation term extension. In the guaranteed program, borrowers with 

balances of more than $30,000 can elect a 25-year extended repayment term on their 

original loans. 
 26

Table 4: Default Claims as a Percentage of the Outstanding Federal Loan Portfolio

Budget Year 1990 1996 2005

Outstanding Loan Portfolio (millions of dollars) 49,890 57,557 242,581

Default Claims (millions of dollars) 2,384 1,428 3,818

Loans in Default (percent) 4.8 2.5 1.6

Table 5: Base-Case Market-Based Subsidy Estimates for New Stafford Loans Originated 

Award Year 2006 

(Percent) 

 Direct Guaranteed Difference

Unsubsidized Loans 

$0- 20,000 17.6 25.8 8.2

$20,000 – 60,000 19.6 28.7 9.1

$60,000 + 21.2 30.8 9.5

Weighted Average Subsidy of Unsubsidized 

Loans 19.5 28.4 8.9

 

Subsidized Loans 

$0- 20,000 30.0 37.0 7.1

$20,000 – 60,000 32.6 40.3 7.8

$60,000 + 34.2 42.3 8.1

Weighted Average Subsidy of Subsidized Loans 32.2 39.9 7.6

 

Program Average 25.9 34.1 8.3
 27

Table 6: Parameter Sensitivity of Subsidy Rates

(Percent) 

Direct Guaranteed Difference

Base-Case Subsidy Rate 25.9 34.1 8.3

Varying Credit Risk and Credit-Risk Premium 

High Credit-Risk Premium (3.58% p.a.) 31.8 39.1 7.3

Low Credit-Risk Premium (1.58% p.a.) 19.1 28.5 9.4

No Credit-Risk Premium 6.8 18.8 12.0

No Default or Credit-Risk Premium 

Speed of Repayment 

25% Faster than Base Case 22.2 29.5 7.3

25% Slower than Base Case 29.0 38.0 9.0

Not Sensitive to Interest Rates 25.3 33.6 8.3

Other 

Longer Stafford Repayments/Reduced Consolidation 26.0 36.5 10.5

Table 7: Components of Subsidy Rate

(Percent)

 Direct Guaranteed

Base-Case Subsidy Rate 25.9 34.1

Up-Front Fees -2.3 -3

Federal Noncollection Administrative Expenses 2.2 0.4

Lenders Spread Above CP Rates - 12.1

2% Guarantee Shortfall -0.5

Liquidity Charge 2.1 2.1

Default Losses net of Recovery and Collections Costs 7.2 7.2

Risk Premium for Credit Risk 12.9 12.9

Residual: Net Interest 3.7 3.7
 28

Table 8: Subsidy Rates Under Alternative Policies 

(Percent)

Direct Guaranteed Difference

Base Case 25.9 34.1 10.5

Current Commercial Paper Spreads less 0.5% 25.9 31.3 5.5

Current Commercial Paper Spreads less 1.0% 25.9 28.6 2.8

Floating Rates, as Under 1998-2006 Law 23.4 32.7 9.3

Floating Rates but Without Special Allowances Floor 20.1 27.9 7.8

3.4% Interest Rate on Loans—Without Interest Rate 

Response 

42.1 49.7 7.6

3.4% Interest Rate on Loans—With Interest Rate 

Response 

44.9 52.4 7.5

90% Federal Guarantee 25.9 32.1 6.1

75% Federal Guarantee 25.9 28.0 2.1
 29

Figure 1: The Direct Program Share of New-Loan Volume 

0

5

10

15

20

25

30

35

1993-

1994

1994-

1995

1995-

1996

1996-

1997

1997-

1998

1998-

1999

1999-

2000

2000-

2001

2001-

2002

2002-

2003

2003-

2004

2004-

2005

2005-

2006

Award Year

Direct Loan Share (%)

 Source: The Department of Education. 
 30

Figure 2: Distribution of Loan Lifetimes 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 3 5 7 9 11 13 15 17 19

Years Since Loan Origination

Source: Estimates from 2006 sample of the National Student Loan Database.
 31

Figure 3: Status of Direct and Guaranteed Loan Portfolio, January 2006 

Direct Loans

Grace

21%

Repayment

46%

Default

11%

Forbearance

11%

Deferment

11%

Guaranteed Loans

Grace

19%

Repayment

54%

Default

8%

Forbearance

8%

Deferment

11%

Source: Estimates from 2006 sample of the National Student Loan Database.
 32

Figure 4: Default Rates (Weighted by Loan Value) by Years Since Borrower Entered 

Repayment 

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0123456789

Time Since Entering Repayment (yrs)

Guaranteed Stafford

Guaranteed Consolidated

Direct Stafford

Direct Consolidated

 Source: Estimates from 2006 sample of the National Student Loan Database. 
 33

Figure 5: Distribution of Future Subsidy Costs Given Interest Rate Uncertainty in the 

Direct Lending Program 

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

2008 2010 2012 2014 2016

10th percentile

50th percentile

90th percentile

 Source: Estimates from 2006 sample of the National Student Loan Database. 
 34

Figure 6: Distribution of Future Subsidy Costs Given Interest Rate Uncertainty in the 

Guaranteed Lending Program 

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

2008 2010 2012 2014 2016

10th percentile

50th percentile

90th percentile

 Source: Estimates from 2006 sample of the National Student Loan Database. 
 35

Appendix 1 

Description of NSLDS Data 

The Department of Education administers the National Student Loan Database System 

(NSLDS), a recordkeeping system that tracks the status of individual loans and 

borrowers. The Congressional Budget Office receives an annual subsample of loan and 

borrower records each January, which it uses to make cost estimates. The database 

consists of multiple linked files containing current and historical information about 

borrowers and their loans. The files used to produce market-based subsidy estimates in 

this paper are as follows: 

Loan File: The file consists of one record per loan on the type of loan (direct or 

guaranteed, consolidated or original), the date the loan was taken, the amount disbursed, 

the principal outstanding at the time the sample was drawn, the current status of the loan, 

and the academic level of the student when the loan was taken. Each loan record also 

contains a unique identifier for the borrower, school, and guaranty agency associated with 

the loan, making aggregation of loans by borrower possible. The file contains 5.42m loan 

records on 1.30m distinct borrowers. 

Loan Status History File: The file contains a sequence of records with dates and codes for 

each loan’s status changes. A status change occurs for various reasons, including: 

entering repayment, default, deferment, forbearance, consolidation and payment in full. 

The historical timing of status changes provides a basis for estimating the probability that 

new loans transition through the various statuses over their lifetime. The file contains 

25.60 million status change records on 5.42 million distinct loans. 

IRS and Guaranty Agency Collections Files: These files track the timing and amount of 

payments collected by the Internal Revenue Service, guaranty agencies, the Department 

of Education, and their contracted agents from borrowers whose guaranteed loans are in 

default. No recovery information is available on direct program loans in default. The files 

contain the amount collected and date of collection for each defaulted loan. The amounts 

recovered by issuing the borrower with a consolidation loan are treated inconsistently. 

Collection amounts are combined with historical loan status changes of defaulted loans in 

the loan status history file to compute a recovery rate on defaulted guaranteed loans, 

which we assume is very similar to that in the direct program. The IRS offset file 

contains 340,000 IRS collection records on 156,000 loans (the file contains few 

collections per loan owing to the short history of the IRS offset program). The combined 

guaranty agency and departmental collection file contains 4.05 million collection records 

on 355,000 distinct borrowers. 

Several features limit the usefulness of this data set for estimating loan cash flows over 

time. Except for the collections on defaulted loans, the CBO sample of NSLDS loans 

does not contain a record of borrower payments over time. Similarly, when the sample is 

drawn each January, only the current level of outstanding principal is recorded. Another 

problem is that repayment plans are not reported, making it difficult to infer loan 

lifetimes and to distinguish on-time repayment from prepayment. 
 36
 37

Appendix 2 

Modeling Assumptions18

Interest Rates

We adopt the Cox-Ingersoll-Ross (CIR) model to simulate future paths of Treasury rates. 

In the CIR model, the instantaneous interest rate, R(t), is the sum of a constant and n 

factors, zi(t), i = 1,...,n, the state variables in the model: 

( ) ( )

1

n

i

i

R tR z t == +∑ (1) 

 Each factor obeys a mean reverting square root process: 

dz t z t dt z t dZ i ii i i i i ( ) =− + κθ σ ⎡ ⎤ () () ( )t ⎣ ⎦ (2) 

where θi is the mean reverting rate, κi is the speed of mean reversion, σi is the volatility, 

and dZi(t) is a standard Weiner process independent across factors. 

Under the risk-neutral (or equivalent martingale) measure 

dz t z t dt z t dZ i ii i i i i ( ) =− + κθ σ ⎡ ⎤ () () ( )t ⎣ ⎦ (3) 

where 

κκλ i = +i i (4) 

and 

i

i

i i

κ θ θ κ λ = + (5) 

 

λi is the constant market price of risk for factor i. The time t price of a zero coupon bond 

with unit coupon and expiring at T is 

( ) ( ) ( ) ( ) () ,

1

, , i i

n R T t B tT y t

i

i

p tT e A tT e −− −

=

= ∏ (6) 

where 

 

18 This appendix uses some of the text, figures, and equations contained in Appendix 2 of Lucas and 

Moore (2007). 
 38

( ) ( )( )

( ) ()

2 2 /

2 exp / 2 , exp 1 2

i i i

i ii

i

ii i i

T t

A tT

T t

κθ σ

γ γκ

γκ γ γ

⎡ ⎤ ⎡ ⎤ + − ⎣ ⎦ = ⎢ ⎥

+ − −+ ⎡ ⎤ ⎡ ⎤ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

 (7) 

( ) ( )

( ) ()

2exp 1 , exp 1 2

i

i

i i i i

T t

B tT

T t

γ

γ κ γ γ

⎡ ⎤ − − ⎣ ⎦ = + − −+ ⎡ ⎤ ⎡ ⎤ ⎣ ⎦ ⎣ ⎦ (8) 

and 

2 2

i i i γ = + κ σ (9) 

The yield to maturity, y, of a zero-coupon bond maturing at T is 

( ) ln , ( ) , p t T

y tT T t

− = − (10) 

Jagannathan, Kaplin, and Sun (2001) estimate the following factors from the two-factor 

model using weekly LIBOR rates of various maturities from 1995 through 1999: 

Table 2-1: Parameters for the Cox-Ingersoll-Ross Two-Factor 

Interest Rate Model 

Factor κ θ σ λ

1 0.392 0.272 0.0153 -0.00038 

2 0.0532 0.0162 0.0430 -0.0592 

R = -0.229 

Under these parameters, factor 1, with the stronger degree of mean reversion, drives the 

gap between long- and short-term rates, whereas factor 2 determines long-term rates. We 

subtract 20 basis points from R to reflect the average spread between three-month 

Treasury and LIBOR yields. With these parameters, the Model implies a long-run 

average three-month Treasury bill rate of 3.57 percent (standard deviation, 1.57 percent) 

and 10-year zero-coupon rate of 3.98 percent (standard deviation 1.79 percent). 

For each Monte Carlo run, initial levels of the states variables are calibrated to fairly 

price an initial three-month T-bill and 10-year Treasury bond rate. For each simulation, 

the instantaneous rate is sampled monthly for as many months as the maximum maturity 

of the student loan, using a discrete approximation of the risk-neutral process in equation 

(3). For each sample path of interest rates, the monthly discount rate dt used to discount 

interest-rate-sensitive cash flows from month t + 1 back to month t is: 

1 ln , 12 12

j

t

t t d p⎛ ⎞ + = − ⎜ ⎟ ⎝ ⎠ (11)
 39

Averaging the discounted value of the set of cash flows over all sample interest rate paths 

provides the net present value of any interest-rate-sensitive stream of cash flows.

Cash Flows

Loans originate at time 0, begin repayment at time TR, and have a maturity of T,M so the 

loan is repaid in TR

+TM months. TM depends on whether the consolidation option is 

exercised or, in the counterfactual case, the loan term is extended. The original maturity 

of Stafford loans is 10 years. Figure 2-3of this appendix describes the stochastic rules 

governing consolidation and extension. 

Interest accrues on outstanding principal every month, except for in cases in which the 

borrower of a subsidized loan is in school, deferment, or default. The borrower interest 

rate in period t, denoted ,

j RS t , is either 0, 6.8 percent, or 6.875 percent, depending on the 

type and status of the loan.19

The variable Pt

j denotes the evolution of principal (prior to default) over time in each 

simulation j. Given an initial principal of P0

j

 = P0, principal evolves according to: 

1 , 1 1 jj j j Pt+ + PrA t St t = +− ⎡ ⎤ ⎣ ⎦ (12)

where 

( )

1

12 , , 1 1 j j

St St r R =+ − (13)

is the monthly compounding student rate. The prescribed monthly payment, At

j

, depends 

on the loan’s status and is based on amortizing the principal at the current interest rate 

over the remaining life of the loan: 

( )

,

1 ,

,

1 1

0,

j j

t St R

k j j

t S t

R

P r

t T

A r

t T

−

+

⎧

⎪ ≥ ⎪ = ⎨ − +

⎪

⎪⎩ <

 (14)

Borrowers may pay more or less than this prescribed amount in instances of default, 

prepayment, consolidation, deferment, or forbearance. Because we do not have reliable 

data on actual payments, we assume that borrowers make the prescribed payment unless 

they default on their loans, prepay their loans in their entirety, defer, or receive 

forbearance on their loans. In the direct program, the government’s cash flows on 

performing loans are the student loan payments less an administrative charge:

 

19 The numerical implementation of the model is flexible enough to accommodate floating interest 

rates tied to particular rates on the yield curve. 
 40

j j At t − fP (15) 

where f is the proportional administrative fee. The fee is 0.50 percent per annum in the 

benchmark calibration, reflecting typical servicing and other administrative costs of the 

direct program. In cases of default, the government recovers in proportion to the present 

value of remaining payments. 

In the guaranteed lending program, the government cash flows are the quarterly payments 

to lenders—the SAP less any consolidation fee paid by lenders to the government—while 

the loan is in good standing, and the lump-sum payment of outstanding principal and 

accrued interest in the event of default. We ignore administrative costs because they are 

largely borne by the guaranteed lender. 

The quarterly SAP is the difference between the student rate and the three-month 

commercial paper rate plus a spread but has a floor of zero. We assume that the 

annualized three-month commercial paper rate, RC, tracks the T-bill rate with a 20 basispoint spread: 

, exp 4 3 ,3 3/12 .002 1, 1,2,..., ( ) j j RC t = + + − ∀= ⎡ ⎤ y kk t T ⎣ ⎦ (16) 

Absent default, the government cash flow in each month is the SAP less any 

consolidation fee paid from lenders to the government (1.05 percent of principal). The net 

guarantee payment to the government is

( )

3 ,3 ,3

3 ,3 ,3

3 ,3 ,3

1.74% / 4, 3 and 3 0,1,2,...

2.34% / 4, 3 and 3 0,1, 2,...

2.64% 1.05% / 4, 3 0,1,2,...

0,

jj j R C

k Ck Sk

jj j R C

k Ck Sk j

t jj j C

k Ck Sk

PR R kT kT k

PR R kT kt k

G

P R R kt k

otherwise

⎧ − + − < < ∀= ⎡ ⎤ ⎣ ⎦ ⎪

⎪ − + − ≥ < ∀= ⎡ ⎤ ⎪ ⎣ ⎦ = ⎨

⎪− + − − ≥ ∀= ⎡ ⎤ ⎣ ⎦ ⎪

⎪⎩

 (17) 

In cases of default, the government pays the outstanding principal, j Pt , to the lender, 

assumes the loan, and recovers in proportion to the present value of the remaining 

outstanding payments. The default and recovery rates used in the calibration are 

described in Section 2.5 of the paper. 

Stochastic Rules Governing Borrower Behavior 

Borrowers make a variety of decisions that can dramatically shorten or lengthen the life 

of their loans and correspondingly raise or lower their monthly payments. A borrower 

does not enter repayment until six months after completing his or her course of study, so 

loans taken early in a borrower’s degree will have longer periods of nonrepayment than 

loans taken later. Some students shorten or extend the duration of their studies, which 
 41

adds an uncertain element to the time until a borrower begins repayment. Upon entering 

repayment, a borrower typically opts for a standard 10-year repayment plan. But a 

borrower with a larger balance can choose a longer repayment plan of 25 years or 

consolidate multiple loans into a new loan with term as long as 30 years. Some borrowers 

who have left school but decide to take further studies are entitled to payment deferment. 

Those borrowers experiencing financial hardship are entitled to loan forbearance. We 

model the take-up of these options using a sample of loans from the NSLDS (as 

described in Appendix 1). 

In estimating the time that elapses before a borrower enters repayment, we abstract from 

the uncertainty and simply assume that all loans experience an in-school plus grace 

period of two years.20 Conversely, we assume that loan consolidation and loan 

prepayment behavior are random and sensitive to prevailing interest rates. Prepayment 

and consolidation may also be related to default rates but, for simplicity, we ignore this. 

Default rates are discussed in the next section of this appendix. 

We posit a rule for the intensity of consolidation for a given loan that is consistent with 

the Probit model described in Appendix 1. Specifically, the probability of consolidation is 

decreasing in the student interest rate and decreasing in the elapsed time since repayment 

began. We assume that borrowers consolidate loans during the grace period at a level 

consistent with the rule for consolidation at other times, but that they cannot consolidate 

at all while they are in school.21 Thus, the annualized probability of consolidation, qC,t, at 

month t is 

( ) ( ) ,

1 2

0, 6

Φ max /12,0 ,

R

j

C t R R

t T

q β β tT tT

⎧ < − ⎪ = ⎨ +− ≥ ⎡ ⎤ ⎪ ⎣ ⎦ ⎩

 (18) 

where Φ is the cumulative standard normal distribution function and β1 and β2 are loantype-specific parameters based on Probit regression estimates as reported in Lucas and 

Moore (2007). Table 2-2 summarizes these parameters for loan type. 

Forbearance and deferment rates are likely to exhibit correlation with both interest rates 

and borrower default rates as well as with the borrower’s cumulative loan balance. For 

simplicity, we ignore these correlations and just assume that, each year, a loan has a 6 

percent chance of entering deferment or forbearance for a fixed duration of three years. 

Under that assumption, each loan enters deferment or forbearance one time at most, 

which results in a cumulative 10-year rate of deferment and forbearance of approximately 

0.55 in base-case calibrations. During this period, borrowers do not make payments, 

hence At = 0 for each period t. 

 

20 Averaging the subsidy costs over a distribution of repayment start dates yields similar results 

when the mean of the distribution is the same as that used for the fixed repayment rate. 

21 For the 2006 academic year, borrowers were allowed to consolidate during their in-school period. 
 42

Table 2-2: Parameters Determining the Annual Frequency of Consolidation 

Maximum Eligible Consolidation Loan Term 

(Loan type) 

Model 

Coefficient 

Estimates 

Proportion of 

Loans 

Consolidating 

over 10 years 

β1 β2

 

10 years -1.94 -0.03 0.16 

20 years -0.6 -0.09 0.55 

30 years -0.43 -0.16 0.51 

 

Adjusting Discount Rates for Default Risk 

Under the CIR model, the risk-neutral monthly compounded discount rate, dt, for defaultfree but possibly interest-rate-contingent monthly cash flows is 

( )

1 1 0,1, 2,... , 1/12

d t t ptt= −∀=

+ (19) 

In both the direct and guaranteed lending programs, the underlying payments between 

parties are contingent on default. We assume that default occurs with probability q in 

each month until the borrower completely repays the loan and that default risk is 

orthogonal to interest rate risk. To establish a simple no-arbitrage pricing mechanism for 

interest rate and default sensitive cash flows, we suppose that there is a pair of simple 

one-period securities traded in every period. The first is risk-free and offers a certain 

payoff of $1 in one period’s time. The second is a risky claim that pays $1 if the borrower 

does not default and α if the borrower does default. The fair price of the default-free 

claim along a particular interest-rate-simulation path is:22 

1

1 t + d (20) 

With a constant monthly risk premium of π and a default probability of q, the fair price of 

the risky claim is:23 

( )( )

1 (1 )

1 1 t

q

d

α

π

− −

+ +

 (21) 

 

22 We omit the subscript j in the remainder of this appendix. 23 The probability of default and the risk premium can be time-varying, but this is suppressed for 

simplicity. 
 43

More conveniently, we can define state price deflators to value cash flows in t+1 paid if 

the borrower defaults: 

1 t

h

+ d (22) 

and if the borrower does not default: 

1

1 t

h

d

−

+ (23) 

where h is the risk-neutral probability of default: 

( )

( )( )

1

1 1

q hπ α

π α

+ − = + − (24) 

Calibrating State Prices for Default-Contingent Prices 

Data from the NSLDS suggest a cumulative default rate over the life of a typical Stafford 

loan of 15 percent. Default rates vary over the life of a loan, with the rate decreasing as 

the loan ages. Abstracting from the time pattern, an annual default rate of 2 percent is 

consistent with this cumulative experience. Hence, the quarterly default rate, q, is set to 

0.25 percent. Estimates from the NSLDS suggest a recovery rate on defaulted loans in the 

range of 40 percent to 60 percent. We assume the midpoint of 50 percent in the 

computation of subsidy cost for the two programs. 

Present Value of Program Cash Flows 

For a given sequence of interest rates, the transition of a loan through defaulting and nondefaulting states can be represented as a binomial tree. Figure 2-1 shows borrower 

payments on a direct loan in a two-period binomial tree. The tree tracks the status of the 

loan over time, with discrete intervals of time indicated on the horizontal axis. From a 

given node, each upward move indicates the borrower does not default in the subsequent 

period, and each downward move corresponds to a borrower’s default. To ensure a 

stationary representation, rather than terminate the loan after default, we assume that the 

borrower and lender agree to a new loan with payments reduced to fraction α of the 

originally prescribed payments (reflecting failed collections and collection costs). 24 That 

is, the lender recovers a lump sum proportional to the present value of remaining 

payments. Cash flows in each state can be priced back to the previous period by using the 

default and nondefault state prices in equations (26) and (27) and to earlier periods by 

applying (26) and (27) recursively. The present value of loan cash flows is then: 

 

24 This makes it possible to calibrate the risk premium using the observed loan spread above the riskfree rate (s) and the recovery adjusted default rate q(1-α), as in equation (30). 
 44

( )( )

1

0

0

1 1

t

t t t

k

k

A

d s

∞

− =

=

⎛ ⎞

+ + ⎜ ⎟ ⎝ ⎠

∑

∏ (25) 

where 

( )

1 1

1 1

s

q

π

α

+ = − − − (26) 

The variable s has an interpretation as the monthly credit spread, which depends on the 

rate of default (q), the rate of recovery (α), and the risk premium for credit risk (π). 

Figure 2-1: Binomial representation for the cash 

flows of a two-period student loan for a given 

simulation of interest rates. 

Assuming that the administrative fee is paid only as long as the loan is not in default 

(only along the uppermost branches of the binomial tree), the present value of 

administrative fees is: 

( )

( )

1

0

0

1

1

t j

t

t t

k

k

h fP

d

∞

− =

=

−

⎛ ⎞

+ ⎜ ⎟ ⎝ ⎠

∑

∏ (27) 

Thus the present value of a direct loan is the difference between (25) and (27). The cash 

flows for the guarantee also have a binomial tree representation, as shown in Figure 2-2 

for the two-period case. 

A1 

αA1 

αA2 

α

2

A2 

A2 

q 

q 

q 

1 – q

1 – q

1 – q
 45

Figure 2-2: Binomial representation for the 

cash flows of a two-period loan guarantee for a 

given simulation of interest rates. 

These cash flows can be decomposed into two simpler binomial trees, as displayed in 

Figure 2-3. The first is just the binomial tree for the student loan, and the second is a 

residual that captures the net payments to lenders as described in Section 5.3. Those 

lender payments have only two nonzero branches in each period because the loan is 

assumed to become federal property following default. 

 

Figure 2-3. 

Valuing the two components using the risk-neutral discount rates and probabilities of 

default gives the following present value of cash flows in the FFEL program (excluding 

federal administrative expenses and guaranty agency payments): 

( )( )

( )( )

( )

( )( )

( )

1

1 11

0 00

0 00

1 1

11 1 1

t t

t t t ttt

t tt t t tt

k kk

k kk

A h G A h hP G A

ds d d

− ∞ ∞∞

− −− = ==

= ==

− + − ++ − − ⎛⎞ ⎛⎞ ⎛⎞

++ + + ⎜⎟ ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ ⎝⎠

∑ ∑∑

∏ ∏∏

 (28) 

A1 

αA1 

αA2 

α2A2 

A2 

q 

q 

q 1 – q

1 – q

1 – q

αA2 

−A1 

−G1 

−A1 

−G1 

−P1 

−A2 

−G2 

−P2 

q 

q 

1 – q

1 – q

−A2 

−G2 

−G1 

−P1 

−A1 

−G1 

+αA1

−P2 

−A2 

−G2 

+αA2

α

2

A2 

q 

q 

q 

1 – q

1 – q

1 – q

αA2 

−G2 
 46

References 

Center on Federal Financial Institutions (2005), Student Loans: A Budget Primer, 

available at http://www.coffi.org/pubs/Student%20Loans%20A%20Budget%20Primer% 

20v2.pdf. 

Congressional Budget Office (2005), Estimating the Value of Subsidies for Federal 

Loans and Guarantees, Washington, D.C. 

De Fraja, G. (2002), “The Design of Optimal Education Policies,” The Review of 

Economic Studies, vol. 69, no. 2, pp. 437-466. 

Dynarski, S. (2002), “The Behavioral and Distributional Implications of Aid for 

College,” The American Economic Review, vol. 92, no. 2, pp. 279-285. 

Edlin, A.S. (1993), “Is College Financial Aid Equitable and Efficient?” The Journal of 

Economic Perspectives, vol. 7, no. 2, pp. 143-158 

Gale, W. (1991), “Economic Effects of Federal Credit Programs,” American Economic 

Review, vol. 81, no. 1, pp. 133-152. 

Hanushek, E.A. (1989), “Expenditures, Efficiency, and Equity in Education: The Federal 

Government’s Role,” The American Economic Review, vol. 79, no. 2, pp. 46-51. 

Jagannathan, R., A. Kaplin, and S.G. Sun (2001), “An Evaluation of Multi-Factor CIR 

Models Using LIBOR, Swap Rates, and Cap and Swaption Prices,” Journal of 

Econometrics, vol. 116 (1-2), pp. 113-146. 

Keane, M.P. (2002), “Financial Aid, Borrowing Constraints, and College Attendance: 

Evidence from Structural Estimates,” The American Economic Review, vol. 92, no. 2, 

pp. 293-297. 

Lucas, D. and D. Moore (2006), “The Student Loan Consolidation Option,” manuscript, 

Northwestern University. 

Lucas, D. and M. Phaup (2007), “The Cost of Risk to the Government and Its 

Implications for Federal Budgeting,” working paper. 

New American Foundation, “History of Guaranteed (a.k.a. Federal Family Education 

Loans) and Direct Student Loans,” available at http://www.newamerica.net/programs/ 

education_policy/student_loan_watch/history. 

Price Waterhouse Coopers (2005), “The Limitations of Budget Score-Keeping 

in Comparing the Federal Student Loan Programs,” available at http://www.studentloan 

facts.org/resources/. 
 47