Default Risk and Private Student Loans: Implications for Higher Education Policies

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Default Risk and Private Student Loans: Implications for Higher Education Policies Felicia Ionescu and Nicole Simpson 2014-066 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Default Risk and Private Student Loans: Implications for Higher Education Policies∗ Felicia Ionescu† Nicole Simpson‡ Federal Reserve Board Colgate University December 15, 2015 Abstract Inrecentyears,theproportionofstudentsfacingabindingconstraintongovernment studentloanshasgrown. Thishasledtosubstantiallyincreaseduseofprivateloansasa supplementarysourceoffinanceforhouseholds’highereducationinvestment. Acritical aspect of the private market for student loans is that loan terms must reflect students’ risk of default. College investment will therefore differ from a world in which government student loans, whose terms are not sensitive to credit risk, are expanded to no longerbind. Moreover,beyondsimplycrowdingoutprivatelending,expansionsofthe governmentstudentloanprogramwillfeedbackintodefaultriskonprivateloans. The goal of this paper is to provide a quantitative assessment of the likely effects of the private market for student loans on college enrollment. We build a model of college investment that reflects uninsured idiosyncratic risk and a well-defined life-cycle that is consistent with observed borrowing and default behavior across family income and collegepreparedness. Wefindthathighergovernmentborrowinglimitsincreasecollege investment but lead to more default in the private market for student loans, while tuitionsubsidesincreasecollegeinvestmentandreducedefaultratesintheprivatemarket. Consequently, higher limits on government student loans have small negative welfare effects,whiletuitionsubsidiesincreaseaggregatewelfare. JELCodes: D53;E21;I22;I28 Keywords: CollegeInvestment;CreditRisk;StudentLoans;Default ∗Theauthorswouldliketothankparticipantsatvariousseminarsandconferences. SpecialthankstoKartik Athreya, Satyajit Chatterjee, Simona Hannon, Jonathan Heathcote, Dirk Krueger, Geng Li, Lance Lochner, BorghanNarajabad, MakotoNakajima, MichaelPalumbo, VictorRios-Rull, ViktorTsyrennikov, EricSmith, GianlucaViolante,TomWise,EricYoung,ChristianZimmermann,anonymousreferees,andseveralpeoplein variousfinancialaidofficesandprivatecreditinstitutionswhoprovideduswithvaluableinsight. Allerrorsare areown. † felicia.ionescu@frb.gov ‡ nsimpson@colgate.edu.

1 Introduction More than half of undergraduate students in the United States borrow to finance their college education and an increasing number of students borrow the maximum available in the government student loan program (Berkner, 2000). This has led to substantially increased use of private loans as a supplementary source of finance for households’ higher education investment. In fact, undergraduate borrowing from nonfederal sources peaked at 25 percent in2007-08(CollegeBoard,2014). Thisisimportanttopolicymakersbecauseasmorefunds are borrowed for student loans (from all sources), the repayment process becomes complex, especially in light of recent policy changes in both the government and private student loan markets.1 Infact,defaultratesonallformsofstudentloanshaveincreasedinthepastdecade (refer to Figure 2 in the Appendix). The goal of this paper is to provide a quantitative assessmentofthelikelyeffectsoftheprivatemarketforstudentloansoncollegeenrollmentin ordertobetterassesstheeffectivenessofhighereducationpolicies. A critical aspect of the private market for student loans is that, unlike in the government student loan market, loan terms must reflect students’ risk of default. Eligibility, interest ratesandloanlimitsintheprivatemarket,alldependoncreditscores. Inaddition,defaultin the private market affects credit risk and in turn, results in worse loan conditions. The rise ofstudentloansoriginatinginprivatecreditmarketssuggeststhatindividualcreditriskmay affect college investment. In particular, individuals with good credit may not be constrained intheircollegeinvestmentbylimitsonFederalstudentloanssincetheycanaccesstheprivate market,whereastheoppositemaybetrueforthosewithbadcredit. Moreover,beyondsimply crowding out private lending, expansions of the government student loan program will feed back into default risk on private loans. More generally, higher education policies may affect the distribution of borrowers, and as a result, may have different implications for default behavior,creditrisk,andconsequentlywelfare. This discussion raises the following question: What are the implications of the private market for student loans in the presence of public funding for student loans? In answering this question, we shed light on two additional issues: How important are credit risk and the privatestudent loanmarketfor collegeinvestment? How doborrowingand defaultbehavior in both the government and private markets for student loans vary across individual characteristics? To our knowledge, this is the first paper to quantify these effects in a model thatisabletoreplicateobservedpatternsinborrowinganddefaultbehaviorinstudentloans. We demonstrate the importance of accounting for the interaction between government and 1Section 1.2 includes a discussion about recent policy changes in the government and private market for studentloans. 1

privatestudentloanmarketswhenstudyinghighereducationpolicies. We develop a general equilibrium heterogeneous agents life-cycle model where agents differwithrespecttoanindexofability(orcollegepreparedness),resources(expectedfamily contributions for college), and credit risk type which summarizes the likelihood of default, all of which are observable. We assume that ability, credit type, and family income are positively correlated and that the returns to college increase in ability (consistent with the data). Students can invest in college and use expected family contributions, intra-family transfers and student loans to finance their college education. Students borrow from the government student loan program, where eligibility conditions depend on their expected familycontributionsandcollegecosts. Dependingontheirfinancialneed,studentsmayface a binding borrowing limit on Federal student loans. These students can turn to the private credit market to finance the rest of their college costs. Private creditors assess individual defaultriskbasedoncredittypeandoffertype-contingentcreditterms. In order to provide a credible laboratory for our policy counterfactuals, we ensure that ourbenchmarkeconomyisconsistentwithborrowinganddefaultbehaviorinthedata. First, students from high-income families invest more in their college education, but borrow less thanthosefromlow-incomefamilies. Inaddition,defaultratesamongrichstudentsarelower thanthoseofpoorstudents. Thesameholdstrueforstudentswithmorecollegepreparedness (or innate ability): high ability students have higher college enrollment rates, lower borrowing levels and lower aggregate default rates than those with low ability. As for credit type, we are the first to document that college investment is higher for students with good credit comparedtothosewithbadcredit. We study the policy implications of the importance of credit risk for college investment and the interaction between the government and private student loan markets. Specifically, we analyze the 2008 increase in borrowing limits that the U.S. government student loan program implemented. Undergraduate students can now borrow $31,000 over the course of their undergraduate education, up from $23,000. Using our model, we find that this policy induces an increase in college investment by almost 10 percent, and students borrow more from the government and less from the private market. At the same time, an increase in the borrowing limit by the government induces a change in the riskiness of the pool of borrowers,whichadverselyaffectstheprivatemarketforstudentloansandresultsinhigherdefault rates (7.8 percent compared to 3.1 percent in benchmark). Consequently, the lending terms intheprivatemarketbecomelessfavorabletocompensateforgreaterdefaultriskinequilibriumandthecostofdefaultistransferredtoborrowersviahigherinterestrates. Wefindthat 2

theseeffectshaveimportantwelfareimplications. Inparticular,inapartialequilibriumanalysis where interest rates do not adjust with an increase in default risk, the model overstates the (positive) welfare impact of the policy (+0.12 percent). However, when the interaction between the private and the government sectors are accounted for in general equilibrium, the welfare gain induced by the government policy is completely negated so that welfare is lower with high government borrowing limits compared to the benchmark economy, albeit thelossissmall(-0.04percent). We then compare the effects of increasing government borrowing limits in the government student loan program to a set of budget-neutral tuition subsidies (equal, need-based and merit-based subsidies). Our main results are two-fold. First, we find that tuition subsidies lead to more college investment and higher aggregate welfare compared to higher government borrowing limits. This result hinges on the fact that, unlike higher government borrowing limits, subsidies increase college investment without increasing the default risk in the private market for student loans. Therefore, interest rates in the private market are lower under a tuition subsidy compared to an environment with higher government borrowing limits. Our second result is that merit-based tuition subsides lead to larger welfare gains than need-based subsidies, even though need-based subsidies encourage more college investment. Compared to the higher government limits policy, merit-based subsidies reduce default risk in both the government and private markets since they increase college enrollment rates among high-ability students. Need-based subsidies, on the other hand, induce a smallerdeclineindefaultriskintheprivatemarketandanincreaseindefaultriskinthegovernment student loan program. In this case, low-income students are more likely to invest in college and borrow relatively more to finance their college education. Consequently, the welfaregaininducedbymerit-basedsubsidiesis0.45percentcomparedto0.35percentwith need-basedsubsidies. Our results suggest that if the goal of education policy is to improve aggregate welfare, then merit-based tuition subsidies are preferable to both need-based subsidies and higher government borrowing limits, as merit-based subsidies promote college investment without increasing default rates in the student loan market. However, if the goal is to deliver high college enrollment rates, then need-based subsidies are preferable to merit-based subsidies and higher government borrowing limits, but come at the cost of higher default rates on studentloans. Therichnessofourmodelallowsustoexploreotherdimensionsofstudentloanmarkets that are currently not well understood because of the lack of a comprehensive dataset of 3

credit risk, borrowing levels and default. Specifically, we find that low-income students benefit from having access to the private market for student loans. They are most likely to hitthegovernmentborrowinglimitsincetheyhavelargeamountsofunmetfinancialneed. In addition, low-income borrowers have higher incentives to default in the government market than in the private market, and especially those with good credit. For them, having good credit creates better loan conditions in the private market (for the entire life of the loan), encouraging college investment. Indeed, our results show that low-income students with good credit have college enrollment rates that are 22 percent higher than those with bad credit(comparedtoonly4percenthigherforhigh-incomestudents). Ouranalysisalsodeliversaninterestingpatternofdefaultbehavioracrossborrowerswith differentabilitylevels. Inthemodel,thedisutilityofdefaultingintheprivatemarketislower than the disutility of defaulting in the government market. This feature induces borrowers to default at higher rates in the private market for student loans. However, default in the private market results in exclusion from unsecured credit and this penalty is quite costly for individuals with low ability levels (and hence low earnings) and more than offsets the disutilityeffect. Consequently,low-abilityagentshavehigherdefaultratesinthegovernment loanmarket,whilehigh-abilityagentshavehigherdefaultratesintheprivatemarket. Atthe same time, the model delivers declining default rates in income and credit type for both government and private student loans. This type of interaction between the government and private market for student loans is very difficult to uncover in existing datasets and points to the importance of using a rich general equilibrium heterogeneous agent model to begin to understandthesecomplexities. 1.1 Contribution to the Literature Our paper adds to the rich literature on the determinants of college investment in several ways: (1) we account for the role of credit risk in college investment (alongside the roles played by family income and college preparedness); (2) we model private student loans as a source of financing college (in addition to family income and government student loans); and(3)weallowfordefaultinbothgovernmentandprivateloansandarguethatthisfeature isimportantwhenstudyinghighereducationpolicies. First, the role of family contributions in the college investment decision has been extensively studied, with important contributions by Becker (1975), Keane and Wolpin (2001), Carneiro and Heckman (2002), Cameron and Taber (2004), and more recently by Belley and Lochner (2007) and Stinebrickner and Stinebrickner (2007). College preparedness (or ability) has long been considered an important determinant of college investment, as docu- 4

mented in Heckman and Vytlacil (2001) and Cunha et al. (2005). Our analysis contributes to this body of work by showing how credit risk affects college investment, in addition to differencesinfamilycontributionsandability. In recent years, the focus in the higher education literature has been on the effectiveness of financial aid in promoting college investment, and specifically student loans. Papers that study the implications of student loan policies within a quantitative macroeconomic framework include Garriga and Keightley (2007), Schiopu (2008), Ionescu (2009), Johnson (2010), Lochner and Monge-Naranjo (2011), Chatterjee and Ionescu (2012), and Abbott et al. (2013). For example, Chatterjee and Ionescu (2012) examine the value of offering insurance against the risk of taking a student loan and failing to graduate from college. Ionescu (2009) and Schiopu (2008) analyze the effects of alternative student loan policies on human capital investment. Garriga and Keightley (2007), Johnson (2010), and Abbott et al. (2013) extend the analysis beyond student loan policies and study the effects of need-based versus merit-based tuition subsidies on education choices and earnings. Our analysis contributes to this work by accounting for the role of the private market for student loans in the college investment decisionwhen analyzing theimplications of studentloan policies. We shedlight on the interaction between the government and the private market for student loans and, in particular,ontheimportanceofaccountingfordefaultriskinequilibrium. To our knowledge, the only papers that incorporate both the private and government student loan markets are Abbott et al. (2013) and Lochner and Monge-Naranjo (2011). The first paper focuses on the partial and general equilibrium effects of education policies and incorporates an experiment where the private market absorbs the excess demand for student loans when the government student loan is removed. However, the focus is on wealth-based and merit-based tuition subsidies and their implications for inequality. The second paper focuses on the student loan market and considers an environment where credit constraints arise endogenously from a limited commitment problem for borrowers. The framework is used to explain the recent increase in the use of private credit to finance college as a market response to the rising returns of a college degree. Our study adds to this body of work in an importantway,namely,wecapturedefaultbehaviorinthestudentloanmarketinequilibrium and we account for the individual default risk in both markets. We endogenize interest rates intheprivatemarketforstudentloanstoaccountforindividualdefaultriskandincorporatea feedback of default behavior into loan conditions. These modeling features allow us to take intoaccounttheinteractionbetweenthegovernmentandtheprivatemarket,whichprovesto beimportantinprovidinginsightsforongoingpolicychanges. 5

Our paper is related to studies that focus on the role of credit worthiness in unsecured credit markets, and in particular Chatterjee et al. (2011) and Athreya et al. (2012). The first paper considers the amount of information that can be gleaned from credit scores to explain the rise of unsecured credit, bankruptcy rates and credit discounts. Specifically, Chatterjee et al. (2011) provide a theory where lenders learn about the agent’s type from an individual’s borrowing and repayment behavior, and credit scores are based on the agent’s reputation of default. Athreya et al. (2012) develops a theory of unsecured credit and credit scoring consistent with the data and shows that improved information held by unsecured creditorsregardingindividualdefaultprobabilitiescanaccountformanyofthechangesseen in unsecured credit markets. Consistent with these theories, we model an observable credit risk as a proxy for the probability of default. However, given that our paper focuses on college investment and higher education policies, we simplify the model in terms of credit scoresbynotmodellinginformationalasymmetries. Instead,creditriskisaperfectsignalof theindividualprobabilityofdefault. We also add (in a small but important way) to the large literature that analyzes various types of tuition subsides for college investment in quantitative macroeconomic frameworks. For example, Caucutt and Kumar (2003) find that merit-based aid that uses any available signal on ability increases educational efficiency with little decrease in welfare. Akyol and Athreya (2005) find that college subsidies improve outcomes (including aggregate welfare) byreducingcollegefailureriskwithoutaffectingmeanreturns. Consistentwithourfindings, Johnson(2010)findsthatmoregeneroussubsidieshavealargerimpactoneducationalattainment than relaxing borrowing limits and Abbott et al. (2013) find that general equilibrium effects are important when analyzing education policies. However, in contrast to this literature, we consider the effects of tuition subsidies and higher government borrowing limits in a model where the private market for student loans and default in the student loan markets are explicitly accounted for. Different from the papers mentioned above, we find that merit-based subsidies induce larger welfare gains than need-based subsidies, even though need-basedsubsidieshavealargerimpactoncollegeinvestment. Ourpaperiscloselyrelated toGarrigaandKeightley(2007)whoarriveatsimilarconclusions,albeitthroughadifferent mechanism. Specifically, Garriga and Keightley (2007) focus on the role of in-school labor supplyandshowthatneed-basedsubsidiesincreasecollegeenrollmentbyattractingstudents from the lower end of the ability distribution (many of these students eventually drop-out or take longer than average to complete college). In the same vein, we find that need-based subsidiesencouragecollegeenrollmentforlow-incomestudents. 6

Tothisend,whatmakesourpapernovelisthatweanalyzeeducationpoliciesinaframework that incorporates both the private and government market for student loans with individual default risk in both markets. To our knowledge, no other paper has done this, despite the rising importance of the private market for student loans in financing college and recent concernsaboutincreaseddefaultonstudentloansandcallsformoretransparencyinlending practices. 1.2 Student Loan Market Overview Federal student loans are administered through the U.S. Federal Student Loan Program (FSLP), and include Stafford, PLUS, and Perkins Loans. Government student loans come in two forms: (1) direct loans issued by the Federal government, and (2) indirect loans which are administered by private credit institutions but are guaranteed by the U.S. government.2 Complete details on the FSLP, including recent changes to the system, can be found in Ionescu (2009). However, some general features of the program are important to our analysis. First, students and their families can borrow from the U.S. government at partially subsidized fixed interest rates. Specifically, interest rates on Federal student loans are set in statute, following the Higher Education Reconciliation Act of 2005. In 2006, the interest rate for Federal student loans was set at 6.8 percent and it remained at this level for both subsidized and unsubsidized loans for several years.3 Second, no credit history is required for the majority of government student loans. Third, Federal student loans are need-based and take into account both the cost of attendance (total charges) and the expected family contribution. Inturn,familycontributionsforcollegedependonparentalincomeandassets. There is a limit to how much students can borrow from the government. Prior to 2008, dependent students could borrow up to $23,000 over the course of their undergraduate career using Stafford loans (U.S. Department of Education).4 Borrowing from the government is quite common, with approximately half of all full-time college students borrowing from the government (Steele and Baum, 2009). Of those who borrow from the government, approx- 2In2010, indirectloanswereeliminatedandafterJune30, 2010theonlytypeofFederalloansborrowed are direct loans. However, in the current paper we focus on repayments of student loans disbursed in 2007. Also, in our analysis, we focus on Stafford student loans, which represent 80 percent of the FSLP in recent years. 3TheratefurtherdecreasedfornewundergraduatesubsidizedloansafterJuly1,2008.Before2006,therate wasvariable,rangingfrom2.4to8.25percent. Currently,interestratesonnewFederalstudentloansmadeon orafterJuly1,2013arebasedonthe10-yearTreasuryrate,plusafixedmargin,buttheyarestillfixedforthe lifeoftheloan. Fordetails,seeU.S.DepartmentofEducation(2014b)andhttps://www.edvisors.com/collegeloans/federal/stafford/interest-rates/#sthash.NFFt7mdv.dpuf 4http://studentaid.ed.gov/PORTALSWebApp/students/english/studentloans.jsp#03 7

imately one-half borrow the maximum amount (Berkner, 2000; Titus, 2002), and thus may turntotheprivatemarkettofinancecollege. Typically, repayment of government student loans begins six months after college graduation, and can last up to 25 years. In reality, most borrowers pay their loans in ten years. If studentsfailtomakeapaymentontheirstudentloanin270days,theyareconsideredtobein default. Theaveragenationaltwo-yearcohortdefaultrateintheFSLPwas7percentin2008 (U.S.DepartmentofEducation,2014a)andhassinceincreased,asFigure2intheAppendix shows. Students cannot typically discharge their FSLP debt upon default, and penalties on defaultersincludegarnishmentoftheirwages,seizureofFederaltaxrefunds,possibleholds on transcripts and ineligibility for future student loans. Default status on a government studentloanmayappearonacreditreport. However,theU.S.DepartmentofEducationreports thatdefaultstatusisdeletedfromacreditreportwhenthedefaulterrehabilitatestheloan,and mostdefaultershavetheincentivetorehabilitatetheirloansgivenIRStaxwithholdings.5 The system for obtaining private student loans is much different. First, most private student loans require certain credit criteria. Second, loan limits in private loans are set by the creditor and do not exceed the cost of college less any financial aid the student receives (from all possible sources). Third, interest rates and fees vary significantly by credit risk and hence vary across individuals and during the life of the loan. In contrast to subsidized Federal student loans, interest accumulates on private student loans while students are in college. PrivatestudentloansarenotguaranteedbytheFederalgovernment. Estimates of how many students borrow from private markets to finance their education vary, as schools are not required to report these numbers. Based on the 2007-08 National PostsecondaryStudentAidStudy(NPSAS)data,19percentoffull-timeundergraduatesborrowfromprivatemarkets(SteeleandBaum,2009),whileSallieMaereportsthat14percent borrow from private sources. Similar to other credit markets, private student lenders report information to credit bureaus, including the total amount of loans extended, the remaining balance,repaymentbehaviorandthedateofdefault. Defaultintheprivatestudentloanmarket is somewhat rare; the annualized default rate was 3.3 percent in 2008. Private student loans,likeFederalstudentloans,arenotdischargeableinbankruptcy. Thus, the key difference in borrowing from the private market to finance college (compared to borrowing from the government) is that eligibility and interest rates depend on the credit type of the student. In addition, default penalties differ across the two markets. Our study incorporates these features and discusses their implications for borrowing and default 5http://www.finaid.org/loans/rehabilitation.phtml 8

behavior and points to the importance of these features for college investment and in evaluatingpolicy. 2 Model Description We consider a life-cycle economy where agents live for T periods. Time is discrete and indexed byt =1,...,T wheret represents the time after high school graduation. Agents are heterogeneous in family contributions b∈B, ability (i.e., college preparedness) a∈A, and creditrisk f ∈F,whicharejointlydrawnfromthedistributionsG(b,a, f)onX =B×A×F. Agents can borrow from both the government student loan program and the private market forstudentloanstofinancetheircollegeeducation,whichlastT <T years. 1 2.1 Credit Risk In our model, credit risk f represents a signal about the agent’s probability of repayment. We refer to f as credit risk type (in short, credit type) and assume it represents a perfect signal about individual default risk. There are no informational asymmetries in our model.6 We assume that individuals of different credit types differ in default costs. In particular, we model two types of individuals: those with bad credit (f = 0) and those with good credit (f = 1). Our allowance for heterogeneity in default costs follows Chatterjee et al. (2011) and Narajabad (2012). These costs of default capture pecuniary and non-pecuniary costs associated with default (see Athreya, 2008, and Chatterjee et al., 2007). An important observation is that this previous work focuses on credit card debt, while we model credit risk and default cost in the context of the student loan market. This fact has two important implications. First,unlikecreditcarddebt,studentloansarenotdischargeableinbankruptcy, andthusdefaultinthestudentloanmarketsimplymeansadelayinrepayment,whichcomes with several costs. These costs include wage garnishments, attorney fees, withholding of tax refunds, and the stigma associated with default. Second, for student loans the difference between high and low credit types may be attenuated by the fact that, unlike for credit card debt,therecoveryratesfordelinquentloansarehigh. Heterogeneity in borrowers’ income processes may also have implications for heterogeneityinborrowinganddefaultdecisions(seeWhite,1998). Wecapturethisheterogeneity by allowing labor income to depend on f, among other characteristics (details are provided in Section 2.3). Consequently, even with the same debt level in the student loan market, 6Whilerelaxingthisassumptionwouldallowforadverseselectionwhichwoulddeliverinterestingpolicy implicationsforthegovernmentstudentloanprogram,thisisoutsidethescopeofthecurrentpaper. 9

defaultismorecostlyforsomeborrowersthanforothers.7 2.2 Student Loans Our model captures key features of the student loan program. Specifically, each year during g college, t = 1,...,T , young agents can borrow from the government the amount d > 0 1 t that represents college cost net of grants and education credit, d, less family contributions, b.8 Students may borrow from the government up to an exogenous borrowing limit d . max Thus, in the government market, students can borrow up to the borrowing limit each year: d g =min[max{d¯−b,0},d ]atafixedinterestrateRg. TheinterestrateonFederalstudent t max loansdoesnotchangeduringthelifeoftheloan. The amount students can borrow from private credit markets each year for college cang not exceed the difference between the cost of college, d, government loans, d , and family t contributions, b.9 Thus, the annual borrowing limit in the private market for student loans p g is given by: d = d−d −b. The interest rate charged in the private market depends on t t the credit type of the agent, so that Rp(f). Therefore, the interest rate on private loans may changeduringthelifeoftheloandependingontheevolutionoftheborrower’scredittype. Interest on government student loans does not accumulate during college. At the end of college,totaldebtowedtothegovernmentisDg=d g =∑ T 1 d g .Thisisincontrasttothe T +1 t=1 t 1 privatemarketforstudentloans,whereinterestaccumulatesduringcollege. Thus,totaldebt owedtotheprivatecreditorinthefirstperiodaftercollegeisDp=d p =∑ T 1 d p [Rp(f)] t . T +1 t=1 t 1 Students start repaying their loans after college (at t =T +1) and the duration of each 1 loan is set to T −T periods. Required payments, denoted by pi with i =∈ {g,p}, are 2 1 t calculatedeveryperioduntiltheloanispaidinfull,t =T +1,...,T ,wherei=grepresents 1 2 government loans and i = p represents loans in the private market. Default occurs if the borrower does not repay, pi = 0. Since student loans are not dischargeable in bankruptcy, t 7Inreality,badcreditmayalsohavenegativeconsequencesforthecostofreceivingsecureddebt,insurance costs, and rental costs (Chatterjee et al., 2011). We therefore take a conservative approach in modeling the impact of credit risk on college investment. However, as argued in Narajabad (2012), with constant relative risk aversion, all pecuniary default costs could be represented by non-pecuniary costs as long as they are proportionaltothedefaulter’sconsumption. 8Notethatd,whichisexogenousinourmodel,representsthesumoftuition,room,boardandotherconsumptionexpenditureslessanygrantsoreducationcreditsforayear. 9To keep focus on the trade-off between private and government student loan markets, we abstract from modelingothersourcesoffinancingcollege, suchascreditcardloansorloansfromfamilyandfriends. Our motivationforthisassumptionisthatthesesourcesoffundsarenotaccountedforwhenthegovernmentdecides how much students can borrow under the student loan program. At the same time, we recognize that these sourcesoffundsmightbeimportant,andsoweaccountforameasureofadditionalfundsusedforcollegein theformofintra-familytransfers(Section2.5.1). 10

agents need to reorganize their debt and repay the student loan in the period after default. Theinterruptionofdefaultpenaltiesprovidessufficientincentivesforborrowerstodoso,as weexplainbelow. Thetotaldebtofanagentattimet+1dependsontheoutstandingbalance of each type of student loan (di), his repayment (pi ∈{pi,0}), and the interest rate in each t t t market(Ri). Hence,debtsevolveaccordingto: d g =(d g −p g )Rg andd p =(d p −p p )Rp(f). (1) t+1 t t t+1 t t When agents default on a student loan, they experience a utility loss µi(f) > 0. When agents make the required minimum payment on either government or private student loans (pi = pi),thereisnoutilityloss, µi(f)=0. t t Depending on the default/repayment behavior in the private market for student loans, credittypeevolvesaccordingtothefollowingrules. Define f asthecredittypeintimet and (cid:48) f as the type at timet+1. The agents’ repayment choices determine a transition matrix for f and f(cid:48),namelyF∗ :F×F →[0,1]:  1 if pp =0    F∗(f (cid:48) =0)= 1−α if pp = pp and f =0 (2)    0 otherwise  1 if pp = pp and f =1    F∗(f (cid:48) =1)= α if pp = pp and f =0 (3)    0 otherwise When the agent defaults (pp = 0), he will have bad credit in the next period (f(cid:48) = 0) regardless of his current credit type. When the borrower pays the amount that it is required (pp = pp), his credit type changes as follows: if he has good credit (f =1), his credit type does not change. If he has bad credit (f = 0), he may become a good credit type with probability α, or remain a bad type with probability 1−α. This mechanism captures the feedbackbetweenrepaymentbehaviorintheprivatemarketforstudentloansandcreditrisk. Also,weassumenodefaultinotherassetmarketssowecanisolatetherelationshipbetween the repayment behavior for private student loans and the credit risk of young borrowers.10 10Itisimportanttonotethatparentsmayco-signonstudentloansintheprivatemarket,suggestingthatthe creditscoresofthestudentandtheirparentsmaymatterforthecollegeinvestmentdecision. Inourmodel,we focusonthecreditriskoftheindividualratherthanonthecreditriskoftheparent. Therelationshipbetween the credit risk of the parent and the child’s investment in college is an interesting topic, which we leave for futureresearch. Atthesametime,eventhoughyoungagentshaveshortcredithistory,theircreditscoresdiffer 11

To summarize, in our framework, default on student loans in both markets is penalized in two ways during the period when default occurs: through a utility cost and by not having the option to borrow in the risk-free market. Avoiding the continuation of these penalties gives defaulters an incentive to start repaying their defaulted loans. In addition, default in theprivatemarketforstudentloansispenalizedbymakingagentswithgoodcredithavebad credit,whereasgoodrepaymentbehaviorisrewarded(bygaininggoodcreditormaintaining goodcreditasshowninequations2and3). Inourmodel,peoplecareaboutcredittypesince borrowers with bad credit are excluded from borrowing in the risk-free market, and face a penalty which captures the immediate impact of bad repayment behavior on participation in other credit markets.11 This feature gives defaulters in the private market an additional incentivetostartrepayingtheirloans. 2.3 Labor Income Agentsareendowedwithexogenouslaborincomethatdiffersacrosseducationgroupswhich is intended to mimic the returns to college investment for different types of students as well as the risks faced over the life cycle. We disaggregate endowments into three components: anage-specificmeanoflogincome,persistentshocks,andtransitoryshocks.12 An empirically accurate description of the labor income process, and in particular the incomerisksthatcollegestudentsface,iscentraltoourapproach. First,earningsuncertainty is one of the leading causes of default among young households (Sullivan et al., 2000), and heterogeneity in borrowers’ income processes has implications for heterogeneity in default decisions (White, 1998). Second, credit type has an important role in an environment with earnings uncertainty. For students who borrow from the private market, interest rates are higher for someone with bad credit compared to someone with good credit (Sallie Mae, 2008). Thus,thecostofastudentloan,especiallywhenfinancedovertenormoreyears,can be significantly higher for students with bad credit. Earnings uncertainty (and in particular, the persistent component) amplifies the effects that credit type has on college investment, compared to an environment without earnings uncertainty. Both persistent and transitory incomeshocksarerelevanttoreplicatetherepaymentanddefaultdecisionsrelatedtocollege investment. Inaddition,wespecifyanincomeprocessthataccuratelycapturesthereturnsto collegeinvestment,andinparticular,howthesereturnsvaryacrossindividualswithdifferent significantlyandareprimarilybasedonthenumberofcreditaccounts(Averyetal.,2009). 11This modeling follows Chatterjee et al. (2007), Livshits et al. (2007), and Athreya et al. (2012), and assumesthatanindividualwith(observable)badcreditisexogenouslyexcludedfromborrowing. 12AstandardspecificationofthisprocessisinStoreslettenetal. (2001). 12

levelsofability. Lastly,welinkcredittypetoearningsinordertocapturethefactthatcredit scoresareasignalabouttheprobabilityofdefaultconditionalonobservables(suchaswealth andincome). Wespecifylogincome,lnyh,ofanagentattimet withabilitya,credittype f andhuman t capitalh={h ,h ,h },whichrepresentthethreeeducationgroupsinthemodel(nocollege, 0 2 4 some college but no bachelor’s degree, and four-year college graduates, respectively). The age-specific mean depends on education, ability, and credit type, while the persistent and transitoryshocksdependonlyoneducation. Theincomeprocessevolvesaccordingto: lnyh =λ h λ hlnµ h+zh+ε h (4) t a f t t t whereλh andλh representfixedeffectsforabilityandcredittypeontheage-educationspea f cific mean µh.13 The terms zh and εh represent the persistent and the transitory shocks to t t t earnings,respectively,wherezh=ρzh +ν ,andεh∼i.i.d.N(0,σ2 )andνh∼i.i.d.N(0,σ2 ) t t−1 t t ε,h t ν,h areindependentinnovationprocesses. Agents begin life (at t = 1) as unskilled households and receive their initial realization of the persistent shock, zh, from a distribution with a different variance than at all other 1 ages. That is zh =ξh where lnξh ∼N(0,σ2). This modeling of the income process reflects 1 ξ heterogeneity prior to any direct exposure to labor market risk, i.e., households first draw a realizationofthepersistentshockzh fromtherandomvariableξh withdistributionN(0,σ2). 1 ξ Insubsequentperiods,theagent’slaborincomeisdeterminedasthesumoftheunconditional mean of log income scaled by ability, credit type, and innovations to the persistent and transitory shocks. These shocks depend on human capital to reflect the fact that the risk characteristicsoflaborearningsappeartodiffersystematicallybyeducation(e.g.,Abbottet al.,2013;Hubbardetal.,1994;Storeslettenetal.,2001). 2.4 Means-Tested Transfers and Retirement Income In addition to labor income, agents receive means-tested transfers from the government, τ , t which depend on age t, income y , and net assets s . These transfers provide a floor on t t consumption. FollowingHubbardetal. (1994),wespecifythesetransfersas τ (y ,s )=max{0,τ−(max(0,s )+y )}. (5) t t t t t 13Ideally, wewould allowthe riskiness ofthe incomeprocessesto dependoncredit type. However, given datalimitationsfortheestimationprocess,weinsteadcaptureearningsdifferencesbycredittypeinthesame mannerthatwecaptureabilitydifferencesinearnings. Explanationsontheestimationprocedureareprovided inSection5. 13

Total pre-transfer resources are given by max(0,s )+y and the means-testing restriction is t t represented by the term τ −max((0,s )+y ). These resources are deducted to provide a t t minimal level of income, τ. For example, if s +y >τ and s >0, then the agent receives t t t no transfer. By contrast, if s +y <τ and s >0, the agent receives the difference, in which t t t hehasτ unitsoftheconsumptiongoodatthebeginningoftheperiod. Agentsdonotreceive transfers to cover debts, which requires the term max(0,s ). Lastly, transfers are required t to be nonnegative. After periodt =T when agents start retirement, they receive a constant 3 fractionoftheirincomeinthelastperiodasworkingadults,φy ,whereφ >0. Theydonot T 3 receivethemeans-testedtransfersduringretirement. 2.5 Household decisions 2.5.1 Overview Recall that agents are heterogeneous in three dimensions: family contributions (b), ability (a), and credit type (f). Each agent’s life is characterized by four phases: college, young adult,maturity,andretirement. Figure1illustratesthetimingofdecisionsforatypicalagent inthemodel. Figure1: Timingofdecisions Phase 1 Phase 2 Phase 3 Phase 4 College Young adult Maturity Retirement Life cycle earnings; risk−free savings + repayment / default Graduates College Life cycle earnings; risk−free savings risk−free savings Borrow Life cycle earnings; risk−free savings + repayment / default Dropouts Life cycle earnings; risk−free savings risk−free savings No College In the first period, agents make a one-time decision of enrolling in college or going directly to work as non-college workers, hence h=h . In our environment, the college in- 0 vestment decision is purely a financial decision. If they decide to enroll in college, agents financetheirconsumptionandcollegeinvestmentwhenyoungbyusingfamilycontributions for college, b, intra-family transfers Q(b), and student loans from the government and the privatemarket. Weassumethereisnochoiceincollegequalityandhenceconsideronlyone type of college in the model. This assumption may be a bit restrictive given that drop-out rates,joboutcomes,anddefaultratesonstudentloansvaryacrossdifferenttypesofcolleges, 14

such as public, private and for-profit institutions (see Cellini and Darolia, 2015; Looney and Yannelis,2015). However,thisresearchshowsthatstudentswhoenrollatfor-profitcolleges areoflowerability,onaverage,andcomefrompoorerbackgrounds. Thesearepreciselythe type of individuals in our model who are more likely to get lower returns on their college investment and to default on their student loans (recall that our earnings function depends on the ability of the individual, following Abbott et al., 2013). Empirical findings show that returns to schooling are mostly driven by the ability of the student rather than the quality of the school (Dale and Krueger, 1999). Even though our model does not fully capture heterogeneity in behavior by individuals enrolled in different types of colleges, to the extent that we account for heterogeneity in drop-out rates and job outcomes across ability levels, our modelhasimplications(albeitingeneralterms)fortheobservedheterogeneityinborrowing anddefaultbehaviorbyschooltypes.14 We assume that at the end of the college phase, students may complete college and receive a bachelor’s degree with probability π(a); in this case, h = h . With probability 4 1−π(a), students fail to receive a bachelor’s degree, so that h=h . In this way, our model 2 captures drop-outs from four-year colleges, which represent a significant portion of college students (Gladieux and Perna, 2005). However, there are several assumptions that we make concerning drop-outs. First, the probability of dropping outdepends on the ability ofthe individual. This is motivated by the fact that students’ college preparedness is a strong signal for college success (Chatterjee and Ionescu, 2012). Second, we assume that college risk is realized at the end of college since the majority of drop-outs intend to complete a four-year degree (rather than dropping out early in their college career).15 Third, we model dropping out as a pure risk of failing to acquire a four-year college degree, whereas in reality, students who do not complete four years of college may simply choose to leave college (see Arcidiacono, 2004; Manski and Wise, 1983; Stange, 2012; Stinebrickner and Stinebrickner, 2012). However,asshowninChatterjeeandIonescu(2012),failingtograduatefromcollege isquantitativelymoreimportantasareasontodrop-outthanvoluntarilyleavingcollege.16 Agentsinthesecondphaseoftheirlifeareworkingadultswhousetheirlaborearningsto consume, pay off their student loans (both public and private), save or borrow in a risk-free 14Webelievethataccountingforheterogeneityinschoolqualitycouldbeanaturalextensionofthecurrent study. 15Ourmodelingismotivatedbyempiricalevidencethatdocumentsanaverageenrollmenttimeof3.5years fordrop-outs(Boundetal.,2009;Ionescu,2011). 16Infact, ChatterjeeandIonescu(2012)alsoshowthatthefractionofcollegestudentswhodrop-outearly is small using BPS data. Therefore, we believe our assumptions about drop-out behavior are not restrictive. Ourmodelcouldbeextendedinthespiritofthispreviousworktoaccountfordifferentreasonsandtimesfor droppingout. 15

market, and pay a lump sum tax which finances the government student loan program. The keydecisionsthatindividualsmakeinthisphasearerepayment/defaultdecisionsonstudent loans in the two markets. Then, in the third phase (maturity), agents use their labor income to consume, save or borrow, and pay taxes. In the last phase of life, retired agents receive retirement income and earn interest on their savings. We assume that old agents die with certainty at the end of this period. Young agents who do not invest in college start their life cycleasworkingadultsandthenretireinthelastphaseoflife. Lifetimeutilityconsistsofthediscountedstreamofconsumption,andisdiscountedatthe rateβ ∈(0,1). Theagent’sproblemistomaximizeutilitysubjecttotheirbudgetconstraints (describedbelow). 2.5.2 DynamicProgrammingFormulation We describe the problem in a dynamic programming framework and solve recursively for choices in the model. In any period t, variable x is denoted by x and its period t+1 value t by x(cid:48). The value function is defined as VK(t), where t = T represents the terminal node j j of each phase j ={1,2,3,4} and K ={C,N} represents the college (C) and no-college (N) paths.17 For the terminal node (the last period of phase 4 when t = T = T), we assume 4 that the value function is defined as: VK(s,T)=u(φy +Rs) where s represents the stock 4 T 3 of savings, R is the risk-free interest rate, and φy represents retirement transfers, where φ T 3 representsretirementtransfersasafractionoflastperiod’searnings(y ). T 3 College Forindividualswhoenrollincollege,thevaluefunctionsforthefourphasesofthelife-cycle are given below. For the retirement phase (j = 4) when t < T , the agent faces a simple 4 consumption-savingsproblem,withthevaluefunction VC(s,t)=maxu(φy +sR−s(cid:48))+βVC(s(cid:48),t+1). 4 s(cid:48) T 3 4 Forthematurityphase(j=3),thevaluefunctionVC isdenotedas: 3 VC(h,a, f,s,z,ε,t) =max u(y(h,a, f,z,ε)+τ(y,s)−Θ+sR−s(cid:48)) 3 s(cid:48) +βE VC(h,a, f,s (cid:48) ,z(cid:48),ε(cid:48),t+1) z(cid:48) ,ε (cid:48) 3 17T andT alsodifferacrosseducationgroups, asweexplainbelow. Foreaseofexposition, however, we 1 3 suppressthisnotation. 16

with the state space (h,a, f,s,z,ε,t), representing education, h, ability, a, credit type, f, savings, s, and income shocks (z,ε), respectively. Credit type does not change during this phasesinceagentsnolongermakerepayment/defaultdecisionsontheirprivatestudentloans. During the maturity phase, agents earn labor income y(h,a, f,z,ε) and the means-tested (cid:48) transfer τ(y,s), save or borrow s, pay a lump sum tax Θ, and earn (pay) the risk-free rate R on their previous period’s saving/borrowing. Note that VC(h,a, f,s,z,ε,T +1) =VC(s,1) 3 3 4 foranygivenh,a, f,z,ε.18 Fortheyoungadult(j=2),thevaluefunctionisgivenby: VC(h,a, f,s,dp,dg,z,ε,t) = max u(y(h,a, f,z,ε)+τ(y,s)−Θ+sR−s(cid:48)−pg−pp)− 2 pg,pp,s(cid:48) (Λg µ g(f)+Λp µ p(f))+βE VC(h,a, f(cid:48),s(cid:48),dp(cid:48) ,dg(cid:48) ,z(cid:48),ε (cid:48),t+1) z(cid:48) ,ε (cid:48) ,f(cid:48) 2 withtheevolutionofdebt,di(cid:48) ,asgivenbyequation1,andtheevolutionofcredittype, f(cid:48),by equations2and3. As young adults, agents consume, save/borrow s(cid:48), earn labor income y(h,a, f,z,ε), receivethetransferτ(y,s),payalumpsumtaxΘ,earn/paytherisk-freerateonsavings/borrowings R,andrepayordefaultontheirstudentloans, pi,fori∈g,p. DenoteΛi∈{0,1}anindicator function for default for loans of type i∈{g,p}. When agents default on their student loans (Λi=1),theyfaceautilityloss µi(f).Agentswithbadcredit(asaresultofdefaultinginthe previousperiod)arepenalizedinthecreditmarket,suchthats (cid:48) ≥0.19 Recall that in the first year after colleget =T +1, the amount owed to the government 1 g p atthebeginningofthisperiodisgivenbyd andd ,definedinequation1. Forperiod T +1 T +1 1 1 t =T +1,...,T , debt accumulates according to equation 1 above. We require that in period 1 2 t = T , agents must pay off all of their student loans during the young adult phase; this 2 requires pi =di for i=g,p. This assumption is consistent with the fact that in reality the T T 2 2 majorityofborrowerspayofftheirloanswithin10yearsafterenteringrepayment.20 Finally, for the college phase (phase 1 of their life), agents may complete a bachelor’s degree with probability π(a), which varies by ability, in which they begin phase two with education level h . In the case they do not acquire a college degree, however, agents start 4 phasetwoascollegedrop-outswitheducationlevel,h . Thus,thevaluefunctionforthelast 2 18Thesamemethodologyisusedwhendefiningtheotherphasesofthelifecycle. 19Notethatthisconstraintisnotincludedinthevaluefunctionaboveforeaseofexposition. Inaddition,we assumethatthispenaltydoesnotextendbeyondphase2tobeconsistentwiththefactthat,inreality,penalties associatedwithdefaultarenotlong-lasting(seeMustoandSouleles,2006). 20Relaxing this assumption is a natural extension, in particular with the prevalence of income driven repayment plans, which extend the life of the loan up to 25 years. This will simply result in lower per period paymentswithoutchangingthenatureofouranalysis,giventhattheserepaymentplansareavailableforboth governmentandprivatestudentloans. 17

periodincollege(t =T )isgivenby: 1 VC(a,b, f,T ) = maxu (cid:0) b−d¯+dp(b, f,h)+dg(b,h)+Q(b) (cid:1) + 1 1 dp,dg β[π(a)E VC(h ,a, f(cid:48),s(cid:48),dp(cid:48) ,dg(cid:48) ,z (cid:48) ,ε (cid:48) ,T +1)+ (z(cid:48),ε (cid:48),f(cid:48) 2 4 1 (1−π(a))E VC(h ,a, f(cid:48),s(cid:48),dp(cid:48) ,dg(cid:48) ,z (cid:48) ,ε (cid:48) ,T +1)]. z(cid:48),ε (cid:48),f(cid:48) 2 2 1 Foranyotherperiodincollegethevaluefunctionisgivenby: VC(a,b, f,t) = maxu (cid:0) b−d¯+dp(b, f)+dg(b)+Q(b) (cid:1) +βVC(a,b, f,t+1) (6) 1 1 dp,dg withVC(a,b, f,1) being the value function associated with the college path. The parameter d¯represents the direct cost of college (tuition and fees) per year. During college, agents use expected annual family contributions b and intra-family transfers Q(b) to finance college.21 g p They may also borrow from the government d and from the private sector d during each t t period in the college phase,t =1,2,3,4. We assume that agents do not save or borrow from the risk-free market during college and do not pay the lump sum tax or receive government transfers. We also assume that college students forgo four years of labor income and attend collegefull-time(iftheyattendcollegeatall).22 Nocollege Agents who do not go to college h = h earn labor income y(h ,a, f,z,ε) and solve a 0 0 consumption-savings problem for the first three phases of their lives. For agents who do notinvestincollege,weassumethattheymayallocatefamilycontributions(b)toconsumption or savings in the first period. Agents start life in the working phase and remain there until period T , after which they retire. There are no student loans and thus no repayment 3 or default behavior. As a result, there is no change in credit type during the young adult phase, and thus the credit type in this value function is the one drawn at the beginning of the cycle. Similar to the college path, agents incur some adverse effects from having bad 21Ourmodelingrecognizesthefactthatwhileexpectedfamilycontributionsareimportantforeligibilityfor student loans, actual family contributions during college may be different. In our model, Q(b) captures the difference. This feature is also in accordance with empirical evidence in Johnson (2010) and Kaplan (2012) who show that there is risk-sharing for young adults within a range of networks including families, friends, firms,andunions. Weestimatetheseparameterswithinthemodel,asdescribedinthenextsection. 22Since most of the data on participation in student loans programs (both private and public) significantly varywithfull-timeandpart-timeenrollment,weneedtofocusononegroup.Also,eligibilityforthemaximum amountofgovernmentstudentloansdifferswithfull-timeandpart-timecollegeenrollment. 18

credit in that they cannot borrow in the risk-free market during phase two.23 Agents receive a means-tested transfer τ(y,s) and face a lump sum tax Θ during their working periods of life. In phase 4, agents retire, receive a fixed retirement income φy , and consume their T 3 savings. Thevaluefunctionsintheretirementandmaturityphasesare: VN(s,t) = maxu(φy +sR−s(cid:48))+βVN(s(cid:48),t+1), and 4 s(cid:48) T 3 4 VN(h ,a, f,s,z,ε,t) = maxu(y(h ,a, f,z,ε)+τ(y,s)−Θ+sR−s(cid:48))+βE VN(h ,a, f,s(cid:48),z(cid:48),ε (cid:48),t+1), 3 0 s(cid:48) 0 z(cid:48) ,ε (cid:48) 3 0 respectively,andfortheyoungadult,thevaluefunctionisgivenby: VN(h ,a, f,s,z,ε,t)=maxu(y(h ,a, f,z,ε)+τ(y,s)−Θ+sR−s(cid:48))+βE VN(h ,a, f,s(cid:48),z(cid:48),ε (cid:48),t+1) 2 0 s(cid:48) 0 z(cid:48),ε (cid:48) 2 0 In the first phase of life (which lasts only one period), the agent who does not go to college hasthevaluefunction: VN(a,b, f,z,ε,1) = maxu(b+y(h ,a, f,z,ε)−s(cid:48))+βE VN(h ,a, f,s (cid:48) ,z(cid:48),ε (cid:48),1) 1 s(cid:48) 0 z(cid:48),ε (cid:48) 2 0 At the beginning of life, agents choose between the college and no-college paths and hencesolve: max{VC(a,b, f,1),VN(a,b, f,1)}. (7) whereVN(a,b, f,1)=E VN(a,b, f,z,ε,1)andVC(a,b, f,1)asdefinedinequation6. z,ε 1 2.6 Private creditors The private market for student loans is competitive: the representative private creditor takes prices as given and the creditor can borrow and lend in the risk-free capital market at interestrateR. Asstandardintheliterature,thelendingrateintheprivatemarketforstudent loans covers the transaction cost of intermediation, q, which captures the per-unit cost of servicingaccounts(seeAthreyaetal.,2012;LiandSarte,2006). Pricingofprivatestudentloansinthemodelarisesfromtheconditionthatprivatestudent lenders earn zero profits on any contract type. The private creditor uses the credit type of borrowerstoassesstheprobabilityofdefaultandsuppliesloansforall(Dp, f)-typecontracts inordertomaximizethepresentdiscountedvalueofprofits,where f istheinitialcredittype andDp representstheaccumulateddebtattherateRp duringcollege,givenby: 23Boththeseassumptionsaremadesothatthecollegeandthenocollegepathsaresymmetricregardingthe roleofcreditrisk. 19

T 1 Dp(d p ,...,d p ,Rp)= ∑Rp(T 1 −1)d p . (8) 1 T 1 t t=1 The lender has perfect information about the agent’s probability of default and so loan contracts areactuarially fair. Our problemis consistent withtheories of default, asstandardized by Chatterjee et al. (2007). In contrast to their paper, we have features specific to the privatemarketforstudentloansrequiringthatourpricingmechanismbeslightlydifferentfrom thoserepresentingcreditcardmarkets. Forexample,onlyindividualswhogotocollegehave access to this market and they make borrowing decisions during college. Recall that this is one-timedecisionandindividualsdonotgobacktocollegelaterinlife. Therefore,thecreditor in the private student loan market solves his optimization problem at the beginning of the model when borrowing in the private market takes place. In other words, the expected presentvalueofcash-flowsiszero,discountingattherisk-freerate. Let Φ (Dp, f) be the set of all agents of type f who decide to go to college and take out p privateloansofsizeDp fortheentirecollegeperiod,suchthat: Φ (Dp, f)={k∈B×A×F |VC(k)≥VN(k),Dp(k)=Dp and f(k)= f}. p Recall that loan repayments start in the first period after college, t = T +1. The expected 1 presentvalueofprofitsforeach(Dp, f)-typecontractisgivenby: ∑ k∈Φp(dp,f) (cid:110) ∑ t T = 2 T 1+1Rt 1 −1 (1−ωp(d 1 p ,...,d T p 1 ,f,t)) (cid:104) p t p (d 1 p ,...,d T p 1 ,f,Rp) (cid:105)(cid:111) −(1+q)∑ t T = 1 1R d t− t p 1 .(9) Profits for each type of contract (Dp, f) depend on the expected present value of repayment on student loans less total debt owed to the private creditor. The first term of equation (9) represents the expected present value of total payments made by all agents of type f who borrowed Dp from the private market for the entire college period and who do not default on their loans in period t during the repayment phase. Recall that the per period payment aftercollegeisgivenby p p ((dp, f,Rp)∈{p p ((dp, f,Rp),0}where p p ((dp, f,Rp)represents t t t the fixed payment due each period, which in turn depends on the size of the loan, dp, the interest rate, Rp (which in turn depends on the credit type f), and the duration of the loan, T . There is no payment during the period of default; that is, if default occurs in period 2 t, p p (k) = 0. The term ωp(dp, f,t) in equation 9 represents the probability that an agent t of type f with the size of the loan dp defaults on his loans at time t.24 Also recall that defaulters enter repayment in the period after default occurs. Therefore, the private creditor 24Thisprobabilityofdefaultalsodependsontherealizedshockstoearningsinperiodt. Foreaseofexposition,however,wesuppressthisnotation. 20

collects repayments every period until the loan is paid in full from all participants in the privatemarket,includingdefaulters(exceptfortheperiodwhendefaultoccurs). Thesecond term ofthe equation representsthe present value oftotal debt owedto the private creditorin periodT +1andthetransactioncostfacedbytheprivatecreditor,qdp. 1 TosolveforRp(dp, f),wefirstnotethatweknowhowlargethepaymentsneedtobefor thelendertobreakevenandsoasimpleapplicationoftheannuityformuladeliversthat: 1−Rp(−T 2 −T 1 ) Dp(d p ,...,d p ,Rp)= pp(d p ,...,d p , f,Rp)( ). (10) 1 T 1 1 T 1 Rp−1 Then, to get from the zero profit condition to the contract-specific interest rate we use equation 10 and replace Dp determined by equation 8 and pp(·) from the zero profit condition. This results in an equation that can be solved for the interest rate Rp and the solution delivers that the interest rate on private student loans depends on the credit type (f) and the size of the loan (dp). Specifically, optimization implies Rp(dp, f)≤(R+q)(1−ωp(dp, f)) with q being the transaction cost per unit of loan. This modeling feature captures the fact thatdifferentborrowershavedifferentlikelihoodsofdefaultandtheprivatelenderpricesthe loans accordingly. Also recall that credit type may change over time depending on the individual repayment and default behavior. Therefore, the interest rate on private student loans maychangeovertime. 2.7 Government Our policy analysis takes into account the limited size of the government budget. In this economy, the government finances the student loan program through a lump sum tax. We assumethattherearetwolumpsumtaxes: onetofinancethestudentloanprogram(Θ )and 1 onetofinancethemeans-testedtransfersandretirementbenefits(Θ ). Thus,Θ=Θ +Θ . 2 1 2 Related to the student loan program, government expenditures consist of the present value of government student loans and the subsidization of interest rates on government student loans during college. The government borrows in the risk-free capital market at the interest rate R. The interest rate on government student loans (set to the data) is greater than the risk-free interest rate. The revenue from the repayment of government student loans is usedtocoverthecostsassociatedwithsubsidizinginterestduringcollege. As in practice, the government does not collect any repayment from defaulters during the period when default occurs. Loan collections may not suffice to cover the interest rate subsidizationduringcollege. Tobalancethebudget,thegovernmentcollectstaxestofinance the remaining cost. Lump sum taxes are paid by all consumers in the economy during each 21

periodintheworkingphases(phases2and3inthemodel). As before, let Φ (dg)⊆X be the set of all agents who decide to go to college and take g outgovernmentstudentloansofsizedg eachperiodduringcollege: Φ (dg)={k∈A×B× g F |VC(k)≥VN(k)anddg(k)=dg}.Thegovernmentbudgetconstraintisgivenby (cid:32) (cid:33) (cid:34) (cid:35) (cid:34) (cid:35) T T T 1 1 2 1 3 1 ∑ ∑ dg = ∑ (1−ω g) ∑ pg + ∑ ∑ Θ . (11) Rt Rt−1 Rt−1 1 k∈Φg(dg) t=1 k∈Φg(dg) t=T 1 +1 k∈X t=T 1 +1 Equation11representsalifetimegovernmentbudgetconstraint. Theterminthelefthand side represents the present value of loans. The right hand side consists of the present value ofrevenues,whichincludesloanpaymentsfromindividualswhotookoutgovernmentloans and do not default on their loans, and lump sum taxes, Θ , collected each period during the 1 working phase from all agents in the economy. Recall that loan repayment starts at period t =T +1 and there is no interest accumulated on government student loans during college. 1 Asinthecaseofprivateloans,theperperiodpaymentisgivenby p g (k)={pg(dg),0}where t pg(dg) represents the fixed payment due each period, which depends on the size of the loan dg,thedurationoftheloan,T ,andthefixedinterestrate,Rg. Also,inthecasewheredefault 2 occurs in periodt, p g =0. The term ωg in equation 11 represents the probability of default t in the government program. Separate from the student loan market, the government collects lumpsumtaxesΘ andpaysmeans-testedtransferstoallagentsduringtheirworkingphases 2 of life, and issues retirement benefits φy during the retirement phase. We assume that T 3 the revenues and expenses associated with these government programs must also balance in equilibrium.25 2.8 Equilibrium Our general equilibrium analysis is consistent between individual decisions and decisions madebythegovernmentandfinancialintermediariesintheprivatemarketforstudentloans, such that interest rates in the private market arise from zero-profit conditions in equilibrium and taxes are set so that the government budget constraint balances. This formulation captures the interaction between the private and the government market for student loans (cid:104) (cid:105) 25 The budget constraint associated with these programs is given by ∑ k∈X ∑ t T = 4− T3 1 R 1 t φy T3 (k) + (cid:104) (cid:105) (cid:104) (cid:105) ∑ k∈X ∑ t T = 3− T1 1 R 1 t τ(k) =∑ k∈X ∑ t T = 3− T1 1 R 1 t Θ 2 . 22

alongside the pricing of default risk in equilibrium, both of which are essential for our analysis. Definition 1. An equilibrium in this economy is a collection of: i) individual choices: educationlevelh,consumptionc,savingss(cid:48);defaultanddebtpaymentsinthepublicandprivate market of student loans, {ωg,ωp,pg,pp,dg,dp}; ii) credit type f; and interest rates in the private market for student loans {Rp(f)}; given earnings y(h,a,z,ε), intra-family transfers Q(b), the risk-free rate and the government student loan rate{R,Rg}, and policy parameters {τ,d φ,Θ ,Θ }suchthat: max, 1 2 1. Agentssolvetheirdynamicprogrammingproblem(outlinedinSection2.5.2). 2. Thegovernmentbudgetconstraintshold(equation11). 3. Theprofitsoftheprivatecreditorsforeach(dp, f)-typecontractarezero(equation9). Therearetwoimportantcommentsworthmentioninghere. First,wefollowAthreya(2008) andkeeptherisk-freeinterestrateexogenous. Second,weabstractfromdeliveringwages fromalabormarketconditioninequilibrium. Endogenizinglabormarketsisnotcrucialfor theanalysisandwillincreasethecomputationintensitygiventhehighdimensionofthe statespaceandthenumberofperiodsintherepaymentphase.26 Thefirststepofthealgorithmsupposesthatonthecollegepath,theagent x∈X=B×A×F maximizesutilitybychoosing{h,c,s(cid:48),pg,pp,dg,dp, f},takinginterest ratesandearnings{R,Rg,Rp(f),y(h,a, f,z,ε)},utilitylosses{µg(f),µp(f)},probability ofcompletingfouryearsofcollegeπ(a),andpolicyparameters{τ,d ,Θ ,Θ }asgiven. max 1 2 Theset{VC(s,t),VC(h,a,s,z,ε,t),VC(h,a, f,s,dp,dg,z,ε,t),VC(a,b, f,t)}containsthe 4 3 2 1 associatedvaluefunctions. Ontheno-collegepath,theagentx∈X maximizesutilityby choosing{c,s(cid:48)}andtakingtherisk-freeinterestrateandearnings{R,y(h,a, f,z,ε)}as given. Theset{VN(s,t),VN(h,a,s,z,ε,t),VN(h,a,s,z,ε,t),VN(a,b, f,1)}containsthe 4 3 2 1 associatedvaluefunctions. Lastly,theagentoptimallychoosesbetweenthecollegeand no-collegepaths(equation7). Ourmodeldeliversinequilibriumthatindividualswithbad creditarechargedhigherinterestratesintheprivatestudentloanmarketthanindividuals withgoodcreditforanysizeofloan,consistentwithevidencefordefaultpricinginthe creditcardmarketprovidedinMustoandSouleles(2006). 26Our model therefore has limited scope for the analysis of the relationship between default behavior and labormarketconditions. However,thisisaninterestingavenuetopursueinlightofthetrendsindefaultrates duringandafterthefinancialcrisiswhenborrowersfacedworsejoboutcomes(seeFigure2intheAppendix). 23

3 Calibration Each model period represents one year, and agents live for 58 years (T =58), which corresponds to 18-76 years of age. On the college path, the first phase (college) lasts four years (T =4). Theyoungadult/repaymentphaselasts10years(T =14),thematurityphaselasts 1 2 24years(T =38),andtheretirementphaselasts20years(T =58). Ontheno-collegepath, 3 4 the young adult and maturity stages last 38 years and retirement lasts 20 years. The model parameterscapturethebehaviorofhighschoolgraduateswhoenrollincollegein2003;thus, themodeleconomyiscalibratedtotheyear2003. Allvaluesaregivenin2003dollars. There are four sets of parameters that we calibrate: 1) standard parameters, such as the discount factor, the coefficient of risk aversion, and the risk-free interest rate; 2) parameters for the initial distribution of individual characteristics: family contributions for college, credittypeandability;3)parametersspecifictoeducationandstudentloanssuchas,college costs, tuition, borrowing limits, default consequences, and interest rates on student loans; and 4) parameters for the earnings dynamics of individuals by education and ability groups. Our approach includes a combination of setting some parameters to values that are standard in the literature, calibrating some parameters directly to data, and jointly estimating the parameters that we do not observe in the data by matching moments for several observable implicationsofthemodel. There are several sources of data that we use to calibrate the economy. For earnings profiles, we use the Current Population Survey (CPS) 1968-2002 and National Education LongitudinalStudy(NELS:1988). WealsousetheNELS:1988forenrollmentrates.27 Inaddition, we use several other data sources to test the predictions of the model across different groups of individual characteristics, namely the Beginning Postsecondary Student Longitudinal Survey (BPS) 2004/2009, the Credit Panel Equifax data, and the Survey of Consumer Finances data. A detailed description of all these data sets, the samples used and the computedmomentsareincludedintheAppendix(Section7.1). We assume constant relative risk aversion in the utility function such that u(c) = c1−σ 1−σ with σ =2. We set the risk-free rate (R) at 4 percent. In what follows, we discuss in detail the parametrization of the initial distribution of individual characteristics, the parameters specifictothestudentloanmarket,andearningsdynamics. Lastly,weexplaintheestimation 27MorerecentdataforenrollmentratesacrossexpectedfamilycontributionsandSATgroupsarenotavailable. For our purpose, the use of this enrollment dataset is suitable: enrollment behavior for full-time recent high schoolgraduates has notchanged significantlybetween 1992 and2003. According to NPSASdata, the enrollmentrateforrecenthighschoolgraduatesin2003is67percent;oursampledeliversanenrollmentrate of65.6percent. 24

strategy for the remaining nine parameters and discuss the fit of the model when matching thetargetsinthedata. Table1: Exogenousparameters Parameter Name Value {T,T ,T ,T ,T } Modelperiodsandphaselengths {58,4,14,38,58} 1 2 3 4 σ Riskaversion 2 R Risk-freeinterestrate 4% µ Meanability(SATscores) 1016 a σ Stdevofability(SATscores) 226 a µ Percentwithgoodcreditscores 0.75 f ρ Correlationbetweenincomeandcreditscores 0.30 bf ρ Correlationbetweenincomeandability 0.35 ba ρ Correlationbetweenabilityandcreditscores 0 af π(a) Probabilityofcompletingcollegebyability {0.60,0.72,0.845} d Netpriceforoneyearofcollege $52,140/4 d Borrowinglimitingovernmentstudentloans(forfouryearsofcollege) $23,000 max Rg Interestratesinthegovernmentstudentloanprogram 6.8% q Transactioncostintheprivatestudentloanmarket 0.05 α Percentchancethatbadcreditimprovestogoodcredit 0.10 3.1 Initial Distribution of Characteristics For family contributions for college, we consider a uniform grid, B = [0,...,$28,500]. For initial credit type, we consider two types: bad and good credit. We measure ability level by SATscoresandconsiderthreegroupsofSATscores: A={<900,900−1100,1101−1600} onthe1600-pointtest. Weestimateajointdistributionofexpectedfamilycontributions(b),credittype(f),and ability(a)accountingforcorrelationsbetweenallthreecharacteristics. Thesecharacteristics aredrawnfromadistributionwithmoments(µ ,σ ,µ ,σ ,µ ,ρ ,ρ ,ρ )where µ isthe b b a a f ba bf af i mean, σ represents the standard deviation for i=b,a, µ is the probability of having good i f credit,andρ thecorrelationcoefficientsofb, f,anda. ij Inourmodel,abilityrepresentscollegepreparedness,whichembodiesbothinnateability and acquired ability. Thus, we directly consider a measure of ability that reflects college preparedness: for the distribution of ability, A(a), we assume a normal distribution and use thenationaldistributionofSATscorestosetµ =1016andσ =226(CollegeBoard,2007). a a Ourcalibrationprocedureconsidersallhighschoolgraduateswhointendtogotocollegeand take the SAT. This allows us to better capture the effects of government and private student 25

loan policies on college investment decisions. At the same time, our procedure recognizes thatcollegepreparednessmattersforcollegeinvestment.28 ToestimatethedistributionofcredittypeF(f),weusetheSurveyofConsumerFinances (SCF) and the FRBNY Consumer Credit Panel (Equifax) data. In the SCF data, we define individualswithbadcreditas20to30yearoldrespondentswhoreportthattheywereturned downforcreditordidnotgetasmuchcreditastheyappliedforbasedontheircredithistory (or lack thereof). The 2001 and 2007 SCF data indicate that 75 of young adults have good credit, while 25 percent have bad credit. Thus µ = 0.75. This distribution is consistent f with the Equifax Risk Score in 2001 Equifax data, where young individuals with bad credit are subprime borrowers who have an Equifax Risk Score below 560, while those with good credithaveanEquifaxRiskScoreabove560. Expectedfamilycontributions(EFC)areagoodpredictorforactualfamilycontributions forcollege,butEFCestimatesvaryacrossvarioussurveysanddifferencesmayarisebetween EFC and actual family distributions.29 Therefore, we take the following approach in calibrating EFC and accounting for actual contributions during college. Given the importance ofEFCforreceivingstudentloansinbothmarkets,weestimatemomentsofthedistribution forexpectedfamilycontributions(µ ,σ )suchthatourmodelmatchesparticipationratesin b b the government and private student loan markets (45 percent and 17.5 percent, respectively) rather than assuming an exogenous distribution. In addition, we recognize that differences between EFC and actual family contributions may arise and allow for intra-family transfers during college, Q(b), in addition to EFC and we jointly estimate these transfers to match college enrollment rates by family contributions for college. Details on the estimates are providedinSection3.4. Wesetthecorrelationsbetweenallthreeinitialcharacteristics(b, f,a)asfollows. Based on Equifax and Census block data, the correlation between credit scores (identified as the Equifax Risk Scores) and income is ρ = 0.3. In addition, data suggest a strong positive bf correlation between SAT scores and parental income (College Board, 2009). We therefore assume ρ = 0.45, which is in the middle of the estimates (Ionescu, 2011). We assume ba ρ =0becausethereisnodatathatlinksabilitytocredittype. af 28WhileothermeasuresofabilitysuchasArmedForcesQualificationTest(AFQT)scoresmaybeused,SAT scoresrepresentamoreappropriatemeasuresincewefocusonstudentswhointendtogotocollege. 29TheU.S.DepartmentofEducationcalculatesEFCforstudentsusinganeedanalysismethodologywhich takesintoaccountdependencystatus,income,assets,numberofsiblingsincollege,andotherrelatedfactors. Theformulaisdesignedtocomparetheability-to-payacrossfamiliestopromotetheequitabledistributionof availableaid. 26

3.2 College and Student Loan Parameters We use 2003 college enrollment data from the BPS to set the probabilities of completing four years of college across ability groups. We consider only students who enroll without delayinafour-yearcollegefollowinghighschoolgraduation. Becausewedonothaveparttime enrollment in the model, we consider students who enroll full-time in college. The surveyrecordsthefraction ofstudents(byability)who,six yearslater,reporthavingearned a bachelor’s degree. We use these as proxies for the probability of completing college π(a). Weobtaincollegecompletionratesof{0.60,0.72,0.845}acrossthethreelevelsofability. We calibrate the cost of college to academic years 2003-2004 through 2007-2008. The net price of college for these years, which is total student charges (tuition, fees, room, and board) net of grants and education credits was $33,849 for public universities and $78,570 forprivateuniversities,asreportedbytheCollegeBoard(2007). Sincecollegeismodeledas aconsumptiongood,wemustalsocalculatethetotaldirectcostofcollegeintermsoftuition and fees. Total tuition and fees for four-year private and public colleges were $98,584 and $20,925,respectively,usingthesameCollegeBoarddata. Tomatchtheactualcostsofattendingfouryearsofcollege,weuseBPSdataondrop-out and completion rates for the cohort of students starting college in 2003-2004 who obtained their bachelor degree by 2009. Approximately 55.6 percent of students completed a fouryear degree (59.1 percent of these students attended a public institution and 40.9 percent a private institution). Using these weights, the average net price for four years of college is $52,140. Theaveragedirectcost(tuitionandfees)usingthesameweightsis$52,687. Thelimitson(Stafford)governmentstudentloansfordependentundergraduatesis$23,000 for up to five years of post-secondary education. Dependent students who enroll in college are eligible for $2,625 in the first year, $3,500 in the second year of college, and $5,500 in additional years. Limits in the private market for student loans are set by the creditor and do not exceed the cost of college less any financial aid the student receives, including government student loans. Interest rates in the government student loan program are fixed at 6.8 percent, which is consistent with the 2004-2008 period. Recall that interest rates in the private market are derived in equilibrium such that the creditor earns zero profits across levelsofcredittypeanddebt. Weconsiderthreelevelsofdebtintheprivatemarketforeach credittype. Thethreeloansizesare: below$5,700,between$5,700and$10,700,andabove $10,700. We assume that the transaction cost in the private student loan market is the same as in the credit card market, and set q=0.05 as in Li and Sarte (2006), close to the cost of servicingcreditcardaccountsof5.3percentfoundinEvansandSchmalensee(1999). 27

We calibrate the default punishments to match the default behavior in the data, as explained in Section 3.4. In addition, when default occurs in the private market, credit type is penalized: individuals will have bad credit following default. In the case of no default, we assume that there is a 10 percent chance that bad credit improves to good credit (α =0.1). This is consistent with estimates in Livshits et al. (2007) and Chatterjee et al. (2011), and mimics the fact that in practice, having bad credit remains on your credit report for a while (e.g.,10years). 3.3 Earnings Our earnings estimation consists of the following steps. First, we use 1969-2002 CPS data toestimateage-earningsprofilesfordifferenteducationgroups. Second,weuseNELS:1988 data to determine the fixed effect of SAT scores on earnings. Third, we use SCF data to determine the fixed effects of credit type on earnings. Lastly, for the stochastic component ofincome,wefollowHubbardetal. (1994). First, for the age-earnings profiles by education groups, we generate synthetic cohorts for each year in the CPS by using earnings for heads of households age 25 in 1969, age 26 in 1970, and so on until age 58 in 2002. We consider a five-year bin to allow for more observations,i.e.,byage25at1969,weincludehighschoolgraduatesinthesamplethatare 23to27yearsold. Weincludealladultswhohavecompletedatleast12yearsofschooling. Peoplewith16and17yearsofeducationareclassifiedaspeoplewithfouryearsofcollegein the model. For individuals with some college in the model, we estimate earnings for people with more than 12 years but less than 16 years of education in the data. For people who do notgotocollege,weusetheearningsofpeoplewith12yearsofeducation. Second, the calibration of λh (the ability fixed effect from equation 4) is challenging a because of the lack of data needed to distinguish between the independent effects of ability –asmeasuredbySATscores–andeducation. WefollowChatterjeeandIonescu(2011)and use the NELS:1988 dataset. We group students into our three education groups and terciles of ability and compute mean earnings for students who are five years out from the year they acquiredtheirhighestdegreeandareemployedfull-time.30 Theresultingparametersforthe three ability levels are: 0.99, 1.01, and 1.01 for high school graduates; 0.99, 1.08, and 0.95 for individuals with some college; and 0.94, 1.02 and 1.11 for college graduates. We then usetheseestimatestocomputethemeanearningsofeachability-educationgrouprelativeto 30WedidnotwantearningsofstudentswithverylowandveryhighSATscorestooverlyaffecttheresults of their respective groups. We employed a 1 percent Winsorization with respect to SAT scores to reduce the sensitivityofgroupearningstooutliers. 28

themeanearningsofitseducationgroup. Ourcalibrationisconsistentwithempiricalevidenceshowingindividualsofhigherabilitylevelsexperiencinghigherreturnstotheireducationinvestment(RosenandWillis,1979; Heckman and Vytlacil, 2001; Cuhna et al., 2005). An important question is whether these returns are due to the innate ability of the individual, the quality of the high school these individuals attend before college, the quality of college itself, or family characteristics. In our case, we directly consider a measure of ability that embodies both innate ability and acquired ability because we think of ability as college preparedness. Empirical findings show thatreturnstoschoolingaremostlydrivenbytheabilityofthestudentratherthanthequality of the school (Dale and Krueger, 1999). In addition, Bound, Lovenheim and Turner (2009) document that the average number of years of college for people with a bachelor’s degree is 5.3 years. Thus, the college degree premium implied by our estimation delivers an average return per additional year of college education of roughly 14 percent, which is consistent with estimates in the literature (Willis, 1986; Restuccia and Urrutia, 2004). Furthermore, our estimates suggest that the premium from completing four years of college relative to no collegeincreasesinSATscores,butatadecliningrate. Third,todeterminethefixedeffectsofcredittype(λh inequation4),wefollowthesame f procedure as the one used in determining ability fixed effects. Specifically, we use SCF data and compute the mean earnings of each of our credit-education groups relative to the mean earnings of its education group. The resulting parameters for the two credit types are λh = {0.95,1.06} for high school graduates and λh = {0.8,1.06} for those with a college f f education.31 Lastly, in the parametrization of the stochastic idiosyncratic labor productivity process, we follow Hubbard et al. (1994) whose estimates use after-tax and transfer income, and also feature a shock-structure for earnings that is now standard. They report the following values for high school graduates: ρ =0.95, σ2 =0.021, σ2 =0.025, and σ2 =0.5; and for ε ν ξ college graduates: ρ = 0.95, σ2 = 0.021, σ2 = 0.014, and σ2 = 0.5. We use the first set ε ν ξ of values for people with no college, h , and for those with some college education, h=h , 0 2 andthesecondsetofvaluesforindividualswhocompleteacollegedegree,h=h . Wehave 4 approximatedtheseprocessesastwo-stateMarkovchains,normalizingtheaveragevaluefor theidiosyncraticshockto1. TheresultingsupportsarethesetsZ0/2={0.9285,1.0715}and Z4 ={0.9314,1.0686}. 31Note that we group college drop-outs together with college graduates because of the small number of observationsforcollegedrop-outswithgoodcredit. 29

3.4 Parameters estimated within the model We jointly estimate nine parameters in the model (reported in Tables 2 and 3): the default penalties for government and private loans, the mean and standard deviation from the initial distribution of expected family contributions, the discount factor, and the average amount of transfers across terciles of expected family contributions for college. These parameters are set to match the following targets: the national two-year cohort default rates in both the governmentandprivatestudentloanmarketsin2008(7percentand3.3percent),theratioof defaultratesforbadandgoodcredit(12.5:1ratio),participationratesinthegovernmentand private student loan market (45 percent and 17.5 percent, respectively), college enrollment ratesacrossincometerciles(Table3),andthewealth-to-incomeratio(3.3). Table2: ModelPredictionsvs. Data Parameter Name VariablesTargeted Data Model µg(f =0) Defaultpenaltyforbadcredit-govt Defaultrateingovtmarket 7% 7% µp(f =0) Defaultpenaltyforbadcredit-private Defaultrateinprivatemarket 3.3% 3.1% µ(f =1) Defaultpenaltyforgoodcredit Ratioofdefaultrates 12.5 11 µ Meanoffamilycontribution Participationingovtmarket 45% 48.2% b σ St. dev. offamilycontribution Participationinprivatemarket 17.5% 17.8% b β Discountfactor Wealth-incomeratio 3.3 2.95 Q(b) Transfersbytercilesoffamilycont Collegeenrollmentrates seeTable3 i Table3: CollegeEnrollmentRatesbyFamilyContributions Collegeenrollment Data Model Lowb 52.5% 52.7% Mediumb 65.5% 65.8% Highb 78.5% 78.3% To estimate these parameters, we start with an initial guess of the nine parameters and implement the following algorithm: 1) we first solve for the decision problems for each education path; 2) we endogenize the college decision as well as the borrowing decisions in the government and the private markets; 3) we iterate until the profit conditions for each contract type and the government budget constraints hold; and 4) we simulate the economy andcomputetheninemomentstargetedinthecalibration,averagingthevaluespredictedby the model over 500 economies. We repeat these four steps until the distance between the model and data is minimized and delivers estimates for the nine parameter values as well as thepredictionsofthemodelforstatisticsnottargetedinthecalibration.32 32Notethatwemaptheestimatedparameterstoobservableimplicationsofthemodel. However,thereisno one-to-onemappingsoparametersarejointlyestimated. 30

Weobtain adiscountfactorof 0.9627tomatch theratioofmean wealthtomean pre-tax income provided in Heathcote et al. (2010).33 We allow utility losses µi(f) to differ across the government and private markets for individuals with bad credit and set these costs equal forindividualswithgoodcredit, µp(1)=µg(1). Ourestimationstrategyismotivatedbythe factthatthereareimportantdifferencesintheconsequencesofdefaultingongovernmentstudent loans and defaulting on private student loans. Recall that the consequences for default on government loans include wage garnishments, seizure of Federal tax refunds, possible holds on transcripts and ineligibility for future student loans, all consequences that are absent in the private student loan market.34 One challenge in the calibration of default costs to match default behavior is that we observe aggregate default rates for each market (from the U.S.DepartmentofEducationreleasesandSallieMaesurveys)butnotacrossindividualsof different credit types. In addition, we observe various measures of delinquency rates across individuals of different credit types but for both government and private student loans together (from Equifax data). To overcome these issues, we construct our own measure of the default rate (in Equifax data) as follows: we use the measure for 120+ days delinquency for studentloansandfurtherrestrictittoindividualswhoreportbeingdelinquentforatleasttwo quartersinayear. Thismeasureistheclosestonetothenationaltwo-yearcohortdefaultrate for student loans (which is based on 270+ days). As illustrated in Figure 2 in the Appendix, the two measures match up quite well. Using these measures, we have three moments to match for default behavior: the average two-year cohort default rate for government student loans in 2008 (7 percent), the two-year default rate for private student loans in 2008 (3.3 percent), and the ratio between the delinquency rate for bad credit and the delinquency rate for good credit in 2008 (12.5:1).35 We obtain the utility cost for default for individuals with bad credit in the government student loan market µg0)=0.00991 and in the private market µp(0)=0.00766. Forindividualswithgoodcredit,theutilitycostisµg(1)=µp(1)=0.013. Our estimates imply that individuals with good credit have a higher cost associated with default,whichisconsistentwiththeliterature,andthatdefaultingongovernmentloansmaybe morecostlythandefaultingonprivateloans(apartfromthenegativeconsequencesoncredit 33ThisestimateisbasedontrimmedSCFdatawhichisconsistentwithouruseoftheCPSintheearnings calibration. 34State affiliated private lenders may also garnish wages. However, a court order is needed for this action andwagegarnishmentfordefaultonprivatestudentloansislimitedinpractice. 35Weusethedefaultratefor2008tobeconsistentwiththecalibrationofthecollegephasebetween2003- 2007. Recallthatborrowersneedtostartrepayingtheirloanssixmonthsaftertheyfinishcollege. The2008 two-year cohort default rate represents the fraction of borrowers who entered repayment in FY2008 and defaulted by the end of FY2009. In the model, this is the sum of default during the first two periods of the repaymentphase. 31

type),whichisinlinewiththedefaultconsequencesimplementedinthetwomarkets. We estimate moments of the distribution for family contributions (µ ,σ ) to match parb b ticipationratesinthegovernmentandprivatestudentloanmarkets. Weobtainµ =$17,700 b and σ = $6,900. The participation rate in the government market is consistent with estib mates from the U.S. Department of Education (2008) and Wei and Skomsvold (2011) who reportthatbetween42to45percentofundergraduatesin2003-04borrowedfromthegovernmentstudentloanprogram. Estimatesfortheprivatemarketforstudentsloansaremoredifficulttoobtain,asschoolsarenotrequiredtoreportthisinformation. SteeleandBaum(2009) report that, in 2007-08, 19 percent of undergraduates borrowed from nonfederal sources, while the survey from Sallie Mae reports that 14 percent borrow from private sources (for thesameyears). Wechoose17.5percentasatarget. Finally, we estimate intra-family transfers during college, which is in accordance with research that shows that there is risk-sharing for young adults within a range of networks including families, friends, firms, and unions (Johnson, 2010; Kaplan, 2012). We estimate thesetransferstomatchcollegeenrollmentratesacrosstercilesofexpectedfamilycontributions, based on NELS:1988 data. As evidenced by Table 2, the model does a good job in matching these moments. The model delivers intra-family transfers that increase by family contributions: $12,945, $13,347, and $13,923. These estimates imply that students from higher income groups have extra funds available, funds which are not captured by expected familycontributions. As shown in Tables 2 and 3, the model does well in matching the targeted moments. In addition, we compare and discuss our model predictions to the data on a variety of nontargetedmomentsinSection4.3. 4 Benchmark Results In this section, we analyze the benchmark economy and study how credit risk interacts with other characteristics — namely, family contributions and student ability — to affect the collegeinvestmentdecision. Weevaluatetherelationshipbetweenthegovernmentstudentloan programandtheprivatemarketforstudentloans,andstudytheimplicationsofthisrelationship for college investment, borrowing, and default behavior across individual characteristics. We then assess the performance of our model by comparing our results to observed patternsinthedata. Before presenting the quantitative predictions of the model, we describe the economic intuition behind college enrollment, borrowing, and repayment decisions in our economy. The structure of our model is such that individuals who enroll in college will first use their 32

ownassetstofinancecollege,thengovernmentloans(thatarebasedoninitialassetsb)and,if therearestillcollegecoststocover,theywillborrowprivateloans(basedonbothbandcredit type f). Atthesametime,ability,credittype,andreturnstocollegearepositivelycorrelated. Given the logic of our model, individuals will self-select into college and then decide how to finance their college education. For instance, individuals with low ability will not go to college if they have few assets and/or their credit type is bad. Individuals with enough assets and high ability will chose to attend to college. Those with high ability and median assets will use both their own resources and government loans to finance college. Finally, individuals with high ability and low assets will use all three sources of funds, regardless of their credit type. Thus, credit type and the private student loan market are relevant for the firstandlastsetofagents. Turning to the quantitative predictions, our economy delivers results that are consistent with the data. First, the college enrollment rate is 65.6 percent and the four-year college completion rate conditional on enrolling in college is 74.8 percent (compared to 65.5 and 74.9 percent in the data, respectively). This implies that 49.1 percent of agents in the model haveafour-yearcollegedegree. Second,individualsinthemodelborrow$13,227onaverage to finance college: $8,157 from the government and $5,070 from the private market.36 The amount borrowed from the government is close to the estimates of $8,859 (in 2003 dollars) from Wei and Skomsvold (2011) for 2003-04. About 40 percent of borrowed funds is from theprivatemarketforstudentloans,whichisconsistentwiththeCollegeBoard(2009). Furthermore, interest rates in the private market decrease with individual credit type, which depends on default behavior. Specifically, the model delivers no default in the private market for individuals with good credit, but positive default that increases in the amount of debt for individuals with bad credit. Our model yields a 9 percent interest rate for all debt contractswithgoodcreditandinterestratesbetween10.1and12.1percentfordebtcontracts with bad credit; notice that for the latter, interest rates increase with the size of the loan. Our predictions about interest rates are consistent with several key facts. First, interest rates are higher on private loans than in the government student loan program (which are fixed at 6.8 percent). Second, individuals with bad credit face higher interest rates than individuals with good credit. And third, interest rates increase with the loan size, conditional on having bad credit. An important observation is that interest rates in the private market may be a bit lower than those in the data. This discrepancy is because the recovery rate in the model is 100percentandthusdefaultriskisrelativelysmall,whereasinrealitytherecoveryratemay 36Recallthat48percentofstudentswhogotocollegetakeoutstudentloanstofinancecollegeeducation. 33

belessthan100percent,althoughstillhighgiventhenon-dischargeabilityoftheseloans.37 The importance of the private market for student loans as a source of financing college suggests that credit type may have an important quantitative effect on college investment, in addition to family contributions and ability. Such an effect is exactly what we find, as we describebelow. 4.1 Importance of family income and ability Table 4 presents the model’s predictions regarding college investment, borrowing, and defaultbehaviorforstudentswithdifferentlevelsofexpectedfamilycontributions,ability,and credittype. Wereportcollegeenrollmentrates,thepercentofagentswithafour-yearcollege degree,38 debtlevelsanddefaultratesinbothstudentloanmarkets. The model predicts that poor individuals (in the bottom tercile of family contributions) need to borrow much more than wealthy individuals. Notice that students in the top onethird of family contributions do not borrow from the private market and borrow little from the government. However, low- and middle-income students rely on both the government and the private student loan market. Poor individuals take on the most student loan debt (approximately $16,758 in both markets, on average). Recall that these individuals experiencerelativelylowreturnstocollegeinvestmentgivenapositivecorrelationbetweenability and income, and between ability and earnings. The combination of high student loan indebtedness and low lifetime earnings leads to high default rates for this group, as Table 4 shows. Wealsofindsignificantdifferencesincollegeinvestmentandborrowingbehavioracross abilitytypes. Thepositivecorrelationwithabilityandcollegeenrollment,asobservedinthe data,isdrivenbythetrade-offbetweenthereturnstocollege(whicharepositivelyrelatedto ability) and the financial need for loans (which is negatively related to ability).39 An interestingresultisthatdefaultpatternsacrossabilitylevelsarequitedifferentinthegovernment market compared to the private market for student loans. As illustrated in Table 4, lowability individuals have high default rates in the government market and low default rates in theprivatemarketforstudentloans,whereastheoppositeistrueforhigh-abilityindividuals. The economic intuition behind this result is as follows. The disutility of defaulting in the private market is lower than the disutility of defaulting in the government market (which is 37Precisedataonrecoveryratesforprivatestudentloansarenotavailable. 38The latter consists of multiplying the enrollment rates (which are endogenous in the model) by college completionrates(whichareexogenous). 39Table6inSection4.3deliversallofthedatacounterpartsforthemodel. 34

Table4: BenchmarkResults College Percentwithafour-year Averagedebt Defaultrates enrollmentrate collegedegree (govt/private) (govt/private) Familycontributions(b) Low 52.7% 36.6% $9,885/$6,873 15.7%/1.2% Medium 65.8% 49.0% $10,165/$1,138 5.4%/7.1% High 78.3% 61.9% $4,401/$0 0.6%/NA Abilityofthestudent(a) Low 50.3% 30.2% $9,161/$6,403 14%/0.7% Medium 53.3% 38.4% $8,586/$5,008 6.9%/0.9% High 93.7% 79.2% $7,372/$3,616 3.5%/8.5% Credittype(f) Bad 53.7% 40.6% $8,800/$5,775 23.9%/11.3% Good 69.6% 52.0% $7,969/$4,806 2.1%/0% Note:Forfamilycontributions,thelowgrouprangesfrom$0-$14,997,themediumgroupfrom$14,998-$20,957,andthehighgroupover $20,958in2003dollars. Forability,thelowgrouphasSATscoresthatarelessthan900,themediumgroupfrom900-1100SATscores, andthehighgroupover1100.Recallthatthecollegecompletionratesbyaarecalibratedtothedataandthecollegeenrollmentratesbyb weretargetedinthecalibrationprocedure.Forcredittype,thebadgrouprepresents25percentandthegoodgroup75percent. an estimation result). This feature alone would induce borrowers to default at higher rates in the private market for student loans. However, default in the private market triggers exclusion from borrowing in the unsecured credit market. For low-ability borrowers, access to credit markets is quite valuable. For them, the negative impact on credit risk resulting from defaulting on private student loans is costly and the difference between the disutility levels from defaulting in the two markets is not large enough to compensate for less access to credit. As a result, low-ability individuals would rather default on government loans than private loans. In contrast, for high-ability borrowers, exclusion from credit markets is not too costly, and therefore the difference in disutilities of default in the two markets is sufficiently large to make high-ability borrowers prefer to default on private student loans rather than government loans.40 Our results regarding borrowing and default behavior in the two markets for student loans across groups of family income and ability are novel and provide insightsforpolicydesign,whichweexploreinSection5. 4.2 Importance of credit type Inadditiontofamilycontributionsandability,wefindanimportantroleforcredittypeinthe collegeinvestmentdecision. Table4illustratesthatcollegeenrollmentratesare53.7percent 40Thesetrade-offsdonotexcludethepossibilitythatborrowersmayalsoborrowintherisk-freemarketto repaytheirstudentloans. 35

for agents with bad credit and 69.6 percent for agents with good credit. What drives this result? Webelievetherearethreeforcesatplay. First, we document differences in default costs and earnings across individuals of different credit types. Specifically, borrowers with good credit have a higher disutility of default than borrowers with bad credit. Higher default costs may discourage college investment for individuals with good credit, although the effect is small. In addition, borrowers with good credit have higher earnings, on average, than individuals with bad credit, and these differences are larger on the college path than on the no-college path (this is a direct implication of the data, as explained in Section 3.3). Earnings differences encourage college investment forindividualswithgoodcreditrelativetoindividualswithbadcredit. Second,thereisapositivecorrelationbetweeninitialcredittypeandfamilycontributions for college. Given that individuals with high family contributions enroll in college at high rates, this positive correlation works towards increasing college investment for individuals withgoodcreditrelativetothosewithbadcredit. Third, there are differences dictated by institutional details. Credit type is negatively affected when borrowers default in the private student loan market and individuals with bad creditarepenalizedintheiraccesstotheunsecuredcreditmarket. (Notethatourquantitative resultsarelowerboundssincewedonotincorporateallofthemechanismsincreditmarkets that could affect interest rates.) These penalties decrease the incentive to invest in college for individuals with good credit. They have the most to lose from defaulting in the private market: if they default, their credit type will be revised downward and the penalty is longlasting. At the same time, the pricing of private student loans accounts for the individual probabilityofdefaultinequilibrium,afeaturewhichresultsinbetterloantermsforindividualswithgoodcreditrelativetothosewithbadcredit. Asexplainedearlier,theinterestrates faced by individuals with bad credit are significantly higher than the interest rates faced by individuals with good credit. Moreover, the gap in interest rates across credit type increases with the size of the loan as default risk increases, conditional on having bad credit. These differences in loan termsamplify the incentive to invest in college for individuals with good creditanddiminishitforthosewithbadcredit. A natural question arises: How much of the importance of the credit type for college investment is driven by the correlation between initial family income and credit type? And how much is driven by institutional arrangements and differences across individuals with different credit type? To isolate the effects of these channels, we look at college enrollment ratesbycredittypeconditionaloninitialfamilyincome,b(reportedinTable5). 36

Table5: CollegeEnrollmentRatesbyCreditType Familycontributions(b) Low Medium High Credittype(f) Bad 38.5% 63.8% 73.4% Good 60.7% 66.4% 78% Note that there are gaps in enrollment rates by credit type for all terciles of b. More importantly, the gap in college investment between bad and good credit type is larger for the poorest individuals (with low levels of b). The government borrowing limit binds for nearlyhalf ofcollegestudents, andmostnotably forstudentswith lowfamilycontributions. Goodcreditrelaxestherelevanceofthegovernmentborrowinglimit. Studentsinthebottom tercileoffamilyincomearemostlikelytohitthegovernmentborrowinglimitandhavelarger amounts of unmet financial need. They must turn to the private market to finance college. For them, having good credit creates better loan terms in the private student loan market. These findings imply that credit risk is quantitatively important for college investment, and in particular for poor students. This set of results contributes to the literature in showing that credit type is an important dimension to consider when analyzing college investment decisions, in addition to those traditionally studied in the literature (e.g., ability and family income). 4.3 Model Implications and Data Counterparts Before exploring the policy implications of our research, we compare our model to the data and asses how well the model does in capturing the observed behavior along the three dimensions of heterogeneity in our framework (most of which are not targeted in the calibration). In addition, we analyze borrowing and default behavior for different levels of college attainment in the model and the data. Before presenting our findings from the data, it is important to note that there is not a single data source that contains information on family contributions/income, ability, credit type, educational attainment, borrowing and default behavior. Wethereforeusefourdifferentdatasets: BeginningPostsecondaryStudentLongitudinal Survey (BPS 04/09), National Education Longitudinal Study (NELS:1988), Survey of Consumer Finances (SCF) and FRBNY Consumer Credit Panel (Equifax), all of which are described in detail in the Appendix. There are two important points to make: (1) we target only college enrollment rates across different levels of family contributions using NELS data and default rates across credit types from Equifax, a, and (2) none of the data sources fully distinguish between private and public student loans, so at best we can compare our 37

model and its implications to the government student loan market or to aggregate measures ofstudentloanstothoseinthedata. Alloftheothermomentsarenottargeted. Thefindings fromthedataarereportedinTable6.41 Table6: DataCounterpart College Percentwithafour-year Averagedebt Defaultrates enrollmentrate collegedegree (total) (govtonlyunlessnoted) Familycontributions(b) Low 52.5% 24.6% $13,565 11.5% Medium 65.5% 43% $14,734 3.9% High 78.5% 56.5% $11,586 1.5% Abilityofthestudent(a) Low 53% 30% $14,391 6% Medium 65.6% 50.4% $14,269 3.1% High 85.5% 68.7% $13,190 1.3% Credittype(f) SCF/Equifax Defaultforgovt+private Bad 54% 37% $17,312/$15,048 30% Good 57% 50% $11,237/$20,718 1.4% Ourfindingsarebroadlyconsistentwiththedataintermsofeducationalattainment,debt levelsanddefaultratesacrossvariouscharacteristics(compareTable6withTable4). College enrollmentandcollegecompletionincreaseinfamilycontributions,abilityandcredittypein the data, which is what we find in our model. Quantitatively, we do very well in replicating enrollment and completion rates, especially by family contributions and ability. We nearly match college completion rates for individuals with bad and good credit with the data. SCF datasuggestthatcollegeenrollmentrates,however,arenotthatdifferentforindividualswith different credit types (a 3 percentage point different), whereas our model suggests a much higher enrollment rate for those with good credit (a 16 percentage point difference). Much ofthisisduetodifferencesbetweentheSCFdataandthestructureofthemodel(suchasthe timing of credit status and educational attainment, which are described in the Appendix). In themodel,individualsknowtheyfacedifferentinterestrates,whicharebasedoncredittype, whereas in reality students may not fully understand their loan terms at the time they enroll in college. Still, we are satisfied that our model is delivering important features of the data inavarietyofdimensions. In the third column of Table 6, we report average (total) student loan debt. Similar to our model predictions, total student loan debt generally falls in family contributions and 41PleaserefertoTable10intheAppendixforadetailedlistofsourcesusedtoproduceTable6. 38

ability(theoneexceptionisthatdebtisslightlyhigherformiddle-incomestudentsthanlowincome students in the data). As for debt levels by credit type, the evidence is mixed. Debt levelsarelowerforindividualswithgoodcredit,whereasinEquifaxdatathereverseistrue: studentswithgoodcredithavehigherdebtlevelsthanthosewithbadcredit. Thisisprimarily driven by the fact that the debt levels in SCF represent outstanding college debt, while in Equifax they represent outstanding balances at the time when the data was collected (which coincideswithwhencreditscoresarereported).42 Therefore,itislikelytherearesomeother interactions between repayment/delinquent behavior, the credit score, and the outstanding balance in Equifax data. In our model, however, debt represents the amount students walk away from college with and is in line with SCF data. In fact, our model predictions are consistentwiththefindingsfromtheSCF. The last column of Table 6 reports default rates in the government market using BPS data. Importantly, default rates are lower in BPS data than in both the model and Equifax data given the differences in measurements. In particular, given the short time span after entering repayment on student loans, we expect the measure of default in the BPS data to be lower than the measure in Equifax and the overall aggregate number.43 Still, at least qualitatively,defaultratesongovernmentstudentloansfallinincomeandability,consistent withourfindings(recallthatdefaultratesbycredittypearetargetedinthecalibration). Next, we take a close look at constrained borrowers in both the model and the data. Specifically, using BPS data, we compute the percent of student borrowers who borrow the maximum amount from the government; we find that the percent who hit the borrowing limit increases in both ability and family contributions. For example, for individuals in the lowesttercileofincome,36percenthitthegovernmentborrowinglimit,whilefortherichest students,52.5percentborrowthemaximumamount. However,inourmodel,richstudentsdo nothitthegovernmentborrowinglimitsincetheyareborrowingverylittle. Thediscrepancy between the model versus the data is because there is no choice regarding college quality in our model. Given that all agents in our model face the same college costs, our model does notcapturethefactthatthericheststudentsareattendingmoreexpensivecollegesandhence need to borrow more to finance their college education. Certainly, future work could allow foracollegechoicemechanismthatcouldexploitvariationincollegequality. Inaddition,wecomparethemodelpredictionswiththedataintermsofcollegegraduates 42DebtlevelsingeneralarehigherinEquifaxthaninSCF,asdocumentedbyBrownetal. (2014). 43The default question in the BPS is asked in 2009, right after students are out of college with or without a degree (and it is available only for Federal student loans). This measure is not the exact counterpart of our model, which represents a two-year cohort default rate, in line with the official release from the U.S. DepartmentofEducationandourmeasurefromEquifaxdata(asexplainedinSection3). 39

versuscollegedrop-outsgiventhatcollegedrop-outsareanimportantpartofthestorywhen thinkingaboutthepopulationofstudentloandefaulters. Inourmodel,collegedrop-outsare thosewhodonotcompleteafour-yeardegreebytheendofT ;thus,theyincludethosewith 1 a two-year degree. This is consistent with how we define college drop-outs in the BPS data, namely the fraction of students who report not having earned a bachelor’s degree by 2009 and are no longer enrolled in college. We find that the model does a good job in predicting the observed borrowing and default behavior for college drop-outs and college graduates. Specifically, in both the model and the data, college graduates are more likely to participate in the government student loan program than drop-outs (90 percent versus 22 percent in the model and 82 percent versus 18 percent in BPS data); in addition, college graduates have higher average (total) debt levels and more often hit the government borrowing limit than college drop-outs, again consistent with the data. The default rates of college graduates (in the government market) are much lower then those of college drop-outs (3.8 percent versus 45 percent in the model and 0.2 percent versus 6.75 percent in the data).44 This points to theimportanceofthedebt-to-incomeratiosindefaultbehavior: withhighreturnstocollege, college graduates experience higher income levels which reduces the likelihood that they willdefault,eventhoughtheirborrowinglevelsarehigher. Our analysis across individuals with different default status also confirms this fact: we findthatdefaultershavehigherdebt-to-incomeratiosrelativetonon-defaulters. Forinstance, the ratio of Federal student loans to annual income in 2009 in the BPS is 66.8 percent for defaulters versus 56.1 percent for non-defaulters.45 Our model is consistent with this fact: wefindthatdefaultershavelowerEFCandabilitylevels,onaverage. Butthisinturnimplies bothhigherstudentdebtlevelsandlowerreturnstocollege. Indeed,wefindthat,onaverage, defaulters have higher debt levels than non-defaulters. The differences between defaulters and non-defaulters are not as large, however, compared to the differences in debt-to-income ratios. Defaulters experience much lower income levels, on average, which drives up their debt-to-incomeratiosrelativetonon-defaulters. To conclude, our model is able to explain observed behavior regarding college investment,borrowinganddefaultacrosskeyindividualcharacteristics,andinparticularbycredit type. There is currently very little known about the role of credit type in the college invest- 44Thedifferencesindefaultratesismostlyduetodifferencesinmeasurement,aswediscussinSection7.2. 45BPSdataprovidesthisratioforcumulativeFederalloansrelativetoreportedannualincomein2009. The dataistop-codedsothatthosewithcumulativeFederalloansover100percentofincomeweresetto100.Also, recallthatthereisnoincomeinformationinEquifaxandthatthemeasurementofoutstandingdebtinEquifax isnottheexactcounterpartofourmodel. Therefore,wecompareourmodelpredictionswiththesemoments intheBPSdata. 40

ment decision and the implications of credit type on borrowing and default behavior in the student loan market. Our model matches important features of the data in this dimension alongwithotherindividualcharacteristics,namelyabilityandfamilycontributions. Wenow turntoexploringthepolicyimplicationsofourmodel. 5 Policy Analysis Our analysis so far shows that the private market for student loans plays a considerable role in college investment. Yet, borrowing in this market has declined significantly since 2007, in part due to the financial crisis and in part due to a recent expansion of the government student loan program. We focus on the latter channel and analyze the effects of such a policy on college investment, borrowing and default behavior, and welfare. We consider both the partial and general equilibrium effects of higher government borrowing limits. We then compare the effects of increasing the government borrowing limit with a set of budgetneutraltuitionsubsidies. 5.1 Increase in the government borrowing limit For the first time since the early 1990’s, the U.S. government increased the amount undergraduate students can borrow. Beginning in 2008, undergraduate students can borrow up to $31,000totalforcollege(upfrom$23,000).46 Weanalyzetheeffectsoftheexpansionofthe government student loan program in a general equilibrium (GE) and in a partial equilibrium (PE) framework. A general equilibrium is defined in definition 1 in Section 2.8, while a partial equilibrium does notrequire equations9 and11 to hold. Intuitively, the feedbackbetweenthepublicandprivatestudentloanmarketsisshutdowninthePEframeworkbecause interest rates in the private market do not adjust to deliver zero profits for the private lender. Table7providestheaggregateresultsforallofthepolicyexperiments. 5.1.1 Generalequilibriumanalysis With a higher borrowing limit, we find that college enrollment increases to 75.3 percent (up from65.6percentinthebenchmarkeconomy)andthefractionoffour-yearcollegegraduates 46Theincreaseingovernmentloanlimitsismoregenerousintheearlystagesofacollegeeducation: loan limits for the first and second year of college are now $6,000 per year (up from $2,625 the first year and $3,500 the second year); the increase in the loan limits for additional years of college are now $7,000 per year (up from $5,500). Source: www.finaid.org/loans/historicallimits.phtml. Also, this increase consisted of unsubsidized student loans, in that the government does not pay for the interest accumulated during college. Forsimplicityandeaseofcomparability,weassumethattheseloansweresubsidized.LucasandMoore(2007) findthatthereislittledifferencebetweensubsidizedandunsubsidizedStaffordloans. 41

increases to 55.8 percent (compared to 49 percent). Individuals have increased access to cheaper funds (since they can borrow more from the government at lower interest rates), and, as a result, invest in more college. Participation rates in the government student loan program increase by 7.5 percentage points while participation rates in the private market decrease by eight percentage points. In addition, students are borrowing more (in levels) from the government ($9,589 versus $8,157 in the benchmark) and borrowing less from the private market ($3,998 versus $5,070). Our results suggest that students are treating governmentandprivatestudentloansassubstitutes. The expanded government program leads to increased risk in the private market for studentloans: thedefaultrateintheprivatemarketincreasesfrom3.1percentinthebenchmark economy to 7.8 percent. Our key result is that while a higher government borrowing limit leadstomorecollegeinvestment,italsoleadstoashiftinthedistributionofborrowersaway from the private market towards the government market. The remaining pool of borrowers in the private market has lower levels of family contributions and higher levels of ability, on average, relative to the pool of borrowers in the benchmark economy. Students with low family contributions and high ability have a large incentive to default in the private market forstudentloans,asexplainedinSection4. Consequently,thepoolofstudentsparticipating in the private student loan market as a result of the policy is comparatively more risky. This shift in the distribution of borrowers is the reason why aggregate default rates in the private market more than double. As a result, interest rates in the private market increase relative to the benchmark to account for the extra default risk. At the same time, the default rate in the government market increases slightly (by 0.6 percentage points), which is attributable to higher debt-to-income ratios for borrowers in the government market. Low-ability and low-income students borrow more as a result of higher debt limits to finance their college education;however,theyexperiencerelativelylowreturnstotheirinvestment. Consequently, thehighercostofthegovernmentstudentloanprogramrequirestaxestoincreasesincewage garnishmentsarefixed. The equilibrium adjustments have important welfare implications. On the one hand, the increases in college investment and therefore earnings in the economy increase welfare. On the other hand, higher interest rates and taxes reduce welfare. Quantitatively, the latter channel dominates so that the policy induces a small reduction in aggregate welfare relative to the benchmark economy (-0.04 percent). Note that the welfare calculations depend on the welfare function, which is assumed to be an equally-weighted aggregate function. Our 42

Table7: AggregateResults: Benchmarkvs. PolicyExperiments Variables Benchmark Highergovt Highergovt limit: GE limit: PE Collegeenrollmentrate 65.6% 75.3% 70.9% Percentwithafour-yearcollegedegree 49.1% 55.8% 52.7% Participationingovtmkt 48.2% 55.7% 52.4% Participationinprivatemkt 17.8% 9.8% 9.2% Defaultrateingovtmkt 7% 7.6% 7.7% Defaultrateinprivatemkt 3.1% 7.8% 9.3% Averagegovtdebt $8,157 $9,589 $9,585 Averageprivatedebt $5,070 $3,998 $3,978 Aggregatewelfarechange — -0.04% +0.12% Avgrateintheprivatemktw/badcredit 11.2% 11.7% 11.2% Avgrateintheprivatemktw/goodcredit 9% 9% 9% welfarecalculationsassumeexogenousearningsandhighrecoveryratesforstudentloans.47 5.1.2 Generalequilibriumversuspartialequilibriumanalysis As shown in Table 7, there are several important differences between the PE and GE cases. College enrollment and participation rates in the two markets are lower in PE than in GE (but still higher than in the benchmark), and there is more default in both markets. In the partialequilibriumsetting,thereisnoadjustmentintheprivatemarketforstudentloansand therefore no feedback between default behavior and loan terms for private student loans. Consequently,thedefaultrateintheprivatemarketissignificantlyhigher(9.3percentinthe PE case compared to 7.8 percent in the GE case) and interest rates in the private market are relativelylowforthemostriskyborrowers(thosewithbadcredit). These equilibrium effects have important implications for welfare. Unlike in the GE analysis, the policy in the PE case delivers a 0.12 percent increase in welfare relative to the benchmark economy, with the poorest individuals and those with high ability experiencing the larger gains in welfare. The negative effects of higher interest rates and taxes are absent inthePEsetting. 47Welfareinoureconomyignoresthechangingskillpremiainducedbyhavingahigherfractionofeducated peopleintheeconomyanditassumesarelativelylowerriskpremiumimbeddedintointerestratesforstudent loans. Bothoftheseeffectsmaynegativelyaffectwelfare. 43

Table8: HigherGovernmentBorrowingLimit: GeneralEquilibrium College Percentwithafour-year Avgdebt Defaultrates Welfare enrollmentrate collegedegree govt/private (govt/private) change Familycontributions(b) Low 65.3%(+12.6) 45.1%(+8.5) $12,983/$3,998 17.5%/7.6% +0.1% Medium 78.1%(+12.3) 57.5%(+8.5) $10,670/$0 4.2%/NA -0.1% High 82.4%(+4.1) 64.8%(+2.9) $4,480/$0 0.7%/NA -0.14% Abilityofthestudent(a) Low 63.3%(+13) 38.0%(+7.8) $11,054/$4,779 16%/0% -0.05% Medium 63.4%(+10.1) 46.4%(+8.0) $10,108/$3,883 4.6%/9.5% -0.09% High 99.6%(+5.9) 84.2%(+5.0) $8,321/$2,460 4.5%/21.1% +0.01% Credittype(f) Bad 66.6%(+12.9) 49.8%(+9.2) $10,586/$3,996 17.5%/22.6% -0.03% Good 78.2%(+8.6) 57.8%(+5.8) $9,273/$3,999 4.2%/0% -0.05% Note:Numbersinparenthesesrepresentchangesfromthebenchmark. 5.1.3 Allocationalconsequences Who benefits the most from this policy? As Table 8 illustrates, college investment increases for all types of students.48 Poor individuals (those with low b) experience the largest increases in government student loans (compared to the benchmark results in Table 4), which suggests that looser credit constraints make college more affordable for them. Poor students, however, borrow much less from the private market. Middle-income students also take out slightly more government student debt, but do not borrow from the private market any longer. In fact, the poorest individuals are the only ones who participate in the private market for student loans. Although they borrow less in the private market relative to the benchmark economy, overall they have slightly more total student debt. Poor individuals now experience higher earnings levels (since college investment is higher) and cheaper sourcesoffunds(sinceinterestratesinthegovernmentprogramarelowerthanintheprivate market) and therefore benefit from the policy (in welfare terms). At the same time, middleand high-income students experience welfare losses. For them, the positive effect of higher earningsisnotlargeenoughtocompensateforthenegativeeffectofhighertaxes. Similarly, students across all ability groups increase college investment with a higher government borrowing limit, with larger increases for low- and medium- ability students. However,amoregenerousgovernmentstudentloanprogramencouragesalltypesofstudents to substitute away from private loans towards government loans to finance their increased 48Forbrevity,weshowthequantitativeresultsfortheGEcase,butalloftheotherresultsareavailablefrom theauthors. 44

collegeinvestment. Overall,high-abilitystudentsexperienceasmallwelfaregainasaresult of the policy, whereas students with low and medium levels of ability face welfare losses. Unliketheformer,studentswithlowandmediumlevelsofabilityexperiencelowerreturnsto educationandeventhoughtheyhavehighereducationalattainmentrelativetothebenchmark economy, the positive impact of higher earnings for them is not enough to compensate for moreexpensiveprivatestudentloansandhighertaxes. Students with bad and good credit invest in college at higher rates with a higher government borrowing limit: they borrow larger amounts from the government and less from the private sector. However, because students with bad credit receive worse loan conditions in the private market (in equilibrium), they benefit the most from substituting away from private loans to government loans. They borrow from the government at high levels, and this borrowing behavior is more pronounced as the government increases its borrowing limits. As a result, individuals with bad credit experience smaller welfare losses than those with goodcredit. To summarize, an increasein governmentborrowing limitsleads tomore college investmentforeverytypeofstudent,withthelargesteffectsforstudentswithlowlevelsofability, income and credit type. The policy triggers much higher default rates in the private market, despite lowering average private debt. This is caused by the fact that the remaining pool of borrowers in the private market is relatively risky. Consequently, borrowers with bad credit face even higher interest rates on private loans (11.7 percent on average relative to 11.1 percentinthebenchmark,asreportedinTable7). Overall,thedistributionaleffectsofthepolicy suggest that the poorest individuals and those with high levels of ability experience welfare gains whereas other groups of individuals lose out (albeit with small welfare losses). Our findingspointtotheimportanceofunderstandingthecharacteristicsofstudentswhoborrow fromboththegovernmentandstudentloanmarketasstudentloanpoliciesevolveovertime. Infact,thereisanationalconversationtakingplacerightnowthatcallsforincreasingtransparency in the borrowing and repayment process for student loans. In addition, borrowers are participating at higher rates in income-driven repayment (IDR) plans, especially in the government student loan program. While these plans are more generous in that they reduce financial distress, especially for students with high debt-to-income levels and allow for partialdischargeability,IDR’sentailmultipleeligibilitycriteriaandrepaymentrules,especially in the private market, and thus introduce more complexity into the process. This suggests that expansions in the government borrowing limits and, in general, a more generous student loan program, should consider the consequences on borrowing and default behavior in 45

studentloanmarkets. 5.2 Tuition subsidies We study three budget-neutral subsidy policies: an equally distributed tuition subsidy, a merit-based subsidy and a need-based subsidy. Our analysis assumes that instead of subsidizing the cost of higher borrowing limits, the government simply reallocates these funds to tuition subsidies. Our analysis delivers the following subsidy amounts each year per enrolled student: an equally distributed subsidy of $255, a merit-based subsidy of $654 for high-abilitystudentsandaneed-basedsubsidyof$702forlow-incomestudents.49 Our main finding is that compared to the government policy of raising the borrowing limits on government student loans, all three types of tuition subsidies increase college investment and improve aggregate welfare, as reported in Table 9. The gains in aggregate welfare are 0.38 percent with an equal tuition subsidy, 0.35 percent in the case of a needbased subsidy and 0.45 percent in the case of a merit-based subsidy (compared to -0.04 percent induced by higher government borrowing limits in GE). There are two main factors that contribute to these welfare results. First, tuition subsidies reduce the cost of college enough to promote college investment without increasing borrowing levels. We find that tuitionsubsidieshavealargerpositiveeffectoncollegeinvestmentcomparedtohighergovernment borrowing limits. A key second factor that explains these welfare gains is that unlike an increase in government borrowing limits, subsidies do not increase default rates in the private market for student loans. Recall that low-income and high-ability students are risky borrowers in the private market and tuition subsidies lower the net cost of college faced by these high risk individuals. Consequently, they need to borrow less (in levels) in the private market, although their participation rates increase (because more students go to college). The two forces offset each other so the default rate in the private market remains close to its benchmark level for need-based and equal subsidies and a bit lower in the case of merit-based subsidies. Consequently, the interest rates in the private market for student loansremainatlowlevels(asinthebenchmarkeconomy). Why do merit-based subsidies induce higher welfare gains relative to the benchmark economy compared to need-based subsidies? This result may seem counter-intuitive, espe- 49We acknowledge several caveats of our model regarding tuition subsidies. First, we assume that college costs are not adjusted in response to subsidy policies. Second, agents cannot choose to improve college preparedness(orability)inresponsetomerit-basedsubsidiesorcannotadjustfamilycontributionsforcollegein responsetoneed-basedsubsidies. 46

cially given the larger increase in college enrollment with the need-based subsidy.50 Importantly, the two types of subsidies have different implications for default in the government market for student loans. Specifically, the need-based subsidy induces a significant increase inthedefaultrateinthegovernmentmarket(10percentcomparedto7percentinthebenchmark economy), whereas the merit-based subsidy decreases the default rate slightly (to 6.7 percent). Recall that low-income students exhibit high default risk for government loans, whereashigh-abilitystudentshavelowdefaultrisk. Withneed-basedsubsidies,low-income studentsinvestincollegeathigherrates. However,low-incomestudentsstillneedtoborrow from the government. Note that participation in the government market increases significantly in the case of a need-based subsidy. Unlike in the private market, the increase in theparticipationrateinthegovernmentmarketcomingfromlow-incomeborrowersislarge, andasaresult,averagedebtlevelincreasesslightly(comparedtothebenchmarkeconomy). The pool of borrowers in the government market is relatively riskier and therefore default increases. In the case of a merit-based subsidy, however, the pool of borrowers in the government market is relatively less risky, given that high-ability students invest in college at higherratesandhavelowerdefaultincentivesforgovernmentstudentloans. Consistentwith this default behavior, taxes are higher in the economy with a need-based subsidy than in the economywithamerit-basedsubsidy. Atthesametime,thedefaultrateintheprivatemarket declinesabitmoreinthecaseofmerit-basedsubsidyandtheinterestrateforprivatestudent loans is lower. As a result, welfare gains are higher in the case of a merit-based subsidy comparedtotheneed-basedsubsidy. OurresultsarecomparabletothoseinAkyolandAthreya(2005),GarrigaandKeightley (2007), and Abbott et al. (2013), who find that tuition subsidies (in general) are welfareimproving. We contribute to this literature in two important ways. First, we analyze the effects of different tuition subsidies across students who differ in their credit type. As evidentinTable9,studentswithgoodcreditbenefitrelativelymorefrommerit-basedandequal subsidies (compared to those with bad credit). This contrasts to the case of need-based subsidies where welfare gains are exactly the same across credit types. Individuals with bad credit receive higher subsidies given the correlation between income and credit type. They also face slightly higher interest rates in the private market (relative to other types of subsidies). The need-based subsidy makes college more attractive for low-income students who 50Notethattheneed-basedsubsidyincreasescollegeenrollmentbyalmost20percentagepointsrelativeto higher government limits, whereas the merit-based subsidy increases enrollment about 11 percentage points. Thisresultisnotsurprisinggiventhathigh-abilitystudentsalreadyinvestincollegeathighratesinthebenchmarkeconomy. 47

Table9: AggregateResults: TuitionSubsidies Variables Benchmark Highergovt Equal Need-based Merit-based limit: GE subsidy subsidy subsidy Collegeenrollmentrate 65.6% 75.3% 83.8% 84.9% 76.1% Percentwithafour-yearcollegedegree 49.1% 55.8% 61.6% 62.1% 56.4% Participationingovtmkt 48.2% 55.7% 62% 63.6% 54.8% Participationinprivatemkt 17.8% 9.8% 23.5% 28.5% 19.5% Defaultrateingovtmkt 7.0% 7.6% 9.2% 10% 6.7% Defaultrateinprivatemkt 3.1% 7.8% 2.75% 3.1% 2.4% Averagegovtdebt $8,157 $9,589 $8,279 $8,505 $7,993 Averageprivatedebt $5,070 $3,998 $5,065 $5,073 $4,780 Aggregatewelfarechange — -0.04% +0.38% +0.35% +0.45% Avgrateintheprivatemktw/badcredit 11.2% 11.7% 11.2% 11.3% 11% Avgrateintheprivatemktw/goodcredit 9% 9% 9% 9% 9% borrow more in the private market and have relatively high default risk. We find that the most effective policies (in terms of aggregate welfare) are merit-based subsidies; this contrasts to Abbott et al. (2013), for instance, who find that need-based subsidies lead to larger welfare gains. Default rates in the government market are high in the case of need-based subsidies. Thisleadstohighertaxeswhentheneed-basedsubsidyisimplementedrelativeto the merit-based subsidy. At the same time, the two subsidies have similar effects on default intheprivatemarketforstudentloansandthereforedelivercomparableinterestratesinequilibrium. The equilibrium adjustments dampen the welfare effects of the need-based subsidy relative to those of the merit-based subsidy. However, our findings are similar in spirit to those in Garriga and Keightley (2007) who show that, although merit based subsidies have smallenrollmentresponses,theycounteractadverseselectionproblemsthatneed-basedsubsidiescreate. To summarize, by providing tuition subsidies (of any sort), the government is reducing financialneedforstudents,andthislowersdefaultincentivesintheprivatemarketforstudent loans. Thisisincontrasttoahighergovernmentborrowinglimit,whichinducesmoredefault in the private market for student loans and higher interest rates. Overall, our results imply thattuitionsubsidiesrepresentgoodinstrumentstoencouragecollegeinvestment,asopposed to an expansion of the government student loan program. More generally, while student loan default provides some insurance and repayment relief to some borrowers, the negative consequences of default can be significant. Tuition subsidies minimize the negative effects ofdefaultingonstudentloansandprovetobesuperiorintermsofaggregatewelfare. 48

6 Conclusion Itisquitecommonforundergraduatestudentstoborrowforcollegefromprivatecreditmarkets. Incontrasttothegovernmentstudentloanprogram,privatecreditorssettheconditions for student loans based on the credit type of the student. As a result, credit type may affect the college investment decision which in turn affects borrowing and default behavior. Due to limitations in the data, little is currently understood about how different types of college students use the combination of government and private student loans to finance their college expenditures. We build a life-cycle model where agents are heterogeneous in family income,abilityandcredittypeanddocumentimportantdifferencesinborrowinganddefault behavioracrossdifferentindividualcharacteristics. We find that credit type plays a role for college investment and that there are significant interactionsinborrowinganddefaultbehaviorbetweenthegovernmentandtheprivatemarkets for student loans, which have important policy implications. Specifically, our results revealthatarecentpolicythatincreasedtheborrowinglimitsinthegovernmentstudentloan program increases college investment as students borrow more from the government and less from the private market. However, we find that this policy results in a riskier pool of students participating in the private market, which causes higher default rates and negative profits to private creditors. Consequently, both interest rates in the private market and government taxation increase in equilibrium. We show that if these adjustments are ignored in equilibrium, an increase in government borrowing limits is welfare-improving. However, the general equilibrium effects negate the welfare gains from a more generous student loan program,whileinducingimportantdistributionaleffectsintheeconomy. Furthermore, our analysis shows that tuition subsidies are welfare superior to increasing government borrowing limits because subsidies minimize the adverse effects on private credit markets. Merit-based subsidies lower default rates in both the government and the private markets, while need-based subsidies lower default in the private market but increase default risk in the government student loan program. Thus, it is important for policymakers to consider how borrowing and default decisions for student loans vary under different tuitionsubsidyprograms. The private market for student loans is still evolving. Our analysis suggests that the private market is playing an important role for college investment and that the government should consider how the private market for student loans reacts to policy changes. We hope this paper represents a starting point for more analysis of this important source of funding forcollegestudents. 49

7 Appendix 7.1 Description of data sets and samples We present the datasets we use to study observed patterns of college enrollment and attainment, borrowing and default behavior across various individual characteristics. It is importanttonotethatthereisnotasingledatasourcethatcontainsinformationonfamilycontribution, ability, credit type, educational attainment, borrowing and default behavior. Therefore, we use four data sets: Beginning Postsecondary Student Longitudinal Survey (BPS 04/09), National Education Longitudinal Study (NELS:1988), Survey of Consumer Finances (SCF) and FRBNY Consumer Credit Panel (Equifax). Specifically, the Equifax dataset contains detailed credit-related information (e.g., repayment and various measures of delinquencies), but does not provide demographic characteristics (with the exception of age). Most notably, it lacks any information about income or educational attainment/enrollment. Contrast this with data from the U.S. Department of Education (namely, the BPS and NELS), which provide detailed information about enrollment, educational attainment, sources of financing, and demographic characteristics. U.S. Department of Education data also contain some information about default behavior, but does not provide any information on credit type. The Survey of Consumer Finances (SCF), on the other hand, provides self-reported information aboutcredittype(asdiscussedinSection3.1ofthepaper)andeducationalattainment,butit doesnotprovideinformationaboutstudentloandefaultbehavior. Wenextprovideadetailed descriptionofeachdatasetandsampleusedintheanalysis. BeginningPostsecondaryStudentLongitudinalSurvey(BPS04/09) The Beginning Postsecondary Student Longitudinal Survey (BPS 04/09) is one of several National Center for Education Statistics (NCES)-sponsored studies that is a nationally representativedatasetwithafocusonpost-secondaryeducationindicators. BPScohortsinclude beginners in post-secondary schools who are surveyed at three points in time: in their first year in the National Postsecondary Student Aid Study (NPSAS), and then three and six years after first starting their post-secondary education in follow-up surveys. BPS collects dataonavarietyoftopics,includingstudentdemographics,schoolexperiences,persistence, borrowing/repaymentofstudentloans,anddegreeattainmentsixyearsafterenrollment. Our sample consists of students aged 20-30 who enroll in a four-year college following high school graduation. For demographic characteristics, we use SAT (and converted ACT) scores as the measure of ability (or college preparation) and expected family contribution 50

(EFC), a measure which we check with reported family income. The survey records the fraction of students who, six years later, report having earned a bachelor’s degree. We exclude students who continue with graduate studies since they are not part of our model. We divide the population into terciles of ability and family contribution and compute our model counterparts, including the fraction with a four-year degree, the amount of debt owed at the end of college (total student loan debt in the BPS includes both Federal and private student loansbutitdoesnotincludeParentPlusloans),anddefaultrates. Itisimportanttonotethat the information on default status is limited. The question is asked in 2009, right after studentsareoutofcollege(withorwithoutadegree)anditisavailableonlyforFederalstudent loans. Therefore this measure is not the exact counterpart of our model, which represents a two-year cohort default rate, in line with the official release from the U.S. Department of Education and our measure from Equifax data (as explained in Section 3). In particular, we wouldexpectthemeasureofdefaultintheBPSdatatobelowerthanthemeasureinEquifax andtheoverallaggregatenumber. In addition, we use the BPS data to compute the fraction of borrowers who are constrained(e.g.,hitthemaximumgovernmentborrowinglimit)acrossdifferenttercilesofEFC andSATscores. WealsousetheBPSdataforcollegedrop-outs,definedasindividualswho donothaveabachelor’sdegreeby2009andarenolongerenrolledincollege. NationalEducationLongitudinalStudy(NELS:1988) TheNationalEducationLongitudinalStudy(NELS:1988)isanationallyrepresentativesample of eighth-graders who were first surveyed in the spring of 1988. A sample of these respondents were then resurveyed through four follow-up surveys in 1990, 1992, 1994, and 2000. Weusethethirdfollow-upsurveywhenmostrespondentscompletedhighschooland report their post-secondary access and choice. As in the BPS, demographic information, including SAT scores and EFC, are available. We use this data set to compute college enrollmentratesbyabilityandfamilycontributions. Oursampleconsistsofrecenthighschool graduatesaged20-30whohavetakentheSAT(orACT). SurveyofConsumerFinances(SCF) Weusethe2007SCFdatatoproduceestimatesacrosshouseholdswithgoodandbadcredit. Importantly, unlike Equifax, which is individual data, the SCF surveys households. Therefore, the variables about bad credit are based on the household’s credit history. We define households with bad credit as those who report being turned down for credit or did not get 51

as much credit as they applied for based on their credit history (or lack thereof). The SCF includesthehighesteducationalattainmentofthehouseholdheadsoitisthebestsourcefor linking credit type and educational attainment (but does not contain SAT scores or EFC). TheSCFdatareportacompositeamountowedfromallsourcesofstudentloans,butitdoes not contain any details about default on student loans. To be consistent with the BPS and NELSsamples,ourSCFsampleconsistsofhouseholdheadswhohaveatleastahighschool degreeandarebetweentheagesof20and30. WeusetheSCFtocomputeenrollmentrates, the percent with a four-year college degree and (total) student loan debt across households withdifferentcredittypes(notethat25percentofoursamplehasbadcredit). FRBNYConsumerCreditPanel(Equifax) The FRBNY Consumer Credit Panel/Equifax data is a nationally representative five percent sample of all credit files and has a rich set of variables on consumers’ credit behavior, including risk scores, various measures of delinquency and outstanding balances for all types of loans, including student loans. It is a longitudinal database and collects information derived from consumer credit reports to track individuals’ and households’ access to and use of credit at a quarterly frequency. There is no distinction, however, between Federal and private student loans and there are no demographic characteristics except for age. Consistent with samples in the other data sets we employ, our Equifax sample consists of young individuals (20-30 year-olds) who have positive student loan balances.51 We use this data for default behavior and loan amounts by credit type. Consistent with our definition in the SCF,wedefinethosewithbadcreditasinthebottomquartile,whichtranslatesintoEquifax riskscoresbelow560;thosewithgoodcredithaveariskscoreatorabove560. Toconstruct default rates, we use the measure for 120+ days delinquency for student loans and further restrict it to individuals who are 120+ days delinquent for at least two quarters in a year. This measure is the closest one to the national two-year cohort default rate for student loans (which is based on 270+ days). We discuss the compatibility between the two measures of defaultinSection7.2. AswediscussinSection4.3,debtlevelsandcreditscoresinEquifaxarecaptured(quarterly) at the time of data collection. Therefore, it is likely there are some other interactions between repayment/delinquent behavior, the credit score, and the outstanding balance in Equifax data. This contrasts to SCF data which captures (household) outstanding debt and 51SincethereisnoeducationinformationinEquifax,weusethissampleassumptiontoinsurethateveryone hasatleastsomecollegeeducationtobeconsistentwithourBPSsample. 52

credittypeforthepreviousyear. Torecap,wereportthevarioussourcesofdataforeachcomponentofourmodelinTable 10. Table10: DataSources College Percentwithafour-year Averagedebt Defaultrates* enrollmentrate collegedegree (total=govt+pvt) (govtstudentloansonly) Familycontributions(b) NELS** BPS BPS BPS Abilityofthestudent(a) NELS BPS BPS BPS Credittype(f) SCF SCF Equifax&SCF Equifax** Note:*CohortdefaultratesarereporteddifferentlyacrosstheBPSandEquifax.**Thesemomentsaretargeted inthecalibrationprocedure. 7.2 Default rates on student loans The official national default rate on student loans is released by the U.S. Department of Education and it represents a two-year cohort default rate, that is, the fraction of borrowers who enter repayment in a particular fiscal year and default by the end of the next fiscal year. Recall that borrowers who have not repaid on their student loans for 270+ days are considered to be in default. We also compute a measure of the default rate from Equifax, as explained before. The purpose of this exercise is two-fold: to validate our measure of the default rate in Equifax and to fill in the gaps for trends in default rates for the periods when datafromtheU.S.DepartmentofEducationarenotavailable. (In2011,theU.S.Department of Education stopped releasing the two-year cohort default rate and instead released a three year-cohort default rate - this measure is available for fiscal years 2010, 2011 and 2012). Figure 2 shows the two series of default rates for the past two decades (with the first year availableinEquifaxbeing1999). There are two important observations. First, the two measures of default match up quite well for the entire period and in particular, during the peaks and troughs. Note that the Equifax default rate is greater or equal to the default rate released by the U.S. Department of Education for most of the period. This is expected since the former includes default in both government and private student loan markets, whereas the latter represents default only for Federal student loans. Thus, we are confident to use this measure of default for borrowerscharacteristics(namely,credittype),whichisnotavailableintheU.S.Department of Education data or surveys from the private market. Second, both measures of default indicate a constant decline between 1999 and 2007, but then an increase after 2007. While the two-year cohort default rate seems to suggest a further increase after 2011, the three- 53

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