Econometric Models of Student Loan Repayment in Canada

Transcription

1 003s-68 Econometrc Moels of Stuent Loan Repayment n Canaa Mare Connolly Claue Montmarquette Al Béjaou Sére Scentfque Scentfc Seres Montréal Décembre Mare Connolly Claue Montmarquette Al Béjaou. Tous rots réservés. All rghts reserve. Reproucton partelle permse avec ctaton u ocument source ncluant la notce. Short sectons may be quote wthout explct permsson f full cret nclung notce s gven to the source.

2 CIRANO Le CIRANO est un organsme sans but lucratf consttué en vertu e la Lo es compagnes u Québec. Le fnancement e son nfrastructure et e ses actvtés e recherche provent es cotsatons e ses organsatonsmembres une subventon nfrastructure u mnstère e la Recherche e la Scence et e la Technologe e même que es subventons et manats obtenus par ses équpes e recherche. CIRANO s a prvate non-proft organzaton ncorporate uner the Québec Companes Act. Its nfrastructure an research actvtes are fune through fees pa by member organzatons an nfrastructure grant from the Mnstère e la Recherche e la Scence et e la Technologe an grants an research manates obtane by ts research teams. PARTENAIRE MAJEUR. Mnstère u éveloppement économque et régonal [MDER] PARTENAIRES. Alcan nc.. Axa Canaa. Banque u Canaa. Banque Laurentenne u Canaa. Banque Natonale u Canaa. Banque Royale u Canaa. Bell Canaa. BMO Groupe Fnancer. Bombarer. Bourse e Montréal. Développement es ressources humanes Canaa [DRHC]. Féératon es casses Desjarns u Québec. Gaz Métropoltan. Hyro-Québec. Inustre Canaa. Mnstère es Fnances [MF]. Pratt & Whtney Canaa Inc.. Raymon Chabot Grant Thornton. Vlle e Montréal. École Polytechnque e Montréal. HEC Montréal. Unversté Concora. Unversté e Montréal. Unversté u Québec à Montréal. Unversté Laval. Unversté McGll Les organsatons-partenares / The Partner Organzatons ASSOCIE A :. Insttut e Fnance Mathématque e Montréal (IFM ). Laboratores unverstares Bell Canaa. Réseau e calcul et e moélsaton mathématque [RCM ]. Réseau e centres excellence MITACS (Les mathématques es technologes e l nformaton et es systèmes complexes) Les cahers e la sére scentfque (CS) vsent à renre accessbles es résultats e recherche effectuée au CIRANO afn e suscter échanges et commentares. Ces cahers sont écrts ans le style es publcatons scentfques. Les ées et les opnons émses sont sous l unque responsablté es auteurs et ne représentent pas nécessarement les postons u CIRANO ou e ses partenares. Ths paper presents research carre out at CIRANO an ams at encouragng scusson an comment. The observatons an vewponts expresse are the sole responsblty of the authors. They o not necessarly represent postons of CIRANO or ts partners. ISSN

3 Econometrc Moels of Stuent Loan Repayment n Canaa * Mare Connolly Claue Montmarquette Al Béjaou Résumé / Abstract Sx mos après avor ms fn à leurs étues complétées avec succès ou non les ex-étuants sont tenus e rembourser leurs prêts étues. Une majorté entre eux rembourseront la totalté e leurs prêts sur une péroe e 10 ans. D autres connaîtront es ffcultés à respecter leur engagement. Dans cette étue nous proftons une base exceptonnelle e onnées nvuelles sur les prêts étues au Canaa pour étuer les étermnants es remboursements ou non es prêts et la urée avant le remboursement complet. Les résultats économétrques montrent l mportance e termner ses étues ans les temps requs à la fos pour évter e fare éfaut et auss pour accélérer la péroe e remboursement. Une poltque à envsager serat e gommer une parte es prêts lorsque l étuant complète ses étues ans les temps requs. L autre résultat est que le programme u report es ntérêts n a pas semblé très effcace pour faclter le remboursement es prêts étues pour la cohorte étuée. Fnalement un programme trop généreux e prêts étues sans mse en gare sur les rsques encourus par les étuants nvestr ans certans programmes notamment ceux opérés par le secteur prvé a es effets mportants non seulement sur la pérennté u programme es prêts mas auss sur les mauvases écsons e la part es étuants ans leur chox étues. Mots clés : prêts étues remboursement fallte Sx months after a stuent ceases beng enrolle full-tme n an eucatonal nsttuton a loan contracte wth the Canaa stuent loans program s sa to be consolate an ts repayment s expecte. Many ex-stuents wll repay ther loan n total (captal an nterest) wthn a ten-year pero. However a non-neglgble proporton of borrowers wll experence ffculty n the repayment of ther loans. We are able to she a new lght on these ssues because we have access to unque ata to estmate econometrc moels of the etermnants of nterest relef an clams (efaults) as well as uraton moels for the repayment of stuent loans. We foun that fnshng the program supporte by a loan s essental to avong efault. Therefore t may be worth conserng polces that wll rewar anyone who completes hs or her program. On the other han too much flexblty n access to loans mght encourage experments by stuents that coul turn sastrous for the stuent an the natonal loan program. A loan program shoul also come wth some nformaton on the rsk nvolve for the stuent before he or she nvests n a partcular fel or program. One partcular concern s the relatvely hgh level of efault for stuents attenng prvate schools. Relatvely easy access to loans coul be an nvtaton for prvate nsttutons to captalze on that fact wth varous eucatonal programs havng lttle bearng on the realty of the labour market. Eventually serous nsttutons wll establsh a reputaton but for some stuents t wll be too late. Another result concerns the nterest relef measure that seems not to have playe ts role of helpng the cohort of stuents to pass through ffcult tmes. Keywors: stuent loans rembursement efault Coes JEL : I11 I18; C35 * We are grateful to Nathale Vennot-Brot for her assstance an to the Soco-Economc Analyss Group of the Canaa Stuent Loans Program HRDC for help an comments. Any errors or omssons are our sole responsblty. CIRANO an Department of Economcs Prnceton Unversty CIRANO an Department of Economcs Unversty of Montreal emal: [email protected]. Senor Analyst Soco-Economc Analyss Group Canaa Stuent Loans Program HRDC.

4 1. Introucton In a knowlege base economy nvestment n human captal s a key etermnant of economc growth. Globalzaton wll accentuate the compettveness between economes an therefore to mantan our stanar of lvng many beleve that a substantal amount of our collectve resources shoul be evote to hgher eucaton. One polcy to acheve ths goal s to facltate access to hgher eucaton to anyone regarless of hs or her fnancal stuaton. Investments n human captal are fferent from other types of nvestment n that they cannot be backe by materal collateral. Unlke nvestments n machnery or real estate human captal has nothng tangble to offer to the lenng nsttuton n case of efault. Thus the captal market s an mperfect nsttuton when t comes to offerng loans to stuents. The Canaa Stuent Loans Program (CSLP) proves the necessary loans to stuents wth emonstrate nee. Loans ssue from the creaton of the CSLP n 1964 up to August 1995 were grante uner a program whch requre the government to cover the entre cost of the loan. Loans that were three or more months n arrears were transferre to the feeral government whch then remburse the lener for the efaulte loan. From August 1995 to March the CSLP backe loans mae by fnancal nsttutons through a rsk-sharng agreement. Now all loans come rectly from the Government of Canaa through the Natonal Stuent Loans Servce Centre (NSLSC). In the fscal year the CSLP ha mllon ollars n ts portfolo as a total of both loans n stuy an loans n repayment. By that amount ha ouble to $581.4 mllon an by t ha more than trple to a value of $ mllon. For stuents of the cohort average nebteness for all types of learnng nsttutons was $5834. That number went up to $9346 n for a total of stuents wth loans. Over the same pero the average nebteness for unversty stuents went from $859 to $ More escrptve statstcs an nsttutonal etals concernng Canaa stuent loans ata can be foun n Plager an Chen (1999).

5 Sx months after a stuent ceases beng enrolle full-tme n an eucatonal nsttuton a loan contracte wth the Canaa stuent loans program s sa to be consolate an ts repayment s expecte. Many ex-stuents wll repay ther loan n total (captal an nterest) wthn a ten-year pero. However a non-neglgble proporton of borrowers wll experence ffculty n the repayment of ther loans. The CSLP nclues varous measures to help them. One of them s the nterest relef opton. An ex-stuent usng ths program sees hs or her monthly payment of nterest put on hol for a certan pero of tme. The CSLP s responsble for payng nterest to the lenng nsttutons but the nterest s ae to the loan to be repa by the stuent. The value of the nterest relef affore by ths system went from $4. mllon for the loan year to $36.1 mllon n 1997 to $67.4 mllon n In the meantme the number of recpents went from 3136 n to n Another realty of the eucatonal loan system s those ex-stuents who smply cannot repay. A loan s eeme n efault f t s n arrears for three or more months. In per cent of loans were n efault. That proporton reache a peak n at 9.8 per cent an then went own to 4.9 per cent n Furthermore for the consolaton cohort the efault rate of former stuents was 1.9 per cent of stuents from unverstes 6.0 per cent of those from communty colleges an 43.6 per cent of those from prvate nsttutons. Untl 1994 banks smply ha to clam loans n efault from the CSLP whch woul then try to recover the funs from the stuent. Between 1994 an 001 the fnancal nsttutons ssung loans ha a rsk-sharng agreement wth the CSLP uner whch they ha to recover the loans that went nto clams n return for a government payment of fve percent of the value of the loans gong nto repayment. Snce 001 the new NSLSC s responsble for all phases of the program. Although the government s able to recover a porton of the loans that go nto efault after a clam by the bank some of the borrowers smply never repay. Hgh levels of efault are a threat to the vablty of the system. Snce the CSLP s constantly n efct t s actually subszng hgher eucaton when n fact t was create to correct the mperfect captal market. Wth nebteness an the number of stuents who requre fnancal a growng larger an larger the health of the whole system s at stake. It s thus crucal to

6 unerstan the etermnants of loan repayment an efault. Ths paper stues those etermnants as well as the probablty of usng the nterest relef opton. We are able to she a new lght on ths ssue because we have access to unque ata through Human Resources an Development Canaa (HRDC). We use ths ata to estmate econometrc moels of the etermnants of nterest relef an clams (efaults) as well as uraton moels for the repayment of stuent loans. In the next secton we present the ata use n these analyses an some escrptve statstcs. In secton 3 we scuss the smultaneous etermnants of an nvual s resortng to the nterest relef opton an clams. In secton 4 we look at a smple uraton moel for repayment of stuent loans. We summarze the results an scuss polcy ssues n a conclung secton.. The ata an some escrptve statstcs The ata set use n ths paper conssts of nformaton about the consolaton cohort of After cleanng the fles we were left wth observatons per cent of the stuents never went on nterest relef or efaulte. The proporton of stuents efaultng on ther payments whether or not they use nterest relef s 13. per cent. Lookng at Fgure 1 gves us a goo general escrpton of the stuaton Cohort stuents Breakown of stuents usng nterest relef an/or efaultng 10.6%.6% 9.7% Never usng nterest relef No efault Usng nterest relef No efault Usng nterest relef Default 77.1% Fgure 1 Consolaton occurs sx months after the en of the stues so the ata we have here covers nvuals who consolate ther loans urng the years

7 The ata not nclue a varable for grauaton or whether or not stuents successfully complete ther programs or qut before completon. In orer to get an ea of the grauaton rate an the mpact of grauaton on the rembursement of loans we create a varable for the rato of the years of stuy n the last egree ve by the number of years normally requre to complete the program. Although ths varable s not a perfect substtute for a grauaton ncator we can speculate that an nvual havng a rato lower than one probably n t complete the egree. If the rato s one or more t mght have been successfully complete. As shows n Fgure about 77 per cent of the stuents ha a rato of 1 whle the remanng 3 per cent ha a rato uner one Cohort YRIN/YRTOTAL Rato All observatons Number of stuents Percentage stuents Rato percentage Fgure 3. The etermnants of nterest relef optons an clams The nterest relef opton was mplemente to help stuents wth the repayment of ther loan when they go through a ffcult fnancal pero. It s mportant for the CSLP to unerstan whether that measure meets ts goal whether t s use for the rght purpose. To acheve ths we nee to unerstan the etermnants of the probablty of a stuent resortng to the nterest 4

8 relef opton. However to what extent oes frequent resortng to the nterest relef opton sgnal nherent ffcultes n loan repayment that coul lea the stuent to efault? To aress ths ssue we have to know the factors affectng the probablty of a stuent havng a clam wth among other explanatory varables the number of nterest relef peros use. Both probabltes wll be estmate jontly. 3.1 A jont moel of nterest relef an clams To analyse what nfluences the probablty of a stuent usng the nterest relef opton an gong on to efault we nee to estmate the parameters of two equatons smultaneously. Ths s because we explan the probablty of clams wth the number of nterest relef peros but the probablstc latent varable corresponng to ths number s also a varable explane by nepenent varables. What s the probablty that a stuent never resorts to the nterest relef opton or resorts to t only once twce three tmes.? To answer ths queston an orere probt explanng the number of nterest relef peros usng a seres of explanatory varables wll be use. To explan the probablty of havng a clam wth the same set of explanatory varables plus ummy varables for the number of nterest relef peros a probt moel of clams wll be jontly estmate wth the orere probt for nterest relef peros. The entfcaton of the parameters of the complete moel s a tenuous exercse conserng the complexty of the moel. There are no obvous excluson restrcton an we strongly rely on the non-lnearty of the moel to ensure entfcaton. We are comforte by the fact that n the process of estmatng the moel the lkelhoo functon has converge wth fferent ntal values for the parameters. The probt specfcaton for the probablty of a clam s the followng: * LAIM X 1 D 1 D 3 D 3 4 D 4 5 D 5 6 D 6 C = β + δ + δ + δ + δ + δ + δ +. I CLAIM * s a latent varable. It s the utlty erve by havng a clam. It s not observe. What s observe however s whether or not the borrower has use a clam. Thus we efne CLAIM such as: 5

9 CLAIM 1 f CLAIM * > where X = = 0 otherwse 0 that s f the utlty of a clam s postve s a vector of exogenous varables efne below. Dj are ummy varables relate to the number of nterest relef peros NBIR use by. Thus D D D D D D 1I I 3I 4I 5I 6I = 1 f NBIR = 1 an D = 0 otherwse = 1 f NBIR = 1 f NBIR = 1 f NBIR = 1 f NBIR = 1 f NBIR I I I I I I = an = 3 an = 4 an = 5 an = 6 or more an D D D D D 1I I 3I 4I 5I 6I = 0 otherwse = 0 otherwse = 0 otherwse = 0 otherwse = 0 otherwse. The β an δ s are parameters to be estmate. Each estmate parameter gves us the effect of a specfc varable on the la tent utlty varable CLAIM *. We can obtan the effect of a specfc varable on the probablty of havng a clam by the approprate computatons. The orere probt specfcaton for the latent v arable NBIR * (the utlty of nterest relef) s: NBIR * = where X + X s a vector of exogenous varables efne below. The observe varable corresponng to the latent varable s NBIR the number of nterest relef peros an s efne accorng to fve threshols: 6

10 NBIR = 0 f NBIR * 0 = 1f 0< NBIR* 1 = f 1< NBIR * = 3f < NBIR* 3 = 4 f 3 < NBIR * 4 = 5f 4 < NBIR* 5 = 6+ f 5 < NBIR *. In wors for example NBIR 0 f NBIR * 0 I = smply means that nvual oes not resort to a sngle per o of nterest relef f the utlty of ong so s nonpostve. Note that > > s a vector of parameters to be estmate. 1 >... 5 The errors for those equatons follow a normal bvarate strbuton: ~ NB(0011 ρ) wth zero means unt varances an a correlaton coeffcent ρ. In Table 1 the vector of exogenous varables X s efne. 7

11 Varable name Weeks Amount borrowe Weeks of stuy * amount Age Years of stuy/ years requre n program Female Prvate nsttuton Amount * prvate Marre Fels of stuy Amount * entstry Amount * health scences Amount * law Levels of stuy Provnce of stuy Defnton Table 1 The exogenous varables Total number of accumulate weeks of stuy Natural log of the total amount borrowe Number of weeks tmes the amount borrowe Age as of September of the consolaton year Constructe varable t s the rato of the number of actual years of stuy n the last certfcate of loan to the number of years normally requre to complete the program. A rato lower than one suggests that the stuent not fnsh hs program hence not grauate. Dummy = 1 f female =0 f male Dummy =1 f prvate nsttuton =0 f publc nsttuton Amount borrowe tmes the prvate nsttuton ummy Dummy=1 f martal status s marre =0 f not marre Ten ummy varables = 1 f t s the scplne of the fnal egree =0 f t sn t. Possble fels: busness/amnstraton agrculture arts/scence communty servce/eucaton entstry engneerng/technology health scences law mecne traes an theology (use here as the reference varable) Amount borrowe tmes the entstry ummy Amount borrowe tmes the health scences ummy Amount borrowe tmes the law ummy Three ummy varables =1 f t s the level of stuy of the stuent. Possble levels: non-egree unergrauate masters an octoral (use here as reference) Nne ummy varables =1 f t s the provnce of ssue of the last loan certfcate. Possble provnces: Alberta Brtsh Columba Mantoba New Brunswck Newfounlan Nova Scota Ontaro Prnce Ewar Islan Saskatchewan an Yukon (use here as reference) 8

12 3. The estmaton results The jont clam - nterest relef pero moel has been estmate by maxmum lkelhoo programme n Gauss (see the etale lkelhoo functon n the Appenx). The results are reporte n Table. Coeffcent estmates of the number of weeks of stuy are negatve whle those assocate wth the amount borrowe an the nteracton varable weeks tmes amount are postve. We can see that an ncrease n the number of weeks of stuy ecreases the probablty of clams an of resortng to large numbers (6+) of nterest relef peros owng to the mpact of the rect coeffcent but that these probabltes ncrease wth an ncrease n the weeks*amount-borrowe nteracton varable. 3 Thus stuyng more helps war off clams an nterest relef probably because of completon of the program or a more avance egree; but at the same tme stuyng for a longer pero may also mean borrowng more an hence havng more ffculty repayng. 3 A postve coeffcent ncreases the probablty of a clam wth an ncrease n the value of the corresponng varable. In the case of an orere probt (the nterest relef equaton) ths one-to-one relaton s only val at the extremes: no nterest relef pero an 6+ nterest relef peros. An ncrease n the value of a varable wth a postve coeffcent estmate ncreases (ecreases) the probablty of resortng to sx or more nterest relef peros (no nterest relef pero). Between these categores the fnal effect has to be nvually compute. 9

13 Inepenent varables Table Results of the clam-nterest relef pero jont estmaton Clams Interest relef Clams Interest relef beta estmates gamma estmates Inepenent varables Beta estmates Gamma estmates Constant Engneerng/Techn ology (-6406) (-6045) (0773) (1053) Number of weeks Health Scences of stuy (-9808) (-8056) (-145) (-1184) Amount borrowe Law (ln) (31600) (30904) (4316 (3398) Weeks of stuy * Mecne amount (1134) (9781) (-10158) (-9947) Age Traes (4360) (3447) (6494) (531) Years of stuy/years Theology ref. ref. requre n program (-11199) (-10083) Male ref. ref. Amount borrowe * Dentstry ummy Female (-4733) (-597) (1598) (3588) Amount * Health Scences ummy Prvate nsttuton (-380) (-446) (9553) (883) Amount * Law ummy Publc nsttuton ref. ref. (-5944) (-4951) Amount * prvate nsttuton ummy (-5803) (-536) Marre Level of stuy (-1430) (-1788) Non-egree Not marre ref. ref. (5501) (4085) Unergrauate Fels of stuy (718) (1897) Busness/Amnst raton Masters (4379) (3994) (010) (0084) Agrculture Doctorate ref. ref. (0396) (0760) Arts/scence Provnce of stuy (780) (6980) Alberta Communty (-07) (-005) Servce/Eucaton (0858) (0658) Brtsh Columba Dentstry (0893) (0583) (0938) (183) Mantoba Yukon ref. ref. 10

14 Number of IR peros ρ (correlaton coeffcent) ero ref. - (5336) One (-17) - - (63487) Two (-4954) - - (8183) Three (-711) - - (953) Four (-801) - - (99933) Fve (-8377) - - (10481) sx or more (-14754) - Number of observatons: Log-lkelhoo: Mean log-lkelhoo: The coeffcent estmates for the years of stuy/years requre ratos are hghly sgnfcant an negatve whch ncates that a greater rato lowers the probablty of gong nto clams or usng the nterest relef opton. Assumng that a hgher rato s assocate wth completon of the program an grauaton we realze how crucal t s for stuents to pursue ther stues untl the en. Stuents who have complete ther programs have a lower rsk of experencng ffculty n repayment of ther loans. Ths s explane by the well-known fact that a egree holer has a much better chance of fnng goo employment than someone who hasn t fnshe hs or her egree. The coeffcents of the prvate nsttuton ummy are all postve whch mples that attenng a prvate school ncreases the probablty of efaultng an usng more nterest relef peros. An nterestng result s the one regarng the nteracton varable amount borrowe*prvate nsttuton. A negatve estmate tells us that attenng a prvate school actually ecreases the probablty of clams an nterest relef n proporton of the amount borrowe. The effect of gong to a prvate school then works n both rectons. Ths mxe result may n fact capture the fact that a stuent from a prvate nsttuton tens to borrow more 11

15 because of hgher tuton fees but mght n return get a goo techncal egree that leas to a well-pa job. Relatve to the theology coeffcent the coeffcents of the mecne ummy varable are all very sgnfcant an negatve so we can magne gong to mecal school sgnfcantly lowers the rsk of efault an nterest relef. Although the results for the coeffcents of the fel of stuy ummes are not very sgnfcant n general the estmates for the cross-varables ummes of amount an entstry amount an health scences an amount an law are all negatve an sgnfcant but one. We can conclue that stuyng n one of those fels actually reuces the probablty of havng a clam or usng nterest relef n proporton wth the amount borrowe. To stuy how usng the nterest relef opton affects the probablty of efault we cannot smply conser the coeffcents assocate wth the fferent numbers of peros of nterest relef owng to the jont estmaton of our two-equaton moel. To obtan the probablty of havng a clam contonal to the number of peros of nterest relef the followng formula must be use: Pr(CLAIM = 1NBIR = j) Pr ( CLAIM = 1/NBIR = j) = ; j = Pr(NBIR = j) Wth the coeffcents of Table an wth the exogenous varables taken at ther mean values the mean amount borrowe the mean number of weeks etc. Fgure 3 shows the probabltes of havng a clam contonal on the number of peros of nterest relef. 1

16 Fgure 3 We see that the probablty of clams s very low less than 10 per cent when the stuent never uses the nterest relef opton. That probablty rses ramatcally to aroun 70 per cent for stuents wth one or more peros of nterest relef. Interestngly enough that probablty oesn t vary much wth the number of nterest relef peros between one an sx. Wth other varables taken at ther mean values Fgure 4 shows the probablty of havng a clam expresse relatve to the total amount borrowe. The sol one represents the probablty for publc nsttutons an the otte one prvate nsttutons. We observe that the probablty of a clam s strctly monotoncally ncreasng wth the amount borrowe an that the curve for prvate nsttutons s above the one for publc nsttutons. Ths tells us that the more stuents borrow the more lkely they are to have ffculty repayng an that attenng a prvate nsttuton rases the probablty of efaultng. 13

17 Fgure 4 Fgure 5 represents the probablty of havng a clam ths tme plotte aganst the rato of actual years of stuy to the expecte tme neee to complete the program. Ths probablty s strctly ecreasng from 5 per cent when the rato s zero to aroun per cent wth a rato of one to almost zero as the rato ncreases. Thus the hgher the rato an so hypothetcally the hgher the probablty of grauatng the lower the probablty of a stuent efaultng. Fgure 5 14

18 We turn next to the etermnants of the probablty of usng the nterest relef opton a certan number of tmes. Table 3 presents some smulaton results by sub-groups of the explanatory varables. Usng the coeffcent estmates of Table these smulatons were one by calculatng the probablty of usng the nterest relef opton for each possble value of the varable NBIR from none to sx or more for each nvual n the atabase. The sample was then separate nto sub-groups accorng to the characterstcs of the nvuals. For example the group was ve between males an females. The probabltes shown n the Tables are the means of the probabltes for the observatons n that sub-group. The stanar evaton s presente n talcs. There are two ways to rea these Tables. One s by lne from left to rght. That way we can observe how the probablty vares for the fferent numbers of peros of nterest relef wthn each sub-group. The other way s by column. By comparng two numbers n the same column we see the fference n the probablty of requrng nterest relef a certan number of tmes for the fferent sub-groups. In Table 3 we can see that for a marre nvual the probablty of never resortng to nterest relef s 79 per cent of resortng to t once 7 per cent twce 4 per cent an so on. If we look at the column none for the fferent ranges of amount borrowe we see that the probablty of never usng nterest relef greatly mnshes wth the amount borrowe gong from 90 per cent for amounts uner $500 to 69 per cent for amounts above $1500. As expecte stuents n the fel of mecne have the hghest probablty of never usng the nterest relef opton. 15

19 Table 3 Smulaton of the probablty of usng nterest relef Cohort Number of nterest relef peros None One Two Three Four Fve Sx an more Categores Marre Sngle Weeks< <=Weeks< Weeks>= Amount borrowe <500$ <=Amount< <=Amount< <=Amount< <=Amount< <=Amount Age< Age>= contnue on the next page 16

20 Years n program/years requre< Years n program/years requre>= Female Male Prvate Insttuton Publc Insttuton Fels of Stuy Busness/Amnstraton Agrculture Arts/scence Communty Servce/Eucaton Dentstry Engneerng/Technology Health Scences Law Mecne contnue on the next page 17

21 Traes Theology Level of Stuy Non-egree Unergrauate Masters Ph.D Provnce of Stuy Alberta BC Mantoba New Brunswck Newfounlan Nova Scota Ontaro Prnce Ewar Islan Saskatchewan contnue on the next page 18

22 Yukon Total number of observatons *The numbers below the category names are the number of observatons n each category. *The probabltes n the columns are the mean probablty of usng nterest relef for the observatons n that category. *The numbers n talcs are the stanar evatons of the probabltes for that category. 4. A uraton moel for the repayment of stuent loans Now that we have looke at the etermnants of havng a clam or nterest relef we want to focus on the rembursement tself. What characterstcs make one nvual repay n a shorter pero of tme than another? Do people ten to repay ther loan quckly or slowly? How oes the tme spent n the rembursement phase affect the probablty of full remttance at any gven tme? Those are questons that can be answere through the use of an econometrc uraton moel. A uraton moel proves us wth a survval functon whch characterzes the probablty of survval n the repayment state the tme spent before total rembursement. It s also assocate wth a hazar functon whch gves us the rate at whch a stuent exts the repayment phase gven that he has not alreay exte. Lookng at the shape of the hazar rate functon wll tell us more about the pattern of loan repayment. A uraton moel can also nclue nepenent varables whch o not change the shape of the hazar but rather ts vertcal poston. A varable that affects the uraton negatvely wll make the hazar functon shft upwars leavng t more lkely for an nvual to ext the state at any gven tme. The ata we have for uratons before stuents repay ther loans conssts of observatons for the cohort. The uraton varable s efne as follows: the tme n months before total loan repayment by the stuent startng at consolaton ate. The varable s censore f at the tme the atabase was constructe the stuent was stll n repayment phase. There are censore observatons or 3 per cent of the total. 19

23 A loan eeme n efault s not consere repa except f t s recovere by a collecton agency or the government. We nclue ummy varables for clams an nterest relef n the regresson thus ncatng a stuent who experences fnancal ffcultes. Thus these varables are treate here as exogenous. Three reasons justfy our choce. Frst a ten-year pero s relatvely short for the repayment of stuent loans therefore we conser ths uraton moel an nvestgatve exercse. Secon we o not have strong nstruments to use for the clam an nterest relef varables. Fnally a jont estmaton of clam-nterest relef-uraton of repayment of loans wll mpose a lognormal hazar rate to form a trvarate normal strbuton wth the probt for clams an the orere probt for nterest relef The uraton moel We estmate a uraton moel wth a Webull hazar an a Gamma correcton for unobserve heterogenety. The unobserve characterstcs or varables such as the nvual s motvaton to fn a job health status nee partcular attenton n uraton moel. The log-lkelhoo functon estmate for ths moel s: p1 p [ ln( ) ( )] + + p λ p ( λ ) ln 1 θ ( λ ) ln 1 θ ( λ 1 = θ ln( L ) δ t + t uncensore all t) where ' ( x) = exp λ β an X I = (one correcton ummy weeks of stuy amount borrowe age years of stuy/years requre nterest relef ummy clams ummy sex type of nsttuton [prvate ummy] martal status fel of stuy ummes level of stuy ummes provnce ummes. See Table 1 for etals). The δ coeffcent s equal to one for the observatons on nvuals who exte the repayment phase (the uncensore observatons). About 10% of nvuals repa ther loan mmeately when the consolaton pero starte. Most lkely for these nvuals the loan was not essental to ther pursut of stues. Snce we take the natural log of the uraton varable 0

24 t we a to the observatons for whch t = 0. Those observatons are then gven a value of one for a correcton ummy zero otherwse. The survval functon of ths moel s: S ( t) = 1 p [ 1+ θ ( λt) ] θ an the hazar functon s: λ p 1 () t = λp( λt) [ S() t ] θ We wll see n the results that θ s larger than zero an thus our correcton for heterogenety s necessary. 4.. The emprcal results The coeffcents for the uraton moel are estmate usng maxmum-lkelhoo optmzaton from Gauss. The results are presente n Table 4. The graphs of the hazar functons are presente n Fgure 6. Interestngly enough when a Webull hazar s correcte for heterogenety the shape of the hazar changes an s no longer strctly ncreasng or ecreasng. We can see n Fgure 6 that the hazar rate s ncreasng up to a certan pont close to two years an then ecreasng as the uraton goes up. Ths shape s what we expecte: The probablty of fully rembursng a loan starts at a certan level at consolaton ate then ths probablty goes up wth tme as the ex-stuents fn employment then get experence a better salary an an overall mprove fnancal stuaton. After a certan tme represente by the peak n the hazar functon the probablty of ext goes own ue to the fact that those nvuals stll n the repayment phase at that pont ten to have ffculty repayng because of an unerpa job or a heavy ebt loa. Ths leas to a lower hazar rate an that rate contnues ecreasng as tme goes by. What ths shows us s that t becomes less lkely for an nvual to ext the repayment spell the longer t s been snce the consolaton. Whle ths general shape was the one expecte for such a moel we woul have thought that the return pont n the hazar rate functon here at aroun two years woul be further to the rght after a longer pero of tme. Two years seems a short tme to get r of a stuent loan especally when you conser the amounts borrowe an 1

25 the avantageous nterest rates. What coul explan that ths curve s skewe to the left? Frst t coul be because of the number of ex-stuents who remburse ther loan n one shot at the consolaton ate or rght after. These people probably n t really nee a loan an borrowe only for a strategc reason. The secon explanaton for that early return pont mght be a phenomenon of ebt averson. Even f borrowers on t have to repay quckly they prefer to o so because they feel uncomfor wth nebteness.

26 Table Cohort wth correcton for heterogenety Parameters Estmates St. Dev. T-stat Prob. Parameters Estmates St. Dev. T-stat Prob. Health Scences Constant Law Correcton for Mecne uraton=0 Duraton>0 ref. Traes Number of weeks of Theology ref. stuy Amount borrowe e Age Level of stuy Years of stuy/years Non-egree requre Interest Relef = Unergrauate Interest Relef = 0 ref. Masters Clams= Doctorate ref. Clams=0 ref. Female Provnce of stuy Male ref. Alberta Prvate Insttuton Brtsh Columba Publc Insttuton ref. Mantoba Marre New-Brunswck Not marre ref. Newfounlan Nova Scota Fels of stuy Ontaro Busness/Amnstrat on Agrculture Prnce Ewar Islan Arts/scence Saskatchewan Communty Yukon ref. servce/eucaton Dentstry Engneerng/Technolo P gy θ Number of observatons: Log- lkelhoo : Mean log-lkelhoo :

27 Fgure 6 It s nterestng to look at the sgns of the estmate coeffcents presente n Table 4. A negatve (postve) sgn means that the varable has a negatve (postve) effect on the uraton an nuces a shft upwars (ownwars) n the hazar rate functon. The coeffcent assocate wth the correcton ummes for a uraton equal to zero s very large hghly sgnfcant an negatve. Of course f an observaton has a value of zero for a uraton ths greatly lowers ts uraton. But ths result s nterestng mostly because t shows us that there are nvuals who fully remburse ther loan the mnute they get out of school. Clearly they ha a loan for a fnancally strategc reason an not because of nsuffcent funs to atten school. Ths s part of the realty of stuent loans: stuents who get fnancal a but on t really nee t. Varables havng a postve coeffcent nclue: the amount borrowe age the nterest relef ummy an the marre ummy. It comes as no surprse that the amount borrowe has a postve an sgnfcant effect on the tme before repayment. Just lke the amount borrowe ncrease the probablty of efaultng or resortng to the nterest relef measure here t ncreases the tme spent n the repayment phase. The age varable has a postve effect too but qute small. It s sgnfcant but perhaps oesn t play a major role. Same scenaro for the marre varable but wth a slghtly larger effect. Ths result shows us that a marre person s less lkely to ext 4

28 the repayment phase than an unmarre one. Ths s consstent wth the assumpton that marre nvuals mght nee to support ther partners an/or chlren makng t more ffcult for them to remburse ther stuent loans. Another realty of stuent loans we have to keep n mn s the fact that those loans generally have very low nterest rates. For those who have ebt from fferent sources lke cret car blls car payments or mortgage payments t mght be part of a fnancal strategy to repay the stuent loan last. To avo payng hgh nterest on the cret cars for example one mght fully pay ther cret car blls thus postponng payment of the stuent loan. Snce stuent loans present such avantageous rates they are often at the bottom of the prorty lst when t comes to payng the blls. The nterest relef ummy coeffcent s very sgnfcant qute large an postve. It clearly ncates that a stuent who s on nterest relef has a much lower hazar rate for extng the repayment spell. Now whle the nterest relef ummy s an ncator of a stuent n fnancal ffculty there mght be a smpler explanaton for the strength of ts mpact on the hazar rate of ext. Usng the nterest relef opton lengthens the repayment because that s what t precsely oes: help stuents go through a ffcult pero lettng them efer payments untl a later ate. For the clam ummy the postve coeffcent suggests that havng a clam makes the uraton before repayment longer whch s what we woul normally expect: a stuent who efaults s one who has ffculty meetng hs payments an t wll probably take a long tme for a collecton agency to collect the money owe. Lookng now at the fels of stuy coeffcents we see that only the ones for entstry health scences an mecne are sgnfcant. They are all negatve an relatvely large especally the one for mecne. Ths comes as no surprse at all: grauatng as a mecal octor or a entst greatly lowers the uraton of the repayment pero. Smple to unerstan: they make more money on ther jobs have fewer or no fnancal ffcultes an so repay much faster. The other sgnfcant varables we have are busness agrculture art an scence eucaton an traes all of whch are postve. Invuals grauatng n those fels ten to take more tme to remburse ther loans an ther hazar rate s lower compare to the reference fel whch s theology. 5

29 If we turn now to the level of stuy ummes we see that the non-egree an unergrauate varables are sgnfcant an postve. Ths mples that compare to borrowers who stuy at the Ph.D. level the ones wth an unergrauate egree or no egree show a longer pero of repayment. Another measure we can look at whle analysng the results of an econometrc uraton moel s the mean tme. It s efne as the length of tme after whch half of the stuents have repa ther loan or exte the repayment phase. It s the value of uraton for whch the survval functon equals 0.5. The mean tme for the cohort s about 41 months or 3½ years. Ths tells us that half the stuents fully repay ther loan after 3½ years. Ths result s certanly affecte by those nvuals who repa ther loan mmeately at the consolaton ate. Despte aressng several mportant questons t woul be nterestng for further stues to have access to more extene atabases. Other extensons coul nclue a more complex moel wth tme-varyng covarates such as unemployment economc growth or changng personal characterstcs. Wth a longer tme pero t wll be worthy to aress the enogenety ssue wth regars to the clams an nterest relef varables an to better account for those nvuals repayng ther loan at the consolaton ate. 5. Concluson an polcy ssues Ths paper has benefte from access to a unque set of ata for the stuy of patterns of stuent loans repayment n Canaa. Bllons of ollars are at sake an more than three hunre thousan stuents have been assocate wth the program n recent years. The justfcaton for ths program stems from a government polcy ame at facltatng access to hgher eucaton for all Canaans (the same apples to Québec whch has ts own program) n the context of a knowlege base economy. Unlke real or fnancal nvestments human captal nvestment has nothng tangble to offer to the lenng nsttuton n case of efault. Thus the captal market s an mperfect nsttuton when t comes to offerng loans to stuents. The Canaa Stuent Loans Program (CSLP) s an answer an proves the necessary loans to stuents wth emonstrate 6

30 nee. But nvestment n human captal s lke any other nvestment a rsky enterprse. A realty of the eucatonal loan system s that close to one ex-stuent n fve smply cannot repay hs or her loan. Many more experence ffcultes n payng back ther loan. Hgh levels of efault are a threat to the vablty of the system. Snce the CSLP s constantly n efct t s actually gvng subses to hgher eucaton when n fact t was create to correct the mperfect captal market. Wth nebteness an the number of stuents who requre fnancal a growng larger an larger the health of the whole system s at stake. It s thus crucal to unerstan the etermnants of loan repayment an efault. Ths paper has stue those etermnants as well as the probablty of usng the nterest relef opton a specfc measure to ease repayment of the loan when a partcpant goes through a pero of unemployment or partal employment. Among the many results erve from our econometrc moels a few are partcularly nterestng for polcy ssues. Frst fnshng the program supporte by a loan s essental to avong efault. Therefore t may be worth conserng polces that wll rewar anyone who completes hs or her program. For example by transformng part of the loan nto a grant f ths objectve s met n ue tme. On the other han too much flexblty n access to loans mght encourage experments by stuents that coul turn sastrous for the stuent an the natonal loan program. A loan program shoul also come wth some nformaton on the rsk nvolve for the stuent before he or she nvests n a partcular fel or program. Better nformaton about the labour market s essental. One partcular concern s the relatvely hgh level of efault for stuents attenng prvate schools. Relatvely easy access to loans coul be an nvtaton for prvate nsttutons to captalze on that fact wth varous eucatonal programs havng lttle bearng on the realty of the labour market. Eventually serous nsttutons wll establsh a reputaton but for some stuents t wll be too late. The secon result concerns the nterest relef measure that seems not to have playe ts role of helpng stuent pass through ffcult tmes. Ths coul explan why recently mportant mofcatons were brought to ths program. It wll be mportant to revew ths queston wth a new cohort. Fnally not all stuents neee the loan program to pursue hgher eucaton. Wth scarce resources funng these wnfall gans s a flaw n the program. Whether by chance because of ebt averson or out of a partcular sense of cvc uty many partcpants repa ther stuent loans n a relatvely short pero of tme. A 7

31 polcy systematcally remnng the benefcary of hs own commtment to the perpetuaton of the collectve loan program mght be useful to conser startng two years after the loan s consolate. More work nees to be one however to complete the stuy of patterns of loan repayment n Canaa. In aton to some methoologcal ssues rase earler our estmates nee to be upate wth new an revse ata. 8

32 References FINNIE Ross an SCHWART Saul (1996) Stuent Loans n Canaa. Past Present an Future C.D. Howe Insttute Toronto Observaton 4 16 pages. PLAGER Laure an CHEN Ewar (1999) Stuent ebt from to : An analyss of Canaa Stuent Loan ata Eucaton Quarterly Revew Statstcs Canaa- Catalogue no vol 5(4) The Canaa Stuent Loan Program webste 9

33 Appenx Invual contrbutons to the lkelhoo functon of the clam-nterest relef pero (probtorere probt) moel are calculate usng a bvarate normal strbuton of the resuals ) NB(0011 ~ ρ wth a correlaton coeffcent of ρ. Specfcally the jont probabltes are efne as follows for all cases: P(CLAIMS =1 NBIR =0) = ( ) β φ - -X P(CLAIMS =1 NBIR =1) = ( ) δ β φ X P(CLAIMS =1 NBIR =) = ( ) 1 δ β φ X P(CLAIMS =1 NBIR =3) = ( ) δ β φ X 3 3 P(CLAIMS =1 NBIR =4) = ( ) δ β φ X P(CLAIMS =1 NBIR =5) = ( ) δ β φ X P(CLAIMS =1 NBIR =6) = ( ) 6 5 δ β φ X P(CLAIMS =0 NBIR =0) = ( ) β φ X P(CLAIMS =0 NBIR =1) = ( ) 1 1 δ β φ X P(CLAIMS =0 NBIR =) = ( ) 1 δ β φ X 30

34 P(CLAIMS =0 NBIR =3) = ( ) 3 3 δ β φ X P(CLAIMS =0 NBIR =4) = ( ) δ β φ X P(CLAIMS =0 NBIR =5) = ( ) δ β φ X P(CLAIMS =0 NBIR =6) =. ( ) 6 5 δ β φ X 31