UNIVERSITY TUITION SUBSIDIES AND STUDENT LOANS: A QUANTITATIVE ANALYSIS YAAKOV GILBOA * ** AND MOSHE JUSTMAN Abrac We ue a calbraed macroeconomc model o examne he dfferen effec of unvery and uden loan polce amed a mprovng acce o publc hgher educaon. Suden loan ha condon repaymen on fuure ncome ubanally mprove acce. The gnfcan fcal co of uch loan can be offe by reducng curren ubde, whou gnfcanly mparng acce. The mpac of uch polce on graduaon rae maller han on enrolmen rae and even he mo effecve meaure leave a very large gap beween rch and poor. None of hee polce ha a gnfcan effec on he economy oal oupu. 1. INTRODUCTION Governmen facng fa-growng demand for broader acce o ubdzed publc hgher educaon are fndng hey canno manan he qualy of a rapdly expandng unvery yem whou rang axe. Whng o avod h, many are conemplang, or have already mplemened, reducon n ubde whch are ofen coupled wh uden loan program amed a eang lqudy conran, and n many of hee program repaymen of he loan condoned on fuure ncome o a alo o aborb ome of he rk of a unvery educaon. Thoe who oppoe uch ep warn ha rang undermne he role of he unvery a an nrumen of ocal mobly bu profeonal economc opnon generally uppor hee polce, argung ha nadequae acce o cred raher han he level of ha deer worhy bu dadvanaged uden from enrollng n hgher educaon. Tuon ubde, he argumen goe, nroduce an neffcen doron of ncenve whle uden loan drecly addre he problem of nuffcen lqudy whou wang reource ha could oherwe be channeled o beer purpoe. Moreover, a acce o hgher educaon regulaed no only by bu alo by academc requremen, he uden who benef mo from ubde generally come from hgher-ncome famle, o ha curren ubde are regreve n effec. The am of h paper o gauge he relave mporance of hee dfferen effec by mulang dfferen combnaon of ubde and uden loan whn a * Sapr College; yaakovg@bgu.ac.l. ** Ben-Guron Unvery; juman@bgu.ac.l.
calbraed macro model and quanfyng her effec on acce o hgher educaon, on fcal co, and on aggregae meaure of effcency, ncome drbuon and nergeneraonal ncome mobly. The need for mulaon are becaue of he lmed emprcal evdence we have on hee ue. We have no yemac evdence of he effec of hee polce on effcency: wha we know abou her effec on acce draw largely on raw nernaonal comparon, and fcal co can be een o vary wdely among counre. We know, for example, ha Aurala and New Zealand, depe adopng co-baed and ncome-conngen loan program, manan erary enrolmen rae ha are a hgh a or hgher han counre uch a Denmark, France, Germany, Ireland and Sweden, whch charge lle or no (OECD, 003, Table C.1. 1 However, hee counre educaon yem dffer n many oher way oo, whch mu cloud he comparon. In he Uned Sae, where unvery ubanally hgher, and fundng arrangemen are le comprehenve, economerc analy ndcae ha lqudy conran have lle effec on college enrolmen rae (Carnero and Heckman, 00; Cameron and Taber, 004, hough acce o he mo pregou and mo expenve program reman rongly condoned on ocoeconomc background. The fcal co of uden loan program exhb conderable varaon. Recovery rae are far from perfec even n well-run program due o nere rae ubde, admnrave co, and loan defaul. Barr (004, p. 41 emae ha n he Uned Kngdom a hrd of all money len o uden no repad" and Zderman and Albrech (1995 reach mlar concluon. Chapman and Ryan (005 emae for Aurala lower, beween 15% and 5%. Experence wh loan program n newly nduralzng counre vare even more wdely, wh ome, noably Hong Kong, admnerng relavely low-co loan program whle n oher, uch a Thaland, loan recovery rae are o low a o render her loan program effecvely equvalen o ubde (Zderman, 004. Several recen ude have ued calbraed mulaon o ae he mpac of and loan polce, 3 and we connue n h ven, defnng and calbrang a decon-baed, general equlbrum, macro model wh a cenralzed yem of hgher 1 On Aurala Hgher Educaon Conrbuon Scheme (HECS, ee Deparmen for Educaon Scence and Tranng (004 and Chapman and Ryan (005 among oher; on fundng of hgher educaon n New Zealand, ee Mnry of Educaon/Terary Educaon Common (003. For an overvew of hgher educaon fundng n varou counre ee (UK Deparmen for Educaon Servce (004. On hgher educaon fundng reform n Grea Bran, paerned on Aurala HECS, ee Houe of Common (004 and Barr and Crawford (005. Boh Hong Kong and Thaland program core hgh n reachng needy canddae. Zderman (004 alo decrbe le ucceful program n Souh Korea, he Phlppne and Chna. 3 Among hee are Heckman, Lochner and Taber (1998, Keane and Wolpn (001, Caucu and Kumar (003, Akyo and Ahrea (005, Gallpol, Meghr and Volane (006, Garrga and Keghley (007 and Lochner and Monge-Naranjo (008.
educaon, whch we ue o mulae dfferen and loan polce. However, everal key aumpon e our model apar from earler effor. 4 Fr, we condon boh enrolmen and graduaon on academc achevemen. Thu hgher educaon ac a a "double fler" (Arrow, 1973 n whch academc e mperfecly correlaed wh rue ably regulae boh admon and graduaon. Propecve uden who mee academc enry requremen decde wheher o aend unvery or no, and graduaon a ochac varable povely correlaed wh ably. 5 Th capure he mporance of non-moneary barrer o acce: even when lqudy conran are reolved, academc admon andard mu be me o gan enry; and even f admon andard are waved here no pon aendng unvery unle here a good chance of graduang. Boh fler lm he mprovemen n acce ha can be acheved hrough and loan polce; 6 and graduaon requremen lm he poenal effcency lo ha reul from allowng uden wh a weak pror record of academc achevemen o enrol n hgher educaon. The endogenou deermnaon of wage n he model depar from prevou reamen n wo mporan way. Fr, he margnal produc of klled and unklled labor, on whch ndvdual wage are baed, are derved from a need CES producon funcon n whch capal equpmen a cloe ubue for unklled labor bu no for klled labor. Th follow Kruel e al.' (000 emprcal analy and allow u o capure wha we beleve an eenal pon whch mpler funconal form m: he fall n he educaon premum checked by ncreae n he ock of capal equpmen makng up for he declne n he hare of unklled labor. 7 Aben uch a mechanm, a 3 4 The hgher-educaon yem decrbed n our model, n whch unvery aendance a dcree choce raher han a connuou decon on he quany of educaon purchaed, nearer o he more cenralzed, publc yem of hgher educaon operang n mo European counre, Canada, Aurala, New Zealand and Irael, whch charge unform acro nuon ha offer mlar qualy, han o hgher educaon n he Uned Sae, whch offered n a much wder range of unregulaed quale and prce. (Bu prevou effor geared o modelng hgher educaon n he Uned Sae, whle pobly allowng uden o chooe he quany of educaon hey acqure gnore he wde range of qualy and prce avalable; cf. Lochner and Monge-Naranjo, 008; Caucu and Kumar, 003; Akyol and Ahreya, 005. The qualy-prce dmenon eem crucal for aeng acce n he Uned Sae. Our cenral aumpon regardng he mporance of academc e n deermnng boh enry and graduaon he economy ably o ubue capal equpmen for unklled labor, and he combned role of human capal and gnalng n deermnng wage are vald for boh ype of yem. 5 Modelng he producon of kll hrough hgher educaon a a funcon of maeral reource and uden effor beyond he cope of h paper. Corell (1993, 1994 and Be (1998 model he effec of admon and graduaon polce on uden effor, and Garrga and Keghly (007 offer a quanave analy of college behavor a a mul-perod rky nvemen n whch uden decde how many cred o ake and how much effor o nve n her compleon. However, here are a ye no relable emprcal emae of academc producon funcon ha lnk unvery npu and oupu, largely becaue of he dffculy of meaurng unvery oupu (Ehrenberg, 004. 6 The praccal gnfcance of h pon lluraed by Bra e al. (008 emprcal udy, whch how ha he expanon of hgher educaon n Ialy had lmed effec on nequaly n achevemen precely becaue greaer acce, whle gnfcanly rang enrolmen rae, had a much maller effec on he probably of graduang. 7 Sude of hgher educaon ha do no ake h effec no accoun nclude Heckman, Lochner and Taber (1998, who argue ha gnorng general equlbrum effec overemae he enrolmen repone o a by an order of magnude a ncreae n enrolmen wll be dampened by a
4 large expanon of hgher educaon hould reul n a ubanal fall n he educaon premum, whch ha no been he cae n he la hree decade. 8 In addon, we aume ha ndvdual wage ulmaely reflec no only he pecfc ably of ndvdual worker bu alo he average producvy of klled and unklled labor repecvely, a employer canno mmedaely dcover ndvdual producvy. Th arbue a gnalng effec o hgher educaon n addon o role n buldng human capal. 9 A uch an effec mpue negave exernale o educaon, mple ha a marke oluon whou he ue of academc fler o regulae acce o hgher educaon and graduaon no "fr be" even when uden pay full co (Glboa and Juman, 005. Anoher mporan feaure of our model our dealed analy of nergeneraonal mobly. Broader acce o hgher educaon ndependen of parenal background a he core of he publc debae on fnancng hgher educaon and wdely vewed a a ocal goal n own rgh, no only n erm of effec on he drbuon of ncome. 10 To gauge he effec of dfferen polce on ocal mobly we model ably and parenal ncome a followng a jon bvarae lognormal drbuon, whch we calbrae o emprcal obervaon and hen follow n our mulaon he mpac of dfferen polce on he enrolmen and graduaon rae of propecve uden rafed by parenal ncome qunle, and on an aggregae meaure of nergeneraonal ncome mobly. Lqudy conran play a cenral role n he model. Followng Becker (1975 and Cameron and Taber (004 among oher, we aume ha aben governmen nervenon, uden from poor famle face a hgher rae of nere n fnancng her educaon han do uden from more affluen home, and h alo conran her pendng on conumpon whle hey are udyng. Th capure he flexbly of he lqudy conran ha famle face n fundng hgher educaon and he rercon ha boh formal and nformal lender ypcally place on he ue o whch uden can apply borrowed fund, and yeld a monooncally ncreang relaonhp beween nal human capal before hgher educaon and boh enrolmen and graduaon rae. 11 conequen declne n he wage premum; and Caucu and Kumar (003 and Akyol and Ahreya (005, who ee he man benef of ubde n lowerng he college premum, whch reduce rk. 8 Oher work ha emphazed he role of kll-baed echnologcal change n mananng he educaon premum (e.g., Barel and Scherman, 1999. 9 There exenve evdence ha educaon conrbue o ndvdual earnng hrough boh channel. See We (1995 for an early revew of he emprcal evdence. 10 The leraure ha examne he lnk beween apec of he paren' ocoeconomc au and her chldren' educaonal achevemen nclude recen work by Cameron and Heckman (1998, 001, Ellwood and Kane (000, Keane and Wolpn (001, Carnero and Heckman (00, Reucca and Urrura (004, Juman and Glboa (006 and Belley and Lochner (007. Earler work revewed by Haveman and Wolfe (1995. 11 Many recen ude model lqudy conran a a cap on uden lendng. However, a Lochner and Monge-Naranjo (008 pon ou, aben a rercon on conumpon, h mple a negave lnk beween ably and nvemen n hgher educaon (for emprcally oberved value of he neremporal elacy of ubuon, whch conradc he pove lnk oberved n he daa. They reolve h by combnng a cred cap wh he pulaon ha uden loan canno be ued o fnance
The benchmark we ue o calbrae he model baed on he Irael economy and cenralzed hgher educaon yem, whch offer hree- and four-year bachelor degree a a fxed level of annual. Tuon proporonaely comparable o ha n publc unvere n he Uned Sae, Grea Bran, Aurala and New Zealand, wh full for a degree cong roughly half he average annual alary of a hgh chool graduae, or abou one hrd of annual per capa GDP. There no way of precely eparang eachng co from reearch a a unvery, bu akng he budgeng pracce of Irael' Councl of Hgher Educaon a a gudelne, we aume ha cover abou half of unvery eachng co. Admon are regulaed by academc crera and calbraed n he model o approxmae curren enrolmen and graduaon rae n Irael. There no gnfcan uden loan program, and lqudy conran n he benchmark cae are e o approxmae he drbuon of uden enrolmen by paren' ocoeconomc au. Afer calbrang he model we mulae dfferen combnaon of level and uden loan polce, and compare her effec. The polce we conder are he benchmark cae of paral ubde whou uden loan; uden loan ha cover and lvng expene coupled wh he curren level of ubde; uden loan whou ubde; and uden loan wh conngen repaymen, whch forgve ome or all of he deb ncurred dependng on he uden' wage ncome, combned wh paral ubde and wh no ubde. Each polcy evaluaed aumng appled over he me requred for a full urnover of he labor force, and n each cae we calculae enrolmen and graduaon rae by paren' ncome qunle a a drec meaure of acce; he nergeneraonal correlaon of ncome a an aggregae meaure of ncome mobly; he Gn coeffcen of lfeme wage ncome and he college wage premum a ndcaor of wage nequaly; ndce of aggregae oupu and varaon n aggregae uly a ndcaor of effcency; loan recovery rae; and he ax rae requred o cover ubde and unpad loan. Prevewng he reul of hee mulaon, we fnd ha uden loan n hemelve have only a mall pove effec on acce o hgher educaon, hough provdng uden loan allow ubde o be removed wh lle advere effec on acce, hu freeng fcal reource for oher worhwhle purpoe or enablng a reducon of axe. Aborbng ome of he rk of hgher educaon by condonng repaymen of uden loan on he uden' ncome afer enerng he workforce ubanally mprove acce for uden from low-ncome famle, ncreang boh enrolmen rae and, o a leer degree, graduaon rae. Th uppor Akyol and Ahreya (005 empha on he mporance of rk averon a an nhbng facor ha lm acce o hgher educaon. Nonehele, he cope for mprovemen lmed, and dfference n enrolmen and graduaon rae beween uden from dfferen ocoeconomc background reman large. The hgh fcal co of conngen repaymen of loan can be offe by removng ubde wh lle acrfce of acce. The general ncreae n graduaon rae caued by uden loan lead o a fall n wage nequaly, and generally ha a pove effec on oal oupu, bu hee effec are 5 non-choolng-relaed conumpon. Our nroducon of academc flerng furher renforce he pove lnk, n our model, beween pre-college ably and enrolmen.
6 proporonally o mall a o be dwarfed by mporan elemen gnored n our analy ncludng he co of admnerng he program, he cope for abue, he exen of ncomplee nformaon among college canddae, and he role of non-economc facor n educaon decon. The effec of hee polce on aggregae uly, a an mperfec general ndcaor of welfare, generally even maller n proporonal ncomeequvalen erm and ndeermnae. Our general approach buld on wo mporan economc perpecve on educaon: macroeconomc analye of how he accumulaon of human capal affec nergeneraonal mobly and wage nequaly (e.g., Becker and Tome, 1979; Loury, 1981; Bénabou, 1996; Durlauf, 1996; Haler and Rodrguez-Mora, 000 o whch we add rucural deal; and more rucured analye of hgher educaon (Arrow, 1973; Sglz, 1975; Danzger, 1990; Loury and Garman, 1993; Fernandez and Gal, 1999; Epple, e al., 003 whch we place n a general equlbrum conex. The ue we conder here are cloely relaed o work by Berocch and Spaga (004 and Checch e al. (1999 on he mpac of educaon yem on ncome nequaly and ocal mobly; o emprcal analye of he mpac of dfferen fundng cheme on acce o hgher educaon, uch a Keane (00 and Chapman and Ryan (005, and Barr' (004 negrave eay; and more drecly o calbraed analye of uden loan and ubde by Heckman, Lochner and Taber (1998, Keane and Wolpn (001, Caucu and Kumar (003, Akyol and Ahreya (005, Gallpol, Meghr and Volane (006, Garrga and Keghley (007 and Lochner and Monge-Naranjo (008. None of hee ncorporae academc barrer o enry and graduaon or ue an aggregae producon funcon wh dfferen elace of ubuon beween capal and klled and unklled labor or allow ha hgher educaon ha a gnalng effec n he labor marke. Fnally, he bac rucure of he model developed n h paper draw on our earler calbraed analy of unvery admon andard (Glboa and Juman, 005. The paper organzed a follow: n Secon we decrbe he model; n Secon 3 we calbrae ; n Secon 4 we compare dfferen fundng polce a hey affec acce, drbuon, mobly, oupu, welfare and fcal co; and Secon 5 conclude. In an appendx we fll n ome of he echncal deal and preen envy analye.. THE MODEL We defne a model n whch paren auomacally bequeah nnae able o her chldren and nve economc reource n her early developmen. Chldren hen reach young adulhood wh a record of pror achevemen, whch ndcae her academc poenal. A cenralzed yem of hgher educaon regulae admon on he ba of h pror ndcaor. 1 Thoe offered admon decde wheher o enrol, pay, and 1 The preen analy focue on polce, and o hold fxed an admon creron mlar o ha generally appled n Irael' hgher educaon yem. Th creron ncome-neural. Glboa and Juman (005 focu on academc admon requremen and conder alo ncome-baed affrmave acon admon polce ha favor applcan from low-ncome houehold. The wo ype of polcy could be combned n he model whou dffculy, a decrbed n noe 16 below.
loe pad employmen whle hey udy. In he benchmark cae, hee co are funded hrough he famly a an nere rae ha decreae wh parenal ncome. Thoe who chooe o udy and hen uccefully graduae earn a degree ha open he door o employmen n klled job; hoe whou degree work n unklled job. Worker earn a wage equal o a weghed average of her own margnal produc value and of he average margnal produc value of her occupaon klled or unklled. Young adul ancpae her fuure wage n decdng wheher o udy or no, and we focu on equlbra n whch her ancpaon are realzed..1 The houehold, before hgher educaon Conder an economy wh a connuum of houehold, each comprng a paren and chld, and ake paren' afer-ax ncome a exogenouly gven. 13 Denoe he lfeme dpoable ncome of he paren n houehold by y, and aume drbued lognormally n he populaon wh mean µ y and varance y, ln y ~ N (µ y, y. Denoe by a he unobervable "nnae ably" of he chld n houehold and aume ha povely correlaed wh parenal ncome: 14 (1 ln a = ln y + u a, where u a an ndependen, normally drbued durbance erm wh zero mean and varance ua. The chld' pre-college level of human capal h deermned by her nnae ably and by addonal parenal nvemen, b : ( ln h = A + αln a + δ ln b, where A, α, γ, and δ are conan. Aumng paren' nvemen n her chld' cognve developmen proporonal o ncome, 15 b = ξ y, we have afer ubuon (3 ln h = A + δ ln ξ + (α + δ ln y + α u a, whch mple ha ln h alo normally drbued, wh mean and varance 13 We wll aume a balanced budge conran, for compleene. However, a he hgher educaon fundng polce on whch our analy focue have a very mall effec on governmen pendng, for praccal purpoe, ax rae can be gnored (and a we how n a envy analy. In Irael he oal governmen hgher educaon budge, for eachng and reearch, abou 0.8% of GDP, and aumng half of ha for eachng, oal governmen pendng on eachng n hgher educaon amoun o 0.4% of GDP, whch abou 1% of ax revenue. Moreover, one could argue ha flucuaon n he governmen hgher educaon pendng are generally no ranlaed no varaon n he ax rae bu raher affec oher budge em, uch a repaymen of publc deb. 14 Th correlaon em from genec or culural facor, whch "money can' buy". In Juman and Glboa (006 we how ha even n kbbuzm (communal vllage here a ubanal pove correlaon beween chldren' e core and her paren' educaon whch n he general populaon povely correlaed wh earnng. 15 Th mplcly aume ha paren' nvemen of economc reource n her chldren early developmen canno be fnanced by borrowng agan her chldren fuure ncome h a capal marke mperfecon ha canno be reolved and ha nvemen n educaon ndependen of chldren ably (h hold f he elacy of ubuon beween conumpon and educaon equal one. 7
8 (4 µ h = A + δ ln ξ + (α + δ µ y, (5 h = (α + δ y + α ua. We aume ha ndvdual know her own human capal h bu ha unvery admon offcer have acce only o a ochac enry core ha ummarze her record of pror achevemen, and whch povely correlaed wh h : (6 = ln h + u, where u an ndependen, normally drbued durbance erm wh zero mean and varance u. Afer ubuon we have (7 = A + δ ln ξ + (α + δ ln y + α u a + u, o ha alo normally drbued, wh he ame mean a h bu larger varance: (8 µ = A + δ ln ξ + (α + δ µ y = µ h, (9 = (α + δ y + α ua + u.. Hgher educaon There a cenralzed yem of hgher educaon n he economy ha offer a ngle degree. I pecfe a hrehold θ for he obervable enry core a an academc requremen for admon. 16 Suden who mee h requremen and chooe o enrol, pay an annual fee P (whch may or may no cover he full co of educaon. In order o graduae, hey mu aend chool for T e year and earn a pang grade, where grade are a ochac funcon of human capal: (10 = ln h + u and u an ndependen, normally drbued durbance erm wh mean zero and varance u. Subuon how ha normally drbued wh mean and varance (11 µ = µ = µ h, (1 = (α + δ y + ua + u. Suden who fal o aan a pang grade drop ou of chool afer T d year and ener he labor marke a non-graduae performng unklled job; falure occur before he full coure of udy compleed, T d < T e, o only paral and lvng co are 16 A more general form of admon crera, condered n Glboa and Juman (005, φ + (1 φ ln y > θ, where φ > 1 yeld ncome-baed affrmave acon polce ha favor applcan from lower-ncome houehold, and φ = 1 yeld a purely "mer-baed" creron ha gnore parenal ncome. To focu here on he effec of polce we hold fxed a mer-baed admon creron.
ncurred. Graduaon open he door o klled job. 17 Wheher or no he uden graduae uccefully, here are and lvng co o be funded, and we aume n he benchmark cae ha he capal marke for fundng hem mperfec. Suden may be able o fund ome of hee co hrough par-me work bu are dependen on her paren for ubanal uppor, wheher from he paren' own reource or from exernal ource for whch he paren co-gn. We aume ha h dependence conran uden' borrowng for conumpon whle hey udy wheher hrough formal conran e by exernal lender or mplc conran whch paren place on her chldren whle hey uppor hem. To mplfy he analy we gnore earnng from par-me employmen whle udyng a unvery, and e annual conumpon whle a unvery exogenouly (and unformly equal o c 0 ; hence, annual fnancng need are P + c 0. We aume ha he co of fnancng hee need a decreang funcon of parenal ncome, o ha uden from lower-ncome home face hgher fnancng co. Th may em from he lower (opporuny co of fundng h expene by reducng avng a oppoed o he hgher (ou-of-pocke co of ncurrng addonal deb; or from he hgher expeced recovery co ha lender may ancpae when lendng o paren wh le lqud ae. Denoe by r(y he rae of nere pad by a houehold wh parenal ncome y, and aume ha weakly decreang n ncome wh (13 r(y > r 0, where r 0 he marke rae of nere, and rc nequaly hold a lea for lower ncome. I follow from he precedng expoon ha he four varable ln y, ln h, and hare a jon mulvarae normal drbuon. Sraghforward calculaon yeld he followng correlaon beween par of varable: (14a y = (α + δ y /, (14b y = (α + δ y /, (14c yh = (α + δ y / h. (14d h = h /, (14e h = h /, (14f = h / [ ]. 9 17 A dcued n noe 4 above, graduaon a dchoomou varable employer do no look a grade, and do no dnguh beween hoe who fal a college and hoe who do no enroll. The model could be exended o allow graduaon o enhance human capal by a varable facor of β > 1, o ha a peron enerng college wh human capal h graduae wh human capal β h, where β a funcon of unvery npu. However, no poble o denfy β from macro daa when klled and unklled labor are dnc facor of producon; and denfyng from mcro daa would requre an economerc emae of he producon funcon of hgher educaon, on whch here lle agreemen (Ehrenberg, 004. The abence of a quanave emprcal lnk beween educaon qualy and he co of educaon alo preven u from ung he model o explore relaed ue of opmal qualy n hgher educaon.
10.3 Producon and wage We aume ha producon n he economy underaken by a connuum of dencal frm producng a ngle homogeneou good ung he ame conan-reurn-o-cale producon funcon. Aggregae oupu equal (15 Y = F (H u, H, K, where H u he unklled human capal of nongraduae, H he klled human capal of graduae and K he ock of capal equpmen. Le w u denoe he average wage per un of unklled human capal, w he average wage per un of klled human capal, and p he renal co of a un of capal equpmen. 18 We aume ha employer canno fully or mmedaely oberve ndvdual human capal, hence a worker n occupaon k (k = u, earn a pre-ax ncome y k ha proporonal o ndvdual ably, h, and he average ably of worker n her occupaon, denoed h k : (16 y k = w k [υ h + (1 υ h k ], where 0 < υ < 1. Th conen wh he general emprcal fndng (ee Jenck, 197, among oher ha meaured cognve ably ha lle effec on earnng a early age, exercng greaer nfluence laer n he lfe cycle. The co of ubde and of ncomplee recovery of conngen loan, when offered, funded by a proporonal ax on wage ncome, a he ax rae τ. 19 Excep for he decon o udy, he upply of labor nelac. 0 An ndvdual who doe no aend college work for T u year; a graduae ude for T e year and work for T = T u T e year; and one who ude bu fal o graduae ude for T d year and work for T f = T u T d year..4 The decon o udy Aume ha he lfeme uly V of ndvdual a dcouned negral of emporal uly U a he ubjecve dcoun rae η, where emporal uly U = U(c an ncreang concave funcon of conumpon by ndvdual a me. Indvdual eek o maxmze her expeced uly gven her ancpaon of fuure klled (graduae and unklled (nongraduae wage rae and of average klled and unklled human capal, and we aume ha all ndvdual hare he ame ancpaed value, 18 In general, facor prce may vary over me. For mplcy, we lm our analy o an equlbrum n whch ndvdual ancpae aonary facor prce. 19 We aume ha he governmen able o offer (non-conngen uden loan a he marke rae of nere a no exra co hrough an nfrarucure of ax collecon whch allow o recover deb a a lower varable co han ha n he prvae ecor. 0 Gallpol, Meghr and Volane (006 how ha allowng a varable upply of labor ncreae wage nequaly among houehold.
(17 ω = ( w e, w u e, h e, h u e,τ. 11 Conder fr a peron who doe no aend unvery. To mplfy he analy, aume ha he borrowng rae of nere he face no lower han η and ha her lendng rae no hgher han η o ha he ha no ncenve o hf ncome from one perod o he nex. Then her lfeme uly condoned on her human capal h and on ω, gven by T u e e η (18 Vu ( h, ω = U ((1 τ wu [ υh + (1 υ hu ] e d. 0 Nex, conder klled worker who aend unvery and ncur a deb o cover her and lvng expene. The ze of he deb upon graduaon and enry no he workforce depend on parenal ncome and equal T e r ( y (19 B ( y = ( P + c0 e d. 0 Aume ha once he ndvdual n he workforce, h deb can be refnanced a he unform nere rae r 0 o be repad n a connuou conan ream of (0 R (y, h, ω = γ (h, ω B (y r 0 / (1 e r0 ( T u Te where γ (h, ω < 1 rcly le han one when repaymen of uden loan conngen on ncome and graduae ncome y = w [υ h + (1 υ h ] fall below he relevan hrehold. The lfeme uly of a klled worker, condoned on her human capal, on parenal ncome, and on ancpaed ω hen η (1 V ( y, h, = U( c e d+ T e, Tu e e η 0 U(( 1τ w [ υh + (1 υ h ] R ( y, h, ω e d. T ω 0 e Smlarly, an ndvdual who enroll n unvery bu fal o graduae ncur a deb of T f r ( y ( B f ( y = ( P + c0 e d, 0 whch repad n a connuou conan ream of (3 R f (y, h, ω = γ u (h, ω B f (y r 0 / (1 e r ( T u T 0 f where γ u (h, ω < 1 a above, for unklled worker. Her expeced lfeme uly, mlarly condoned, hen equal,
1 Td Tu η e e (4 Vf ( y, h, ω = U( c0 e d + U(( 1τ w [ υh + u (1 υ hu ] Rf ( y, h, ω e 0 Td η d. A peron wh an enry core > θ ha mee he admon requremen wll chooe o enrol n hgher educaon f ncreae her expeced lfeme uly, akng no accoun her probably of graduang, condoned on her human capal h, her paren' ncome y, and ancpaed ω (ee Appendx B for a dervaon of he jon drbuon of lnh and gven lny and. Denong he cumulave deny funcon of condoned on h by G ( h, G ( h he probably ha a uden wh human capal h wll fal o graduae f he enrol, and 1 G ( h he probably ha he ucceed. A propecve uden expec o gan from aendng college f her expeced lfeme uly f he enroll greaer han her lfeme uly f he doe no enrol: (5 V ( h, ω G ( h V ( y, h, ω + ( 1 G ( h V ( y, h, ω.5 Equlbrum u. f We aume ha each cohor ha meaure one; ha all capal, labor and produc marke are compeve, excep for he fundng of educaon and mperfec obervaon of human capal; and ha he upply of capal equpmen perfecly elac a he exogenou prce p. 1 We focu on an equlbrum n whch he value of he margnal produc of each of he facor npu equal prce or wage; all ancpaon are realzed; marke clear; he drbuon of human capal acro graduae and nongraduae labor n each cohor he ame; and he governmen budge balanced. To e ou hee condon explcly, le g(y, h,, denoe he jon deny of y, h, and and aume ha he admon creron θ and he graduaon hrehold are gven. Le ψ(y,ω denoe he e of value of h for whch (5 hold for canddae wh parenal ncome y, gven he vecor of ancpaed value ω; hee are he value of h for whch canddae wh parenal ncome y, ancpang ω, chooe o aend college. Then he hare of graduae n a cohor, gven a vecor of ancpaed value ω, (6 ϕ ( ω = ( y, h,, h ψ ( y, ω θ g d d dh dy. The hare of hoe who ener unvery bu fal 1 In effec we are aumng ha change n he proporon of klled worker are gradual enough for capal o adju whou a change n prce. I eem nuvely plauble ha for every value of y here hould be a unque hrehold level of human capal h(y,ω ha afe (5 wh equaly, uch ha ndvdual apple o udy n hgher educaon f and only f h > h (y, ω. However, we were no able o prove h generally and dd no ue n he numercal oluon of he model, hough we found alway held.
(7 ϕ ( ω = ( y, h,, f h ψ ( y, ω θ g d d dh dy. 13 The hare of hoe who do no aend unvery, eher becaue hey chooe no o or becaue hey do no mee he enry requremen, he remander 3 (8 ϕ n (ω = 1 ϕ (ω ϕ f (ω. I follow ha he meaure of klled worker n he workforce n equlbrum T ϕ (ω; he meaure of unklled worker who enrolled n hgher educaon bu faled o graduae T f ϕ f (ω; and he meaure of unklled worker who dd no enrol n hgher educaon T u ϕ n (ω. Smlarly, he oal human capal of klled worker n equlbrum (9 ( ω = T h g ( y, h,, h ψ ( y, ω θ H d d dh dy, o ha he average human capal of a klled worker (30 h (ω = H (ω / [T ϕ (ω]. The oal human capal of unklled worker who aended hgher educaon bu faled (31 ( ω = T h g ( y, h,, f f h ψ ( y, ω H d d dh dy. θ The oal human capal of unklled worker who dd no aend hgher educaon (3 H n ( ω = Tu + h ψ ( y, ω θ h ψ ( y, ω h h g g ( y, h,, ( y, h,, d d dh dy d d dh dy. Conequenly, he oal human capal of unklled worker equal (33 H u (ω = H n (ω + H f (ω, 3 ϕ ( ω = n h ψ ( y, ω g ( y, h,, d d dh dy + g ( y, h,, θ h ψ ( y, ω d d dh dy
14 and her average level of human capal (34 h u (ω = H u (ω / [T f ϕ f (ω + T u ϕ n (ω ]. An equlbrum hen a vecor ω* = (w *, w u *, h *, h u *, τ and a ock of capal equpmen, K*, uch ha (35 h (ω* = h *, (36 h u (ω = h u *, (37 (38 F H F H u (H u (ω, H (ω*, K* = w *, (H u (ω, H (ω*, K* = w u *, (39 F K (H u (ω, H (ω*, K* = p, and he governmen budge balanced. 3. CALIBRATION Calbrang he model o oberved emprcal varable allow u o derve a quanave ndcaon of how change n he fnancng of hgher educaon affec acce, mobly, drbuon, oupu, and fcal co. Our benchmark he Irael economy wh cenralzed hgher educaon yem. Tuon ubde cover abou half of eachng co and he governmen doe no offer a comprehenve uden loan program. (A ummary of calbraon value preened n Table 1. We decrbe aggregae producon by a need conan elacy of ubuon (CES funcon: ψ ς ς ς ψ (41 Y = A ν ( H + (1 ν [ λ ( K + (1 λ ( H ] }, { u and adop he elace emaed by Kruell e al. (000 for he Uned Sae economy, ζ = 0.495, and ψ = 0.401, whch mply an elacy of ubuon of 1.67 beween klled and unklled labor, and beween capal equpmen and unklled labor, and an elacy of ubuon of 0.67 beween capal equpmen and klled labor. 4 ψ 1 4 We ue Kruell e al.' emae only for he elace. The oher parameer of he producon funcon are calbraed o Irael daa. There are no emae of hee elace for he Irael economy bu we beleve he value derved from he Uned Sae economy provde a beer approxmaon of Irael' advanced nduralzed economy han he more ealy emaed logarhmc form.
Thu capal equpmen a ubue for unklled labor and a complemen of klled labor. The remanng parameer are calng parameer, whch are calbraed o Irael' bune ecor n 003. The (gro reurn on nvemen n capal equpmen e equal o p = 1%. Wage are deermned a an equally weghed average of own human capal and he average human capal of mlarly klled worker, υ = 0.5 (n our envy analy we mulae he model for υ = 0.4 and υ = 0.6. Income, human capal, enry core and coure grade ln y, ln h, and are aumed o follow a mulvarae normal drbuon, 5 he parameer of whch are relaed o oberved emprcal value a follow: The mean and varance of he logarhm of parenal ncome, µ y and y, are derved from he drbuon of ne houehold ncome n Irael n 003. 6 The margnal drbuon of enry core and coure grade are aumed o be andardzed normal, wh µ = µ = 0 and = = 1. Th mple ha he logarhm of human capal µ h alo ha zero mean. The correlaon y beween parenal ncome and enry core e equal o 0.5, whch whn he range of emprcal emae of he correlaon beween parenal ncome and pre-college apude e core. 7 The correlaon beween parenal ncome and coure grade aumed o be he ame a beween parenal ncome and enry core: 8 y = y = 0.5. The correlaon beween enry core and coure grade calbraed o emaed correlaon beween pre-college apude e core and fr-year college grade, 9 and e equal o 0.5. The remanng enre of he varance-covarance marx h, hy, h, and h are hen calculaed drecly from hee value (ee Appendx A for deal of he dervaon. We aume ha graduaon requre four year of udy, T e = 4; 30 oal for he degree equal abou one half of he annual alary of an unklled worker, whch we pread over four year; and annual lvng expene whle udyng equal one hrd of he average wage of an unklled worker. A uden who fal aumed o udy for half he me, T d =, and pay half he. 31 The oal workng lfe of a graduae afer graduaon T = 40; hence T f = 4 and T u = 44. We po an annual houehold 15 5 The mulvarae normal drbuon provde a racable framework for paramerzng he jon drbuon of hee varable. The aumpon ha ncome follow a lognormal drbuon common n emprcal work, hough oher aumpon are clearly poble (ee, e.g., Harron, 1981. 6 Mean gro monhly ncome per houehold n 003 wa NIS 10,385, and medan ncome wa NIS 9,00 (Sacal Abrac of Irael, 005, Table 5.31. 7 Thee vary beween 0.17 and 0.3 (Hearn 1991; Owen 1985; Alwn and Thornon 1984; Paulhu and Shaffer 1981. 8 Th an arbrary deermnaon: becaue of he wde varaon n gradng andard, doe no eem reaonable o calbrae y, he correlaon n he populaon a large, o emprcal correlaon beween parenal ncome and college grade-pon average. 9 Cf. Brdgman, McCameley-Jenkn and Ervn (000 and Kenne-Cohen, Bronner and Oren (1998. 30 Ar and cence degree are hree year program; engneerng, accounng and law are four-year program (o accredaon. Of coure, many uden ake longer o complee her ude. 31 Th accord wh Snebrckner and Snebrckner' (007 fndng ha he medan me o droppng ou wo year.
16 dcoun rae of η = 6% and aume ha he emporal uly funcon ha a conan coeffcen of relave rk averon (CRRA equal o 1., ha, U(c = c 0. (n our envy analy we mulae he model for CRRA value of 1.05 and 1.35. In calbrang he benchmark cae we e he admon hrehold equal o θ = 0., ha, one ffh of a andard devaon below he mean, and e he fnal pa core equal o 0, he mean core n he populaon a a whole. 3 Educaon co, beyond he governmen, are elf-fnanced n he benchmark cae a an nere rae ha decreae wh houehold ncome y: (4 r (y = 0.06 + 0.06 y m / y, where y m medan ncome (n our envy analy we mulae he benchmark cae for x oher nere rae chedule; he nere rae chedule relevan only for he benchmark cae. The nere rae n ubequen perod r 0 = 0.06, whch he ame a he ubjecve ner-emporal dcoun rae. Th yeld an enrolmen hare n hgher educaon of 41.4%, whch lghly lower han he fr-year enrolmen hare n erary educaon n Irael, 43.6%; and a hare of graduae equal o 7.1%, lghly hgher han he hare of graduae n Irael' workforce, whch abou 5% (Sacal Abrac of Irael, 005, Table 14.7. The rao we oban of he average wage of nongraduae o ha of graduae 0.4, whch lower han he rao of 0.54 oberved n he workforce of he wage of worker wh le han a college educaon o ha of worker wh a college educaon or more, (Sacal Abrac of Irael, 005, Table 1.4. 33 Th can be een a reflecng added advanage of a college degree, uch a more able employmen and ocal au. The Gn coeffcen of lfeme wage ncome we oban equal 0.17, whch lower han oberved value of he Gn coeffcen compued for annual ncome. Th can be arbued o our ue of permanen ncome o calculae he Gn coeffcen n he calbraed model, whch le varable han annual ncome ued n emprcal calculaon, 34 and o he mple occupaonal rucure of our model, whch allow only wo kll level. We meaure relave ocal mobly hrough he nergeneraonal correlaon of he logarhm of ncome beween paren and her chldren. I equal 0.389 n he benchmark cae, whch well whn he range of value obaned for advanced nduralzed econome. 35 Fgure A1 n Appendx C compare he 3 Admon n Irael are generally "mer-baed" wh very lle affrmave acon. 33 We were no able o calbrae he model wh he lower, oberved, wage rao. Th conen wh klled job havng oher advanage bede beer pay, uch a hgher ocal au and beer workng condon. 34 Lllard (1977 found ha he Gn coeffcen for annual earnng 50 percen larger han for lfeme ncome, whch ugge ha our benchmark calbraon roughly conen wh oberved value. 35 Th la meaure cloely relaed o he mo commonly ued meaure of nergeneraonal mobly he elacy of ncome wh repec o parenal ncome. If ε denoe he nergeneraonal earnng elacy obaned from a mple regreon of on log earnng y on faher log earnng x, y and x repecvely denoe her ample andard devaon, and r xy denoe her correlaon coeffcen, hen r xy = ε x / y (Johnon, 197, p. 34. Thu f he varance n log earnng are abou he ame for paren and her chldren, he wo are roughly equal (Solon, 00. We ue he correlaon
cumulave drbuon funcon of chldren wage ncome n equlbrum n he benchmark cae wh he paren drbuon of ncome. The dchoomou occupaonal rucure aumed n he model nduce a bmodal deny funcon. The drbuon of college enrolmen hare by qunle of parenal ncome n he benchmark cae preened n he fr column of Table. The econd column preen he drbuon of enrolmen rae n Irael 003 by he ocoeconomc qunle of he uden' local auhory of redence (Sacal Abrac of Irael, 005, Table 8.36. Graduaon rae by paren' ncome qunle are preened n he hrd column of he able. Thee enrolmen and graduaon rae, obaned n he benchmark cae, appear alo n he fr column of Table 3, a a reference pon for comparon o oher polce, wh he ummary meaure of acce, nequaly, mobly, oupu and fcal co, dcued above. 17 4. SIMULATION OF ALTERNATIVE FUNDING POLICIES We now apply our calbraed model o mulae dfferen unvery fundng polce: removng lqudy conran by offerng loan a preferred marke rae o cover and lvng expene durng ude; removng ubde; and offerng conngen loan ha reduce ndvdual rk by allowng repaymen o depend on fuure ncome. We gauge he ncremenal effec of hee polce on acce o hgher educaon, fcal co, ncome drbuon, nergeneraonal mobly, and oupu, afer a full urnover of he labor force. Acce meaured hrough enrolmen and graduaon rae by qunle of parenal ncome; fcal co meaured a an ndex n relaon o fcal co n he benchmark cae; drbuon meaured a he Gn coeffcen of lfeme labor ncome; (relave mobly meaured a he nergeneraonal correlaon of ncome; and oupu meaured a an ndex, n relaon o he benchmark cae. In addon we provde a meaure of aggregae welfare compued, for each polcy j, a he proporonal change n ncome n he benchmark cae requred o acheve he ame aggregae uly ha polcy j acheve. 36 Admon andard and academc graduaon requremen are held fxed hroughou. 4.1 Removng lqudy conran and rang We begn by conderng he mpac of fr removng lqudy conran and hen rang, and compare he reul o he benchmark cae. When lqudy of log ncome o meaure relave mobly, raher han he earnng elacy, n order o dnguh more clearly beween mobly and drbuon. For oher approache o meaurng ocal mobly ee he urvey by Feld and Ok (1999, who oberve ha "he mobly leraure doe no provde a unfed dcoure of analy". 36 Le y j be he vecor of annual ncome of ndvdual under polcy j, where j = 0 denoe he benchmark cae, and le V(y j be her ndrec lfeme uly. Then he welfare enry n Table 3 for polcy j he value ξ ha olve V((1+ ξ y 0 = V(y j.
18 conran are reolved, we aume ha and lvng co can be fnanced a he unform nere rae r 0 = 0.06, rrepecve of parenal ncome. The fr hree column of Table 3 preen he mpac of he followng polce: he benchmark cae, n whch 50% of ubdzed and lqudy conraned; he ame ubde combned wh (nonconngen governmen uden loan ha remove lqudy conran; and removal of ubde, reulng n a doublng of, combned wh (nonconngen governmen uden loan. The op row of Table 3 preen enrolmen and graduaon rae by qunle for each of hee polce; and he boom row preen aggregae enrolmen and graduaon rae, he rao of nongraduae o graduae ncome, he Gn coeffcen of lfeme ncome, 37 he nergeneraonal correlaon of ncome, an ndex of oal oupu, an ncome-equvalen ndcaor of he change n aggregae uly (defned above, and he fcal co of hgher educaon, preened boh a a ax rae and a an ndex of fcal co. We aume ha here full recovery of loan and gnore admnrave co. A comparon of he fr wo column n Table 3 how ha reolvng lqudy conran margnally mprove acce: caue a general ncreae n enrolmen and graduaon rae, wh he relave ncreae decreang a parenal ncome re. The lgh ncreae n he oal hare of graduae n he workforce lead o a mall ncreae n he rao of unklled o klled wage, whch lghly reduce nequaly. The nergeneraonal correlaon of ncome, an ndcaor of mmobly, vare very lghly n he ame drecon a he Gn coeffcen: a maller gap beween unklled and klled wage render hgher educaon le effecve n promong relave ncome mobly. The lgh ncreae n oal oupu neglgble gven ha we gnore admnraon co, and he ncreae n oal uly alo very mall n ncome-equvalence erm. The mall re n fcal co reflec a mall ncreae n enrolmen n ubdzed hgher educaon. Rang ofen an mporan componen of reform of hgher educaon fnance, eher upplemenng publc pendng on hgher educaon or replacng. The hrd column n Table 3 how he reul of removng ubde, whch caue fee o double, whle offerng uden loan. Comparng o he benchmark we fnd mall declne n enrolmen and graduaon rae, wh he large declne occurrng n he hgher-ncome qunle, ndcang ha f lqudy conran are reolved, can be ubanally ncreaed wh lle effec on acce o hgher educaon. The removal of ubde reul n a harp relave declne n fcal co, hough he compued declne overae acual gan a aume perfec loan recovery and cole admnraon. The change n oupu and n aggregae uly are neglgble. 4. Conngen repaymen of loan 37 Thee value are conderably maller han emprcal Gn coeffcen of wage ncome. We made no aemp o adju h a our meaure hould be lower: Where emprcal meaure of nequaly are baed on annual ncome our meaure baed on permanen ncome. I hould be maller, a average ou boh year o year flucuaon n ncome and varaon n annual ncome among people wh mlar lfeme earnng profle who are a dfferen age of her lve.
19 The obervaon ha ndvdual are rk avere and governmen can effcenly pool rk ha led many hgher educaon fundng program mplemened n recen year o ncorporae an elemen of nurance. Typcally, repaymen n each year lmed o a fxed fracon of ncome wh no repaymen below a gven ncome hrehold, unl eher he deb repad or a pre-deermned number of year have paed, a whch pon any ouandng deb forgven. Our model aume ha perfec conumpon moohng poble, o he mng of repaymen rrelevan, and only he fracon repad maer. To fx dea, we aume ha ndvdual earnng le han 0.75 of average ncome pay nohng, hoe earnng 1.5 me average ncome repay her loan n full, and hoe nbeween repay on a lnear cale (e.g., ndvdual earnng average ncome repay half her deb. 38 The fourh column of Table 3 aume ha uch loan are offered whle ubde reman a he benchmark level of 50%, whle he ffh column aume ha ubde are removed. The reul hown n column 4 demonrae he ubanal pove effec of uden loan wh conngen repaymen on acce: n he lowe parenal-ncome qunle hey ncreae enrolmen rae by more han a hrd and graduaon rae by a quarer, compared o he rae acheved hrough an unnured uden loan program. Hgher qunle alo gan, bu relave gan decreae wh parenal ncome and he lowe wo qunle alo have he hghe abolue gan. The nurance mplc n uch loan ubanally ncreae he hare of graduae n he workforce, whch reduce nequaly, rae oupu, and reduce relave ncome mobly. The recovery rae whn he range 75-85% quoed by Chapman and Ryan (005 for Aurala. The fcal co of he program almo doubled becaue of he added co of forgven loan and he expanon of ubdzed hgher educaon. In he ffh column of Table 3, where he ame loan are combned wh a removal of ubde, we fnd agan ha reolvng lqudy conran allow removal of ubde wh very lle effec on acce, whle ubanally reducng fcal co. Combnng hee loan wh a removal of ubde leave governmen pendng a he benchmark level whle achevng large relave gan n boh enrolmen and graduaon rae n he lowe ncome qunle. The large overall ncreae n enrolmen and graduaon rae narrow he gap beween klled and unklled wage and reduce wage nequaly a meaured by he Gn coeffcen of lfeme wage ncome. The mall gan n oupu of 0.8% over he benchmark cae reflec he governmen' nnae advanage n preadng rk, hough agan gnore he admnrave co of he program, poble admnrave neffcence and any abue of he yem. The radeoff mplc n choong beween hee varou polce are lluraed n Fgure 1, whch graph he college enrolmen rae for he lowe qunle of parenal ncome veru fcal co, for he fve polce n Table 3. There are hree polce on he 38 We alo examned a more generou nurance chedule: allowng ndvdual earnng le han average ncome o pay nohng, requrng hoe earnng a lea 50% above average ncome o repay her loan n full, whle hoe n-beween repay on a lnear cale. Th yeld a lower recovery rae of abou wo hrd, whch ubanally ncreae he fcal co of he loan program whle offerng lle mprovemen n acce or n any of he aggregae meaure of equy and effcency.
0 opmal (upper lef-hand froner: offerng uden loan whle chargng full acheve a large reducon n fcal co wh a very lgh reducon n acce; offerng nured uden loan whle chargng full acheve a large mprovemen n acce wh lle change n fcal co; and offerng nured uden loan whle mananng curren ubde acheve a mall furher mprovemen n acce whle ubanally ncreang fcal co. 4.3 Senvy analy To e he robune of our concluon we conduced envy analye and recompued Table 3 under alernave aumpon, whch are preened n Appendx D. Fr, we vared he relave nfluence of human capal and gnalng on wage. We orgnally calbraed he model o a value of υ = 0.5, where υ he relave wegh of ndvdual human capal n deermnng wage, and now re-ran for value of υ = 0.4 and 0.6. The reul, preened n Table A1 and A, how ha hee varaon do affec demand for hgher educaon: a maller mpac of own human capal on wage.e., a larger gnalng effec reul n ncreaed demand for acce o hgher educaon, rang enrolmen and graduaon rae acro he board. However, hee parameer change do no affec our polcy comparon. I ll hold ha removng ubde whle offerng (nonconngen governmen uden loan reduce fcal co wh very lle mpac on acce, whle offerng nured loan and removng ubde markedly mprove acce, compared o he benchmark cae, wh lle change n fcal co, hu decrbng he ame polcy radeoff froner a Fgure 1. Addonally, a n he prncpal calbraon, none of hee polce ha much effec on aggregae oupu or uly. Nex we vared he coeffcen of relave rk averon (CCRA, whch we orgnally calbraed o a value of 1., eng alernave value of 1.05 and 1.35, reul of whch are preened n Table A3 and A4. A mgh be expeced, lowerng he CCRA rae enrolmen and graduaon rae and lghly rae fcal co, whle rang he CRRA ha he oppoe effec, bu hee effec are mall and he quanave concluon are agan unchanged. We alo vared he nere rae rucure of prvae lendng for hgher educaon o e effec on he benchmark cae. In he orgnal calbraon we aumed he nere gven n equaon (4. We now re-ran he model aumng a pecewe lnear rae. The reul hown n Table A5 compare 6 dfferen chedule o he benchmark cae (he nere rae are no relevan when uden loan are offered. The general mlary apparen and our concluon reman nac. Fnally, we ran he model for a fxed (zero ax rae, aumng ha change n pendng on educaon do no reul n varaon of he ax rae bu raher are aborbed a change n oher budge em. The reul hown n Table A6 are very mlar o hoe n Table 3, ndcang ha he ax rae can be gnored (and he model reamlned whou ubanvely affecng he reul.
1 5. CONCLUSION In h paper we conruced a macro-model of an economy wh klled and unklled labor and a cenralzed yem of hgher educaon ha ran klled labor, whch we hen ued o mulae dfferen unvery and uden loan polce. We condered he effec of provdng uden loan a preferred nere rae, of doublng, and of condonng repaymen of he loan on uden' ncome when hey ener he workforce. We found ha uden loan n hemelve have only a mall pove effec on acce o hgher educaon bu hey enable o be raed ubanally wh lle advere effec on acce for uden from low-ncome home. Allowng repaymen of loan o depend on fuure ncome aborb ome of he rk of hgher educaon and ubanally mprove acce. And f ncreaed a he ame me, a large mprovemen n acce can be acheved whou ncreang fcal co above curren level. Increaed acce, reulng n larger number of graduae, caue a fall n he college wage premum and hu n wage nequaly. A he ame me, nergeneraonal relave ncome mobly, a meaured nverely by he correlaon n ncome acro generaon, declne very lghly depe he mprovemen n enrolmen and graduaon rae. Loan wh conngen repaymen generae mall ncreae n oal oupu, n our mulaon reul, bu hee effec are relavely mall compared o he large relave mpac of hee polce on acce and fcal co, and gven he many facor from whch our analy abrac are a be a weak ndcaon of acual effcency gan. Fnally, we noe ha even loan wh conngen repaymen combned wh ubdzed leave ubanal dfference n enrolmen and graduaon rae beween uden from dfferen ocoeconomc background. By he me uden reach college age much ha already been deermned; larger mprovemen n ocal mobly requre nervenon a earler age.
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6 Table 1 Calbraon value Decrpon of varable Value Reference and noe Elacy of ubuon beween (unklled 1.67 labor and (capal equpmen and klled labor Kruel e al. (000 Elacy of ubuon of beween capal 0.67 equpmen and klled labor Reurn on nvemen n equpmen, p (gro 1% Wegh of own human capal n wage, υ 0.5 Alo eed: υ = 0.4, 0.6 Mean of he log of parenal ncome, µ y Varance of he log of parenal ncome, y Calbraed o ne houehold ncome n Irael, 003; ee noe 4 Mean of enry core and grade, µ and µ 0 Varance of enry core and grade, and 1 Sandardzed normal Corr beween paren ncome and enry core, y 0.5 See reference n noe 7 Corr beween paren ncome and grade, y 0.5. Aumed equal o y ; n. 8 Corr beween enry core and grade, 0.5 See reference n noe 9 µ h, h, hy, h, and h Calculaed, ee Appendx A for deal Year of udy o graduaon, T e 4 Year of udy, o dconnung ude, T d Tuon, per year, P w u / 8 Calbraed o Irael Annual lvng expene n college, c 0 w u / 3 Subjecve emae Graduae workng lfe, T (year 40 Admon hrehold, θ 0. Enrolmen rae Graduaon requremen, 0 Graduaon rae Be nere rae for conumer loan, r 0 6% Coeffcen of relave rk averon (CRRA 1. Alo eed: 1.05, 1.35 Annual houehold dcoun rae, η 6% Se equal o r 0 Table Drbuon of enrolmen and graduaon hare: Benchmark mulaon veru oberved value Qunle Enrolmen rae by paren' ncome qunle (benchmark model Enrolmen rae by local auhory' ocoeconomc rankng (oberved Share of graduae by paren' ncome qunle (benchmark model I 18.4% 3.4% 11.0% II 31.4% 8.5% 19.5% III 4.% 4.1% 6.3% IV 51.0% 5.5% 33.7% V 64.7% 63.0% 45.8% Toal 41.4% 43.6% 7.1%
Table 3 Enrolmen and graduaon rae by qunle, and aggregae ndcaor of acce, nequaly, mobly, oupu and fcal co under dfferen and loan polce Qunle Benchmark 50% No uden loan 50% Suden loan No Suden loan 50% Conngen repaymen No Conngen repaymen Enrolmen I 18.4% 0.0% 18.1% 8.% 7.% hare by II 31.4% 33.0% 30.7% 41.6% 40.6% paren' III 4.% 4.3% 40.1% 50.1% 49.3% ncome IV 50.1% 51.7% 49.7% 58.1% 57.4% qunle V 64.7% 64.9% 63.4% 68.7% 68.3% Graduaon I 11.0% 11.7% 10.8% 15.0% 14.6% hare by II 19.5% 0.% 19.1% 3.7% 3.3% paren' III 6.3% 6.8% 5.8% 30.0% 9.7% ncome IV 33.7% 34.1% 33.1% 36.7% 36.4% qunle V 45.8% 45.8% 41.% 47.4% 47.3% Enrolmen rae n hgher educaon 41.4% 4.% 40.% 49.1% 48.4% Share of graduae n he workforce Rao of non-graduae o graduae ncome Gn coeffcen of lfeme ncome Inergeneraonal ncome correlaon Aggregae oupu ndex (Benchmark = 100 Change n aggregae uly (ee ex 7.1% 7.6% 6.7% 30.4% 30.1% 0.389 0.397 0.383 0.44 0.437 0.17 0.14 0.19 0.197 0.199 0.367 0.369 0.366 0.387 0.377 100.0 100.1 99.9 100.8 100.8-0.51% -0.38% -0.80% -0.79% Loan recovery rae 100% 100% 81.7% 8.0% Tax rae 0.9% 0.30% 0 0.57% 0.9% Fcal co ndex 100 103 0 196 99 7
8 Fgure 1. Tradeoff beween acce and fcal co 30% Inured loan, Enrolmen rae, lowe ncome qunle 5% 0% Suden loan, full Inured loan, full Suden loan, No loan, (Benchmark 15% 0% 50% 100% 150% 00% Fcal co
Appendx 9 A. The varance-covarance marx of ln h,, ln y and The mng elemen of he varance-covarance able are he elemen ncorporang he unoberved varable ln h, he logarhm of human capal. From equaon (15a we oban (A.1 α + δ = y / y, and ubung h n equaon (15c gve (A. yh = y / h, mplyng ha (A.3 cov (y, h = yh y h = y y = 0.181 afer ubung he calbraon value from he ex. From equaon (15f (A.4 h = = 0.5, and from equaon (15d (A.5 cov(h, = h h = h = = 0.5. Smlarly, from equaon (15e (A.6 cov(h, = = 0.5. Thu all he elemen of he varance-covarance marx can be expreed a funcon of he oberved correlaon and varance.
30 B. The condonal jon drbuon of ln h and gven ln y and Gven parenal ncome and he pror e core, he jon condonal drbuon of he logarhm of human capal and he fnal exam core have expecaon, ( ( ( ( (ln (ln (1 (, ln (, ( ( ( ( (ln (ln (1 1 (ln, ln (ln + + = + + = y y y y y y y y y y E y E y E y E E y E y h E y h E and varance-covarance marx. (1 ( (1, ln, cov(ln, ( (1 ( (1, (1 ( (1, ln, ln ln = = = y y y y y y y y y y y y y y y y y y h y h
C. Cumulave ncome drbuon 31 Cumulave ncome drbuon (benchmark cae 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0. 0.1 0-3 - -1 0 1 3 Sandard devaon Paren Chldren
3 D. Senvy analy Table A1. Sgnalng effec υ = 0.4 Enrolmen and graduaon rae by qunle, and aggregae ndcaor of acce, nequaly, mobly, oupu and fcal co under dfferen and loan polce Enrolmen hare by paren' ncome qunle Graduaon hare by paren' ncome qunle Qunle Enrolmen rae n hgher educaon Share of graduae n he workforce Rao of non-graduae o graduae ncome Gn coeffcen of lfeme ncome Inergeneraonal ncome correlaon Aggregae oupu ndex (Benchmark = 100 Change n aggregae uly (ee ex Benchmark 50% No uden loan 50% Suden loan No Suden loan 50% Conngen repaymen No Conngen repaymen I 0.% 1.9% 19.8% 30.4% 9.4% II 33.5% 35.1% 3.7% 43.6% 4.7% III 43.1% 44.4% 4.1% 51.8% 51.0% IV 5.6% 53.4% 51.4% 59.3% 58.8% V 65.7% 65.9% 64.6% 69.3% 69.1% I 11.8% 1.5% 11.6% 15.8% 15.4% II 0.4% 1.1% 0.1% 4.3% 4.0% III 7.% 7.7% 6.7% 30.5% 30.3% IV 34.5% 34.8% 34.0% 37.1% 36.9% V 46.% 46.3% 45.7% 47.6% 47.6% 4.8% 44.0% 41.9% 50.6% 50.0% 7.9% 8.4% 7.5% 30.9% 30.7% 0.401 0.409 0.395 0.451 0.447 0.199 0.197 0.0 0.181 0.183 0.343 0.345 0.34 0.353 0.35 100 100.1 99.9 100.7 100.7-0.1% -0.06-0.54% -0.54% Loan recovery rae 100% 100% 80.1% 80.3% Tax rae 0.30% 0.31% 0 0.60% 0.3% Fcal co ndex 100.0 10.4 0 199.1 104.7
33 Table A. Sgnalng effec υ = 0.6 Enrolmen and graduaon rae by qunle, and aggregae ndcaor of acce, nequaly, mobly, oupu and fcal co under dfferen and loan polce Enrolmen hare by paren' Income qunle Graduaon hare by paren' Income qunle Qunle Enrolmen rae n hgher educaon Share of graduae n he workforce Rao of non-graduae o graduae ncome Gn coeffcen of lfeme ncome Inergeneraonal ncome correlaon Aggregae oupu ndex (Benchmark = 100 Change n aggregae uly (ee ex Benchmark 50% No uden loan 50% Suden loan No Suden loan 50% Conngen repaymen No Conngen repaymen I 16.7% 18.1% 16.3% 6.4% 5.9% II 9.3% 30.7% 8.4% 39.8% 39.4% III 39.0% 40.1% 37.8% 48.6% 48.% IV 49.1% 49.7% 47.7% 56.9% 56.5% V 63.5% 63.5% 6.0% 68.0% 67.8% I 10.% 10.8% 10.0% 14.3% 14.1% II 18.5% 19.1% 18.% 3.0%.7% III 5.3% 5.8% 4.8% 9.4% 9.% IV 3.9% 33.% 3.% 36.% 36.0% V 45.% 45.% 44.6% 47.1% 47.0% 39.3% 40.% 38.% 47.7% 47.3% 6.3% 6.7% 5.7% 9.9% 9.6% 0.376 0.383 0.369 0.433 0.431 0.33 0.31 0.37 0.09 0.10 0.386 0.389 0.386 0.39 0.39 100.0 100. 99.8 101.0 101.0-0.16% -0.3% -0.1% -0.1% Loan recovery rae 100% 100% 8.7% 8.9% Tax rae 0.8% 0.9% 0 0.44% 0.6% Fcal co ndex 100 10.0 0 37.4 93.3
34 Table A3. CRRA = 1.05 Enrolmen and graduaon rae by qunle, and aggregae ndcaor of acce, nequaly, mobly, oupu and fcal co under dfferen and loan polce Qunle Benchmark 50% No uden loan 50% Suden loan No Suden loan 50% Conngen repaymen No Conngen repaymen Enrolmen I 19.3% 1.1% 19.0% 9.0% 8.0% hare by II 3.5% 34.% 31.8% 4.3% 41.4% paren' III 4.% 43.5% 41.1% 50.8% 50.0% ncome IV 51.9% 5.7% 50.6% 58.5% 57.9% qunle V 65.4% 65.4% 64.0% 68.9% 68.6% Graduaon I 11.4% 1.% 11.% 15.3% 14.9% hare by II 0.0% 0.7% 19.6% 3.9% 3.6% paren' III 6.8% 7.3% 6.3% 30.% 9.9% ncome IV 34.1% 34.5% 33.6% 36.8% 36.6% qunle V 46.1% 46.1% 45.5% 47.5% 47.4% Enrolmen rae n hgher educaon 4.0% 43.% 41.1% 49.7% 49.0% Share of graduae n he workforce Rao of non-graduae o graduae ncome Gn coeffcen of lfeme ncome Inergeneraonal ncome correlaon Aggregae oupu ndex (Benchmark = 100 Change n aggregae uly (ee ex 7.5% 8.0% 7.1% 30.6% 30.3% 0.396 0.403 0.389 0.446 0.441 0.14 0.11 0.17 0.196 0.197 0.369 0.370 0.367 0.378 0.377 100.0 100.1 99.8 100.8 100.7-0.10% -0.38% -0.8% -0.8% Loan recovery rae 100% 100% 81.3% 81.7% Tax rae 0.30% 0.30% 0 0.57% 0.30% Fcal co ndex 100 100 0 190 100
Table A4. CRRA = 1.35 Enrolmen and graduaon rae by qunle, and aggregae ndcaor of acce, nequaly, mobly, oupu and fcal co under dfferen and loan polce Enrolmen hare by paren' ncome qunle Graduaon hare by paren' ncome qunle Qunle Enrolmen rae n hgher educaon Share of graduae n he workforce Rao of non-graduae o graduae ncome Gn coeffcen of lfeme ncome Inergeneraonal ncome correlaon Aggregae oupu ndex (Benchmark = 100 Change n aggregae uly (ee ex Benchmark 50% No uden loan 50% Suden loan No Suden loan 50% Conngen repaymen 35 No Conngen repaymen I 17.4% 19.% 17.1% 7.4% 6.7% II 30.3% 3.0% 9.5% 40.8% 40.% III 40.0% 41.4% 38.8% 49.5% 49.0% IV 49.9% 50.8% 48.5% 57.6% 57.% V 64.0% 64.% 6.6% 68.4% 68.% I 10.5% 11.3% 10.4% 14.7% 14.4% II 18.9% 19.7% 18.5% 3.4% 3.1% III 5.7% 6.4% 5.% 9.7% 9.5% IV 33.3% 33.7% 3.6% 36.5% 36.3% V 45.5% 45.6% 44.8% 47.3% 47.% 40.1% 41.3% 39.1% 48.5% 48.1% 6.6% 7.% 6.% 30.% 30.0% 0.38 0.390 0.375 0.434 0.435 0.19 0.16 0.3 0.198 0.00 0.366 0.368 0.364 0.377 0.376 100.0 100. 99.8 101.0 100.9-0.07% -0.37% -0.76% 1.86% Loan recovery rae 100% 100% 8.9% 8.1% Tax rae 0.9% 0.9% 0.56% 0.8% Fcal co ndex 100 100 0 193 97
36 Table A5. Benchmark cae wh dfferen form of lqudy conran Enrolmen and graduaon rae by qunle, and aggregae ndcaor of acce, nequaly, mobly, oupu and fcal co under dfferen and loan polce The nere rae lnear n he paren ncome percenle from 0 o P wh he nere rae a P 1 equal o 1% and he nere rae a P and above equal o 6%. Qunle P 1 = 40% P = 80% P 1 = 50% P = 80% P 1 = 30% P = 70% P 1 = 40% P = 70% P 1 = 0% P = 60% P 1 = 30% P = 60% Enrolmen I 16.6% 15.6% 17.6% 16.5% 17.9% 17.% hare by II 30.4% 9.7% 31.6% 30.7% 31.9% 31.5% paren' III 41.1% 41.0% 4.3% 4.0% 4.6% 4.7% ncome IV 51.7% 5.0% 5.5% 5.7% 5.5% 5.7% qunle V 65.1% 65.4% 65.4% 65.5% 65.3% 65.4% Graduaon I 10.1% 9.7% 10.6% 10.1% 10.8% 10.4% hare by II 19.0% 18.7% 19.5% 19.1% 19.7% 19.5% paren' III 6.3% 6.% 6.8% 6.7% 6.9% 7.0% ncome IV 34.1% 34.% 34.4% 34.5% 34.4% 34.5% qunle V 46.0% 46.1% 46.1% 46.1% 46.0% 46.1% Enrolmen rae n hgher educaon 40.8% 40.6% 41.7% 41.3% 41.8% 41.7% Share of graduae n he workforce Rao of non-graduae o graduae ncome Gn coeffcen of lfeme ncome Inergeneraonal ncome correlaon Aggregae oupu ndex (Benchmark = 100 6.9% 6.8% 7.6% 7.% 7.4% 7.4% 0.387 0.385 0.393 0.390 0.394 00.393 0.17 0.18 0.14 0.17 0.15 0.16 0.366 0.366 0.368 0.367 0.368 0.368 100 99.9 100.1 100.06 100.1 100.1
Table A6. Fxed ax rae Enrolmen and graduaon rae by qunle, and aggregae ndcaor of acce, nequaly, mobly, oupu and fcal co under dfferen and loan polce Qunle Benchmark 50% No uden loan 50% Suden loan No Suden loan 50% Conngen loan No Conngen loan Enrolmen I 18.4% 0.% 18.1% 8.% 7.% hare by II 31.4% 33.% 30.7% 41.6% 40.6% paren' III 41.% 4.6% 40.1% 50.1% 49.3% ncome IV 51.0% 51.9% 49.7% 58.1% 57.4% qunle V 64.7% 64.9% 63.4% 68.7% 68.3% Graduaon I 11.0% 11.8% 10.9% 15.% 14.7% hare by II 19.5% 0.3% 19.1% 3.8% 3.3% paren' III 6.3% 6.9% 5.8% 30.1% 9.7% ncome IV 33.7% 34.1% 33.% 36.8% 36.4% qunle V 45.8% 45.9% 45.% 47.5% 47.3% Enrolmen rae n hgher educaon 41.4% 4.4% 40.% 49.1% 48.4% Share of graduae n he workforce Rao of non-graduae o graduae ncome Gn coeffcen of lfeme ncome Inergeneraonal ncome correlaon Aggregae oupu ndex (Benchmark = 100 Change n aggregae uly (ee ex 7.1% 7.7% 6.7% 30.4% 30.1% 0.389 0.398 0.383 0.44 0.437 0.17 0.13 0.19 0.197 0.198 0.367 0.369 0.366 0.377 0.377 100.0 100. 99.9 100.9 100.8-0.09% -0.31% 1.61% 1.88% Loan recovery rae 100% 100% 81.6% 81.9% Fcal co ndex 100.0 10.3 0 190.8 96.7 37