Access to Credit Market and Repeated Moral Hazard. University of Illinois. 1. Background

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1 Ae to Credt Market ad Reeated Mora Hazard Arato A. Patr Uverty o Io T aer dea t te robem o mora azard. We d te tato e te mora azard a be reeated over tme. A me mode t te erod aayzed. I addto, e o more o og-term otrat, rater ta t o ort-term otrat. We are tereted te e o eter or ot a memory ay a roe te og-term otrat. Tat, eter or ot ayo a ge erod deed o te ret o a revo erod. Frtermore, memory doe ay a roe, e od ke to d at te oeqee be te aget a a ae to redt market Bakgrod Tere are to maor robem ra-aget reato de to aymmetry o ormato, amey, advere eeto ad mora azard robem. Advere eeto od et e te aget a reevat rvate ormato beore a otrat ged. O te oter ad, mora azard od or e te aymmetry are ater te otrat a bee ged Mao-Stader ad Perez-Catro, 997. I te mora azard robem, te aget beavor ot obervabe by te ra, or obervabe bt ot verabe. A a oeqee, te aget eort very dt to be ded te term o otrat. T aer dea t te robem o mora azard. We d te tato e te mora azard a be reeated over tme. We ooe to aayze te me mode t te erod. I addto, e o more o og-term otrat, rater ta t o ort-term otrat. Tat, a batera agreemet betee te ra ad te aget over evera erod o reato. Hoever, e at to ko te otma og-term otrat a t be memeted trog ort-term otrat. We are tereted te e o eter or ot a memory ay a roe te og-term otrat. Tat, eter or ot ayo a ge erod deed o te ret o a revo erod. Frtermore, memory doe ay a roe, e od ke to d at te oeqee be

2 te aget a a ae to redt market. I addto to te aay o te roe o memory, e ao ke to d te roe o ommtmet. I t aer e e te mode deveoed by Caor et a 994 tat aayze te roe o bot memory ad ommtmet te robem o mora azard. Tey ao de ter aay te aget ae to redt market ad t mato o aget omto ad avg deo tat tr aet deo o eort eve. Prevo tde a aayzed te roe o memory ad ommtmet earatey, e.g. Rogero 985 or memory, ad Rey ad Saaé or ommtmet 990. Te tde o te roe o memory geeray ame tat aget a o ae to redt market, e te tde o ommtmet ao te aget to ave redt market ae. Caor et a 994 o te oter ad rovde a ed mode or tee to aet. 2. Set Tere are to ayer, a rk-etra ra ad a rk-avere aget. Tere are to erod t =, 2. At te begg o ea erod te aget ooe a eort e a rvate ormato. Let deote otome, ere =,, ad te. Te robabty o attag otome e. Te ra a oberve te otome bt ot te eort. Te aget tty to ea erod U,e = ve ere omto ad U a oave to. Te aget reervato tty U. O te oter ad, te ra tty to ea erod ere a oave to. Net e ao ee tat te aget a ave a eod deo addto to eort eve, amey avg ad borrog deo. Te derto o te aget ad te ra tty me te amto o tmeearabty ad te at tat te rret eort oy aet te rret otome. We ao ame tat bot te ra ad te aget dot te tre at te ame market teret rate, o tat e a dro te dot ator 2. T te ame a amed by Rogero 985. Later ter aato, Caor et a e reeree to or aget tat ebt a otat abote rk avero. T ea ae te ame a to ame tat te aget rk-etra ee Mao-Stader ad Pérez-Catro, Rogero 985 o te oter ad de te dot rate, e e mty amed tat te ra dot rate ad te aget dot rate are ot eeary te ame. To ome etet t more reat, e te dotg o tre reated to degree o atee tat a be very betve. For eame, e te aget vae rret ome more gy, tere a addtoa reao or age 2

3 Trogot te aer e e te deto rom Caor et a tat a og-r otrat ortr memetabe ad oy tere et a eret Bayea eqbrm o te ort-r otratg game oe otome reate te og-r otrat. 3. We aget borrog ad avg are otraed Cae : Aget a o ae to redt market I t rt ae te aget doe ot ave ae to redt market. It mea te aget ot aoed otmay moot tertemora omto roe by borrog or avg agat tre ome. So, te aget rret omto eqa rret age. Te otma og-term otrat ebt memory beae o tertemora mootg ad eat eet. It amed tat te aget omto determed by age oy, ot by bod. Te ra rooe a og-term otrat tat ee 2 otget age te matve otget age rom rt ad eod erod. Soe tat te rt- erod age aoated t otome, ad te eod-erod age t rt-erod otome ad eod-erod otome 3 I tere o memory, te eod-erod age doe ot aeted by te rt-erod otome, tat : = ', ', I T otet t te rooto Rogero, 985: 3 Prooto Soe tat a Pareto-otma otrat. Coder 3, ', I. Soe tat ' te tere mt et a 3 I tat '. aymet to be keed toard te begg o te reato. Smary, te ra vae rret ome more gy, tere a tedey or age to be more keed to te ed o te reato. Hoever, Rogero ao aayzed te ae e te to dot ator are eqa ee Prooto 3 ad t roo. For mty, e dede to oo Caor et a e te trodto o dotg od ot age ay o [ter] argmet, a og a bot arte dot te tre at te market teret rate. 3 A Rogero 985, a otrat a be togt o a a oeto o brae ad te -t bra age tat ae odtoa o, orrg te rt erod. 3

4 Te aget ooe otget eort 4. Soe e 0 te eort take te rt-erod, ad e te eod-erod ato tat odtoa o te rt-erod otome, tat, te rt-erod otome. Te otma og-term otrat mamze te ra obetve bet to a artato otrat ere te aget reervato tty 2U,.e. amato o tty to erod ad tat te aget ateray ooe ato 5. Te ra robem tereore ma e 0,, e0, e = = e.t. e, e arg ma e0 U, e0 0 e U, e e 0, e = = e0 U, e0 e U, e 2U = = I te obetve to, te eod term te braket e ea o te eod-erod eeted tty o te ra otget o te tato orred te rt erod. T obetve to te ra bet reoe to te aget beavor,.e. te rt otrat. Te eod otrat te artato otrat,.e. to make re tat te aget get tty at eat a m a reervato tty. Te ret rom te robem above tat te otma og-term otrat ebt memory 6. Te etee o memory me tat te eod-erod te aget reeve ger age te rt-erod age a g, ad oer te rt-erod age a o. T memory ret de to tertemora mootg ad eat eet tat e d ater. I t otma to make te aget tty otget o te rt-erod otome, te to ao a tertemora mootg betee erod ad erod 2 te eod-erod age od be otget o tat rt-erod otome. I geera, tertemora mootg reqre te rret age, a e a te eeted tre age to be otget o te otome o te rret erod. T otgey motvated by te aget dere to read ga or oe over evera erod. 4 Tat, rereet te rt erod, o otget o otg. 5 Uatera ommtmet reer to te ae e te aget aot ommt ot to break te otrat ad eave at ay ot te reato. I oter ord, t reembe te etve omatbty otrat. 6 Caor et a 994 dtge betee memory o omto te aget omto deed o at otome, ad memory o age te age ad by te ra deed o at otome. Ue te aget a ae to redt market, te to oto are te ame. Rogero 985 doe ot make dtto. 4

5 Nevertee, te tertemora mootg ot or te aget oy are abot tota ome, rreetve o t aoato to te rt- ad te eod erod. A eame or t tato e tty to U e 0 e. Hoever, e a reae aet te aget beavor toard te te deo o, te t geera deed o. I addto, t eat eet o te aget rk avero aet te eod-erod age trtre rater ta t overa eve. 7 It mortat to ote a e tat te mode above e reqre tat te aget eeted tty mt be arger ta at e a get t ay otde oto. I tee otde oto are aeted by te otrat, te te otrat above revet te mootg o ay ga, rovded tat a good otome roded te rt erod or o, rt-erod otome bad. We a ear rom t mode tat te e-ate og-r otma otrat e-ot eet 8. We te rt erod otome, te otato o te otma otrat ot eet, beae tere et a ateratve otrat tat rovde at eat a m a eeted tty or te aget ad ger ayo or te ra. Se e-ot eey me tat o reegotato obe at te ed o te rt erod, te te og-r otma otrat ot reegotabe. Hoever, to re tat t og-r otma otrat ort-r memetabe, te otma eqee o ot otrat od be memorye. T a be ereed a oo: Prooto 2 Let FU deote te ra vae to a tat robem, aoated t aget reervato tty U. I te og-r otma otrat memorye ad te to F oave, te og-r otma otrat te reetto o te tat otrat, ad tereore t ot-memetabe. 7 Maomo ad Sey 988 arge tat memory ret are my beae eat eet, ot beae tertemora mootg. Caor et a 994 oo Rogero 985 te ee tat bot tertemora mootg ad eat od ae memory ret. Gve tat Caor et a e a ed mode, e ave te reao to oo ter amto. 8 Laot 999 ded te odto e e-ate Pareto eey me e-ot Pareto eey. 5

6 Cae 2: Pra motor te aget trade o redt market I te ra a otro te aget borrog ad avg, e at at a a baker or te aget. Caor et a 994 arge tat a og a at eat oe arty a ae to a eret redt market ad te aget avg a be motored, te te otma omto-eort at do ot deed o arty a ave ad borro 9. Soe or o tat bot arte ave ae to redt ad te aget avg a be otrated o 0. Te robem o beome: ma e t 0,, t, e0, e = = e.t. e, e arg ma e0 U, e0 t 0 e U, e e0, e = = e0 U, e0 e U, e 2U = = ere t te ra avg ad te aget avg. I te robem above, t o tat te aget oe o eort eve deed oy o omto. Moreover, eabty otrat me tat tota omto a ever eeed rodto. Tereore, at te otmm, oy te tota avg t tat are determed; ot dvda avg ad t earatey. A a oeqee, oe arty avg a be zero. Se te aget ae motorabe, a og a te ra a ae a e, te tato tereore t be te ame a tat Cae, e tere o ae atoever. I t ae, e te og-r otma otrat t ot reegotabe, t ebt memory o omto. Hoever, e te mat o at otome o te tre omto oy deed o te eeted tty, ot otratg a aeve og-r eey e te aget a ae to a redt market, eve te ra a motor ae. 9 Reet tde ave bee abe to make a dtto betee borrog rom bak ad rom aa market, e.g. Reo ad Sarez So te ra a de te aget mode o avg te otrat. 6

7 Aoter teretg ot ere tat, a o Rogero 985, e te ra rketra, te aget od aay ke to ave more ta te otrat ao m to. We rerode rooto beo: Prooto 3 Soe tat Pareto-otma otrat or te eort e. Te or every I, mt aty, 2 e = ' ' = Ayg Jee eqaty to te ove to / e oave 3, e get Tereore = ' e ' = = e ' e ' T, der every Pareto-otma otrat or every otome o every erod, te aget od ooe to ave ome o age e a te oortty to do tat. From bot ae ded above, e ode tat, e te aget a o ae to redt market or a ae bt otroabe, te otma og-r otrat ot be reegotabe. Hoever, ort-r otrat revet omto mootg. Tat, te otma eqee o ort-r otrat t a reetto o tat otma otrat. I te orga rooto, te rato o ra dot rate ad te aget dot rate aear te rgt-ad de. Beae e amed eqaty, te dot rate ae ot. 2 I te ra rk-avere te odto ' = ' ' e ' = 3 Te oavty o te vere o te aget marga tty ra, a oted ot by Rogero 985. He od tat or te a o yerbo abote rk avero HARA tty to, eeted age are reag or dereag over tme deedg o eter te aget rk toerae - / reae at a rate greater ta or e ta oe. Tey are otat te aget tty ogartm. 7

8 4. We aget borrog ad avg are ot otraed I te ra aot otro te aget avg, e mt take to aot tat te aget read age otmay over tme. I eter te aget omto or avg are oberved -bt o-verabe at te ed o te rt erod, te te aget eat te eod erod rvate ormato. I te abee o ommtmet, t gve re to a advere eeto. Te aymmetry o ormato t ae tat te dde aratert emerge edogeoy rom te rt erod. Tat, tat te eod-erod age ee te aget avg te rt erod. Hee, te rt-erod avg erve a remary vetmet te eod erod. Te robem or ommtmet tereore ormazed a oo: ma e 0,,, e0, e = = e e U, e 0 e0, e, = =.t. e, e, arg ma e0 U, e0 e0 U, e0 e U, e 2U = = Uke te revo ae, t og-r otmzato, te term t te obetve to daear, e o oy te aget a ae to redt market, ad te ra aot otro t. Moreover, avg are o redetermed at te begg o erod to. A a oeqee, te tty o bot te ra ad te aget a be mroved by reegotatg te otrat. For eame, oe tat eort oy eerted erod to 4, ad t take to vae, g H ad o L. Te ot o g eort oe ad te ot o o eort zero. Te g eort gve e t robabty ad are t robabty, ad o eort yed e t robabty < ad are t robabty. Soe tat te ayo o e g eog o tat te ra dede to de g eort. Uder a ommtmet te otrat 4 So tat U = ad U 2 = 2 ve 2. T amto o te aget beg orkg ad omg te eog erod, bt oy omg te rt erod otet t revo tde ke Damod- Mrree, Barverma ad Stgtz et ee Maomo ad Sey,

9 9 od t ot o eod-erod age,. Let ad be te aget rt-erod omto e a deded to rode g eort ad o eort, reetvey. Tereore, or k =,, k mamze k k For te aget o ome ad rode g eort, te eod-erod tty : 2 = U Uder a ommtmet te etve omatbty otrat bdg,.e. 2 U = Hoever, e te otma omto or a aget ag to rode o eort, te t oo tat > Tereore, 0 2 > U T ret ea y a aget o reae te begg o te eod erod ater omg trty reer to eert g eort ta to eert o eort. O te oter ad e deret der a e-ot eet otrat. T ead to a oortty or bot ra ad aget to reegotate te orga otrat order to atta Paretoeror tte. So, a -ommtmet otrat my ommttg e-ate to e-ot eee e tere a remary vetmet.

10 T te aget a a ree ae to redt market, ad tere o eat eet or eame, te aget reeree ebt otat abote rk-avero, te avg deo doe ot aet ay otrat. Tat, eve te aget avg are ot obervabe, te og-r otma otrat ot reegotabe ad a be memeted trog ort-r otrat. 6. Coo Memory ay a roe Pareto-otma otrat. I order to aeve a Pareto-otma otome, a retrto o te aget ae to redt market eeary. Te og-r otma otrat ad te ort-r otma otrat a yed te ame oto te og-term otrat teraze te aget omto over tme, aeted by at tory. I addto, te og-r otma otrat od ot be reegotabe. Tat, te begg o ay termedate erod, o e otrat or reegotato tat od be reerred by bot arte. Te reetto o mora azard reato rovde te oortty or tertemora rkarg. Te otma otrat take advatage o t odto, tat, memory ay a roe te otma otrat. Nevertee, de to etve robem, te aget ot y red ad et t a dere o tertemoray re me trog te e o redt market. Tat, te aget aay et t a dere to ave ome o age ad ever to borro agat tre age. Te mode deveoed by Caor et a a bee abe to rovde a ed rameork or te aayzg te roe o memory ad ommtmet ra-aget reato. It ao gve a more ear dertadg o te mortae o ae to redt market. Hoever, t mode oy ork or te orzo Rogero, 985; Maomo ad Sey, 988. Ao, te amto o ommo dot rate ot aay aabe. Eeay e dvda ave deret degree o atee. Te mode ao avod dg te robem o advere eeto, dete te at tat ome tde ave aready bee abe to aayze bot advere eeto ad mora azard to oe rameork o aay. Ma 99 or eame, tde te robem o advere eeto dyam mora azard, by amg tat otrat a be reegotated ad aget oe o eort a og-r eet. He oded tat e aget ato a og-r eet, te tot a ommtmet eme, oe od eet a rkg beavor to be more ommo. Se te oetee o mora azard ad advere eeto more reat ta t beg to 0

11 earated robem, e tk tat tre deveomet o te mode o Caor et a od ororate te robem o advere eeto. More reet tde ave bee abe to dtg betee redt ae, amey, ae to bak ae ad to market ae, e.g. Reo ad Jarez 2000, Homtro ad Troe 997, et. We beeve tat dtgg betee ore o redt od mrove te mode. Reeree Caor, P.A., Ma. I, Rey P., ad Saae, B Reeated Mora Hazard: Te Roe o Memory, Commtmet, ad Te Ae to Credt Market, Eroea Eoom Reve 38: Laot, J-J Te Eoom o Uertaty ad Iormato. Te MIT Pre. Ma, C.A. 99. Advere Seeto Dyam Mora Hazard, Qartery Jora o Eoom, Vo. 06: Mao-Stader, I. Ad D. Perez-Catro A Itrodto to te Eoom o Iormato. Oord Uv. Pre. Maomo, J.M. ad Sey F. Te Mterod Pra-Aget Probem, Reve o Eoom Stde, LV: Rey, P. ad Saae, B Log-term, Sort-term ad Rebegotato: O te Vae o Commtmet Cotratg, Eoometra, Vo. 58 3: Reo, R. ad J. Sarez Etrereera Mora Hazard ad Bak Motorg: A Mode o te Credt Cae, Eroea Eoom Reve 44: Rogero, W.P Reeated Mora Hazard, Eoometra, Vo. 53. No. :