Determinants of Borrowing Limits on Credit Cards Shubhasis Dey and Gene Mumy

Transcription

1 Bank of Canada Banque du Canada Wokng Pape / Document de taval Detemnants of Boowng mts on Cedt Cads by Shubhass Dey and Gene Mumy

2 ISSN Pnted n Canada on ecycled pape

3 Bank of Canada Wokng Pape Mach 2005 Detemnants of Boowng mts on Cedt Cads by Shubhass Dey 1 and Gene Mumy 2 1 Monetay and nancal Analyss Depatment Bank of Canada Ottawa Ontao Canada K1A 0G9 sdey@bankofcanada.ca 2 Depatment of Economcs The Oho State Unvesty Columbus OH mumy.1@osu.edu The vews expessed n ths pape ae those of the authos. No esponsblty fo them should be attbuted to the Bank of Canada.

4 Contents Acknowledgements v Abstact/ésumé v 1. Intoducton Backgound The Theoetcal Model A bank s poft-maxmzaton poblem Data The Econometc Model esults and Dscusson Conclusons efeences Appendx

5 v Acknowledgements The authos ae gateful to uca Dunn Stephen Cosslett Pee St-Amant Célne Gauthe Gegoy Caldwell and loan Pelgn fo the helpful comments.

6 v Abstact The dffeence between actual boowngs and boowng lmts alone geneates nfomaton asymmety n the cedt cad maket. Ths nfomaton asymmety can make the maket ncomplete and ceate ex post msallocatons. Households that ae dened cedt could well tun out to be ex post less sky than some cedt cad holdes who boow lage potons of the boowng lmts. Usng data fom the U.S. Suvey of Consume nances the authos fnd a postve elatonshp between boowe qualty and boowng lmts contollng fo banks selecton of cedt cad holdes and the endogenety of nteest ates. The estmaton eveals how nteest ates have a negatve nfluence on the optmal boowng lmts offeed by banks. JE classfcaton: D4 D82 C3 Bank classfcaton: Maket stuctue and pcng Econometc and statstcal methods ésumé a dfféence ente le montant des lmtes de cédt accodées et le montant effectf des empunts sufft à cée su le maché des cates de cédt une asyméte d nfomaton. Cette asyméte peut ende ce maché ncomplet et podue a posteo une mauvase allocaton des essouces. Il se pouat fot ben en effet que les ménages qu se voent efuse un pêt epésentent un sque mons élevé que cetans détenteus de cates qu font lagement appel à leu lgne de cédt. À pat des données de l enquête menée pa la éseve fédéale amécane su les fnances des consommateus les auteus concluent à une coélaton postve ente la solvablté de l empunteu et la lmte de cédt une fos ps en compte l endogénété des taux débteus et les effets de la sélecton pa les banques des détenteus de cates. D apès leus estmatons le nveau optmal des lmtes de cédt consentes vae en foncton nvese des taux d ntéêt. Classfcaton JE : D4 D82 C3 Classfcaton de la Banque : Stuctue de maché et fxaton des px Méthodes économétques et statstques

7 1. Intoducton It s well accepted that boowng lmts on collatealzed loans ae pmaly detemned by the amounts of collateal pledged by the boowes. Howeve fo noncollatealzed loans such as those on cedt cads the nfomaton about boowes epayment abltes plays a cucal ole n detemnng the cedt cad boowng lmts o cedt lmts. Asymmetc nfomaton between boowes and lendes and the lack of collateal to mtgate that nfomatonal asymmety ae manly esponsble fo the exstence of cedt atonng n some cedt makets. Impefect nfomaton about boowe sk nduces banks to efuse cedt to some boowes even f the latte would accept hghe nteest ates fo the loans. Cedt bueau epots povde some ctcal nfomaton about boowe skness whch banks use to allevate some of the nfomatonal asymmety and to mpove the qualty of the loan-supply decson. Publcly avalable nfomaton about boowes cedtwothness helps banks sot the clent pool nto boad sk classes. Banks do not howeve have pefect knowledge about ndvdual boowe sk. In the case of lnes of cedt such as cedt cads banks patculaly do not know how much a boowe wll actually boow on the lne whch s a key detemnant of the boowe s epayment pobablty. Theefoe cedt atonng pessts n the unsecued cedt cad maket. Boowes wth no o bad cedt epots ae moe lkely to be efused access to cedt cads by banks. Those cedt cad holdes who have bette cedtwothness ae peceved to have hghe epayment abltes and theefoe ae lkely to be povded wth hghe cedt cad boowng lmts. Poftmaxmzng banks choose to povde exactly the amount of cedt to the boowes that maxmzes the expected pofts. Theefoe a caeful analyss of the elements of boowes cedtwothness and the optmal lne of cedt contacts wll help us undestand the detemnants of cedt cad boowng lmts. We fnd that the dffeence between actual boowngs and offeed cedt lmts s enough to geneate nfomaton asymmety n the cedt cad maket. Moeove ndvduals who ae atoned out of the cedt cad maket could vey well tun out to have been convenence uses 1 and theefoe ex post wee less sky than some cedt cad holdes who boow lage factons of the cedt lmts. Thus not only can nfomaton asymmety n the cedt 1 Convenence uses ae ndvduals who use cedt cads fo tansactons puposes only. 1

8 cad maket make the maket ncomplete though cedt atonng but t can also esult n ex post msallocatons. A typcal cedt cad contact s two-dmensonal. Banks offe a ate of nteest along wth a pe-set boowng lmt to the potental boowes. The two-dmensonal natue of loan contacts makes cedt cad nteest ates endogenous. Empcal dentfcaton of the detemnants of cedt cad boowng lmts eques us to coect fo ths endogenety. Moeove not all ndvduals have cedt cads. The set of cedt cad holdes s a selected sample and theefoe ou estmaton needs to account fo the sample selecton bas. Contollng fo the banks selecton of cedt cad holdes and the endogenety of cedt cad nteest ates we fnd a postve elatonshp between boowe qualty and boowng lmts on cedt cads. Ou estmaton also eveals how the endogenous nteest ates negatvely nfluence the optmal cedt cad boowng lmts. In secton 2 we descbe the backgound and pevous eseach on these ssues. In secton 3 we ntoduce the theoetcal model. The data ae descbed and the econometc model bult n sectons 4 and 5 espectvely. Secton 6 descbes the empcal esults and secton 7 offes some conclusons. 2. Backgound Begnnng wth Ausubel 1991 eseaches have examned consume lnes of cedt especally wth egads to cedt cads. The bulk of the lteatue on cedt cads concentates on explanng why the aveage cedt cad nteest ates eman stcky at a hgh level. Ausubel 1991 agues that the eason fo the downwad gdty of cedt cad nteest ates and supenomal pofts s the falue of competton n the cedt cad maket. He patly attbutes ths falue to myopc consumes who do not foesee ndebtedness and nteest payments on the outstandng balances. Bto and Hatley 1995 howeve ague that consumes cay hgh-nteest cedt cad debt not because of myopa but because low-nteest bank loans nvolve tansactons costs. Meste s 1994 vew s that low-sk boowes who have access to low-nteest collatealzed loans leave the cedt cad maket. Ths makes the aveage clent pool of the cedt cad maket ske theeby peventng nteest ates fom gong down. Pak 1997 ponts to the opton-value natue of cedt cads to explan the pce stckness. He agues that the 2

9 nteest ate that poduces zeo poft fo cedt cad ssues s hghe than the nteest ates on most othe loans because atonal cedt cad holdes boow moe money when they become ske. An empcal pape by Calem and Meste 1995 fnds evdence that consumes ae eluctant to seach fo lowe ates because of hgh seach costs n ths maket. Cagll and Wendel 1996 suggest that due to the hgh pesence of convenence uses even modest seach costs could keep the majoty of consumes fom seekng out lowe nteest ates. Ke 2002 focuses on nteest ate dspeson wthn the cedt cad maket. He studes a two-fold nfomaton asymmety: one between the banks.e. the lendes and the boowes and the othe wthn the banks themselves. Some banks the extenal banks have access to only the publcly avalable cedt hstoes whle othes the home banks have addtonal access to boowes pvate fnancal accounts. Ke agues that n equlbum the aveage ate of nteest chaged by the so-called extenal banks would be hghe than that chaged by the home banks because the aveage boowe assocated wth the extenal banks would be ske. Most of the exstng lteatue on the cedt cad maket focuses on analyzng the vaous aspects of ts pcng. Despte the fact that cedt cad loan contacts ae essentally two-dmensonal eseaches have lagely gnoed the cedt-lmt dmenson of the contact. Goss and Souleles 2002 utlze a unque new data set on cedt cad accounts to analyze how people espond to changes n cedt supply. They fnd that nceases n cedt lmts geneate an mmedate and sgnfcant se n debt consstent wth the buffe-stock models of pecautonay savng as cted n Deaton 1991 Caoll 1992 and udvgson Dunn and Km 2002 ague that banks n ode to stategze aganst Ponz-schemes n the cedt cad maket tend to povde lowe cedt lmts to hgh-sk boowes despte gvng them a lage numbe of cads. Though they fnd some empcal suppot fo the hypothess on cedt lmts Dunn and Km choose to focus the fomal empcal analyss on an estmaton of cedt cad default ates. Castonova and Hagstom 2004 usng smple two-stage least squaes estmaton fnd that the acton n the cedt maket s mostly n the lmts and not n the balances. In ths pape we buld a geneal theoetcal model that captues the key elements of cedt cad loan contacts and we test the elatonshp between boowe qualty and 3

10 cedt cad boowng lmts coectng fo the banks selecton of cedt cad holdes and the nfluence of endogenous nteest ates. 3. The Theoetcal Model Consde a model whee banks ae compettvely offeng non-collatealzed lnes of cedt such as cedt cads. A lne of cedt s a boowng nstument wheeby the boowe s offeed a boowng lmt o cedt lmt and an nteest ate. The boowe can boow up to the cedt lmt. Inteest chages accue only f some postve amount s boowed on the lne. A lne of cedt contact ncopoates the tadtonal fxed-loan contact as a specal case when the ente cedt lmt s boowed at the vey outset. Banks ae assumed to pocue funds at a ate. Based on publcly avalable cedt epots banks ae able to patton the clents nto boad sk classes. et us assume that these classes epesented by ae such that [ ]. The vaable can be consdeed the cedt scoe that cedt bueaus constuct fo all potental boowes. et us also assume fo smplcty that thee s only one boowe n evey sk class. 2 A typcal cedt cad contact offeed to class conssts of a vecto whee s the cedt lmt and s the nteest ate. Usng the famewok put fowad by Dey 2004 we ague that boowes pmaly use lnes of cedt to smooth consumpton acoss vaous states and tme peods. Ths famewok essentally makes the desed boowngs on lnes of cedt become andom vaables functons of the nteest ates and the undelyng wealth shocks. et epesent the undelyng wealth shock such that we have the optmal boowng as B = B ~ G whee. We can wte B B B = f B whee B. Moeove s ae assumed to ~ be ndependent of each othe and so ae B s. Usng the optmal boowng functon we can deve an nvese demand cuve fo boowe as = B. The epayment pobablty fo a boowe nceases wth the sk-class measue and deceases wth the 2 We theefoe assume that banks offe the same contact to all ndvduals wthn a patcula sk class wth the same cedt scoe despte the potental heteogenety n the epayment abltes. 4

11 5 amount owed D whee D = B and = 1 + = B. 3 We epesent the class epayment pobablty as D ρ ρ = such that. < 0 D ρ. > 0 ρ and ]. [01 ρ The only uncetanty that banks have about boowes epayment pobabltes esults fom the nablty to know the actual boowngs to be undetaken on the lnes they extend. In the followng secton we consde a typcal bank s poft-maxmzaton poblem whee t s offeng an unsecued lne of cedt such as a cedt cad. 3.1 A bank s poft-maxmzaton poblem The expected poft fom offeng an unsecued lne of cedt contact to class s epesented by. o class a bank s poft-maxmzaton poblem s gven by: + = db B f B B B B Max ] [ ρ db B f ] [ ρ = + db B f B B B B ] [ ρ. ] ][ 1 [ ρ et us assume that. < 0 Patally dffeentatng wth espect to and settng t to zeo we get + = ]. [ f ρ }.. { ][ [1 D ρ ρ ]. ρ ]. [ f ρ = 0 3 Banks know that actual boowngs undetaken on cedt cads change boowes epayment pobabltes. Snce banks have no way of knowng how much a boowe n a patcula sk class wll boow lne of cedt contacts cannot be condtoned on actual boowngs.

12 o = [1 ][ { ρ. D + + ρ. ρ. ] = 0. 1 } + Poposton: Banks choose and = such that = 0 =. o all sk classes yeldng < 0 the banks choose 0. o all banks maxmzng the total expected poft ove all sk classes s equvalent to ntegatng ove all sk classes the maxmzed expected poft of evey sk class. 4 The optmal cedt cad contact offeed to boowe gven by the pa s chosen such that f s actually boowed at pce = ou bank s poft maxmzaton and zeo-poft condtons ae smultaneously satsfed fo the sk class that boowe epesents. We show that the dffeence between actual boowngs and offeed cedt lmts s enough to geneate nfomaton asymmety n the cedt cad maket. Moeove ndvduals who ae atoned out of the cedt cad maket could vey well tun out to have been ex post less sky than some cedt cad holdes who boow lage factons of the cedt lmts. Thus not only can nfomaton asymmety n the cedt cad maket make the maket ncomplete though cedt atonng but t can also esult n ex post msallocatons. Ou bank s optmal cedt cad contact fo sk class can be epesented by the followng tangula stuctue: The equlbum cedt lmt equaton = 2 The equlbum pce equaton 4 Ths follows fom the fact that wealth shocks s and theefoe actual boowngs B s ae ndependent of each othe and banks ae foced to make zeo expected pofts n evey sk class. 6

13 =. 3 Theefoe ou theoy of lnes of cedt contacts yelds to a bvaate equaton system that can be used fo empcal analyss. Usng household-level data we can potentally test the sgns of the followng patal devatves: 5 and. Gven the second-ode condton < 0 and assumng that > 0 > 0 and < 0 ou devatons shown n the appendx can geneate the followng testable pedctons out of ou theoetcal model of lne of cedt contacts: < 0 and > 0. Though we have unambguous sgns fo the educed-fom patal devatves the sgns fo the patal devatves of the stuctual-fom optmal boowng lmt functon such as and ae ambguous. 6 We hope to use ou econometc model and the empcally vefed esults to shed some lght on these ambguous sgns. 4. Data The data used n ths study ae fom the 1998 U.S. Suvey of Consume nances SC. SC s a natonwde suvey conducted by the Natonal Opnon eseach Cente and the U.S. edeal eseve Boad. The 1998 SC povdes a lage and ch data set on household assets labltes demogaphc chaactestcs and a numbe of vaables that captue household atttudes. In households wee suveyed and 3233 of them had at least one bank-type cedt cad whch amounts to 75.1 pe cent of the total numbe of households n the sample. Table 1 defnes the vaables used n ou econometc analyses. Table 2 compaes the mean chaactestcs of consumes wth cedt cads aganst those wthout. 5 See the appendx fo a dscusson of the patal devatves. 6 The ambguty egadng the stuctual paametes ases fom the fact that t s mpossble to theoetcally dentfy a supply functon when the pce s endogenous. Identfcaton of the stuctual paametes eques futhe estctons whch wll be addessed n moe detal n secton 5. 7

14 Table 1: Defnton of Vaables Vaables Type Explanaton HI Contnuous HEOC nteest ate Maxmum nteest ate chaged among the dffeent HEOCs taken out by the household 1 Got behnd n payments by two months o moe DEINQUENCY Bnay 0 Othewse 1 Declaed bankuptcy BANKUPTCY Bnay 0 Othewse CI Contnuous Cedt cad nteest ate OGCIMIT Contnuous ogathm of cedt cad boowng lmt OGINCOME Contnuous ogathm of ncome APHAI Contnuous HOUSEHODSIZE Contnuous Household sze AGE Contnuous Age of the household acton of HEOC and/o motgage debt epad EMPOYMENT1 Bnay 1 Not wokng 0 Othewse EMPOYMENT2 Bnay 1 eted 0 Othewse EMPOYMENT3 Bnay 1 Wokng and not self-employed 0 Othewse EMPOYMENT4 Bnay 1 Wokng and self-employed 0 Othewse Bnay 1 Dd not obtan as much cedt as appled fo despte IQCONSTAINT eapplyng o dd not eapply afte the fst efusal 0 Othewse HEOC Bnay 1 Has taken out a HEOC 0 Othewse 0 Almost no shoppng fo the vey best tems SHOPINVEST Categocal 1 Modeate shoppng 2 Geat deal of shoppng HEOC = Home equty lne of cedt 8

15 Table 2: Cedt Cad Holdes and Non-Holdes Vaables Cedt cad Holdes Cedt cad Non-holdes Mean Mean HOUSEHODSIZE DEINQUENCY BANKUPTCY OGINCOME EMPOYMENT EMPOYMENT EMPOYMENT SHOPINVEST APHAI AGE IQCONSTAINT HEOC HI CI OGCIMIT Note: All monetay vaables ae n thousand dollas. 5. The Econometc Model Household now epesents the sk class o boowe. et denote the poft-maxmzng boowng lmt that all banks collectvely extend to household. Accodng to ou theoetcal model descbng the equlbum n the cedt cad maket we have =. The vaable has no vaaton acoss households. Theefoe the effect of on cannot be empcally tested. Moeove let the vecto X 1 denote the nfomaton on household that banks use to defne the household s sk measue. The vecto X 1 conssts of vaables ncluded n publcly avalable cedt epots and the vaables that banks gathe whle pocessng cedt cad applcatons. Table 3 povdes a complete lst of vaables ncluded n an ndvdual cedt epot. Hence the vecto X 1 conssts of 9

16 Pesonal nfomaton Cedt Hstoy Publc ecods Inques Souce: TansUnon Table 3: Cedt epot Detals Name Cuent and pevous addess Socal secuty numbe Telephone numbe Date of bth Cuent and pevous employes Type of accounts: 1. etal cedt cads 2. Bank loans 3. nance company loans 4. Motgages 5. Bank cedt cads Infomaton avalable: 1. Account numbe 2. Cedto s name 3. Amount boowed 4. Amount owed 5. Cedt lmt 6. Dates when accounts wee opened updated o closed 7. Tmelness of payments 8. ate payments Tax lens Bankuptces Cout judgments st of all pates who have equested a copy of you cedt epot pesonal nfomaton such as employment status age and the sze of the household. It also contans nfomaton on cedt hstoy vaables such as access to altenatve lnes of cedt e.g. HEOCs the facton of motgage and/o HEOC debt epad tmelness of payments bankuptcy ecods and cedt nques. The vecto X 1 also ncludes nfomaton on household ncome whch s gatheed dung the applcaton pocess fo a cedt cad. We postulate a lnea stuctual-fom equaton fo as = γ + β 1 X 1 + v

17 In equaton 4 the banks oppotunty cost of funds contbutes to the constant tem and the undelyng wealth shock that nfluences a household s desed boowng level goes nto the eo tem v 1. Snce the optmal cedt cad nteest ate s gven by = the lnea educed-fom equaton fo s gven by = β 2 X 2 + v 2. 5 Also n equaton 5 the vaable contbutes to the constant tem and the undelyng wealth shock goes nto the eo tem v 2. The vecto X 2 conssts of all the vaables pesent n vecto X 1 and some dentfyng vaables whch ae nfluental yet absent n publc cedt epots that captue aspects of a household s seach behavou such as a household s popensty to shop aound fo the best ates befoe makng majo savngs and nvestment decsons and the nteest ates on altenatve lnes of cedt such as HEOCs. The combnaton s obseved f the banks decde to offe a cedt cad to household.e. f > 0. et us theefoe consde the followng econometc model: = = = γ ' = β X 2 ' + β X v v 1 f >0 and = 0 = 0 In the equatons above othewse. and epesent the obseved cedt cad boowng lmt and nteest ate espectvely X 1 and X 2 ae vectos of exogenous vaables v 1 and v 2 follow bvaate nomal wth means zeo vaances σ 1 2 and σ 2 2 espectvely and covaance s 12. If X 2 contans at least one vaable that s not ncluded n X 1 then all the paametes of the model ae dentfed. To dentfy the effect of the endogenous nteest ate on the cedt cad boowng lmt that s offeed to household we use the estmated cedt cad nteest ate ˆ as an nstument. 7 Maxmum-lkelhood estmaton s used to estmate the poposed econometc model. To fom the lkelhood functon we have to elate the dependent vaables to 7 See ee Maddala and Tost 1980 and Wales and Woodland 1980 fo techncal detals. 11

18 the empcal countepats and descbe the pocess by whch the obsevable countepats ae geneated n tems of the undelyng stochastc components. Household s obseved to have a cedt cad f > 0. Substtutng the equaton fo the cedt cad nteest ate nto the boowng lmt equaton the decson on whethe to offe a cedt cad can be wtten as o β 1 X 1 + γβ 2 X 2 > - v 1 + γv 2 I > v whee v N 0 σ γ 2 σ γσ 12 N 0 σ v 2 and I = β 1 X 1 + γβ 2 X 2. The lkelhood of obsevng household wthout a cedt cad s ϖ 1 I 2 I Pob I < v = e dϖ = 1 Φ = Φ 2 σ σ I / σ v whee Φ s the standad nomal cumulatve densty functon. 2 Hence the lkelhood of obsevng the data consstng say of N households wth M households wthout cedt cads s = M = 1 I Φ σ v N = M + 1 M N I b v1 v2 = Φ n v2 n v1 v2 σ = 1 v v = M + 1 whee b. s the bvaate nomal densty functon n. s the nomal densty functon and v 1 = - β 1 X 1 - γ v 2 = - β 2 X 2. Now v 2 ~ N 0 σ 2 2 v v1 v2 ρσ 1v2 2 2 N σ 1 1 ρ σ 2 σ 12 whee ρ =. σ σ et σ = σ 1 ρ and c

19 v T = 1 ρσ v σ 2 σ c 1 2. The coespondng log-lkelhood functon can be wtten as log = M I log[ Φ σ ] + v φ σ σ = 1 v = M N N = M + 1 whee φ. s the standad nomal densty functon. φ T σ A mult-step pocedue s used to estmate the paametes of the model. st the paametes of the econometc model ae estmated usng the two-stage pobt method descbed by ee Maddala and Tost Ths two-step pocedue yelds consstent estmates of all the paametes of the model. c To obtan asymptotcally effcent paamete estmates the consstent estmates ae used as ntal values fo the fnal maxmzaton of the log-lkelhood functon. et δ D such that I = and σ v λ δ D = 1 f household has a cedt cad.e. = 0 othewse. o cedt cad holdes = β 1X 1 + γ + σ vλ δ + v3 = β 2 X 2 + µλ δ + v4 2 γσ 2 + σ 12 whee µ =. σ v φ δ =. et us futhe defne a dummy vaable 1 Φ δ > 0 Consstent estmates of δ can be obtaned by unnng a pobt of the decson to offe a cedt cad. Then we can estmate the followng equaton usng odnay least squaes OS and obtan ˆ : = β X + µλ δˆ + v

20 We then estmate the followng equaton usng OS: = β X + γ + σ λ δˆ + v 1 1 ˆ v 3. Ths two-step pocedue afte coectng fo the standad eos gves us consstent estmates of all the paametes of the model whch ae used as statng values fo the maxmum-lkelhood pocedue. 6. esults and Dscusson Table 4 epots the esults of a pobt estmaton that explans a bank s decson to offe a cedt cad to a potental boowe. 8 The household s ncome age and selfemployed status sgnfcantly mpove the lkelhood of gettng a cedt cad. The fact that self-employed households ae moe lkely to eceve cedt cads seems counte- Table 4: A Bank s Decson to Offe a Cedt Cad Vaables Coeffcent Standad eo S.E. CONSTANT HOUSEHODSIZE DEINQUENCY BANKUPTCY OGINCOME EMPOYMENT1 EMPOYMENT2 EMPOYMENT4 SHOPINVEST APHAI AGE IQCONSTAINT HEOC HI Sgnfcant at 1 pe cent sgnfcant at 5 pe cent sgnfcant at 10 pe cent. ntutve. Self-employed households face hghe vaatons of ncome and ae lkely to have hghe default sks theefoe banks should extend lowe amounts of cedt to them. The sze of the household unemployment delnquency and a declaaton of bankuptcy 8 Table 1 defnes the vaables used n all the tables of ths secton. 14

21 dmnsh the chance of obtanng a cedt cad. If the household s lqudty constaned then thee s a hghe pobablty that they wll be dened a cedt cad. The moe the household looks aound fo the best ates o f they have taken out a HEOC the moe lkely they ae to have a cedt cad. In geneal the esults ndcate that the hghe the household s cedtwothness the geate the lkelhood of obtanng a cedt cad. Table 5: Two-Stage Pobt fo Inteest ates Vaables CONSTANT HOUSEHODSIZE DEINQUENCY BANKUPTCY OGINCOME EMPOYMENT1 EMPOYMENT2 EMPOYMENT4 IQCONSTAINT APHAI AGE SHOPINVEST HEOC HI AMBDA a Two-stage pobt Coeffcent S.E = value = 5.11 σ 2 = 4.5 N = 3233 Sgnfcant at 1 pe cent sgnfcant at 5 pe cent sgnfcant at 10 pe cent. φˆ a AMBDA =. 1 Φˆ Table 5 epots the esults fo the two-stage pobt egesson fo nteest ates among cedt cad holdes. Delnquency o a declaaton of bankuptcy nduces banks to chage hghe cedt cad nteest ates. If the household s lqudty constaned then t s also lkely to esult n a hghe cedt cad nteest ate offeed by banks. If the household 15

22 shops aound then they can obtan a lowe nteest ate on the cedt cads. The ate on an altenatve lne of cedt such as a HEOC also educes the offeed cedt cad nteest ate. nally the estmated value of µ s Snce ths estmated value s not sgnfcantly dffeent fom zeo we conclude that thee s no empcal evdence of sample selecton n ou estmates of the equaton fo the cedt cad nteest ate. We conclude that the bette the cedtwothness of the household the lowe the cedt cad nteest ate chaged by banks whch means that we have empcal suppot fo the followng: < 0. Moeove contollng fo the cedt sk of the household the moe ponounced s the seach behavou the lowe s the cedt cad nteest ate. Table 6 epots the two-stage pobt estmates of the equaton fo the cedt cad boowng lmt fo the cedt cad holdes. The hghe the ncome of the household the hghe the cedt lmt offeed by banks. If the household s self-employed o has aleady taken out a HEOC then agan they eceve a hghe cedt cad boowng lmt fom banks. The endogenous vaable the cedt cad nteest ate has a negatve effect on banks lne of cedt supply. Chagng a hghe cedt cad nteest ate wll ase the default pobablty of a boowe of any gven sk type. A typcal bank s optmal cedt lmt should theefoe fall to compensate fo ths se n default sk. nally the estmated value of σ v s Snce the estmated value s also sgnfcant we conclude that thee s empcal evdence of sample selecton n the estmates of the equaton fo the cedt cad boowng lmt. Moeove the estmated effect of sample selecton s postve. Theefoe the hghe the cedtwothness of the boowe the hghe s the lkelhood of beng offeed a cedt cad and the hghe s the boowng lmt extended by banks. Hence ou empcal esults suppot the followng pedctons: < 0 and > 0. 16

23 Table 6: Two-Stage Pobt fo Cedt mts Vaables CONSTANT HOUSEHODSIZE DEINQUENCY BANKUPTCY OGINCOME EMPOYMENT1 EMPOYMENT2 EMPOYMENT4 APHAI AGE IQCONSTAINT HEOC CI AMBDA Two-stage pobt Coeffcent S.E og = σ 1 = s 12 = N = 3233 Sgnfcant at 1 pe cent sgnfcant at 5 pe cent sgnfcant at 10 pe cent. φˆ a AMBDA = 1 Φ ˆ. Table 7 epots the full-nfomaton maxmum lkelhood IM estmates of the equaton fo the cedt cad nteest ate. Delnquency o a declaaton of bankuptcy nduces banks to chage hghe cedt cad nteest ates. If the household s unemployed o lqudty constaned then t s agan lkely to esult n banks offeng a hghe cedt cad nteest ate. The ncome of the household o the self-employed status depesses the offeed nteest ate n cedt cad contacts. If the household shops aound fo the best ates then they can obtan a lowe nteest ate on cedt cads. Hence an actve seach fo a lowe ate esults n a lowe ate fo a household of any sk type. Moeove ou maxmum-lkelhood estmates confom to the two-stage pobt pedcton of < 0. 17

24 Table 7: IM Estmates fo Inteest ates Maxmum kelhood Vaables Coeffcent S.E. CONSTANT HOUSEHODSIZE DEINQUENCY BANKUPTCY OGINCOME EMPOYMENT EMPOYMENT EMPOYMENT IQCONSTAINT APHAI AGE SHOPINVEST HEOC HI Sgnfcant at 1 pe cent sgnfcant at 5 pe cent sgnfcant at 10 pe cent. Table 8 epots the IM estmates of the equaton fo the cedt cad boowng lmt. The hghe the ncome o the age of the household the hghe the cedt lmt offeed by banks. If the household s self-employed o aleady has taken out a HEOC then agan they eceve a hghe cedt cad boowng lmt fom banks. Unemployed households howeve obtan lowe cedt cad boowng lmts fom banks. The endogenous vaable the cedt cad nteest ate agan has a negatve effect on the bank s loan supply. Hence ou maxmum-lkelhood estmates ae consstent wth the two-stage pobt esults suppotng < 0 and > 0. 18

25 Table 8: IM Estmates fo Cedt mts Vaables CONSTANT HOUSEHODSIZE DEINQUENCY BANKUPTCY OGINCOME EMPOYMENT1 EMPOYMENT2 EMPOYMENT4 APHAI AGE IQCONSTAINT HEOC CI Maxmum kelhood Coeffcent S.E σ 1 σ 2 ρ og- = Sgnfcant at 1 pe cent sgnfcant at 5 pe cent sgnfcant at 10 pe cent. 7. Conclusons ne of cedt contacts such as cedt cad contacts ae fundamentally dffeent fom tadtonal fxed-loan contacts. An undestandng of the key elements of cedt cad contacts eques a theoetcal sepaaton of the choce of the amount of boowng and the choce of the amount of cedt lmt the two-dmensonal natue of the contact and the maket stuctue unde whch the boowes and lendes opeate. We have shown that the dffeence between actual boowngs and offeed cedt lmts s enough to geneate nfomaton asymmety n the cedt cad maket. Moeove ndvduals who ae atoned out of the cedt cad maket could vey well tun out to have been ex post less sky than some cedt cad holdes who boow lage factons of the cedt lmts. Theefoe not only can nfomaton asymmety n the cedt cad maket make the maket ncomplete though cedt atonng but t can also esult n ex post msallocatons. 19

26 We have theoetcally dentfed the cucal featues of cedt cad contacts offeed by banks and examned the assocaton between boowe qualty and the offeed menu of cedt cad boowng lmt and nteest ate. We have also been able to captue the effect of endogenous nteest ates on the offeed boowng lmts of households. Ou esults suppot the fact that banks use publcly avalable nfomaton on potental boowes to assess the cedt sk and to fomulate the type of cedt cad contacts to offe. The cedt cad maket shows clea evdence of cedt atonng. Banks efuse lowest-qualty boowes access to cedt cads. Among the cedt cad holdes those wth bette cedt epots ae peceved to have hghe epayment pobabltes and theefoe ae povded wth hghe cedt cad boowng lmts and lowe nteest ates. Contollng fo the boowe s sk type we fnd that a geate seach fo the best ates on loans sgnfcantly educes the nteest ate that they ae chaged on cedt cads. We also have found empcal suppot fo a negatve elatonshp between the cedt cad boowng lmt loan supply and the cedt cad nteest ate the pce of the loan. A hghe nteest ate wll ase a boowe s default pobablty egadless of the sk type theefoe the optmal boowng lmt should fall to compensate fo ths se n default sk. Seveal empcal studes have shown that a household s actual amount of boowng on cedt cads o the cedt cad utlzaton ate does affect the cedt cad boowng lmt that banks offe them. o nstance the cedt cad boowng lmt offeed to a convenence use of a gven sk class s typcally hghe than that offeed to a household n the same sk class and yet aleady boowng up to the cedt lmt. As an extenson to ths pape one could postulate a dynamc theoetcal model whee banks update the ex ante epayment pobabltes and the cedt cad contacts afte obsevng the actual amount boowed on cedt cads. The extended econometc model should have among othe thngs the cedt cad nteest ate and the obseved cedt cad boowng as endogenous vaables. 9 9 Such a model may be able to explan why we found self-employed households ecevng hghe cedt cad boowng lmts and lowe cedt cad nteest ates. Self-employed households ae pmaly convenence uses because they use cedt cads not fo boowng puposes but to mnmze the lqudty sks of the day-to-day busness opeatons. 20

27 efeences Ausubel.M The alue of Competton n the Cedt Cad Maket. Amecan Economc evew 811: Bto D.. and P.. Hatley Consume atonalty and Cedt Cads. Jounal of Poltcal Economy 1032: Calem P.S. and.j. Meste Consume Behavo and Stckness of Cedt Cad Inteest ates. Amecan Economc evew 855: Cagll T.. and J. Wendel Bank Cedt Cads: Consume Iatonalty vesus Maket oces. Jounal of Consume Affas 302: Caoll C The Buffe-Stock Theoy of Savng: Some Macoeconomc Evdence. Bookngs Papes on Economc Actvty 2: Castonova E. and P. Hagstom The Demand fo Cedt Cads: Evdence fom the Suvey of Consume nances. Economc Inquy 422: Deaton A Savng and qudty Constants. Econometca 595: Dey S ne of Cedt as Instuments of Consumpton Smoothng acoss State and Tme: The Choce between Cedt Cads and Home Equty nes of Cedt. The Oho State Unvesty Columbus OH. Unpublshed pape. Dunn.. and T.H. Km An Empcal Investgaton of Cedt Cad Default: Ponz Schemes and Othe Behavos. The Oho State Unvesty Columbus OH. Unpublshed pape. Goss D. and N.S. Souleles Do qudty Constants and Inteest ates Matte fo Consume Behavo? Evdence fom Cedt Cad Data. Quately Jounal of Economcs 1171: Ke S Inteest ate Dspeson Due to Infomaton Asymmety n the Cedt Cad Maket: An Empcal Study. The Oho State Unvesty Columbus OH. Unpublshed pape. ee.. G.S. Maddala and.p. Tost Asymptotc Covaance Matces of Two-Stage Pobt and Two-Stage Tobt Methods fo Smultaneous Equatons Models wth Selectvty. Econometca 482: udvgson S Consumpton and Cedt: A Model of Tme-Vayng qudty Constants. evew of Economcs and Statstcs 813:

28 Meste.J Why Ae Cedt Cad ates Stcky? Economc Theoy 44: Pak S Opton Value of Cedt nes as an Explanaton of Hgh Cedt Cad ates. edeal eseve Bank of New Yok eseach Pape No Wales T.J. and A.D. Woodland Sample Selectvty and the Estmaton of abo Supply unctons. Intenatonal Economc evew 212:

29 23 APPENDIX The optmal lne of cedt contact offeed to sk class can be epesented by the followng tangula stuctue: = A1 =. A2 Substtutng equaton A2 nto equaton A1 we obtan the followng educed-fom epesentaton of the optmal cedt cad boowng lmt: =. A3 Usng equatons A2 and A3 we can wte the followng: 0 = A4 0. = A5 Patally dffeentatng equaton A4 wth espect to we have + + = 0. A6 Patally dffeentatng equaton A5 wth espect to we have + + = 0. Usng the fst-ode condton of a bank s poft-maxmzaton poblem we can wte + = 0. A7 Solvng equatons A6 and A7 and suppessng the aguments we obtan 0 D C = = A8

30 D E = = A9 Smlaly we can solve fo 0 D = = A D G = = A11 Moeove we know that =. Hence we have + = A12. + = A13 Theefoe the theoetcally pedcted sgns of the patal devatves deved above and those of and wll depend on the sgns of the detemnants C E G and D. We know that the epayment pobablty fo boowe D ρ ρ = satsfes. < 0 D ρ. > 0 ρ and ]. [01 ρ Theefoe we have 0 >. The bank s poft functon also makes 0 < and 0 <. et us assume that > 0 > 0 and < 0.

31 25 Gven ou assumptons and the second-ode condton 0 < we have 0 < 0 > 0 > and 0 <. om equatons A12 and A13 we conclude that the sgns of and ae ambguous.

32 Bank of Canada Wokng Papes Documents de taval de la Banque du Canada Wokng papes ae geneally publshed n the language of the autho wth an abstact n both offcal languages. es documents de taval sont publés généalement dans la langue utlsée pa les auteus ls sont cependant pécédés d un ésumé blngue Monetay Polcy unde Model and Data-Paamete Uncetanty G. Cateau Y a-t-l eu sunvestssement au Canada duant la seconde moté des années 1990? State-Dependent o Tme-Dependent Pcng: Does It Matte fo ecent U.S. Inflaton? Pe-Bd un-ups Ahead of Canadan Takeoves: How Bg Is the Poblem? Sylvan Matel P.J. Klenow and O. Kyvtsov M.. Kng and M. Padalko The Stochastc Dscount acto: Extendng the Volatlty Bound and a New Appoach to Potfolo Selecton wth Hghe-Ode Moments. Chab-Yo. Gaca and E. enault Self-Enfocng abou Contacts and the Dynamcs Puzzle C. Calmès Tade Cedt and Cedt atonng n Canadan ms An Empcal Analyss of the Canadan Tem Stuctue of Zeo-Coupon Inteest ates The Monetay Ogns of Asymmetc Infomaton n Intenatonal Equty Makets Une appoche éclectque d estmaton du PIB potentel pou le oyaume-un Modellng the Evoluton of Cedt Speads n the Unted States The Tansmsson of Wold Shocks to Emegng-Maket Countes: An Empcal Analyss eal etun Bonds Inflaton Expectatons and the Beak-Even Inflaton ate Intenatonal Equty lows and etuns: A Quanttatve Equlbum Appoach. Cunnngham D.J. Bolde G. Johnson and A. Metzle G.H. Baue and C. Vega C. St-Anaud S.M. Tunbull and J. Yang B. Desoches I. Chstensen. Don and C. ed. Albuqueque G. Baue and M. Schnede Copes and a complete lst of wokng papes ae avalable fom: Pou obten des exemplaes et une lste complète des documents de taval pèe de s adesse à : Publcatons Dstbuton Bank of Canada Dffuson des publcatons Banque du Canada 234 Wellngton Steet Ottawa Ontao K1A 0G9 234 ue Wellngton Ottawa Ontao K1A 0G9 E-mal: publcatons@bankofcanada.ca Adesse électonque : publcatons@banqueducanada.ca Web ste: Ste Web :