DETERMINANTS OF BORROWING LIMITS ON CREDIT CARDS. Shubhasis Dey + Gene Mumy ++

Transcription

1 DETEMINANTS O OOWING IMITS ON CEDIT CADS Shubhass Dey + Gene Mumy ++ ASTACT In the credt card market banks have to decde on the borrowng lmts of ther potental customers when the amounts of borrowng to be ncurred on these lnes are uncertan. Ths borrowng uncertanty can make the market ncomplete and create ex post msallocatons. Households who are dened credt could well turn out to have ex post hgher repayment probabltes than some credt card holders who borrow large portons of ther borrowng lmts. Smlar msallocatons may exst wthn the credt card holders as well. Our setup also explans how new nformaton on borrowng patterns wll generate revsons of exstng contracts and counter offers such as balance transfer offers from competng banks. Usng data from the U.S. Survey of Consumer nances we propose an emprcal soluton to ths msallocaton problem. We show how ths dataset can be used by banks to explan the observed borrowng patterns of ther customers and how these borrowng estmates wll help banks to better select and retan ther customers by enablng them to devce better contracts. We fnd support for a postve relatonshp between the proxes of borrower qualty and the approved borrowng lmts on credt cards controllng for the banks selecton of credt card holders and the endogenety of nterest rates. We also fnd evdence for a postvely-sloped credt supply functon. JE classfcaton: D4 D8 G2 We are grateful to uca Dunn Stephen Cosslett Perre St-Amant Celne Gauther Gregory Caldwell and loran Pelgrn for ther helpful comments. The opnons expressed heren need not necessarly reflect the vews of the ank of Canada. + Senor Analyst ank of Canada Canada; emal: sdey@bank-banque-canada.ca phone: Assocate Professor Department of Economcs The Oho State Unversty USA; emal: mumy.1@osu.edu phone:

2 1. Introducton We envson an envronment consdered by Dey 2006 where consumers use lnes of credt as payment nstruments and to smooth consumpton across states and tme perods wthn a complete market framework. Gven the nterest rates nsurance premums dscount factors wealth and the wealth shocks all consumers n ths model know when and how much to borrow n all the states of the world. Some consumers decde not to borrow at all tmes and n all states savers and/or convenence users. 1 A porton of consumers decde to borrow a fxed amount n all states and at some tme n ther lfe-cycle pure ntertemporal borrowng. nally some consumers have statecontngent borrowng behavor. ased on observed customer borrowng patterns and prmarly lackng or not utlzng nformaton on customer wealth banks can only generate a borrowng dstrbuton of every consumer belongng to a rsk class. 2 anks are forced to treat the borrowng of a consumer n a rsk class as a random varable because lackng or not utlzng manly the customer wealth nformaton all varatons n customer borrowng patterns are ndstngushable for them from the varatons caused by the realzatons of the wealth shocks alone. Ths borrowng uncertanty whch s unque to lnes of credt can make the market ncomplete and create ex post msallocatons. Usng data from the U.S. Survey of Consumer nances we propose an emprcal soluton to ths msallocaton problem makng banks better select and retan ther customers by enablng them to devce better contracts. Publcly avalable nformaton about borrowers credtworthness helps banks sort ther clent pool nto broad rsk classes by way of ther credt scorng systems. anks do not however have perfect knowledge about ndvdual borrower rsk-type. Even f they dd n the case of lnes of credt such as credt cards banks face a new source of uncertanty.e. they do not know how much a borrower wll actually borrow on the lne a key determnant of the borrower s repayment probablty. Proft-maxmzng banks choose to provde exactly the amount of credt to ther borrowers that maxmze ther expected profts. acng the borrowng uncertanty banks tend to offer every rsk class a credt lmt and charge an nterest rate based on full exposure. anks may also 1 These are consumers who use lnes of credt for transactons purposes alone. 2 The envronment consdered here s of nformaton asymmetry because clearly for the case of the frst two sets of consumers the banks have nferor nformaton set. 1

3 prefer to raton out some less credtworthy consumers. However ndvduals who are ratoned out of the credt card market could very well turn out to have ex post hgher repayment probabltes than some credt card holders who borrow large fractons of ther credt lmts. Smlar msallocatons may exst wthn the credt card holders as well. Thus not only can borrowng uncertanty n the credt card market make the market ncomplete exstence of credt ratonng but t can also result n ex post msallocatons. Our modelng setup also explans how new nformaton on borrowng patterns wll generate revsons of exstng contracts changes n credt lmts and/or nterest rates and counter offers such as balance transfer offers from competng banks. Even f standard theory tells them that credt card borrowngs are functons of borrowers wealth banks typcally do not have or do not use that nformaton for ther customers except for ncome whch s self-reported and often unrelable. ackng manly the consumer wealth nformaton banks are unable to explan some systematc varatons of ther customer borrowng patterns and hence treatng borrowng as a pure random varable seems lke the only reasonable alternatve for them. ut here comes the use of external surveys such as the US Survey of Consumer nances. Just as banks use the publcly avalable credt bureau nformaton to generate credt scores of ther customers they may fnd the avalable and yet unused consumer wealth nformaton n the US Survey of Consumer nances to be qute helpful n explanng customer borrowng patterns and thus mprovng ther credt supply decsons. The emprcal contractng scheme goes as follows frst explan the observed borrowng patterns based on avalable and yet unused consumer wealth nformaton; second use the estmated borrowngs to generate the correspondng nterest rates nverse demand functons; fnally use the nterest rates to determne the borrowng lmts credt-supply functons. A typcal credt card contract s two-dmensonal. 3 anks offer a rate of nterest along wth a pre-set borrowng lmt to ther potental borrowers. orrowers then decde on how much of that credt to utlze at the offered rate of nterest. The two-dmensonal nature of the loan contracts makes credt card nterest rates endogenous. Emprcal dentfcaton of the determnants of credt card borrowng lmts requres us to correct for 3 Although the non-prce terms of credt contracts were always mportant n corporate lnes of credt and are becomng ncreasngly mportant n consumers lnes of credt here we choose to focus on a twodmensonal contract lmt and prce only. See Strahan 1999 and Agarwal et al for a dscusson. 2

4 ths endogenety. Moreover not all ndvduals are gven credt cards by the banks. The set of credt card holders s a selected sample and therefore our estmaton needs to account for ths sample selecton bas as well. We fnd that wealther consumers borrow less on credt cards. Our estmaton also reveals how the credt card nterest rates are postvely affected by the credt card balances carred by households. Controllng for rsk f banks exogenously charge lower rates for ther credt n response to lower balances of wealther customers they should be nduced to extend less credt as well. Hence we fnd evdence for a postvely-sloped optmal credt supply functon as expected. We also fnd a postve relatonshp between the proxes of borrower qualty and the borrowng lmts on credt cards. In secton 2 we descrbe the background and prevous research on these ssues. In secton 3 we ntroduce the theoretcal model. The data are descrbed and the econometrc model bult n sectons 4 and 5 respectvely. Secton 6 descrbes the emprcal results and secton 7 offers some conclusons. 2. ackground egnnng wth Ausubel researchers have examned consumer lnes of credt especally wth regards to credt cards. The bulk of the lterature on credt cards concentrates on explanng why the average credt card nterest rates reman stcky at a hgh level. Ausubel 1991 argues that the reason for the downward rgdty of credt card nterest rates and supernormal profts s the falure of competton n the credt card market. He partly attrbutes ths falure to myopc consumers who do not foresee ndebtedness and nterest payments on ther outstandng balances. Ausubel 1999 fnds emprcal evdence of adverse selecton and a lack of foresght among consumers regardng ther credt card ndebtedness. rto and Hartley 1995 however argue that consumers carry hgh-nterest credt card debt not because of myopa but because lownterest bank loans nvolve transactons costs. Mester s 1994 vew s that low-rsk borrowers who have access to low-nterest collateralzed loans leave the credt card market. Ths makes the average clent pool of the credt card market rsker thereby preventng nterest rates from gong down. Park 1997 shows the opton-value nature of credt cards n order to explan ther prce stckness. He argues that the nterest rate that produces zero proft for credt card ssuers s hgher than the nterest rates on most other 3

5 loans because ratonal credt card holders borrow more money when they become rsker. An emprcal paper by Calem and Mester 1995 fnds evdence that consumers are reluctant to search for lower rates because of hgh search costs n ths market. Cargll and Wendel 1996 suggest that due to the hgh presence of convenence users even modest search costs could keep the majorty of consumers from seekng out lower nterest rates. Kerr 2002 focuses on nterest rate dsperson wthn the credt card market. He studes a two-fold nformaton asymmetry: one between the banks.e. the lenders and the borrowers and the other wthn the banks themselves. Some banks the external banks have access to only the publcly avalable credt hstores whle others the home banks have addtonal access to borrowers prvate fnancal accounts. Kerr argues that n equlbrum the average rate of nterest charged by the so-called external banks would be hgher than that charged by the home banks because the average borrower assocated wth the external banks would be rsker. Even though credt card contracts are essentally two-dmensonal researchers n the earler lterature prmarly focused on only the prcng aspect of those contracts. Gross and Souleles 2002 broke that trend by utlzng a unque new dataset on credt card accounts to analyze how people respond to changes n credt supply. They fnd that ncreases n credt lmts generate an mmedate and sgnfcant rse n debt consstent wth the buffer-stock models of precautonary savng as cted n Deaton 1991 Carroll 1992 and udvgson Gross and Souleles also fnd evdence of sgnfcant nterest-elastcty of credt card debt wthn ther sample. Dunn and Km 2002 argue that banks n order to strategze aganst Ponz-schemers n the credt card market tend to provde lower credt lmts to hgh-rsk borrowers despte gvng them a larger number of cards. Though they fnd some emprcal support for ther hypothess on credt lmts Dunn and Km choose to focus ther formal emprcal analyss on an estmaton of credt card default rates. Castronova and Hagstrom 2004 fnd that the acton n the credt market s mostly n the lmts and not n the balances. nally a recent paper by Musto and Souleles 2005 shows how the amount of credt receved by consumers sgnfcantly ncreases wth ther credt scores. 4 abson et al have been very nfluental n renewng nterest of economc researchers n solvng consumpton puzzles that exstng theores have faled to reconcle. 4

6 In ths paper we buld a smple theoretcal model that captures the key elements of credt card contracts. We show how banks facng borrowng uncertanty tend to offer consumers wth dfferent rsk profles dfferent credt lmts and charge nterest rates based on full exposure potentally resultng n market ncompleteness and ex post msallocatons. Our setup also explans how new nformaton on borrowng patterns wll generate revsons of exstng contracts and counter offers such as balance transfer offers from competng banks. We show how banks may fnd the avalable and yet unused consumer wealth nformaton n the US Survey of Consumer nances to be qute helpful n explanng customer borrowng patterns and thus mprovng ther credt supply decsons. 3. A Theoretcal Model Consder a model where banks are compettvely offerng non-collateralzed lnes of credt such as credt cards. A lne of credt s a borrowng nstrument whereby the borrower s offered a borrowng lmt or credt lmt and an nterest rate. The borrower can borrow up to the credt lmt. Interest charges accrue only f some postve amount s borrowed on the lne. A lne of credt contract ncorporates the tradtonal fxed-loan contract as a specal case when the entre credt lmt s borrowed at the very outset. anks are assumed to procure funds at a rate r. ased on publcly avalable credt reports banks are able to partton ther clents nto broad rsk classes. et us assume that these classes represented by are such that [ ]. The varable can be consdered the credt score that credt bureaus construct for all potental borrowers. et us also assume for smplcty that there s only one borrower n every rsk class. 5 A typcal credt card contract offered to class conssts of a vector r where s the credt lmt and r s the nterest rate. Usng the framework put forward by Dey 2006 we argue that borrowers use lnes of credt as payment nstruments and to smooth consumpton across states and tme perods wthn a complete market framework. Gven the nterest rates nsurance premums dscount factors wealth and the wealth shocks consumers n ths model know when and how much to borrow n all the states of the 5 We therefore assume that banks offer the same contract to all ndvduals wthn a partcular rsk class wth the same credt score despte the potental heterogenety n ther repayment abltes. 5

7 world. Some consumers decde not to borrow at all tmes and n all states savers and/or convenence users. A porton of consumers decde to borrow a fxed amount n all states and at some tme n ther lfe-cycle pure ntertemporal borrowng. nally some consumers have state-contngent borrowng behavor. ased on observed customer borrowng patterns and lackng or not utlzng nformaton on customer wealth banks can only generate a borrowng dstrbuton of every consumer belongng to a rsk class. anks are forced to treat the borrowng of a consumer n a rsk class as a random varable because lackng or not utlzng manly the customer wealth nformaton all varatons n customer borrowng patterns are ndstngushable for them from the varatons caused by the realzatons of the wealth shocks alone. The envronment consdered here s of nformaton asymmetry because clearly for the case of the frst two sets of consumers the banks have nferor nformaton set. Moreover the consumers wth credt cards n Dey s model are not lqudty-constraned. 6 Hence for the banks n the credt card market ths framework essentally makes borrowng on credt cards for rsk class become a random varable functons of the ndex nterest rate nsurance premum dscount factor wealth 7 and wealth shock. et P denote the nsurance premum δ denote the dscount factor W denote the wealth and θ represent the wealth shock that borrower faces such that we have the credt card borrowng as = r ; P δ W θ ; θ ~ G θ where θ. We can wrte = f where. ~ Moreover θ s are assumed to be ndependent of each other and so are s. Usng the optmal borrowng functon we can derve an nverse demand curve for borrower as r = r ; P δ W θ. The repayment probablty for a borrower ncreases wth the rsk class measure and decreases wth the amount owed D where D = and = 1 + r = ; P δ W θ. 8 We represent the class repayment probablty as ρ. ρ = ρ D such that < 0 D ρ. > 0 and ρ [01]. The only uncertanty that 6 Average credt card borrowng s usually well below the average credt lmt; see Table 3 for emprcal evdence based on the US Survey of Consumer nance Although a porton of ths unused lne could be explaned by the typcal household s use of credt cards for precautonary purposes t s unlkely to account for the entre gap. 7 Wealth ncludes net worth dfference between gross assets and labltes household sze and ncome. 8 Smlarly = 1 + r. 6

8 7 banks have about borrowers repayment probabltes arses from ther nablty to know the actual borrowngs to be undertaken on the lnes they extend. In the followng secton we consder a typcal bank s proft-maxmzaton problem where t s offerng an unsecured lne of credt such as a credt card. 3.1 A bank s proft-maxmzaton problem The expected proft from offerng an unsecured lne of credt contract r to class s represented by. π or class a bank s proft-maxmzaton problem s gven by: + = d f W P W P Max ] ; ; [ θ δ θ δ ρ π d f W P W P ] ; ; [ θ δ θ δ ρ = + d f W P W P ] ; ; [ θ δ θ δ ρ. ] ; ; ][ 1 [ W P W P θ δ θ δ ρ et us assume that. < 0 π Partally dfferentatng π wth respect to and settng t to zero we get + = ] ;.. [ f ρ π ;.}. ;. ;.. ;. { ][ [1 D ρ ρ ] ;.. ρ ] ;.. [ f ρ = 0 or = π ;.}. ;. ;.. ;. { ][ [1 D ρ ρ = ] ;.. ρ 0. 1

9 Proposton: anks choose and r = r ; P δ W θ r 9 such that π r = 0 = π r. or all rsk classes yeldng π r < 0 the banks choose 0. or all banks maxmzng the total expected proft over all rsk classes s equvalent to ntegratng over all rsk classes the maxmzed expected proft of every rsk class. 10 The optmal credt card contract offered to borrower gven by the par s chosen such that f s actually borrowed at prce r = r ; P δ W θ r our bank s proft maxmzaton and zero-proft condtons are smultaneously satsfed for the rsk class that borrower represents. We fnd how banks facng borrowng uncertanty tend to offer consumers wth dfferent rsk profles dfferent credt lmts and charge nterest rates based on full exposure. anks may also deny credt to some rsk classes who yeld negatve expected profts. However ndvduals who are ratoned out of the credt card market could very well turn out to have ex post hgher repayment probabltes than some credt card holders who borrow large fractons of ther credt lmts. Smlar msallocatons may exst wthn the credt card holders as well. The queston that naturally follows s that can banks do better. anks through ther credt card lendng busness gather nformaton on the borrowng patterns of ther exstng customers. Ths new nformaton helps them revse ther exstng credt contracts through changes n credt lmts and/or nterest rates. Informaton on observed borrowng pattern also generates counter offers such as balance transfer offers from competng banks. The queston that remans s that can the borrowng nformaton of ther customers be used to better desgn ther credt contracts and reduce the possblty of the ex post msallocatons. The answer s no unless they fnd ways to explan the observed borrowng patterns of ther customers. If the credt card borrowngs were solely due to realzatons of wealth shocks then there would have been no way to explan the observed r 9 anks choce of optmal nterest rates based on the assumpton of full exposure may also provde an explanaton for these rates beng so hgh on average. 10 Ths follows from the fact that wealth shocks θ s and therefore actual borrowngs s are ndependent of each other and banks are forced to make zero expected profts n every rsk class. 8

10 borrowng patterns of consumers. However sgnfcant portons of credt card borrowngs among consumers are purely due to ntertemporal consumpton smoothng. Informaton about consumers wealth s crucal n explanng these sorts of borrowng patterns. Even f standard theory tells them that credt card borrowngs are functons of borrowers wealth W banks typcally do not have or do not utlze that nformaton for ther customers except for ncome whch s self-reported and often unrelable. Although avalable demographc varables provde banks some measure of the dscount factors of ther customers they possess no knowledge of the nsurance premums ether. ackng manly the consumer wealth nformaton banks are unable to explan some systematc varatons of ther customer borrowng patterns and hence treatng borrowng as a pure random varable and offerng the contract seems lke the only reasonable alternatve. ut here comes the use of external surveys such as the US Survey of Consumer nances. Just as banks use the publcly avalable credt bureau nformaton to generate credt scores of ther customers they may fnd the avalable and yet unused consumer wealth nformaton n the US Survey of Consumer nances to be qute helpful n mprovng ther credt supply decsons. elow we put forward an emprcal contractng scheme. Our emprcal results are solely based on the US Survey of Consumer nances data; however banks may wsh to customze ther emprcal contractng schemes by explotng ther own customer nformaton and the nformaton present n the US Survey of Consumer nances data. 11 Step 0: Estmate the selecton crteron of credt card holders as a functon of exogenous varables. Step 1: Estmate the observed credt card borrowng as a functon of exogenous varables: D r = D W δ θ r. 2 Step 2: Estmate the nverse demand functon of observed credt card borrowng: r = r D ; δ θ r arge commercal banks often fal to fully ntegrate all the nformaton they have on ther customers prmarly due to a lack of communcaton among the varous busness lnes under ther umbrella. The emprcal scheme suggested n ths paper can lead to mprovements n ther decson-makng process f they just manage to utlze the nformaton they already possess even wthout relyng on outsde surveys such as the US Survey of Consumer nances. 9

11 Step 3: Estmate the credt card borrowng lmt functon: = r ; δ θ r Data The data used n ths study are from the 1998 U.S. Survey of Consumer nances SC. SC s a natonwde survey conducted by the Natonal Opnon esearch Center and the U.S. ederal eserve oard. The 1998 SC provdes a large and rch dataset on household assets labltes demographc characterstcs and a number of varables that capture household atttudes. In households were surveyed and 3233 of them had at least one bank-type credt card whch amounts to 75.1 per cent of the total number of households n the sample. Table 1: Defnton of Varables Varables Type Explanaton ogarthm of the dfference between gross assets and OGNETWOTH Contnuous labltes DEINQUENCY ANKUPTCY nary nary 1 Got behnd n payments by two months or more 0 Otherwse 1 Declared bankruptcy 0 Otherwse CEDITATE Contnuous Credt card nterest rate rate on the credt card wth the largest balance or on the one most recently used OGCIMIT Contnuous ogarthm of credt card borrowng lmt OGINCOME Contnuous ogarthm of ncome HOUSEHODSIZE Contnuous Household sze AGE Contnuous Age of the household NOTWOKING nary 1 Not workng 0 Otherwse ETIED nary 1 etred 0 Otherwse EGUAEMP nary 1 Workng and not self-employed SEEMPOYED nary OGCEDITDET Contnuous 0 Otherwse 1 Workng and self-employed 0 Otherwse ogarthm of credt card balances 10

12 Table 1 defnes the varables used n our econometrc analyses. Table 2 compares the mean characterstcs of consumers wth credt cards aganst those wthout and Table 3 shows the pattern of credt card utlzaton rates and a comparson of the average credt card balance and borrowng lmt. Table 2: Credt Card Holders and Non-Holders 12 Varables Credt card Holders Credt card Non-holders Mean Mean OGNETWOTH HOUSEHODSIZE DEINQUENCY ANKUPTCY OGINCOME NOTWOKING ETIED SEEMPOYED AGE CEDITATE OGCIMIT OGCEDITDET Table 3: Credt Card Utlzaton ates Utlzaton Number of % of Credt Card ate Households Holders Utlzaton ate < % Utlzaton ate % Varable Mean Medan OGCEDITDET OGCIMIT Table 1 defnes the varables used n all the tables of all subsequent sectons. 11

13 5. The Econometrc Model Household now represents the rsk class or borrower. Accordng to Step 3 of our emprcal contractng scheme descrbed above we have the credt card borrowng lmt functon as = r ; δ θ r. The varable r has no varaton across households as all banks n the credt card market are assumed have access to a common funds market. The vector X 1 contans all nformaton avalable n credt reports on household that banks use to defne ther rsk measure and the dscount factor δ. The vector X 1 also contans nformaton that banks gather whle processng ther credt card applcatons such as ncome. Table 4 provdes a complete lst of varables ncluded n an ndvdual credt report. We postulate a lnear structural-form equaton for as = γ r + β 1 X 1 + v 1. 5 In equaton 5 the banks opportunty cost of funds r contrbutes to the constant term and the wealth shock that nfluences a household s borrowng level θ goes nto the error term v 1. Snce the choce of the credt card nterest rate accordng to Step 2 of our emprcal contractng scheme s gven by r = r D ; δ θ r the lnear structuralform equaton for r s gven by r = α D + β 2 X 1 + v 2. 6 Also n equaton 6 the varable r contrbutes to the constant term and the wealth shock θ goes nto the error term v 2. ollowng Step 1 of our emprcal contractng scheme we use the expresson of the observed credt card borrowng D = D W δ θ r to postulate the followng lnear reduced-form equaton: D = β 3 X 3 + v 3. 7 Smlarly r contrbutes to the constant term and the wealth shock θ goes nto the error term v 3. The vector X 3 contans all varables ncluded n vector X 1 and the nformaton on household s sze and net-worth. 12

14 Table 4: Credt eport Detals Personal nformaton Credt Hstory Publc records Inqures Source: TransUnon Name Current and prevous address Socal securty number Telephone number Date of brth Current and prevous employers Type of accounts: 1. etal credt cards 2. ank loans 3. nance company loans 4. Mortgages 5. ank credt cards Informaton avalable: 1. Account number 2. Credtor s name 3. Amount borrowed 4. Amount owed 5. Credt lmt 6. Dates when accounts were opened updated or closed 7. Tmelness of payments 8. ate payments Tax lens ankruptces Court judgments st of all partes who have requested a copy of your credt report The combnaton r D s observed f the household possess a credt card.e. f we have > 0. et us therefore consder the followng econometrc model: D = r = r = D = γr = αd ' = β X 3 ' + β X ' + β X v v 1 + v 2 f >0 and D = 0 r = 0 = 0 otherwse. 13

15 In the equatons above r and D represent the observed credt card borrowng lmt nterest rate and borrowng respectvely; X 1 and X 3 are vectors of exogenous varables; v 1 v 2 and v 3 follow trvarate normal wth means zero varances σ 1 2 σ 2 2 and σ 3 2 respectvely and wth covarances σ 12 σ 23 and σ 13. If X 3 contans at least one varable that s not ncluded n X 1 then all the parameters of the model are dentfed. Snce X 3 has varables such as net-worth and household sze that are not present n X 1 we have satsfed the dentfyng restrcton of our econometrc model. The parameters of the econometrc model are estmated usng the two-stage probt method descrbed by ee Maddala and Trost Ths two-step procedure yelds consstent estmates of all the parameters of the model. et us frst defne a dummy varable I such that I = 1 f household has a credt card.e. > 0 = 0 otherwse. We then estmate a probt model on the avalablty of credt card Step 0. Next we estmate the credt card borrowng equaton correctng for the sample selecton Step 1. We use the estmated credt card balances as an nstrument and estmate the structural equaton explanng the credt card nterest rate Step 2. nally we use the estmated credt card nterest rates as an nstrument and estmate the credt card borrowng lmt equaton Step esults and Dscusson Table 5 reports the results of a probt estmaton that explans the avalablty of credt card for a typcal household. eng self-employed havng a hgh ncome and net worth sgnfcantly mprove the lkelhood of gettng a credt card. The sze of the household delnquency bankruptcy unemployment and age dmnsh the chance of obtanng a credt card. In general the results ndcate that the hgher the household s credtworthness the greater ther lkelhood of obtanng a credt card. Table 6 explans the estmaton results of credt card borrowng. We fnd that among credt card holders households wth hgh net worth and ncome and those who are retred or self-employed are less nduced to carry credt card balances. However our results show that bgger-szed households who have an unemployed head wth a hstory 14

16 Table 5: Probt Model for Credt Card Avalablty Varables CONSTANT OGNETWOTH HOUSEHODSIZE DEINQUENCY ANKUPTCY OGINCOME NOTWOKING ETIED SEEMPOYED AGE Coeffcent Standard error S.E Sgnfcant at 1 per cent; sgnfcant at 5 per cent; sgnfcant at 10 per cent. Table 6: Two-Stage Probt for Credt Card Debt Varables CONSTANT OGNETWOTH HOUSEHODSIZE DEINQUENCY ANKUPTCY OGINCOME NOTWOKING ETIED SEEMPOYED AGE SEECTION Two-stage probt Coeffcent S.E og = σ 3 = 3.97 N = 3233 Sgnfcant at 1 per cent; sgnfcant at 5 per cent; sgnfcant at 10 per cent. of delnquency or bankruptcy carry bgger credt card debt. Hence we fnd that rsker households tend to carry larger credt card balances although wealther households borrow less. Moreover from our results we may nfer that the correcton for sample selecton does seem to matter sgnfcantly for our estmaton. 15

17 Table 7: Inverse Demand uncton for Credt Card Debt Varables CONSTANT DEINQUENCY ANKUPTCY OGINCOME NOTWOKING ETIED SEEMPOYED AGE OGCEDITDET SEECTION Two-stage probt Coeffcent S.E og = σ 2 = 5.4 N = 3233 Sgnfcant at 1 per cent; sgnfcant at 5 per cent; sgnfcant at 10 per cent. Table 7 presents the estmates of an nverse demand functon of credt card balances. We fnd that a hstory of delnquency and a hgher ncome do seem to ndcate towards chargng a typcal household a hgher credt card nterest rate by the banks. The sgn of the coeffcent of households ncome s a bt counter-ntutve although the estmates for credt card borrowng lmts later show that controllng for nterest rates a hgher ncome should fetch a hgher credt lmt from the banks. We also fnd that f ther customers exogenously tend to carry lower credt card balances due to the presence of hgher wealth levels t should optmally nduce though not sgnfcantly banks to lower ther credt card rates. Agan our results show that the correcton for sample selecton does seem to matter sgnfcantly for our estmaton. nally Table 8 shows the results for the structural equaton estmaton of the credt card borrowng lmts. We see that hgher ncome and age and beng selfemployed must optmally fetch a hgher borrowng lmt on credt cards. Moreover households wth a hstory of delnquency or bankruptcy should face strcter credt lmts. Hence our results n general tend to support the fact that the hgher the household s credtworthness the greater should be the offered borrowng lmt on credt cards. 16

18 Controllng for rsk f banks exogenously charge lower rates for ther credt n response to lower balances of wealther customers they should be nduced to extend less credt as well. Hence we fnd evdence for a postvely-sloped optmal credt supply functon as expected. nally we also fnd emprcal support for sample selecton n our credt lmt estmates. Table 8: Estmates for Credt mt Equaton Varables CONSTANT DEINQUENCY ANKUPTCY OGINCOME NOTWOKING ETIED SEEMPOYED AGE CEDITATE SEECTION Two-stage probt Coeffcent S.E og = σ 1 = 2.4 N = 3233 Sgnfcant at 1 per cent; sgnfcant at 5 per cent; sgnfcant at 10 per cent. 7. Conclusons ne of credt contracts such as credt card contracts are fundamentally dfferent from tradtonal fxed-loan contracts. In the credt card market banks have to decde on the borrowng lmts of ther potental customers when the amounts of borrowng to be ncurred on these lnes are uncertan. Ths borrowng uncertanty can make the market ncomplete and create ex post msallocatons. Households who are dened credt could well turn out to have ex post hgher repayment probabltes than some credt card holders who borrow large portons of ther borrowng lmts. Smlar msallocatons may exst wthn the credt card holders as well. Our setup also explans how new nformaton on borrowng patterns wll generate revsons of exstng contracts and counter offers such as balance transfer offers from competng banks. Usng data from the U.S. Survey of 17

19 Consumer nances we propose an emprcal soluton to ths msallocaton problem. We show how ths dataset can be used by banks to explan the observed borrowng patterns of ther customers and how these borrowng estmates wll help banks to better select and retan ther customers by enablng them to devce better contracts. Even f standard theory tells them that credt card borrowngs are functons of borrowers wealth banks typcally do not have or do not use that nformaton for ther customers except for ncome whch s self-reported and often unrelable. ackng manly the consumer wealth nformaton banks are unable to explan some systematc varatons of ther customer borrowng patterns and hence treatng borrowng as a pure random varable seems lke the only reasonable alternatve for them. ut here comes the use of external surveys such as the US Survey of Consumer nances. Just as banks use the publcly avalable credt bureau nformaton to generate credt scores of ther customers they may fnd the avalable and yet unused consumer wealth nformaton n the US Survey of Consumer nances to be qute helpful n mprovng ther credt supply decsons. The emprcal contractng scheme goes as follows frst explan the observed borrowng patterns based on avalable and yet unused consumer wealth nformaton; second use the estmated borrowngs to generate the correspondng nterest rates nverse demand functons; fnally use the nterest rates to determne the borrowng lmts credt-supply functons. Our estmaton reveals that wealther consumers borrow less on credt cards. We also fnd that the credt card nterest rates are postvely affected by the credt card balances carred by households. Controllng for rsk f banks exogenously charge lower rates for ther credt n response to lower balances of wealther customers they should be nduced to extend less credt as well. Hence we fnd evdence for a postvely-sloped optmal credt supply functon as expected. We also fnd a postve relatonshp between the proxes of borrower qualty and the borrowng lmts on credt cards. 18

20 eferences Agarwal S. J.C. Drscoll X. Gabax and D.I. abson Two Steps orward One Step ack: The Dynamcs of earnng and acksldng n the Consumer Credt Market. Unpublsher paper. Ausubel.M The alure of Competton n the Credt Card Market. Amercan Economc evew 811: Ausubel.M Adverse Selecton n the Credt Card Market. Unversty of Maryland College Park MD. Unpublshed paper. rto D.. and P.. Hartley Consumer atonalty and Credt Cards. Journal of Poltcal Economy 1032: Calem P.S. and.j. Mester Consumer ehavor and Stckness of Credt Card Interest ates. Amercan Economc evew 855: Cargll T.. and J. Wendel ank Credt Cards: Consumer Irratonalty versus Market orces. Journal of Consumer Affars 302: Carroll C The uffer-stock Theory of Savng: Some Macroeconomc Evdence. rookngs Papers on Economc Actvty 2: Castronova E. and P. Hagstrom The Demand for Credt Cards: Evdence from the Survey of Consumer nances. Economc Inqury 422: Deaton A Savng and qudty Constrants. Econometrca 595: Dey S nes of Credt and Consumpton Smoothng. The Oho State Unversty Columbus OH. Unpublshed paper. Dunn.. and T.H. Km An Emprcal Investgaton of Credt Card Default: Ponz Schemes and Other ehavors. The Oho State Unversty Columbus OH. Unpublshed paper. Gross D. and N.S. Souleles Do qudty Constrants and Interest ates Matter for Consumer ehavor? Evdence from Credt Card Data. Quarterly Journal of Economcs 1171: Kerr S Interest ate Dsperson Due to Informaton Asymmetry n the Credt Card Market: An Emprcal Study. The Oho State Unversty Columbus OH. Unpublshed paper. abson D.I. epetto A. and Tobacman J A Debt Puzzle. NE Workng Paper No

21 ee.. G.S. Maddala and.p. Trost Asymptotc Covarance Matrces of Two-Stage Probt and Two-Stage Tobt Methods for Smultaneous Equatons Models wth Selectvty. Econometrca 482: udvgson S Consumpton and Credt: A Model of Tme-Varyng qudty Constrants. evew of Economcs and Statstcs 813: Mester.J Why Are Credt Card ates Stcky? Economc Theory 44: Musto D.K. and N.S. Souleles A Portfolo Vew of Consumer Credt. Journal of Monetary Economcs 531: Park S Opton Value of Credt nes as an Explanaton of Hgh Credt Card ates. ederal eserve ank of New York esearch Paper No Strahan P.E orrower sk and the Prce and Nonprce Terms of ank oans. ederal eserve ank of New York Staff eport No