DEBT REVOLVERS FOR SELF CONTROL. Carol C. Bertaut and Michael Haliassos DEPARTMENT OF ECONOMICS UNIVERSITY OF CYPRUS. Discussion Paper

Transcription

1 DEPARTMENT OF ECONOMICS UNIVERSITY OF CYPRUS DEBT REVOLVERS FOR SELF CONTROL Carol C. Berau and Michael Haliassos Discussion Paper P.O. Box 20537, 1678 Nicosia, CYPRUS Tel.: , Fax: Web sie: hp://

2 Deb Revolvers for Self Conrol Carol C. Berau Board of Governors of he Federal Reserve Sysem Michael Haliassos Universiy of Cyprus and HERMES Firs Draf: May 18, 2001 This Draf: June 10, 2002 Absrac By 1998, abou wo-hirds of U.S. households held a bank-ype credi card. Despie high ineres raes, mos revolve credi card deb. The majoriy of deb revolvers have subsanial liquid asses, apparenly violaing arbirage. We propose an accounanshopper model ha could provide an explanaion for his puzzle. In our model, he accounan self (or spouse) of he household can conrol he expendiures of he shopper self (or spouse) by limiing he purchases he shopper can make before encounering he credi limi. Since he card balance is used for conrol purposes, he accounan self may also find i opimal o save in lower-reurn riskless asses. Using aiudinal responses and demographic daa from he pooled 1995 and 1998 Surveys of Consumer Finances, we esimae a bivariae probi model of he decisions o have a credi card and o revolve deb on i, allowing for sample selecion. The paern of esimaed coefficiens is consisen wih deb revolvers being moivaed primarily by self-conrol consideraions raher han ineremporal consumpion smoohing. Keywords: credi cards, consumer deb, porfolio puzzles, household porfolios JEL classificaion codes: E210, G110. This paper was wrien when Haliassos was visiing he Finance and Consumpion Chair a he European Universiy Insiue, which provided an excellen research environmen. We are graeful o Giuseppe Berola, Chris Carroll, Luigi Guiso, Sefan Hochguerel, David Laibson, Raffaele Miniaci, Vicor Rios Rull, Nick Souleles, and Guglielmo Weber for very helpful discussions. We would also like o hank paricipans a he 2001 NBER Summer Insiue, he 2001 meeings of he Sociey for Compuaional Economics, he macro workshop a he European Universiy Insiue, and he Federal Reserve Board for consrucive commens. They are no o be blamed for any remaining errors. Haliassos acknowledges parial research suppor by HERMES, he European Cener on Compuaional Finance and Economics a he Universiy of Cyprus, and from he Levenis Foundaion. The views expressed in his paper are he auhors own and do no necessarily reflec hose of he Board of Governors of he Federal Reserve Sysem or is saff.

3 1. Inroducion Credi card holding has increased seadily over he pas 20 years. According o he mos recen Survey of Consumer Finances (SCF), in 1998 more han wo-hirds of U.S. households had a bank-ype credi card, 1 compared o only 43 percen in he 1983 Survey. The majoriy of households wih a bank-ype credi card had no paid off heir las credi card bill in full, and hus carried an ousanding balance--no including new charges--on ha card a he ime of he Survey inerview. Slighly less han half of card holders declare ha hey do no usually pay off heir credi card balance in full each monh. Repored card deb is sizeable: among households revolving deb on bank-ype credi cards, he median ousanding balance in 1998 was $1,800. The majoriy of households ha revolve credi card deb repor subsanial liquid savings in checking, saving, and money marke deposi accouns, wih a median of $4, The median ineres rae paid by such households on he card wih he highes balance was 15 percen, far exceeding reurns on heir liquid asses. The puzzling porfolio behavior of revolvers of high-ineres credi card deb who also save in low-ineres liquid asses is he objec of his paper. The limied research o dae on borrowing behavior hrough credi cards has already idenified hree puzzles. An early puzzle is he use of high- raher han lowerineres credi cards for borrowing (Ausubel, 1991), which he aribued mainly o failure of consumers o anicipae he likelihood ha hey will have o pay ineres on ousanding credi card balances. Brio and Harley (1995) argue ha relaively small coss of arranging for oher ypes of loans can induce raional individuals o borrow on high-ineres credi cards. Gross and Souleles (2001) use a proprieary adminisraive daa se of individual credi card accouns from differen card issuers o esimae consumpion responses o exogenous increases in credi lines and o changes in ineres raes. 1

4 Households differ in he exen o which hey uilize he credi limi allowed by he card issuer. Grouping households according o uilizaion raes, Gross and Souleles remarkably find ha households consumpion response o an exogenous increase in he line is such as o reurn uilizaion near o is iniial level in he space of five monhs or so. They also use he 1995 Survey of Consumer Finances o documen wo credi card porfolio puzzles: he co-exisence of credi card deb (i) wih subsanial holdings of illiquid asses for reiremen, and (ii) wih low-ineres liquid asses. Laibson, Repeo, and Tobacman (2000) deal wih he former, which hey ermed he Deb Puzzle. They show ha consumer preferences wih hyperbolic discouning are consisen wih he endency of consumers o ac impaienly when i comes o credi card borrowing bu paienly when i comes o accumulaion of illiquid asses for reiremen. This paper deals wih puzzle (ii), namely he co-exisence of high-ineres credi card deb and low-ineres liquid asses, which is also documened in Berau and Sarr McCluer (2001). We erm his he Puzzle of Deb Revolvers. I consiues an excepionally difficul porfolio puzzle, as i seems o run conrary o one of he mos fundamenal noions in Economics and Finance, namely ha of arbirage. I would be problemaic o aribue his endency o lack of informaion or irraionaliy, since ineres raes on credi cards and on liquid accouns are prined on he monhly saemens and we show ha his endency characerizes a large segmen of he populaion. Indeed, a recen Federal Reserve sudy finds ha U.S. credi card holders are generally aware of he erms of borrowing on heir credi cards (Durkin, 2000). I may be argued ha deb revolvers find i difficul o borrow in oher ways and need liquid asses o cover coningencies for which credi cards are no acceped. Ye, i is always possible o obain cash advances. 3 Revolving of deb is also no aribuable o he use of auomaic paymen faciliies: 98 percen of deb revolvers are 2

5 presened monhly wih he opion o pay off heir credi card deb and apparenly make a conscious decision no o do so. Finally, hyperbolic discouning enails conrol of fuure selves, and his is accomplished by holding illiquid raher han liquid asses. Lehner and Maki (2001) argue ha a household ha conemplaes bankrupcy may run up unsecured deb and liquid asses, so ha i can discharge a large par of unsecured deb (based on chaper 7 bankrupcy laws) bu conver liquid asses o a bankrupcy-exemp asse caegory (like housing) once i declares bankrupcy. Using daa from he Consumer Expendiure Survey, hey find ha households living in saes wih high bankrupcy exempion levels are 1 o 4.5 percenage poins more likely o have boh liquid asses and oal unsecured deb in excess of a hreshold ranging beween $2,000 and $5,000 (in 1996 dollars). 4 While sraegic bankrupcy consideraions may moivae he behavior of some deb revolvers, hey alone seem unlikely o accoun for he widespread naure of his phenomenon, especially among households whose porfolios show no signs of financial disress. The daa presened in his paper show ha deb revolvers are widespread, especially in he middle class (i.e. households wih incomes beween $25,000 and $100,000). Indeed, among households wih liquid asses in excess of credi card deb, only 14 percen mee he Lehner-Maki amoun requiremens a he $3,000 hreshold. 5 Even if all of hese were considered sraegic defaulers, his would sill leave 86 percen o be explained. We skech a model of credi card behavior ha absracs from defaul moives and ye can generae co-exisence of revolving card deb wih holdings of liquid asses in he absence of financial disress. The model sresses ha saving and consumpion decisions, normally modeled as being simulaneous, cease o be so in he presence of credi cards. The decision of how much o save (or dissave) is assigned o he accounan or financial officer in he household, or more generally o he 3

6 accounan self ha pays bills and is in charge of finances. The shopper self uses he purchasing power offered by he available limi on he card o shop and deermines he consumpion level of he household, in a way no necessarily consisen wih he preferences of he accounan or he financial consrains faced by he household. The accounan self, however, decides how much of he credi line o make available o he shopper self by making a paymen ino he credi card accoun. Manipulaion of he size of his paymen offers a way o he accounan self o exercise (shopper) selfconrol and o limi credi card purchases. Since he revolving balance is now mainly an insrumen of self-conrol raher han a means o borrow, i is no longer inconsisen wih posiive holdings of liquid asses. 6 We hen examine economerically wheher available aiudinal responses and demographic daa from he pooled 1995 and 1998 waves of he SCF provide empirical suppor o a selfconrol explanaion of credi card behavior. New informaion on aiudes of credi card holders in he 2001 Survey of Consumers shows ha abou fory percen of card holders perceive self-conrol problems emanaing from he availabiliy of credi cards and he possibiliy of overspending, hough considerably fewer are willing o admi ha his is a problem for hemselves and no jus for ohers (Durkin, 2002). Exising research in markeing and in consumer psychology sresses ha self-conrol problems occur when he benefis of consumpion arise earlier han he coss (Hoch and Loewensein, 1991). This lieraure also poins o evidence ha liquidiy enhances boh he probabiliy of making a purchase and he willingness o pay for a given iem (see Shefrin and Thaler, 1988; Prelec and Simeser, 2001; Werenbroch, 2002). Moreover, Soman and Cheema (2002) presen experimenal and survey evidence suggesing ha consumers inerpre heir available credi lines as indicaions of fuure earnings poenial and 4

7 adjus heir spending accordingly. Policy makers are also discovering he relevance of self-conrol consideraions for savings decisions. 7 Revolving credi card deb enails ineres coss ha we esimae below. Based on our findings, he coss paid by deb revolvers are neiher negligible nor prohibiive as a means of imposing self-conrol in consumer spending. Cosly self-raioning as a means of self-conrol may be a fairly novel concep in research on financial porfolios, bu i has been sressed in Markeing and in economic research on menal accouning. 8 A elling example refers o deadlines ha various people, including academics, impose on hemselves o avoid procrasinaion even when missing hem enails subsanial coss (Thaler, 1980; Ariely and Werenbroch, 2002). Secion 2 documens he characerisics of hose who revolve credi card deb using he 1998 SCF. In Secion 3, we presen a model of credi card behavior in he absence of defaul moives, firs wihou and hen wih self-conrol consideraions. In Secion 4, we invesigae wheher available survey daa yield empirical suppor o a self-conrol explanaion. Secion 4.1 discusses wha daa are available and how bivariae probi esimaion wih sample selecion can help differeniae self-conrol from ineremporal consumpion smoohing inerpreaions of deb revolvers. Secion 4.2 presens esimaion resuls, while secion 4.3 checks robusness by focusing exclusively on deb revolvers who hold subsanial liquid asses. Secion 5 concludes. 2. Revolvers of Credi Card Deb in he Daa In his secion, we documen he puzzle using daa on bank-ype credi cards and household liquid asses from he 1998 SCF, he mos recen and mos comprehensive survey of household porfolios in he Unied Saes. We also review some poenial explanaions for he puzzling behavior of deb revolvers ha are no borne ou by he daa (in he SCF or in oher sources). 5

8 In 1998, more han wo-hirds of US households had a bank-ype credi card. As indicaed in he firs column of Table 1, bank-ype credi cards are more likely o be held by households wih higher educaion, wih higher income, by married couples, and by households who repor heir race and ehnic origin as whie, non-hispanic. Bank-ype credi cards are held by a noably smaller fracion of households where he household head is eiher less han 35 years old or more han 65 years old. As indicaed in column 2 of Table 1, he majoriy of households ha had a bank-ype credi card had no paid off heir las credi card bill in full. Alhough households ha are younger, have lower educaion, or lower income are less likely o have credi cards, a higher percenage of hose ha do have cards use hem as a source of revolving credi. Some households may emporarily carry a balance because of special circumsances, while heir normal pracice is o pay off he balance in full. The Survey does ask households abou heir normal card paymen pracices. Of households wih a repored balance, only a lile over 20 percen saed ha hey almos always pay off he balance in full, while almos half repored ha hey hardly ever do so. 9 As column 3 indicaes, mos households wih a bank-ype credi card ypically do no pay off heir card balances, and his is again more prevalen for households ha are younger, have lower educaion, or lower income. Recen aenion has been paid o he fracion of households wih relaively high levels of credi card deb and he poenial for such households o defaul on ha deb by declaring personal bankrupcy (see Lehner and Maki, 2001). Daa from he SCF confirms ha some households do indeed have very high levels of credi card deb. However, here is a differen, more prevalen, and puzzling feaure of credi card borrowing: nearly half of all credi card holders repor ha hey do no ypically pay off heir credi card balances each monh, while a he same ime hey hold ample amouns of liquid financial asses asses held in banking, checking, and money 6

9 marke accouns ha amoun o more han half heir average monhly income and are a leas $500 (column 4). This behavior is exhibied by all age groups, all educaion groups, and all income groups. However, i is somewha more common among younger households, among hose wih only a high school degree, or some college (bu no college degree), and among households wih incomes beween $25,000 and $100,000 han for eiher low-income or high-income households. Thus, i ends o be a middle-class puzzle. One migh suspec ha his behavior, hough puzzling, is mainly aribuable o auomaic paymen faciliies ha allow households o make minimum paymens on heir credi card accouns wihou reviewing heir balances every monh. This suspicion is no confirmed by he daa. Of he 2,664 households in he combined 95/98 Surveys who had a balance on a credi card, only 51 used auomaic paymen faciliies for any ype of irregular paymen, which includes credi card paymens. Among hose who usually have a balance, only 44 used such faciliies. In boh cases, 98 percen of hose who carry a balance on heir credi card are presened monhly wih he opion o pay off heir credi card deb and apparenly make a conscious decision no o do so. Households appear o perceive self-conrol problems associaed wih holding a credi card. Alhough he majoriy of cardholders inerviewed in he 2001 Survey of Consumers found ha heir credi cards made managing heir personal finances easier by allowing flexibiliy in smoohing expendiure and repaymen, 10 percen admied ha i was more difficul o manage heir own finances. The possibiliy of overspending and overexending financial resources was he mos common reason noed. Cardholders were much more willing o admi ha ohers faced such problems. When asked abou wheher credi cards make managing finances easier or more difficul for ohers, 40 percen responded ha i made managing finances 7

10 more difficul (Durkin, 2002). Two facors may be creaing hese disparae views regarding personal financial managemen and financial managemen of ohers. Firs, hese quesions were asked only of card holders. A higher percenage for hose having difficuly would be expeced in he broader populaion of ohers, because his includes households who choose no o hold cards because of self-conrol problems. Addiionally, households may be relucan o admi heir own self-conrol problems wih regard o credi cards bu more willing o idenify he problem more generally. 10 Skepics may argue ha households concerned abou overspending could ask insiuions o reduce heir credi line insead of revolving cosly deb. However, his seems o happen very rarely, if a all, in he daa, and i is by no means clear ha i would be an efficien way o handle self-conrol problems. Gross and Souleles (2001) rack credi card accouns over ime and repor ha only 10 percen of line changes are requesed by he household, while in 90 percen of he cases i is he insiuion ha iniiaes he line change. Moreover, households rarely ask for reducions, if a all, and insiuions have been relucan o reduce lines. As a resul, line changes are generally nonnegaive. Households wih self-conrol problems do have he opion no o hold any credi cards. Those who decide o hold credi cards probably do so no only for ease of ransacions (which could alernaively be provided by a debi card or checks), bu also because hey value he abiliy o borrow for unforeseen coningencies wihou filing ime-consuming and cosly applicaions. Reducing he credi line and guaraneeing o pay off in full whaever he shopper charges on he credi card could severely limi he available buffer for unforeseen coningencies. Thus, limiing he credi line is no a cosless way of enforcing self-conrol. How cosly is he alernaive of revolving credi card deb while holding liquid asses? This depends on he size of balances, liquid asses, and ineres raes faced by deb revolvers (Table 2). Among households wih balances on bank-ype credi cards, 8

11 he median ousanding balance in 1998 was $1,800 (col. 1). Households ha ypically carry credi card deb alhough hey have ample amouns of readily available financial resources have similar or even slighly higher levels of credi card deb. Columns 2 and 3 of Table 2 show ha he median level of bank-ype card deb for hese households was $1,900, while median liquid financial asses for his group were abou wice his amoun a $4, Table 2 also shows he median levels of credi card deb by age, educaion, and income. Boh credi card deb and financial asses end o increase wih age (excep for hose aged over 65), and wih income and educaion. Revolving credi card deb may enail negligible cos if ineres raes charged on such deb are low, especially if he deb is financed a ypical inroducory easer raes of 1 o 5 percen. However, his is no he case for mos households. Alhough a small fracion of deb revolvers wih liquid asses do pay low ineres raes on he card mos frequenly used, he median ineres rae for hese households was 15 percen (column 5). The nex wo columns provide an esimae of he ineres cos o each household ha habiually revolves credi card deb from no using available liquid asses o pay off he card balance. The firs compues he minimum of wo amouns, he card balance and he amoun of liquid asses, and repors is median for each caegory. The second muliplies he minimum for each household by he ineres rae he household faces on he card wih he highes balance. 12 The median ineres cos for he enire populaion is abou wo hundred dollars per annum, and i varies somewha across demographic groups. On he whole, i is of he order of he cos of a DVD player per year. This is neiher so low ha households should no boher o eliminae i nor so high as o render i a prohibiively cosly way of imposing selfconrol. 9

12 3. The Model 3.1 A Model of Credi Card Use Consider a household ha maximizes expeced discouned lifeime uiliy of consumpion, possibly subjec o nondiversifiable earnings risk. The household has access o wo financial insrumens: a riskless liquid asse ha offers gross reurn R, and a credi card ha allows he household o revolve credi up o a maximum level B R c c a a gross real rae. The rae depends on wheher he household has paid off is credi card balance in he previous monh. If i has, hen new purchases are given an ineres-free grace period equal o one model ime period ( R =1). If i has no, hen he previous balance and new purchases are subjec o he credi card rae, which is c higher han ha on he riskless liquid asse ( R > R ). For simpliciy, we will absrac from invesmen in illiquid asses and also assume ha he household canno borrow a all a he low riskless rae 13, i.e. ha A 0. There is one consumpion good, and i can be bough using a credi card. The household decides how much o consume in each period, C c R 0, and how much of he ousanding credi card balance, B, o repay in period by making a paymen P 0. All variables are expressed in real erms. Given hese assumpions, he household s opimizaion problem can be wrien as follows: Max { C, P } T 1 = 0 E T 1 0 = 0 β U ( C ), 0< β < 1 (1) +1 ( A + Y P R s.. A = ) (2) R c c ( B P C ) R B + +1 = (3) c R > R > 1 if P < B : (4) c R = 1< R if P B 10

13 C 0, A 0 (5) B B, 0 T 1 (6) A ; B = 0; B 0 (7) 0 = 0 0 T = Equaion (1) saes ha he objecive of he household is o maximize expeced lifeime uiliy over is lifeime of T periods wihou a beques moive. Nex period s feliciy is discouned relaive o curren period s feliciy, so ha β is less han uniy. Equaion (2) describes he evoluion of he real sock of he liquid riskless asse. A he beginning of each period, he household observes he sock of he liquid asse accumulaed o dae, receives labor income equal o Y, and decides wha par of he ousanding credi card balance o pay off using available cash on hand, A + Y. Any remaining cash on hand is held in he liquid asse. 14 Equaion (3) describes he evoluion of he ousanding credi card balance, B. The household sars period wih an accumulaed credi card balance 0. I repays an amoun P 0, and i revolves he remaining balance, B, augmened by new purchases, C, a a gross real rae c R. P Expression (4) deermines he relevan value of c. If he paymen does no cover he ousanding credi card balance ( P < ), he gross ineres rae on credi B card deb applies boh o he inheried balance and o new purchases. If he household R B repays he ousanding balance so as no o revolve card deb P = B ), ( hen new purchases, C, are given a grace period when no ineres is charged and he gross ineres rae is uniy. If he household wans o use he credi card for purchases ha exceed he enire credi limi, i can make a paymen in excess of he ousanding balance ( P > B ) and ake advanage of he grace period on new purchases. Because of he grace period, he household has no reason o pay for he consumpion good direcly ou of liquid asses

14 Iem (5) liss he usual nonnegaiviy consrain for consumpion, and he borrowing consrain ha prevens households from borrowing a he low ineres rae. 16 Relaions (6) and (7) sae ha he credi limi on he card is B and ha he credi card will be aken away prior o he end of life. The maximum amoun ha can be spen on curren consumpion consiss no only of cash on hand (he sum of asses minus ousanding liabiliies plus labor income) bu also of he unused par of he credi line: X A + Y + B B ) (8) ( In view of (2) and (3), he ransiion equaion for consumable resources is X + 1 = ) c ( A + Y P ) R ( B P + C R + Y B (9) All erms are eiher given or exogenous o he household a ime, excep for P, R, C c. Le us fix he consumpion decision. Then, higher paymens simply ransfer mass from he firs o he second parenhesis in (9). Now, given B, he choice of P deermines c R hrough (4). As long as he paymen ino he credi card accoun does no cover he full ousanding balance, R > R c and he household increases fuure consumable resources by ransferring funds from he liquid asse o he card accoun. Moreover, since boh ineres raes are riskless, his ransfer consiues a genuine arbirage opporuniy. 17 c A P =, jumps o uniy and resources are B furher enhanced. Beyond his amoun, arbirage opporuniies cease o exis: R paymens ino he card accoun reduce consumable resources because R < R c, and will be made only if opimal consumpion exceeds he credi limi, B. This simple resul is he essence of he credi card puzzle and is no dependen on preference parameers or he earnings process. In view of arbirage opporuniies shown in (9), revolving credi card deb should no coexis wih posiive holdings of 12

15 cash on hand, le alone wih subsanial holdings of liquid asses relaive o is size, as documened in he Survey of Consumer Finances. 3.2 A Model of Credi Card Use in an Accounan-Shopper Household Now suppose ha he household consiss of wo unis, an accounan and a shopper. The accounan is he member of he household who manages finances. The shopper visis he sores wih credi card in hand. Noe ha he accounan is no necessarily he breadwinner in he family, nor even necessarily a differen person from he shopper. Even a single person can behave differenly when paying bills and when shopping a he sore, and i is more general o hink of he accounan and he shopper as wo selves performing differen asks (hence he erm self-conrol ). The accounan self recognizes ha he shopper self does no necessarily exhibi he same preferences or does no ake ino accoun he same consrains as he accounan self. The accounan self decides he size of paymen o he credi card accoun, P. Given curren cash on hand and he ousanding credi card balance, his deermines boh he amoun o be kep in he form of liquid asses, A + Y P, and he maximum amoun ha can currenly be charged o he credi card for consumpion purchases, B B P. Alhough he accounan self ulimaely derives uiliy from household consumpion, i is he shopper self who visis he sores and underakes consumpion expendiures. The shopper self is old he available credi on he card accoun and decides how much o spend on consumpion as a funcion of available credi. 18 Thus, he shopper deermines he policy funcion C = C ( B P ), where he consan credi limi B has been suppressed. 13

16 The accounan self can exercise shopper-self conrol by manipulaing P and hrough i he amoun of unused credi made available o he shopper. 19 The accounan s problem can be expressed in he following way: Max { P } T 1 = 0 E T 1 0 = 0 β U ( C [ B P ]), 0< β < 1 (1 ) +1 ( A + Y P R s.. A = ) (2) c ( B P + C [ B P ) R B ] + 1 = (3 ) where C B P ] is he policy funcion for consumpion chosen by he shopper, (2) [ is repeaed for convenience, (3 ) replaces (3), and (4)-(7) coninue o hold as before. Denoing he accounan s conrol variable, B P, by u, we can wrie he firs order condiion for he accounan s choice as: U '( C C ) u 1 + β C+ c c C E U '( C 1 ) + + R R R = 0 u + 1 u (10) This condiion can be inerpreed as follows. The derivaive C u represens he amoun by which he shopper changes he curren choice of consumpion level when he accounan changes (infiniesimally) he unpaid credi-card balance. The resuling change in uiliy of he accounan is C U '( C ) u, and i should mach in equilibrium he effecs on nex period s discouned expeced uiliy. Revolving a larger amoun of deb ino he nex period imposes an ineres cos equal o he differenial c R R. On he oher hand, use of he credi card balance as a conrol mechanism reduces curren consumpion by C u, and his in urn reduces c C omorrow s balance direcly by R. u This addiional effec provides a way in 14

17 which using he available credi as a self-conrol device can offse he arbirage opporuniies posed by he ineres differenial beween liquid asses and credi cards. 3.3 An Empirically Moivaed Case of Shopper Behavior Once saving and consumpion decisions have hus been separaed, one can explore various cases of accounan-shopper combinaions and ineracions. In his secion, we illusrae he poenial of such seups o generae co-exisence of revolving credi card deb and liquid asses hrough a simple example of infinie-horizon households and an empirically moivaed assumpion abou shopper behavior. We assume ha shoppers always purchase as much as hey can wihou exceeding a arge uilizaion rae for he credi card limi. Such behavior can be hough of as a rule of humb, bu can also arise opimally in he conex of a homoheic, single-self, buffer-sock model (see Ludvigson, 1999). 20 This assumpion is consisen wih he empirical findings of Gross and Souleles (2001) based on a large proprieary daa se of credi card holders, bu somewha exaggeraes he speed wih which households aain heir arge uilizaion rae. Alhough uilizaion raes differ across households in he Gross-Souleles daa, 21 in each group defined wih reference o uilizaion raes uilizaion reurns back near is iniial level in he long run. The ime span involved is of he order of five monhs. If we denoe he household-specific uilizaion rae by λ, hen he shopper self purchases as much as is consisen wih mainaining a revolving credi card balance B = λb, 0 < λ 1. (11) Given he ransiion equaion (3) for he revolving credi card balance, he implied consumpion rule is 1 C = λ B 1 + P c R (12) 15

18 Because he shopper self is consisen in following he simple rule of humb, he accounan self can perfecly conrol he level of curren consumpion hrough he choice of he paymen P ino he credi card accoun. Noe ha P affecs consumpion no only direcly bu also by deermining c R, in a way given by (4). As long as he accounan chooses o revolve credi card deb ( P < B ), he marginal propensiy of he shopper o spend on consumpion ou of every exra dollar he accounan pays ino he credi card accoun is equal o uniy. Using (12) o subsiue marginal propensiies o consume ino he firs order condiion (10), we ge Τhis simplifies o c c U '( C ) + β [ U '( C 1 )( 1)( R R R )] = 0. (13) E + U '( C ) + β [ U '( C 1 ) R ] = 0 (14) E + This firs order condiion is idenical o ha governing accumulaion of he liquid asse in he sandard saving model wihou credi cards. The reason why can be undersood by observing he naure of he accounan s problem when he shopper follows his rule of humb. The accounan s problem now becomes: Max { P } = 0 E 0 = 0 β U ( C [ P ]), 0< β < 1 (1 ) +1 ( A + Y P R s.. A = ) (2) B λb, 0 < 1 (3 ) + 1 λ C 0, A 0 (5) A = ; B 0 (7) = where he funcionc ( P ) is given by (12) and he shopper s rule of humb has resuled in replacemen of he ransiion equaion (3 ) wih ideniy (3 ). The accounan s choice of he paymen amoun P no longer influences he evoluion of 16

19 credi card deb bu only consumpion and accumulaion of liquid asses, as in he sandard saving model wihou credi cards. Inuiively, sacrificing one dollar of liquid asses o pay off a dollar of he credi card balance increases consumpion by one dollar as in he sandard saving model, bu i does no resul in lower credi card deb. In erms of equaion (13), he ineres savings from paying off one exra dollar of he ousanding balance are exacly offse by he ineres charges on he exra dollar of consumpion his induces. The only remaining effec is o forego he ineres on liquid asses, R as would happen in a sandard model of (liquid) asse accumulaion. Since arbirage canno be effeced, here is no reason why revolving credi card deb should be inconsisen wih posiive holdings of liquid asses Is There Empirical Suppor for he Self-conrol Hypohesis? 4.1 Making Use of Available Daa Alhough he poenial of self-conrol consideraions for explaining credi card puzzles can be shown in he conex of a heoreical model, probing household-level daa for direc empirical suppor is subjec o some limiaions. An imporan obsacle is ha self-conrol problems are largely unobservable, a leas in he conex of exising household surveys ha also conain perinen informaion on porfolios. For insance, while he Survey of Consumer Finances is he mos comprehensive source on household porfolios and associaed demographic characerisics, i conains lile informaion on aiudes and habis ha sugges direcly eiher self-conrol problems or lack of concern for such issues. The limied number of perinen variables of his sor can hen be augmened wih more sandard demographic variables ha conain a self-conrol aspec possibly in addiion o oher ypes of effecs. 17

20 We focus on hree direc aiudinal quesions in he SCF ha seem perinen o he issue a hand. Two of hem ask, respecively, wheher he household member in charge of finances (he accounan in our erminology) hinks i is accepable o borrow in order o purchase fur and jewelry, and wheher i is accepable o borrow in order o cover living expenses. Conrolling for oher facors, posiive answers o hese quesions sugges ha he accounan perceives less of a need o exercise selfconrol in credi card behavior. Addiionally, he Survey idenifies smokers, a habi ha is known o be harmful bu difficul o conrol for some individuals. To he exen ha smoking is a signal of more general self-conrol problems, he smoker variable poins o households ha could benefi from cosly self-conrol mechanisms such as revolving high-ineres deb. In addiion o he relaively scarce aiudinal quesions, household surveys conain a wealh of demographic variables ha can be shown o influence credi card behavior. Alhough we are no aware of exising psychological or economic lieraure ha has esablished clear relaionships beween paricular demographic characerisics and self-conrol problems, i is worh asking wheher here are aspecs of such demographic variables ha are relevan for self-conrol and wheher heir overall effecs on credi card behavior are consisen wih hose aspecs. For example, aaining a college degree is ofen used as a signal of self-discipline as well as of increased undersanding of financial maers. Being young implies ha he household faces boh bigger uncerainy regarding he fuure and a muliude of as ye unaccomplished objecives: self-conrol is imporan for he young on boh couns. Alhough college educaion and young age can influence credi card behavior hrough various channels, i is ineresing o see if heir overall effec is consisen wih wha is implied by a model focusing on heir self-conrol aspec raher han on a hypohesized need of credi card holders o borrow a high ineres raes. 18

21 Modeling economerically he decision o revolve deb on he credi card is somewha involved. Households may be observed o have no credi card balance because hey choose no o carry a balance on heir card, or because hey do no have access o a credi card in he firs place. Furhermore, hese decisions are likely o be correlaed. Unobservable household-specific facors ha deermine he desirabiliy of having a credi card (and he likelihood of receiving a card upon applicaion) are likely o influence also wheher or no he household would wish o use he card as source of revolving credi. Specifically, we observe he dummy variable z 1 = 0,1 for wheher or no he household has a leas one bank-ype credi card. For households ha have credi cards, we observe (in our benchmark model) a second dummy variable z 2 = 0,1 for wheher he household had an ousanding balance on he card afer he las monhly paymen. We wrie he esimaion model for each household i as zi1 = α 1' vi1 + u z u i2 i1, z i2 i2 i1 = α 2' vi2 + u u i2 ~ bivariae normal wih variances1,1and correlaion ρ is observed only when z i1 = 1 We esimae he decision o hold a credi card balance for households ha have a bank-ype credi card. As boh of hese variables are observed as 0,1 dummy variables, we esimae his as a bivariae probi wih sample selecion, allowing for correlaion beween he error erms u 1 and u 2. Esimaion yields wo ses of esimaes: firs, of facors influencing wheher he household has a credi card, and second, of hose deermining wheher i revolves credi card deb. The paern of esimaed coefficiens across hese wo sages can help disinguish beween wo alernaive hypoheses on why households end up revolving high-ineres credi card deb. One hypohesis is ha households revolve credi card deb as par of heir effor o smooh consumpion ineremporally. Under his hypohesis, households 1,2 19

22 revolve such high-ineres deb because i is difficul or cosly for hem o secure loans a more aracive ineres raes. If his is he case, facors ha encourage households o acquire credi cards should also make hem more likely o use he cards for borrowing. Supply-side facors such as screening of applicaions would, if anyhing, reinforce such endencies. I is no an objecive of banks o discourage revolving of credi card deb once hey have deermined he credi limi. As Brio and Harley (1995) pu i, []he mos desirable cusomers are hose who borrow a subsanial amoun on heir cards and ye remain well wihin heir credi limis and herefore are unlikely o defaul (p. 409). 23 By conras, he accounan-shopper self-conrol model implies ha highineres credi card deb is revolved mainly as a self-conrol device raher han for consumpion smoohing purposes. Under his hypohesis, we should observe a paern of sign reversals across he wo esimaion sages: facors ha make households less confiden abou heir abiliy o conrol credi card spending should make hem less likely o have a credi card, and more likely o revolve card deb once hey acquire a card. These reversals should be observed even afer conrolling for difficulies ha households encouner in securing oher ypes of loans. As an addiional check, facors ha explicily signal lack of self-conrol problems or of concern for such issues should no generae sign reversals. 4.2 Esimaion Resuls Our daa se is he pooled samples of he 1995 and 1998 U.S. Surveys of Consumer Finances, he wo mos recen waves of he SCF. The pooled sample has 8,406 observaions, 6,906 of which have a leas one bank-ype credi card, and 2,664 of which carried an ousanding balance on heir bank-ype credi cards. In order o focus on households ha usually raher han accidenally revolve credi card deb, we 20

23 eliminae households responding ha hey always or almos always pay off heir credi card bill. This leaves us wih 2,013 households ha usually revolve credi card deb. Variables are defined in he Daa Appendix. 24 The firs node of he bivariae probi deals wih wheher he household has a bank-ype credi card or no. The second, observed only for credi card holders, deals wih he choice of wheher o (usually) revolve credi card deb or no. Our esimaes are repored in Table 3. Le us firs examine he sign paern of esimaed coefficiens across he wo nodes for he hree aiudinal variables menioned in he previous subsecion. The firs wo such variables are direcly linked o borrowing for consumpion. Conrolling for various demographic characerisics ha include age, educaion, income and non-liquid wealh, households ha find i accepable o borrow for fur and jewelry purchases are more likely o have a card and o usually revolve deb on i. The same holds for hose ha find i accepable o borrow for living expenses. Households giving hese responses are likely o be less concerned abou exercising self-conrol in credi card behavior, and his is consisen wih he observed absence of sign reversal implied by self-conrol consideraions. On he oher hand, being a smoker also has saisically significan effecs for boh nodes: i conribues negaively o having a credi card and posiively o revolving credi card deb if he household has a card. This is wha one would expec o find if smoking signals selfconrol problems in oher areas, such as credi card behavior, and he household uses he revolving balance o conrol credi card purchases. Le us now urn o demographic variables in Table 3. We firs look a variables ha make a household less likely o be holding a bank-ype credi card bu more likely o be revolving deb if i has one. Conrolling for oher facors, household heads under fory years are less likely o have credi cards and more likely o revolve credi card deb if hey have a card. This is observed despie conrolling for difficulies in 21

24 securing oher ypes of loans or credi lines hrough he liquidiy consrains variable. 25 Young households have a number of fuure objecives relaed o homeownership and acquisiion of asses and durable goods, and hey face uncerainy abou heir long sream of fuure earnings. They hus have good reasons o be cauious in conrolling heir impulse spending, including credi card spending. Our finding is consisen wih such consideraions being imporan. Similarly, conrolling for available resources and for difficulies in obaining oher ypes of loans, having more children makes a household less likely o have a credi card and more likely o revolve high-ineres card deb if i does ge a card. I seems plausible ha an increase in he number of children makes i more difficul for a household o exercise full conrol of is credi card spending and our esimaes are consisen wih such facors being imporan. Households headed by a non-whie or Hispanic person are less likely o have a bank-ype credi card and more likely o revolve credi card deb, conrolling for perceived borrowing consrains on oher ypes of loans. If he financial services indusry has made less of an effor o marke iself o minoriy households, more limied familiariy wih financial insrumens or even some culural predisposiion agains aking financial risks or losing conrol of credi card spending may be plausible explanaions for his finding. In fac, his finding parallels findings in he sockholding lieraure ha such groups have a more limied endency o hold socks, where no applicaion or bank screening are involved (see, for example, Berau and Sarr McCluer, 2001). 26 Our esimae of Rho, he correlaion beween he error erms in he bivariae probi wih selecion, is significan and negaive. This suppors our findings of sign reversal beween he influence of he same facor in he card holding and revolving decisions. I implies ha unobserved household-specific characerisics ha make a 22

25 household less likely o hold a card also make i more likely o revolve deb on he card, hus reinforcing he role of observed characerisics consisen wih a self-conrol explanaion of deb revolvers. A he oher end of he specrum are facors ha make household heads more confiden or less concerned abou heir abiliy o conrol spending. Such facors should conribue o a endency o apply for credi cards for he convenience hey afford in making ransacions, and discourage households from revolving deb as a disciplining device. Indeed, he mos exreme way o impose self-conrol is no o apply for a credi card a all. College educaion and higher incomes, non-liquid financial wealh, and non-financial wealh fall in his caegory. The more educaed are no only more knowledgeable abou financial insrumens bu hey also have demonsraed considerable self-discipline in meeing he challenges of college degree programs. For boh reasons, hey can be more confiden abou heir abiliy o exercise self-conrol in heir finances. This is demonsraed in credi card behavior here, bu i is also corroboraed by heir greaer endency o absorb financial risk hrough sockholding (Haliassos and Berau, 1995). Educaion is no he only possible source of confidence. Those wih higher incomes or asses can be more confiden because hey are financially successful, bu also less concerned abou going on a spending spree using a credi card. We find ha all hese facors make households more likely o have a credi card and less likely o be running a balance on i. 27 The SCF also idenifies households whose average monhly expenses were below heir incomes over he previous year and hus could afford o save (hence he label saver in Table 3). The esimaed sign paern is he same for his variable ha clearly signals reduced need o borrow as for educaion, income, and asses. Marial saus presens an ineresing paern of esimaes. Being married makes i more likely ha he household has a credi card, bu i does no have a 23

26 significan effec for wheher he household revolves credi card balances. Married households see an advanage o having a credi card for ransacions purposes, bu do no regard marial saus as a decisive facor for wheher hey will revolve deb. Raher han marial saus being irrelevan for he decision o revolve deb, we consider i as giving rise o wo conflicing (and apparenly muually offseing) facors. The presence of a spouse may help conrol credi card spending, if spending by one spouse mus be jusified o he oher or be consisen wih some overall plan. On he oher hand, having a spouse may creae coordinaion problems beween he wo spouses. Based on our findings, hese wo consideraions cancel each oher ou. Households headed by someone more han 65 years old are significanly less likely han heir middle-aged counerpars o have a credi card and less likely o revolve deb. Findings in he consumpion lieraure ha older households end o experience a downward shif in consumpion sugges ha old age conribues o a smaller propensiy o underake credi card ransacions. This is probably reinforced by a cohor effec, given ha he use of credi cards was no widespread hrough much of heir working lifeime. Mainly for idenificaion purposes, we also included in he firs regression (lef panel of Table 3) variables ha proxy for regional facors likely o influence access o credi cards bu are separae from individual characerisics ha we do conrol for. These include he percenage of households in he census region 28 employed in finance, insurance, or real esae; he median ne worh in he region, relaive o he naional median ne worh; and median income, relaive o naional median income. The moivaion for using such regional variables for idenificaion is ha here may be some endency of banks o offer cards in regions ha are more affluen or have a higher concenraion of finance-relaed professionals. Of hose variables, relaive 24

27 income of he region is srongly saisically significan, enhancing he probabiliy of holding a credi card. An imporan facor no presen in he firs esimaion bu only in he esimaion regarding deb revolving is an SCF variable idenifying households ha are more financially aler, in he sense ha hey end o shop around a lo for he bes ineres raes. As seen in he righ panel of Table 3, such households are less likely o be revolving credi card deb. Given ha revolving credi card deb is cosly, one would indeed expec hose households o be more sensiive o he high ineres rae charged o deb revolvers and o be less willing o use his mechanism in order o achieve oher objecives, such as self-discipline in credi card spending. Incidenally, he finding ha financially aler households are less likely o carry a balance ends o argue agains he idea ha revolving balances are mainly moivaed by sraegic bankrupcy moives. 4.3 Focusing on Coexisence of Credi Card Deb wih Subsanial Liquid Asses As a robusness check, his secion re-esimaes he bivariae probi focusing on households ha no only revolve credi card deb bu also hold subsanial liquid asses ha could be used o repay (a leas par of) he deb. Specifically, we coninue o require ha credi card holders usually revolve credi card deb (in he sense defined above) bu now we also require ha hey hold liquid asses a leas equal o half heir average monhly income and a leas equal o $500. Alhough here is no generally agreed upon hreshold for ransacions balances, his amoun combined wih cash holdings ha are no recorded in he SCF, should be sufficien o cover normal ransacions needs. Households ha saisfy hese requiremens represen abou one half of households wih an ousanding credi card balance and abou sixy percen of hose who do no usually pay off heir credi card balance (see Table 4). 25

28 Our discussion in he previous subsecion is no maerially alered when we confine aenion o households ha combine credi card deb wih significan holdings of liquid asses. One difference is ha households ha find i accepable o borrow in order o buy furs or jewelry or in order o cover living expenses are significanly more likely o be revolving credi card deb bu no significanly more likely o be holding subsanial liquid asses alongside credi card deb. If anyhing, his difference corroboraes he self-conrol sory, since such households do no perceive a need o exercise self-conrol by resricing he available credi card limi. Among demographic variables, young age (below 40 years) is replaced by low educaion (high school dropou) in he lis of facors significanly discouraging households from having a credi card and encouraging hem o revolve deb. Boh young age and low educaion are facors a priori likely o be associaed wih selfconrol problems, bu low educaion is found o be more powerful when explaining he coexisence of credi card deb wih subsanial liquid asses conrolling for he propensiy o shop around for aracive ineres raes. All in all, our conclusions carry hrough regardless of wheher we invesigae all hose who revolve credi card deb or we confine aenion o hose who also hold subsanial liquid asses. 5. Concluding Remarks Credi card usage by U.S. households has increased seadily over he pas 20 years, and by 1998, abou wo-hirds of U.S. households held a general-purpose bankype credi card. Mos card holders carry an unpaid balance on heir cards, and he majoriy of hose hold subsanial liquid asses a he same ime. Because revolving credi card deb ypically involves borrowing a an ineres rae well above ha earned by households on heir riskless liquid asses, his porfolio puzzle is paricularly inriguing, as i suggess violaion of sandard financial arbirage. While sraegic 26

29 bankrupcy consideraions may explain he behavior of some households, we find ha his puzzling behavior is quie widespread, especially among he middle class. We presen an alernaive inerpreaion ha does no rely on bankrupcy moives or financial disress. In our accounan-shopper model of household behavior, he presence of he credi card allows saving and consumpion decisions o be separaed. The financial accounan self of he household can impose conrol on he consumpion decisions of he shopper self by revolving a balance on he card, limiing he amoun of new purchases he shopper can make before encounering he card s credi limi. Since he balance is used for conrol purposes in his framework, he accounan self may also find i opimal o save in a lower-reurn riskless asse o finance fuure consumpion. Using daa from he pooled 1995 and 1998 Surveys of Consumer Finances, we find ha a number of facors make households less likely o hold a credi card bu more likely o revolve deb once hey have a card, and more likely o revolve small amouns relaive o heir liquid financial asses. This combinaion of findings is hard o explain by eiher a pressing need of households o borrow a high ineres raes or by deliberae bank policy o rejec such applicans. I is, however, consisen wih a significan role for self-conrol consideraions ha end o discourage households from applying for credi cards, and o encourage hose who do ge hem o leave lile room o heir (oher) selves o overspend. 27