Do Banks Use Private Information from Consumer Accounts? Evidence of Relationship Lending in Credit Card Interest Rate Heterogeneity

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1 Do Banks Use Prvate Informaton from Consumer Accounts? Evdence of Relatonshp Lendng n Credt Card Interest Rate Heterogenety Sougata Kerr, Stephen Cosslett, Luca Dunn December, 2004 Author nformaton: Kerr, Consumer Rsk Modelng and Analytcs, JP Morgan Chase, Columbus, Oho; Cosslett, Professor of Economcs, Oho State Unversty, Columbus, Oho; Dunn, Professor of Economcs, Oho State Unversty, Columbus, Oho.

2 Abstract Ths paper looks at the mportance of relatonshp lendng n the credt card market. Credt bureaus are the major source of nformaton for banks n ther card approval and prcng processes. They collect nformaton prmarly on the debt sde of a consumer s portfolo rather than on a consumer s assets. However, the latter prvate nformaton s avalable to a home bank wth whch the consumer has other fnancal dealngs. We test whether home banks are usng ths prvate nformaton to make lower nterest offers to ther own customers who are good credt rsks. An endogenous swtchng regresson model ncorporatng the self-selecton of consumers to use a home bank card versus an external bank card s used. The results show that home banks are able to make lower nterest offers to ther nternal customers whose default rsks are lower, and ths has contrbuted to nterest rate heterogenety n the credt card market. In addton, we test whether home banks are able to extract nformaton monopoly rents from the low credt rsks, but fnd no evdence of rents n ths market. Keywords: Credt cards, Relatonshp lendng, Informaton asymmetry, Interest rates, Default heterogenety JEL classfcaton: D12, D82, G21, C34

3 1. Introducton The rapd growth of the credt card ndustry n the last decade has attracted consderable attenton among researchers and polcy-makers. An especally notable phenomenon n ths market s the fact that nterest rates have become much more dspersed n recent years and snce the late 1990s have ranged from 9 to 24 percent. Ths dsperson of rates s largely due to banks greater use of rsk-based prcng whch reflects the credtworthness of dfferent consumers. One crtcal type of nformaton used n ths process comes from credt bureaus and s avalable to all banks. However, much valuable nformaton about credtworthness s not avalable n credt bureaus. The current paper examnes the ssue of whether banks prvate nformaton arsng from relatonshp lendng wth ther own customers s also used n addton to the publcly avalable credt bureau nformaton to assess default heterogenety of borrowers. We fnd that relatonshp lendng does play an mportant role n assessng default heterogenety and leads to heterogeneous prcng n the credt card market beyond what could be expected to arse from the use of credt bureau nformaton. We refer to the bank wth whch a consumer has other fnancal dealngs as the home bank (HB), whle the bank wth only credt bureau nformaton for that consumer s referred to as the external bank (EB). We model nterest rate competton among banks by ncorporatng ths nformaton asymmetry between sellers. The predctons of our model are tested wth a structural econometrc model that takes account of the endogenous decson of the consumer to choose between credt cards. We fnd that HBs are able to select a pool of the more credtworthy by offerng lower nterest rates. We also fnd evdence of a wnner s curse for banks that do not have ths prvate nformaton advantage. 1

4 2. Background Much of the prevous research on the credt card market focused on the phenomena of hgh and stcky rates prevalent n the 1980s. One lne of lterature attrbutes these phenomena to the falure of nterest rate competton due to consumer nsenstvty to nterest rates (Ausubel, 1991) and lack of search (Calem and Mester, 1995). Brto and Hartley (1995), whle retanng the assumptons of consumer ratonalty and competton among banks, ntroduced transacton costs on alternatve forms of borrowng as an explanaton for the hgh average nterest rates on credt cards. Begnnng n the md-1990s, nterest rates n ths market started to declne and have shown much varablty as prce competton has ncreased. Reasons for ths ncreased competton nclude greater consumer senstvty to credt card nterest rates (Gross and Souleles, 2001) and more nterest-rate search by debt-carryng credt card users (Kerr and Dunn, 2002; Km, Dunn, and Mumy, 2004). Gross and Souleles fnd that credt card debt has become ncreasngly nterest elastc, wth approxmately half of the effect resultng from balance swtchng. Another notable feature of the late 1990s credt card market was a wde dsperson of nterest rates, rangng from low ntroductory offers of zero percent up to rates well over 20 percent. Informaton from credt bureaus 1 has been one of the major factors for ths dsperson snce t allows banks to dstngush default heterogenety among consumers and leads to separatng equlbra n nterest rates. In ths context, the current paper dfferentates between publc nformaton (.e., credt bureau nformaton on consumers credt hstores) avalable to all credt card ssuers and prvate nformaton (.e., consumers ncome and expendture cycles, checkng or savngs account balances, net worth, etc.) avalable only to banks nvolved n 1 In conductng pre-approved solctatons, credt card ssuers have broad access to detaled credt bureau nformaton about the entre pool of ndvduals beng solcted, non-respondents as well as respondents. 2

5 addtonal relatonshps wth ther credt card holders. Specfcally, we test whether banks use prvate nformaton to assess default heterogenety of borrowers and select a more credt-worthy clent pool by offerng them lower rates n equlbrum. The beneft of prvate nformaton n lendng has been an actve area of research n corporate fnance. However, ths lterature has, to our knowledge, focused only on commercal lendng and has not been explored for consumer bankng. Theoretcal aspects of relatonshp lendng were developed by Sharpe (1990), Peterson and Rajan (1995), and Boot and Thakor (1994). The frst strand of emprcal lterature n the area sought to address the queston of whether bank-borrower relatonshps over tme are value-enhancng for the borrowng frm (Lummer and McConell, 1989, and Wansley, DeGannaro, Elayan and Collns, 1992). These authors fnd evdence that the renewal of exstng bank lnes of credt nduces postve returns on the borrowng frm s stock. Accordng to these papers, credt renewal by a bank, whch s a repostory of prvate nformaton on the frm, s regarded as a postve sgnal by the market. A second lne of ths lterature has looked drectly at the duraton of the bank-borrower relatonshp (Peterson and Rajan, 1994, and Berger and Udell, 1995). These studes are unanmous n ther fndngs that longer relatonshps result n greater avalablty of credt and lower requred collateral for frms. Berger and Udell also show that borrowers wth longer relatonshps pay lower nterest rates. Recently, usng data from an anonymous Canadan bank, Mester, Nakamura, and Renault (2002) have documented the propagaton of prvate nformaton wthn a bank, focusng on commercal lnes of credt. The earler work on relatonshp bankng was not only confned to commercal bankng, but was also based on reduced form model estmaton. Hence t was not able to capture the endogenous selecton of agents,.e., the borrowers. Ths s a sgnfcant pont because the choce 3

6 made by the borrower between an nsder bank and an external de novo lender depends crucally on the terms of the offers. The terms of the contracts, n turn, are based on the nformaton sets avalable to the two types of lenders. The structural form estmaton used n the current paper, ncorporatng the endogenous selecton of the consumer based on relatve offers, allows us to dentfy the specfc channels through whch prvate nformaton s generated, and how banks use ths nformaton to determne contract terms n consumer lendng. None of the earler work has emprcally modeled these aspects of relatonshp lendng. For our purposes, HBs are those credt card banks that have multple relatonshps wth consumers through addtonal checkng, savngs, or money-market accounts, etc. The provson of such fnancal servces by HBs expands ther nformaton set wth data from the assets sde of the consumers portfolo such as lqud assets, net worth, and the volatlty of the ncome cycle (regularty n checkng cycles, drect depost accounts, etc.). Ths nformaton helps them to assess a consumer s repayment probablty and should then be reflected n the nterest rates offered by HBs to ther customers. On the other hand, EBs, where the consumer merely holds credt card accounts, wll not be prvy to ths nformaton, leadng to an nformaton asymmetry between sellers. The crux of these deas dates back to Stgltz and Wess (1981), where adverse selecton results n the external banks endng up wth a clent pool at the far rght of the rsk dstrbuton a problem prevented n the current case precsely because of the exstence of some publc nformaton (credt bureaus). Incorporatng the nformaton asymmetry arsng from relatonshp lendng nto a framework of nterest rate competton, our model shows that wthn each rsk class based on publc nformaton, banks havng addtonal prvate nformaton are able to select the good credt rsks by offerng them lower rates n equlbrum. The model used n ths paper s smlar 4

7 to the model of commercal lendng used by Sharpe (1990) and von Thadden (2004). In Sharpe s model, low-rsk frms are nformatonally captured and charged a rate that s above the far rate because of a sngle nsder and hgh costs of nformaton revelaton to a potental new lender. Von Thadden shows that the Nash equlbrum for Sharpe s model s a mxed-strategy equlbrum n whch both nsde and outsde banks randomze ther nterest-rate offers. Ths results n only a partal nformatonal capture by the nsde bank and so allows for addtonal dsperson n rates. 2 The assumpton of a sngle nsder s more lkely to hold for commercal loan markets wth collateralzed debt and ts assocated transacton costs of borrowng. 3 In consumer lendng, unlke commercal lendng, there are few, f any, transacton costs that mght prevent a consumer from holdng multple non-credt card fnancal accounts n more than one bank. Ths allows for more than one seller wth prvate nformaton on a customer, thus preventng an nformaton monopoly. Ths, along wth the assumpton of Bertrand competton, results n HBs offerng lower rates to the good credt rsks. The assumpton of multple nsders s not essental, however, because the same outcome would occur f banks can acqure a reputaton for offerng lower rates to ther good customers (or alternatvely, make an actual commtment to do so), whch would affect the consumer s ntal choce of home bank. 4 To test the predctons of the theoretcal model, we use data from the 1998 Survey of Consumer Fnances. We employ an endogenous swtchng regresson model smlar to the unon membershp model of Lee (1978) to capture the aspect of self-selecton by consumers nto two categores those who have ther prmary credt card wth ther HB and those who have 2 The soluton gven by Sharpe (1990) also predcts lmted nformatonal capture and dsperson of rates but s not a Nash equlbrum (von Thadden, 2004). 3 In commercal lendng, because of multple clams n the event of frm bankruptcy, ex-ante contracts need to be wrtten, whch ncreases the assocated transacton costs of borrowng. 4 Sharpe s model, on the other hand, explctly rules out any knd of mult-perod commtment by the bank. 5

8 ther prmary card wth an EB. In our econometrc model, we assume that both banks make nterest-rate offers to consumers based on sgnals receved about ndvduals credtworthness. Indvduals then select ther prmary card based on the nterest rate, as well as on consumerspecfc characterstcs. Thus the complete model contans two nterest rate offer equatons, one by each type of bank, and a selecton equaton for the consumer. Both two-stage and maxmum lkelhood methods are used to estmate the emprcal model. Our results provde strong evdence n favor of the nformaton asymmetry hypothess: prvate nformaton enables HBs to select consumers wth lower rsks of default by offerng them lower nterest rates compared to the EBs, whch have access only to publc nformaton. The testable mplcatons for the emprcal study are derved n the next secton from a theoretcal model whch ncorporates the nformaton asymmetry between banks. The data are descrbed n Secton 4. Secton 5 dscusses the econometrc methodology used to test the propostons of our theoretcal model. The results of the emprcal tests are dscussed n Secton 6, and our conclusons are presented n Secton Models of Interest Rate Competton In ths secton, we model the nature of nterest-rate competton among credt card ssuers faced wth dfferent types of consumers. We assume there are numerous proft-maxmzng banks n ths market, competng on prces,.e., nterest rates, and no sgnfcant barrers to entry. The cost of funds to banks s fxed at r, and nterest s the only source of revenue. The lne of credt extended s determned exogenously and s normalzed to be $1. 5 A contnuum of consumers s characterzed by publc nformaton X E that s avalable to all banks (e.g., from 5 We exclude endogenety n loan amounts and resultng credt ratonng ssues. 6

9 credt bureaus) and by prvate nformaton X H that s avalable only to the one or more HBs wth whom the consumer has other fnancal dealngs. The consumer s repayment probablty s then θ = θ X E, X ). ( H Banks make credt-card offers to the consumer, wth nterest rates based on ther avalable nformaton. Although the consumer can hold multple cards from more than one bank, the prmary card that we focus on here s the one on whch he/she keeps the largest outstandng balance. From a ratonal consumer s pont of vew, ths card should have the lowest nterest rate and can be held ether wth an EB or a HB. If the consumer receves equal offers (whch can happen wth postve probablty f X H s dscrete), and one offer s from a HB, then the consumer selects the HB card wth probablty ρ ; f there are equal offers from dfferent EBs, then each has an equal probablty of selecton. (a) Frst, suppose that all banks have only publcly avalable credt bureau nformaton (or equvalently, that X H s not nformatve about the repayment probablty). Then compettve equlbrum leads to the zero-proft nterest rate for consumers of type 1+ r r 0( X E ) = 1, (1) θ ( X ) 0 X E, where θ 0 s the average repayment probablty, E θ ( X ) = E[ θ X ]. 0 E E In ths case, all banks make zero proft, and the dstrbuton of nterest rates does not depend on the type of bank. (b) Next, suppose that the prvate nformaton X H takes on two dscrete values, h and l, correspondng to hgh and low repayment probabltes, as n Sharpe (1990). The dervaton of the equlbrum s the same for all X E, so wthout loss we can condton on a specfc value of 7

10 the publc nformaton and suppress the argument X E n the followng dscusson. Let λ = λ( X E ) be the fracton of consumers of type h, wth repayment probablty θ = θ (, h), whle the remanng fracton 1 λ are of type l wth repayment probablty θ = θ (, l), where θ h > θ l. Then θ ) 0 = λθh + (1 λ θ l. The benchmark nterest rates r h and r l are defned as the respectve zero proft nterest rates for types h and l: As θ h > θ 0 > θl, ths mples r h r < rl 1+ r 1+ r r h = 1, r l = 1. (2) θ θ h < 0. (b.1) Frst, suppose that each consumer has more than one HB, leadng to the creaton of l l h X E X E multple nsders and so elmnatng any nformaton monopoly. 6 The Nash equlbrum s the compettve outcome: HBs offer the nterest rate r h to ther type h customers and r l to ther type l customers, whle EBs offer the nterest rate r l ndscrmnately and so attract only type l customers. All banks make zero profts. The fracton of consumers holdng HB cards s λ + ρ ( 1 λ), whle the fracton holdng EB cards s ( 1 ρ)(1 λ). The correspondng average nterest rates of the HBs, r H, and the EBs, r E, are λ rh + ρ (1 λ) rl r H =, r E = rl, λ + ρ (1 λ) whle the average repayment probabltes for HB and EB customers are θ λθh + ρ (1 λ) θ λ + ρ (1 λ) l H =, E θl θ =. 6 In the Survey of Consumer Fnances sample, 31.6% of those usng ther HB cards have more than one fnancal account at commercal banks, savngs and loans, or savngs banks. 8

11 (b.2) An alternatve stuaton s that of a sngle nsder, agan wth two dscrete values for the prvate nformaton. Ths s essentally the same as Sharpe s model of nformaton asymmetry n commercal lendng (Sharpe, 1990). In the absence of reputatonal effects or mult-perod commtments by banks, HBs can now extract some rent from ther nformaton monopoly. As shown by von Thadden (2004), the Nash equlbrum s a mxed-strategy equlbrum n whch both HBs and EBs randomze offers and lend to a mx of types h and l. Whle the HBs stll have a hgher proporton of type-h borrowers than the EBs, the average nterest rate of EB customers may or may not be hgher that that of HB customers, dependng on the parameter values of θ l, θ h, λ and ρ. The expected EB proft s zero, as before, whle the expected proft of the HBs s postve. There s lmted nformaton capture n that the average expected HB proft per ndvdual s λ θ r r ) rather than the full monopoly rent of λ θh( rl rh). h ( 0 h (c) Instead of takng two dscrete values, we can consder the case where θ X ) s unformly dstrbuted on the nterval θ, ]. Comparng these two models may gve some [ l θh nsght nto the robustness of conclusons drawn from the mxed-strategy equlbrum outcome. (c.1) The case of multple nsders, HBs, wth a contnuous dstrbuton for θ leads to the unrealstc concluson that all EBs would, n effect, be forced out of the market n equlbrum, and so ths case wll not be consdered here. (c.2) In the nformaton monopoly case, the HBs now pursue a pure strategy, offerng each customer an nterest rate determned by θ, whle the EBs make randomzed offers as n von Thadden (2004). As before, the expected proft s postve for HBs and zero for EBs. Detals and further dscusson of the mxed-strategy equlbrum outcomes n the nformaton-monopoly cases (b.2) and (c.2) are gven n Secton A.1 n the appendx. ( H 9

12 We can therefore draw the followng conclusons and ther testable mplcatons. If HBs have prvate nformaton about θ, then, condtonal on X E (publc nformaton): (I) The HB offered nterest rate should be decreasng wth θ. (II) The EB offered nterest rate should not depend on θ. These two conclusons yeld the testable mplcaton that the prvate nformaton varables that predct repayment probabltes should affect the HB nterest rates and not the EB nterest rates. (III) On average, the repayment probablty θ wll be hgher for HB customers than for EB customers. Accordng to ths predcton, the repayment probablty of HB consumers wll be hgher (lower rsks) compared to the EB consumers. Together wth predctons (I) and (II), ths mples that the average nterest rate for HB consumers wll be lower than the average rate for consumers usng an EB card. If, n addton, the prvate nformaton gves HBs an nformaton monopoly, allowng them to approprate an nformaton rent, then (IV) HBs should make postve profts relatve to EBs. Ths mples that the actual nterest rate charged by the HBs wll be hgher than the zero-proft rate (whch can be estmated from the average default probablty of HB customers and the cost of funds). The randomzaton of offers wll result n a wnner s curse effect on the EBs where some type l ndvduals wll select the EB card precsely because they receve lower rates from EBs than ther own HBs. The magntude of rent approprated by the HBs from ther type h customers and the wnner s curse of the EBs are emprcal questons that would depend on the extent of 10

13 competton prevalng n ths market. We test for both these effects and fnd (1) evdence of a wnner s curse effect for the external banks but (2) no evdence of nformaton rent. 4. Data and Descrptve Statstcs We use the 1998 Survey of Consumer Fnances (SCF), whch contans: () publc nformaton carred by credt bureaus (mortgages, home equty lnes, credt card balances, delnquency, bankruptcy hstory, etc.); and () prvate nformaton on consumer ncome, lqud assets, and net worth data whch would be avalable only to a HB through other accounts and servces provded to ther customers. 7 These varables serve as proxes for the ncome and expendture streams of each consumer, whch n turn serve as proxes for default rsk. The SCF also maps the network of relatonshps that consumers have wth fnancal nsttutons, allowng us to determne whether the prmary credt card used belongs to a bank wth whch they have other fnancal dealngs (HB). Followng the SCF conventon, the prmary card s taken to be the one on whch the consumer has the largest balance, whle for zero-balance consumers t s the card appled for and receved most recently. We use the nterest rate on ths prmary card n all tests snce, from a ratonal consumer s perspectve, the card wth the largest outstandng balance should be the one whch offers the lowest nterest rate among all cards held. 8 Our study s confned to those ndvduals who have some form of bank credt card. 9 Among these we consder only those cases wth nterest rates above 6.5%. Any lower rate n the perod was an ntroductory rate snce the federal funds rate durng ths tme was around 7 Whle the prvate nformaton varables n the SCF may not correspond exactly to the HBs nformaton set, we expect there to be a hgh degree of correlaton. Furthermore, measurement error, f any, n the banks prvate nformaton wll lead to an underestmaton of ts sgnfcance. 8 For our consumer, the prmary card s always the lowest nterest card even when other benefts are assocated wth a card for example, frequent fler mles. Ths s because those benefts are ted to usage of the card and not nterest-payng debt on the card. Hence a ratonal card user should always shft outstandng balances to the lowestnterest card, regardless of other benefts that come wth card use. 9 Vsa, MasterCard, Dscover or Amercan Express cards. 11

14 5.5%. 10 Our fnal sample contans 2,265 cases 861 cases wth HB prmary cards and 1,401 wth EB prmary cards. Varable defntons and descrptve statstcs are gven n Table 1. We see there that consumers whose prmary card s wth an EB have lower net worth, less lqud assets, and are more prone to mss payments or declare bankruptcy than those whose prmary card s wth a HB. Thus a casual look at the data suggests that the average consumer who uses an EB card s on a weaker fnancal footng then the average consumer who uses a HB card. More mportantly, the average nterest rate of consumers wth HB cards s one percentage pont lower than the average rate of consumers wth accounts held at EBs. 11 To see how the nterest rates offered vary across the home and external bank sample, we estmate the probablty densty functon of the rates across these two bank types usng a Gaussan kernel wth a data-based bandwdth suggested by Slverman (1986). Fgure 1 shows the dstrbuton of rates across the two samples. The rates offered to consumers havng a HB card are lower and have a bmodal densty functon wth a roughly 5-pont spread between modes. The dstrbuton of rates clearly shows that the nterest rates on the prmary debtcarryng card of consumers are notably lower f the account s held wth a HB than f t s held wth an EB. Ths valdates one of the testable mplcatons that arse from our theoretcal model. 5. Econometrc Analyss The econometrc model s a three-equaton system representng the HB nterest rate offer, the EB nterest rate offer, and the consumer s choce of the HB card or the EB card as the prmary card. Snce the focus here s on a comparson of HB and EB nterest rates rather than on credt-card holdng, we estmate the model for the populaton of ndvduals holdng at least one 10 It has been documented that credt card-backed securtes offered yelds n the vcnty of 1% above those of Treasury securtes n ths perod. Hence the cost of funds for credt card ssuers was at least 6.5%. 11 Ths result also holds n an OLS regresson after we control for all the consumer characterstcs n Table 1. 12

15 bank credt card. As n the theoretcal model of Secton 3, we assume that both types of banks make nterest rate offers to consumers based on sgnals they receve about ndvduals credtworthness. Indvduals then select whch card to use as ther prmary card based on whch nterest rate s lower, as well as other consumer-specfc characterstcs and non-prce dmensons of the offers. 12 Because the SCF data contan nterest-rate nformaton only for the consumer s prmary card, we therefore estmate the equaton system as a partal-observablty swtchng regresson model. 13 The structural equatons for the nterest rates offers are r H, = X1, 11 + X 2, β12 + u1, β (3a) r E, = X1, 21 + X 2, β22 + u2, β (3b) where r, and H r, are the lowest rates receved by ndvdual from hs/her HBs and EBs, and E X, 1 and X 2, are the vectors of consumer characterstcs whch sgnal credtworthness based on publc and prvate nformaton respectvely. The consumer selects the HB card f r E, rh, > η where η summarzes the preference for a card based on non-nterest terms. It can be represented as η W C + v. = δ 0 + α1 + α2 W s a vector of ndvdual-specfc characterstcs (whether the cardholder s a convenence user, the cardholder s propensty to search for better credt terms, and rato of average monthly payments on rents, mortgages, autos and leases to monthly ncome) that determne preference for a card, and C s a non-prce dmenson of the offer (credt lne). In other words, f the consumer 12 It s, of course, possble that some credt-card holders may not have receved competng offers. We wll treat ths as equvalent to a competng offer wth an nterest-rate dfferental suffcently hgh that the probablty of choosng the competng card s neglgbly small. 13 Ths s smlar to the unon membershp model of Lee (1978). 13

16 selects the HB card, t s because the HB nterest rate s suffcently lower than the EB rate to compensate for all other characterstcs that determne the preference for a card. Substtutng η nto the above nequalty allows us to represent consumer selecton by the latent-varable equaton I δ C + v (4) * = 0 + δ 1 ( re, rh, ) + α1 W + α 2 where the HB card s chosen f I The error terms u, * > jontly normally dstrbuted wth zero means and varances 2 σ 1, 1, u, 2 and v are assumed to be 2 σ 2, and 2 σ v. Endogenety arses from the fact that the nterest rates, whch are the dependent varables n the nterest rate equatons (3a) and (3b), also determne the choce by the ndvdual n the selecton equaton (4). To deal wth ths endogenety, we follow the procedure proposed by Lee (1978) where (3a) and (3b) are used to substtute for the nterest dfferental n (4). Ths gves the reduced-form probt equaton I = * Z γ + ε (5) where Z ncludes X 1,, X 2,, W and C, whle ε s the composte error term 1 ( u 2, u1, + v rescaled so as to gve the conventonal normalzaton σ 2 ε = 1 δ ). Thus the model to be estmated conssts of the three equatons (3a), (3b) and (5), wth the observed dependent varables I * 1 when I > 0 = * 0 when I 0 and 14 * The coeffcent δ 1 was ntroduced to allow for the conventonal rescalng of the latent varable, I, n the probt model. 14

17 r r = r H, E, when when I * * I > 0 0 We estmate the model both by the two-stage method and by maxmum lkelhood. Detals are gven n Secton A.2 n the appendx, and the results are reported below n Secton 5. The magntude of the self-selecton effect s represented n the two-stage estmates by the covarance parameters σ1, ε = cov( u1,, ε ) and σ 2, ε = cov( u2,, ε), whle the ML results gve the correspondng correlaton coeffcents ρ 1 and ρ 2. Accordng to predcton (I) n Secton 3, β 12 should be sgnfcant, wth negatve coeffcents for those varables known to the HB that sgnal lower rsk,.e., lqud assets, net worth, and the proxes correspondng to lower ncome volatlty. On the other hand, accordng to predcton (II), β 22 should not be sgnfcantly dfferent from zero, snce EBs do not possess the nformaton represented by X 2. Self-selecton corresponds to a negatve sgn for σ 1 ε and a postve sgn for σ 2 ε,.e., the expected nterest rate for a partcular card condtoned on selecton s predcted to be lower than the average uncondtonal rate. 15 However, the present data do not allow us to determne the extent to whch the stochastc terms u, 1 and u 2, are due to () unobserved nformaton avalable to the bank, leadng to selecton of more credtworthy customers, () strategc randomzaton of offers, and () random errors. Both () and () lead to a wnner s curse effect. Under the assumpton that no prvate unobserved nformaton s avalable to the EBs, a postve sgn for σ 2 ε mples a wnner s curse effect for the EBs. 15 Note that ths predcton would not hold f unobserved non-prce features of the offer are suffcently attractve that they more than offset a lower nterest rate. 15

18 Delnquency model. The next step s to nvestgate default probabltes. Ths wll allow us to determne whether the prvate nformaton varables X 2 do n fact correspond to lower default probabltes, as was assumed above n testng predcton (I). Modelng the default probabltes wll also allow us to test the remanng predctons from Secton 3,.e., (III) lower average default probabltes for HB customers and (IV) postve HB profts. Assumng that delnquency s an ndcator for future default, we estmate an ordered probt model where the delnquency varable has three categores: D = 1 f respondent had mssed a monthly payment but not fallen behnd by two months, D = 2 f they were behnd n ther payments by two months or more, and D = 0 otherwse. These are treated as an ordered categorzaton of the latent varable D = X β + η where the explanatory varables X are the same publc and prvate nformaton varables as n the nterest rate equatons, other than the delnquency varable. 16 Besdes determnng whether these varables have a sgnfcant effect on delnquency, ths model also allows us to estmate the probabltes Pr( D = 1) and Pr( D = 2), whch serve as proxes for the actual default probabltes n testng predcton (III). Fnally, to estmate the proft dfferental between HBs and EBs, we make the further assumpton that the expected rate of losses (charge-offs) for banks s approxmately equal to the 60 days delnquency rate gven by Pr( D = 2). 16 The ncluson of bankruptcy as an ndependent varable n ths equaton mght create endogenety ssues snce delnquences are often a precursor to bankruptcy. However, ths problem does not occur here as all bankruptces n these data were fled more than one year pror to the survey, and as such precede the delnquency varable whch reflects late payments over the past one year only. 16

19 6. Emprcal Results The two-stage estmates are presented n Table 2. The frst two columns of ths table represent the nterest rate equatons on publc (.e., credt bureau) and prvate nformaton varables for the HB and the EB. The selecton probt n column 3 ncludes four addtonal dentfcaton varables: a dummy varable for convenence users, a dummy for the propensty to search for credt cards, the rato of monthly payments to ncome, and the log of the credt lne. The convenence user varable s mportant because consumers who do not borrow on ther cards mght put more emphass on other features, such as frequent fler mles, rather than nterest rates when selectng among cards. The propensty to search for credt cards s ncluded as a proxy for both the pecunary and nonpecunary search costs of consumers. Average monthly payments on mortgages, rent, auto loans and other leases relatve to monthly ncome are ncluded because hgh-payment consumers are lkely to be more senstve to nterest rates rather than other features of the card. Fnally, the total credt lne offered captures another non-prce dmenson of bank offers and hence also nfluences the lqudty-constraned consumer s choce of cards. The estmates n Table 2 support predctons (I) and (II). We fnd: () all varables reflectng prvate nformaton lqud assets, net worth, and employment proxes for ncome volatlty are sgnfcant n determnng nterest rates for HBs but not for EBs; and () only the credt bureau varables utlzaton rates on credt cards, home equty lnes of credt, as well as past delnquency and the bankruptcy hstory of the consumer are sgnfcant n determnng nterest rate offers for EBs. Surprsngly, none of the publc nformaton varables are sgnfcant n determnng rate offers for the HBs, ndcatng a smaller role for credt bureau nformaton for HBs when determnng offers for ther own customers. Also, three of the four consumerpreference varables are sgnfcant n the selecton equaton. The sgns on all fnancal varables 17

20 are as expected for both HBs and EBs. For nstance, those wth delnquent accounts or bankruptcy flngs are charged a hgher nterest rate by EBs, whle those wth hgher lqud assets and lower ncome volatlty are charged a lower nterest rate by ther HBs. 17 The estmates also provde evdence of selecton, snce σ 1, ε (whch appears as the coeffcent of the nverse Mlls rato n the second-stage equaton (A5) for the HB nterest rate) s negatve and sgnfcant, thereby ndcatng that the expected nterest rate of the home bank card holders condtoned on selecton s lower than the uncondtonal expectaton. On the other hand, there s no evdence of selecton for the EB cardholders. The maxmum lkelhood estmates of the selecton model (Table 3) are qualtatvely smlar to the two-stage estmates. The only dfferences are that () the rato of average monthly payments to ncome s not sgnfcant n the selecton equaton, and () both of the correlaton coeffcents ρ 1 and ρ 2 are now sgnfcant, wth sgns correspondng to a selecton effect (.e., nterest rates are lower when condtonng on selecton). Accordng to the nterest-rate equaton coeffcents, HBs are able to attract the good credt rsks among ther depost customers by makng lower nterest-rate offers on the bass of favorable prvate nformaton. However, as none of the prvate nformaton varables are sgnfcant n the EB nterest-rate equaton, the EB offer s attractve only to customers who are offered hgher rates by the HBs on the bass of adverse prvate nformaton. If we now also consder the unexplaned heterogenety of nterest rate offers, the selectvty effect shows that the average HB card holder receved a below-average HB nterest-rate offer, and accordng to the maxmum lkelhood results, the average EB card holder lkewse had a below-average EB 17 The sgn on the home equty utlzaton rate mght at frst glance appear unntutve. However, home equty lnes are a substtute for credt cards, especally for consumers wshng to consoldate ther debts, and banks must compete for these customers by offerng lower rates. 18

21 offer. 18 For HBs, we can reasonably ascrbe part of ths unexplaned heterogenety to unobserved prvate nformaton, thus further enhancng the HBs ablty to attract good credt rsks through lower offers. For EBs, on the other hand, the absence of observed prvate nformaton strongly suggests that there s no unobserved prvate nformaton ether. Instead, the unexplaned heterogenety of EB offers may be attrbuted to the strategc randomzaton of offers by EBs, and acceptance of below-average offers then leads to a wnner s curse effect for the EBs. These arguments hold provded that HBs actually succeed n attractng cardholders wth lower average default rsk than EB cardholders, and later n ths secton we show that ths s n fact the case. Next we focus on a crtcal underlyng assumpton: prvate nformaton predcts nterest rates because t actually predcts repayment probabltes (mplct n the test of predctons I and II), and so allows HBs to select a lower-rsk pool (predcton III). As dscussed n the prevous secton, we assume that delnquency s an ndcator for future default, and estmate an ordered probt model for the delnquency varable. The results, presented n Table 4, show that lqud assets, net worth, and the employment dummes servng as proxes for ncome volatlty are hghly sgnfcant and are thus key predctors of future delnquences. For example, a thousanddollar ncrease n lqud assets reduces the probablty of gong sxty days past delnquent by approxmately 2.4 percentage ponts. The above analyss s carred out for the entre sample as well as for the EB sample separately. We fnd that the results are qualtatvely smlar for the EB consumers lqud assets and net worth do predct future delnquences even n ths sample. The fact that these varables 18 Below average here means below the average of offers made by that type of bank to all consumers wth the same observable characterstcs. 19

22 are not sgnfcant n the EBs nterest rate equatons s due to the EBs not havng access to ths nformaton. The ordered probt model s also used to estmate Pr( D = 1) (probablty of mssng a payment n the last year) and Pr( D = 2) (probablty of fallng behnd on payments by two months or more) for the HB and EB samples separately. These estmates, presented n Table 5, show that HB customers have lower probabltes for both default states. Agan assumng that delnquency can be used as a proxy for future default, ths valdates predcton (III),.e., HBs succeed n attractng a clent pool from ther own customers who are more credtworthy than the average EB customer. Fnally, to test predcton (IV), we assume that the expected rate of losses for banks s approxmately equal to Pr( D = 2). Then Table 5 mples that the loss rate of the HBs credt card portfolo s one pont lower than that of the EBs. Ths dfference n expected losses s also reflected n the dfference n the average nterest rates between the HBs and EBs (approxmately 1 percentage pont). If we further assume that the EBs are makng zero profts then the cost of funds (.e. prme rate) for the EBs, wth an average nterest rate of r =15.72% and a repayment probablty of θ = 95.04%, s r θ ( 1+ r ) 1 = 9.98%. Gven the cost of funds, we calculate E = E E the zero-proft nterest rate of the HBs, wth repayment probablty θ = 0. 96, as r ( 1+ r ) / θ 1 = 14.56%. The small dfference between the actual nterest rate charged by H = H the HBs (14.75%) and the zero-proft rate suggests that even though some HBs have an nformaton monopoly arsng from relatonshp lendng, t does not result n expropraton of rent from the low credt rsks. Ths, along wth the evdence of wnner s curse for EBs, suggest that randomzaton of offers n ths compettve market envronment have reduced the nformaton capture of the low credt rsks and led to more heterogeneous prcng. E H 20

23 7. Summary and Conclusons Ths paper has examned the ssue of heterogenety n credt card nterest rates. It ntroduces the noton of relatonshp lendng (prevously consdered only n the context of commercal lendng) n the consumer credt market and dstngushes between prvate nformaton held by a card holder s home banks (HBs) as opposed to publcly-avalable credt bureau nformaton held by external banks (EBs). It shows that prvate nformaton arsng from other bankng servces (checkng accounts, savngs, etc.) s used by HBs to assess the default potental of ther own customers and to select a lower-rsk pool by offerng them lower nterest rates. On the other hand, EBs must depend prmarly on nformaton that s avalable through credt bureaus, and ths nformaton asymmetry among card-ssuers ultmately has contrbuted to further rate heterogenety beyond what arses from the use of bureau nformaton. The Survey of Consumer Fnances (1998) data are used to test the mplcatons of the theoretcal model. We assume that both HBs and EBs make nterest rate offers to consumers based on the nformaton set avalable to them. Consumers then select ther prmary card based on the nterest rate, some non-prce dmensons of the offer, and other consumer-specfc characterstcs whch govern the consumers choce of card. An endogenous swtchng regresson model that captures the aspect of self-selecton by consumers nto two categores s used and estmated usng maxmum lkelhood methods. The emprcal results provde strong evdence of the mpact of relatonshp lendng n ths market. Our results nclude the followng. (1) The average rate on EB credt cards s one percentage pont (.e., 6 percent) hgher than home bank cards, and ths holds even after controllng for other observables. (2) Varables representng nformaton from the prvate fnancal accounts of the consumer (and known only by the HBs) are sgnfcant n the HB 21

24 nterest offers but are not sgnfcant n the EBs offer equaton. On the other hand, most of the publc nformaton varables (avalable from credt bureau reports) are sgnfcant n the nterest rate offer equatons of EBs but not n the HBs offers. Ths clearly suggests that HBs, havng access to prvate nformaton, put less weght on publc nformaton. (3) There s evdence of a wnner s curse for EBs. (4) The default rsk of the HB sample s also one percentage pont lower than that of the EB sample. These results pont to a Pareto-mprovng exchange of nformaton arsng out of relatonshp lendng. Consumers havng low rsks of default are better off holdng credt cards wth banks where they have other fnancal accounts. The prvate nformaton gleaned from other fnancal accounts held by the consumer at ther HBs, enables these banks to make the lowrsk consumers nterest offers that cannot be matched by an EB for fear of adverse selecton. Despte result (4) above, however, there s no conclusve evdence that HBs succeed n usng ther nformaton monopoly to extract a rent from low-rsk consumers. Appendx A.1. Mxed-Strategy Equlbrum wth a Sngle Home Bank As dscussed n Secton 3, a sngle HB can extract rent from ts nformaton monopoly, n the absence of any knd of mult-perod commtments by banks. When X H takes on two dscrete values (.e., case (b) n Secton 3), the structure of the game s equvalent to the second stage of Sharpe s model (Sharpe, 1990), f we condton on a partcular rsk class X E and dentfy the types h and l wth Sharpe s frst-stage outcomes S and F. notaton) The two-perod structure of Sharpe s model leads to the parameter restrcton (n our λ θ = 0,.e., the proporton of borrowers who are observed by the HB to be good rsks s 22

25 equal to the average repayment probablty. Because the present model does not have ths restrcton, we restate the results of von Thadden (2004) n a form that apples here. Let F H (r) be the dstrbuton functon of nterest rates offered by the HB to consumers of type h, and let F E (r) be the dstrbuton functon of nterest rates offered by an EB to consumers of type l. As before, the HB offers only r l to consumers of type l. If M competng EBs make ndependent offers, then the dstrbuton of the best offer by an EB s gven by M E M F ( r) = 1 [1 F ( r)]. Then, followng von Thadden (2004), Nash equlbrum mples the offer dstrbutons F F r0 rh rl r r) = 1 for r [ r, rl ] (A1) r r r r H ( 0 l 0 h r0 rh r) = 1 for r [ r, rl ), F M ( r l ) = 1, (A2) r r M ( 0 h whch are expressed n terms of the benchmark nterest rates r 0, r h, and r l defned n equatons (1) and (2). In the alternatve model where θ X ) s unformly dstrbuted on θ, ] (.e., case (c) ( H [ l θh n Secton 3), the followng strateges consttute a Nash equlbrum. 19 As before, we condton on X E. The HBs now adopt a pure strategy, offerng an nterest rate r H 1 ( θ + r ) = 2 1 θ + θ (A3) to ther customers, where θ = θ ( X H ). Note that rh ( θ h ) = r0, where r 0 s defned as before except that the average repayment probablty s now θ = ( θ l + θ ) / 2. The EBs randomze l 0 h ther offers, as n von Thadden (2004), but wth a modfed dstrbuton correspondng to 19 Ths follows by a sutable modfcaton of the argument n von Thadden (2004). However, we do not attempt here to show the unqueness or stablty of ths equlbrum. 23

26 F 2 M ( 0 l 0 (1 + r0 ) rl r r) = 1 for r [ r, r ] 2 l. (A4) r r (1 + r) Comparng these results wth the case of no prvate nformaton, we see that the nformaton monopoly leads to hgher nterest rates for all borrowers. On the other hand, n comparson wth the case of multple HBs, the nformaton monopoly rases nterest rates for good credt rsks whle lowerng nterest rates for bad credt rsks. The expected EB proft s zero, as before, whle the expected proft of the HBs relatve to the populaton sze s λ θ ( r 0 r h ) n model (b) or 1θ r ) n model (c). 20 h 3 h( 0 r h The offer dstrbutons can be used to calculate average nterest rate offers, acceptance rates, and average accepted nterest rates for both types of bank (although the actual expressons are hghly model-specfc.) For the present, we note the followng results: (1) The expected HB-offered nterest rate decreases as θ ncreases, condtonal on publc nformaton. 21 In model (b.2) ths follows mmedately from the fact that type l customers are offered r l, whle type h customers receve an offer dstrbuted between r 0 and r l. In model (c.2) t s clear that r H (θ ) n equaton (A.3) s a decreasng functon of θ. (2) HB card holders have a hgher average θ than EB card holders. To verfy ths n model (b.2), let a h and a l be the proportons of type h and type l customers who accept the HB offer. In ths model, ah = + ( r 0 rh ) /( rl rh ) and a l = ρ( r 0 r h ) /( r l r h ). Thus a h > al, whch mples E[ θ HB] > E[ θ EB]. In model (c.2) drect calculaton of the expected values gves the rato E[ θ HB]/ E[ θ EB] (2θ + θ ) /( θ + 2θ ) > 1. = h l h l 20 These expected profts n model (b) are, n fact, the same as n the outcome proposed by Sharpe (1990). 21 On the other hand, the relatonshp between the average nterest rates pad by those acceptng HB cards and those acceptng EB cards s ambguous, dependng on the model and the parameter values. 24

27 A.2. Estmaton of the Swtchng Regresson Model In the two-stage estmaton method, the regresson equatons n (3a) and (3b) condtoned on selecton (5) become φ( Z γˆ) β ε (A5) r H, = X1, 11 + X 2, β12 + σ1 + e1, Φ( Zγˆ) φ( Z γˆ) β ε (A6) r E, = X1, 21 + X 2, β22 σ 2 + e2, 1 Φ( Zγˆ) where the coeffcents of the Heckman correcton terms are σ 1ε = cov( u 1, ε ) and σ 2ε = cov( u 2, ε ), whle γˆ s estmated from the probt selecton equaton. As usual, φ and Φ represent the standard normal densty and dstrbuton functons. The lkelhood functon for maxmum lkelhood estmaton can be expressed n the form 22 = f ( r ) Φ( A ). f ( r Φ( A ) H I = 1 L (A7) H, 1, E E, ) = 0 I where f H ( ) and f E ( ) are the margnal denstes of the offered nterest rates (3a) and (3b),.e., f f H E ( r ( r H, E, ) = (1/ σ ) φ 2 1 ) = (1/ σ ) φ 2, ( rh, X1, β11 X 2, β12) / σ1) ( r X β X β ) / σ ) E, 1, 21 2, 22 2 The terms Φ ) and Φ ) are the selecton probabltes condtonal on the observed ( A 1, ( A 2, nterest rates r, and H r, respectvely, wth E A 1, = ( Z γ + ( ρ / σ ) ( r X β X β )) 1 1 H, 1, 11 2, 12 1 ρ 2 1 A 2, = 2 ( Z γ + ( ρ 2 / σ 2 ) ( r, X 1, β 21 X 2, β 22 )) 1 ρ 2 E where ρ j s the correlaton between u j, and ε ( j =1, 2 ). 22 See for example Amemya (1985). 25

28 References Altman, Edward I. and Anthony Saunders, Credt Rsk Measurement: Developments over the Last 20 Years, Journal of Bankng and Fnance, 21, Amemya, Takesh, Advanced Econometrcs, Harvard Unversty Press, Ausubel, Lawrence, The Falure of Competton n the Credt Card Markets, Amercan Economc Revew, 81(1), March 1991, Ausubel, Lawrence, Credt Card Defaults, Credt Card Profts and Bankruptcy, Amercan Bankruptcy Law Journal, 71, Sprng 1997, Ausubel, Lawrence, Adverse Selecton n the Credt Card Market, mmeo, Unversty of Maryland, June Ausubel, Lawrence, Personal Bankruptces Begn Sharp Declne: Mllennum Data Update, mmeo, Unversty of Maryland, January Berger, Allen N., and Gregory F. Udell, Relatonshp Lendng and Lnes of Credt n Small Frm Fnance, Journal of Busness, 68(3), July 1995, Black, Sandra and Donald P. Morgan, Rsk and the Democratzaton of Credt Cards, Federal Reserve Bank of New York, Research Paper No. 9815, June Bzer, Davd S., and Peter M. DeMarzo Sequental Bankng, Journal of Poltcal Economy, 100(1), February 1992, Boot, Arnoud W. A., Relatonshp Bankng: What Do We Know? Journal of Fnancal Intermedaton, 9, 2000, Boot, Arnoud W. A., and Anjan V. Thakor, Moral Hazard and Secured Lendng n an Infntely Repeated Credt Market Game, Internatonal Economc Revew, 35, 1994,

29 Brto, Dagobert L., and Peter R. Hartley, Consumer Ratonalty and Credt Cards, Journal of Poltcal Economy, 103(21), 1995, Calem, Paul S., The Strange Behavor of Credt Card Market, Busness Revew, Federal Reserve Bank of Phladelpha, January Calem, Paul S., and Loretta J. Mester, Consumer Behavor and Stckness of Credt Card Interest Rates, Amercan Economc Revew, 85(5), December 1995, Gross, Davd B., and Ncholas S. Souleles, Do Lqudty Constrants and Interest Rates Matter for Consumer Behavor? Evdence from Credt Card Data, Natonal Bureau of Economc Research, Workng Paper 8314, June Kerr, Sougata, and Luca Dunn, Consumer Search Behavor n the Changng Credt Card Market, The Oho State Unversty, Workng Paper No , September Km, TaeHyung, Luca Dunn, and Gene Mumy, Bank Prce Competton, Consumer Search, and Asymmetrc Responses to Credt Card Interest Rates, forthcomng n Economc Inqury. Laderman, Elzabeth, What s Behnd the Problem of Credt Card Loans? Economc Letter, Federal Reserve Bank of San Francsco, July Lee, Lung-Fe, Unonsm and Wage Rates: A Smultaneous Equaton Model wth Qualtatve and Lmted Dependent Varables, Internatonal Economc Revew, 19(2), June 1978, Lummer, S., and J. McConell, Further Evdence on the Bank Lendng Process and the Captal Market Response to Bank Loan Agreements, Journal of Fnancal Econonomcs, 25, 1989, Mester, Loretta J., Why are Credt Card Rates Stcky? Economc Theory, 4, 1994,

30 Mester, Loretta J., What s the Pont of Credt Scorng? Busness Revew, Federal Reserve Bank of Phladelpha, October Mester, Loretta J., Leonard I. Nakamura, and Mchelne Renault, Checkng Accounts and Bank Montorng, Federal Reserve Bank of Phladelpha, Workng Paper No. 01-3/R, July Ongena, Steven, and Davd C. Smth, What Determnes the Number of Bank Relatonshps? Cross-Country Evdence, Journal of Fnancal Intermedaton, 9, 2000, Park, Sangkyun, Effects of Prce Competton n the Credt Card Industry, Economc Letters, 57, 1997, Park, Sangkyun, Opton Value of Credt Lnes as an Explanaton of Hgh Credt Card Rates, Federal Reserve Bank of New York, Research Paper No. 9702, February Peterson, Mtchell A., and Raghuram G. Rajan, The Benefts of Lendng Relatonshps: Evdence from Small Busness Data, Journal of Fnance, 49(1), March 1994, Peterson, Mtchell A., and Raghuram G. Rajan, The Effect of Credt Market Competton on Lendng Relatonshps, Quarterly Journal of Economcs, 110, 1995, Sharpe, Steven A., Asymmetrc Informaton, Bank Lendng and Implct Contracts: A Stylzed Model of Customer Relatonshps, Journal of Fnance, 45(4), September 1990, Stgltz, Joseph E. and Andrew Wess, Credt Ratonng n Markets wth Imperfect Informaton, Amercan Economc Revew, 71(3), June 1981, Trost, R. P., Interpretaton of Error Covarances wth Non-Random Data: An Emprcal Illustraton of Returns to College Educaton, Atlantc Economc Journal, 9(3), 1981,

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