ESSAYS ON CONSUMER LINES OF CREDIT: CREDIT CARDS AND HOME EQUITY LINES OF CREDIT DISSERTATION. the Degree Doctor of Philosophy in the Graduate

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1 ESSAYS ON CONSUMER INES OF CREDIT: CREDIT CARDS AND HOME EQUITY INES OF CREDIT DISSERTATION Presented n Partal Fulfllment of the Requrements for the Degree Doctor of Phlosophy n the Graduate School of The Oho State Unversty By Shubhass Dey, M.A. The Oho State Unversty 2004 Dssertaton Commttee: Professor uca Dunn, Advsor Professor Stephen Cosslett Professor Gene Mumy Approved by Advser The Department of Economcs

2 ABSTRACT nes of credt n the consumer credt market are prmarly n the forms of credt cards (CCs) and Home Equty nes of Credt (HEOCs). In the frst chapter of the dssertaton I focus on the specal usage of lnes of credt as a hedge aganst optmally unnsured rsks. Ths framework helps me understand why some consumers hold lnes of credt and do not draw on them. Consumers wegh the varous non-nterest costs of HEOC borrowng aganst the benefts of low and ncome tax-deductble nterest rates. I show that consumers optmally choose CCs as the preferred rsk-fnancng nstrument for suffcently small amounts of debt. For relatvely large amounts of ndebtedness, they prefer to use HEOCs exclusvely; and for extremely large borrowng needs, the costs of collateralzaton of credt nduce consumers to carry debt on both CCs and HEOCs. The motve to consoldate debt ntroduces smultanety n consumers choce of holdng debt on lnes of credt, whch s addressed wth an approprate econometrc model. In the second chapter of the dssertaton I examne the nature of the nformaton asymmetry prevalent between borrowers and lenders n the market for HEOCs and test how collateral helps overcome ths asymmetrc nformaton. Two dstnct paradgms have emerged from the theoretcal studes nvestgatng the role of collateral n explanng the rsk-spread n the market for collateralzed loans. The sortng-by-observed-rsk paradgm

3 predcts a postve assocaton between collateral and borrower rsk and hence a postve relatonshp between the amount of collateral pledged and the rate of nterest charged. The sortng-by-prvate-nformaton paradgm, on the other hand, postulates a negatve relatonshp between collateral and credt prce. I fnd emprcal support for the sortngby-prvate-nformaton paradgm n the market for HEOCs. In the fnal chapter of the dssertaton I theoretcally and emprcally dentfy the determnants of credt card borrowng lmts when banks can smultaneously choose the borrowng lmt and the nterest rate n ther loan contracts. I fnd a postve relatonshp between borrower qualty and the borrowng lmt on CCs, correctng for banks selecton of credt card holders and for the nfluence of the endogenous varable, the credt card nterest rate.

4 Dedcated to my parents v

5 ACKNOWEDGMENTS I wsh to thank my advser, uca Dunn, for her gudance, encouragement and support n makng ths thess possble, and for her patence n correctng the errors of my scentfc expresson. I thank Stephen Cosslett for ntellectual support and for hs profound nfluence n shapng my economc and econometrc analyses. I am grateful to Gene Mumy for stmulatng dscussons and for hs valuable comments regardng the varous aspects of ths thess. I am mmensely ndebted to Sougata Kerr for helpng me understand the survey data used n ths thess and for provdng a copy of hs unpublshed manuscrpt. Fnally, I wsh to thank all my frends for ther unstnted support, encouragement and enthusasm, wthout whch ths thess would never have been possble. v

6 VITA June 14, Born Calcutta, Inda M.S. Quanttatve Economcs, Indan Statstcal Insttute present. Graduate Teachng Assocate, The Oho State Unversty Major Feld: Economcs FIEDS OF STUDY v

7 TABE OF CONTENTS Page Abstract... Dedcaton..v Acknowledgments...v Vta.v st of Tables.x Chapters: 1. Choce of consumer lnes of credt: secured versus unsecured Introducton The theoretcal model The choce to borrow n the presence of credt card only The choce to borrow n the presence of HEOC only The choce to borrow n the presence of credt card and HEOC Data The econometrc model Results and dscusson Summary Collateral and sortng: an emprcal nvestgaton nto the market for HEOCs Introducton Data The econometrc model Results and dscusson Summary Determnants of borrowng lmts on credt cards Introducton Background The smple model A bank s proft maxmzaton problem The general model A bank s proft maxmzaton problem Data.73 v

8 3.6 The econometrc model Results and dscusson Summary.87 A. Appendx..91 Bblography...94 v

9 IST OF TABES Table Page 1.1 Varable lst. Household s rsk-tolerance vared wthn a 0 to 5 scale Probt equaton explanng the decson to carry HEOC debt OS and probt two-stage estmates of HEOC debt, DHI (DHI = 0 for 4811 obs.) SS and probt two-stage estmates of credt card debt equaton for households wth HEOC debt SS and probt two-stage estmates of credt card debt equaton for households wth no HEOC debt Pattern of ndebtedness on HEOCs and credt cards Means and standard devatons of credt card and HEOC debts Utlzaton rates n credt cards for HEOC debtors Means and standard devatons of credt card and HEOC nterest rates Means of varables for credt card and HEOC debtors Means of varables for HEOC debtors and HEOC non-debtors Full nformaton maxmum lkelhood estmates of HEOC rates of nterest Full nformaton maxmum lkelhood estmates of HEOC debt Means of varables for HEOC debtors and HEOC non-debtors..63 x

10 IST OF TABES (contnued) Table Page 3.1 Varable lst Probt equaton explanng the decson to offer a credt card to a potental borrower Probt two-stage estmates of credt card rates of nterest, RCI (RCI = 0 for 1072 obs.) Probt two-stage estmates of credt card borrowng lmt, OGCIMIT (OGCIMIT = 0 for 1072 obs.) Full nformaton maxmum lkelhood estmates of credt card rates of nterest Full nformaton maxmum lkelhood estmates of credt card borrowng lmt Means of varables for credt card holders and credt card non-holders Credt report detals...90 x

11 CHAPTER 1 CHOICE OF CONSUMER INES OF CREDIT: SECURED VERSUS UNSECURED 1.1 Introducton Ths chapter of my thess addresses some of the fundamental ssues n the market for consumer lnes of credt. I focus on two man lnes of credt facng the consumers credt cards (CCs), the unsecured lne, and the secured Home Equty nes of Credt (HEOCs). My research examnes three prmary questons pertanng to these two lnes of credt. Why do consumers borrow on lnes of credt, as opposed to takng out tradtonal loans?.. What determnes the choce of ncurrng debt on CCs versus HEOCs? Why do some consumers hold debt on both CCs and HEOCs? To answer these questons I develop a theoretcal model, mplcatons of whch are emprcally tested usng the Survey of Consumer Fnances data, recognzng and correctng for the sample selecton and endogenety bas. Consumers face rsky envronments. Rsks are typcally fnanced by nsurances. Consumers hedge aganst the rsks of loss of wealth by purchasng nsurance contracts 1

12 and by payng nsurance premums. However, there are no tradtonal nsurances for fnancng many of the rsks that consumers face. There exst nsurances coverng the loss due to house fre or natural calamty or theft. However, there s no tradtonal nsurance to hedge aganst the loss of wealth due to some sudden need for home repar. Consumers usually nsure themselves through planned savngs (.e. by planned accumulaton of lqud wealth) aganst the permanent fall n ncome due to retrement and aganst the need for lqudty for tems such as college tuton payments. They are, however, unable to nsure themselves aganst the rsk of unforeseen tuton fee ncreases. Hence, there s a need to nvestgate the role that lnes of credt play n consumers rsk management n an envronment lackng tradtonal nsurances for varous rsks they face. So let me frst address the queston as to why consumers borrow on lnes of credt, as opposed to takng out tradtonal loans. Esenhauer (1994) argued that consumers use lnes of credt as nstruments of rsk management. He concluded that n an envronment of rsk together wth an mperfect nsurance market provdng full but unfar nsurance polces, consumers wll optmally keep some losses unnsured and fnance the unnsured losses by borrowng on ther lnes of credt. Hence, he argued that even f consumers have the opton to fully nsure, the presence of lnes of credt would optmally nduce them to under-nsure - for example, to buy only collson nsurance for the car and keep the car repar rsk unnsured, and to be fnanced by borrowng on lnes of credt. The absence of tradtonal nsurances for several types of consumer rsks s therefore lkely to be an equlbrum outcome. However, Esenhauer faled to ncorporate one of the man features of borrowng on lnes of credt - the repayment flexblty. Therefore, he had to rely on the restrctve 2

13 assumpton of mperfect nsurance market. I am able to show that even n the presence of full and actuarally far nsurance polces, consumers wll optmally keep some losses unnsured and borrow on ther lnes of credt to fnance the unnsured losses f the repayment schemes n lnes of credt make borrowng costs accrue at rates lower than consumers rates of dscounts. Should a loss occur, the savngs from not payng full nsurance premums and payng lnes of credt debt overtme wll outwegh the nterest cost for consumers wth suffcently hgh dscount rates. The presence of flexble lnes of credt may also replace a large part of consumers precautonary savngs, as they wll then not need to accumulate lqud wealth for nsurng aganst the so-called rany days. Snce the observed debt on lnes of credt depends, among other thngs, on the occurrence of losses, I can provde an explanaton, other than the argument of convenence use, for the absence of borrowng among holders of lnes of credt. Furthermore, my framework explans why some consumers wth lnes of credt are observed not to use them ether for borrowng or for transacton purposes, a phenomenon partcularly puzzlng n the case of HEOCs, whch nvolve upfront fxed costs. Consumers face heterogeneous envronments of rsk (e.g., rsks from day-to-day household ncome-expendture flows may be small, whle the rsks of unplanned home repars may be substantal). Wealth-ncome profles dctate the nature and magntude of the rsks consumers face. A queston that needs to be addressed n ths context s what roles do the two prmary lnes of credt, namely CCs and HEOCs, play n consumers rsk management under heterogeneous rsk envronments. In other words, I want to understand the factors that determne the choce of ncurrng debt on CCs versus 3

14 HEOCs. In order to address ths ssue, I wll analyze the key propertes of CCs and HEOCs. Propertes of CCs and HEOCs Interest costs are the only sgnfcant costs assocated wth CC borrowngs. However, n order to obtan HEOCs, consumers have to ncur several fxed costs - for example, attorney fees, collateral apprasal costs, ponts, membershp fees etc. Moreover, snce HEOC borrowngs put consumers homes n jeopardy, I postulate some varable costs over and above the nterest costs, called the costs of collateralzaton of credt. Snce HEOCs are secured by consumers homes and CCs are unsecured, the nterest costs on HEOC borrowngs are usually lower than those on CC borrowngs. Fnally, the nterest costs on loans taken on HEOCs (and not those on CCs) are ncome-taxdeductble. Consumers wegh the varous non-nterest costs of ncurrng HEOC debt aganst the benefts of low and ncome tax-deductble nterest rates. I show that for suffcently large amounts of desred debt (as determned by consumers preferences and wealthncome-rsk profles), consumers wll optmally choose HEOCs as the preferred rskfnancng nstrument, and for smaller amounts of desred ndebtedness, they wll prefer CCs. Intutvely, f substantal amounts are desred to be held on HEOCs, then the gans n utlty due to lower nterest rates and ncome tax advantages must outwegh the losses due to the varous non-nterest costs of HEOCs. Hence, consumers facng heterogeneous rsk envronments prefer to use dfferent lnes of credt for fnancng rsks of varyng magntude. For consumers who have already undertaken very large amounts 4

15 of debt on ther HEOCs, the costs of collateralzaton of credt make the motves to consoldate debt nto HEOCs very weak, and hence these consumers can be found to hold debt on both CCs and HEOCs. Therefore, ths research gves a ratonal explanaton for the observed puzzlng phenomenon of consumers holdng both types of debt. Although HEOCs have been around snce the 1980s, the medan CC balance for those wth postve balances on CCs does not show any clear declnng trend. The medan CC balance rose almost 40 percent, from $1,100 n 1992 to $1,500 n However, t remaned more or less unchanged between the years 1995 and By way of modelng the costs (other than the nterest costs) of HEOCs along wth the benefts, I not only analyze the decson to hold debt on HEOCs, but also gan nsght nto the factors hnderng the transfer of balances away from CCs and nto HEOCs. The costs of HEOCs make them unattractve for relatvely small amounts of desred ndebtedness and the non-nterest varable costs make the motves to consoldate debt nto HEOCs become weaker wth ncreased HEOC borrowngs. Therefore, I am able to provde an explanaton for the lack of a pronounced declnng trend n the CC ndebtedness despte the presence of accessble and apparently cheaper alternate lnes of credt, such as the HEOCs. Background and Prevous Research Begnnng wth Ausubel (1991), researchers began to look nto the market for consumer lnes of credt, especally nto CCs. The bulk of the lterature on CCs concentrated on answerng the queston as to why have the average CC nterest rates remaned stcky at such a hgh level. Ausubel (1991) argued that the reason for ths 5

16 downward-rgd nterest rates and the presence of supernormal profts was the falure of competton n the CC market. He partly attrbuted ths falure of competton to the myopc consumers who faled to foresee ndebtedness and nterest payments on ther outstandng balances. Brto and Hartley (1995), vrtually n response to Ausubel (1991), argued that the consumers carred hgh-nterest CC debts, not due to myopa but due to the fact that obtanng low-nterest bank loans nvolved transacton costs. Mester (1994) argued that the low-rsk borrowers who had access to low nterest collateralzed loans left the CC market. Ths made the average clent pool of the CC market rsker and thereby preventng the nterest rates from gong down. Park (1997) explaned the credt card nterest rate stckness usng the opton value nature of lnes of credt. A major emprcal paper n ths lterature put forward by Calem and Mester (1995) found evdence for consumers reluctance to search for lower rates due to hgh search costs n ths market. A more recent paper by Cargll and Wendel (1996) suggests that due to the hgh presence of convenence users, even modest search costs could keep the majorty of consumers from seekng out lower nterest rates. Gross and Souleles (2002) utlze a unque new dataset of credt card accounts to analyze how people respond to changes n credt supply. They fnd that ncreases n credt lmts generate an mmedate and sgnfcant rse n debt, consstent wth the buffer-stock models of precautonary savng, as cted n Deaton (1991), Carroll (1992), and udvgson (1999). HEOC borrowng grew from vrtually nl n 1982 to $40 bllon by By 1993, t was $110 bllon (Canner and uckett 1994); at the end of 1997, the estmated HEOC borrowng was $153 bllon (Canner, Durkn, and uckett 1998) and the most recent estmate of HEOC debt wll amount to $180 bllon. HEOCs have been seen to 6

17 be playng an ncreasngly mportant role n household s ablty to nfluence consumpton patterns (Canner and uckett 1994; DeMong and ndgren 1990). Chen and Jensen (1985) analyzed the propenstes to use HEOCs for consumpton purposes wthn the framework of lfe cycle hypothess. Ther fndngs ndcated a profle of HEOC users who were relatvely young, lved n larger households, and had lower net worths yet larger ncomes. The results, however, showed no sgnfcance wth respect to the value of the housng asset. Accordng to Eugen (1993), recent tax revsons affectng the deductblty of nterest pad, advantageous nterest rates, and ntensve marketng campagn of HEOCs have contrbuted to the dramatc ncrease n ther use. Delaney (1994) noted that wth mortgage payments vewed as a form of forced savngs, one of the largest assets accumulated by a household durng ts lfe cycle s the equty n the home. Ths accumulated equty was largely untapped as a source of fnancal flexblty untl recently. Several authors have tred to provde some explanaton for the growth n HEOC borrowng n US. Salandro and Harrson (1997) used The Survey of Consumer Fnances (1989 and 1992) to dentfy the determnants of demand for HEOCs among households possessng varous lnes of credt, other than CCs or busness lnes of credt. They found that the choce of HEOCs was nfluenced prncpally by the percentage of equty n home, ncome, net worth, age of the borrower, and credt prce. All ths research on CCs and HEOCs dd not answer a smple queston as to why use lnes of credt to borrow when the borrowers have the opton of takng out regular loans. For example, why borrow on HEOCs when there are Home Equty oans (HEs) avalable. In order to answer that queston, one needs to focus on the aspects of lnes of credt that are absent n regular loans and n ths chapter I plan to do just that. 7

18 Snce 1986, lenders have heavly promoted HEOCs. In 1986, nearly half of all large fnancal nsttutons allocated more advertsng funds to home equty accounts than to any other credt products (Canner, Fergus, and uckett 1988). One of the most mportant of all the nfluences on the growth of HEOCs has been the Tax Reform Act of Whle the 1986 Tax Reform Act called for consumer nterest deductblty to be phased out by 1991, only the $100,000 cap now lmts the nterest deductons on equty ndebtedness. Ths means that the nterest pad on HEOCs s stll partally tax deductble, whch s not the case for the nterest pad on CCs. Therefore, t was generally expected that HEOCs would arrest the growth of CC debt n the US. Authors lke Mester (1994) argued that low-rsk borrowers who have access to low nterest chargng collateralzed loans would leave the CC market. Hence for sometme, researchers have been antcpatng and argung about the transfer of balances away from CCs and nto HEOCs. However, despte general expectatons, the lterature on consumer credt has faled to explctly ncorporate the use of HEOCs as nstruments of debt consoldaton. In ths chapter, I wll model and emprcally test the effect of debt consoldaton nto HEOCs on consumers CC debt. 1.2 The theoretcal model I wll model a typcal consumer s choce of borrowng on lnes of credt as a lfetme utlty maxmzaton problem n an envronment of rsk. I consder three dfferent scenaros: 1. The consumer has only CC to borrow on 2. The consumer has only HEOC to borrow on 8

19 3. The consumer has access to both CC and HEOC et me defne the followng: U: Utlty Functon; U > 0, U < 0 W t : Wealth of the Consumer at tme perod t q: Insurance Coverage : oss ; > 0 p: The Probablty of Occurrence of the oss r C : Rate of Interest on CC r H : Rate of Interest on HEOC; r C > r H t: Income Tax Rate; 0 < t < 1 τ: Fxed Cost of Obtanng HEOC; τ > 0 δ: The Dscount Factor; 0 < δ < 1 C: Cost of Collateralzaton of Credt α: The Requred Rate of Repayment; 0 < α < 1 Before I start wth the formal optmzaton problems under my three dfferent scenaros, I need to clearly explan the envronment that the consumer s n and also spell out the assumptons I make n the process. There are two states of the world - the loss state and the no-loss state. There are also two tme perods 0 and 1. Snce I am tryng to explan borrowngs on lnes of credt, I do not consder the use of lnes of credt for transacton purposes. The phenomenon of convenence use s, therefore, not modeled n ths chapter. 9

20 Assumpton 1: The requred rate of repayment, α, s the same n HEOCs and CCs. 1 Assumpton 2: The consumer actually pays back at the rate at whch he/she s asked to. 2 Assumpton 3: C = c(d H ), 1 > c > 0 and D H s the unpad debt on HEOC. The cost of collateralzaton of credt (C) s a cost n the sense that t s costly to take a collateralzed loan as opposed to a non-collateralzed loan. Snce HEOC s secured by household s home, carryng debt on HEOC puts hs/her home at rsk. The varable C captures the cost that HEOC ndebtedness mposes by way of puttng household s home n jeopardy. Moreover, the greater s the amount owed on HEOC, the hgher s the rsk of losng the home. Hence, the cost of collateralzaton of credt s reasonably assumed to be a postve functon of the amount of unpad debt on HEOC. Assumpton 4: Insurance s actuarally far. Hence, Premum = pq. Assumpton 5: Uncertanty about the state of the world s present only n perod 0. Assumpton 6: Wealth of the consumer (W t ) s exogenously determned. The consumer has exogenously chosen the perodc wealth levels n a way that there s no gan n utlty from transferrng wealth from one perod to another. If the consumer fully nsures aganst all states of the world, then the perod 0 expected utlty s gven by V F = U(W 0 - p) and the perod 1 expected utlty s U(W 1 ). It can be shown that wthout any lnes of credt to borrow on and under actuarally far nsurance polcy, buyng full nsurance n perod 0 s n fact optmal for the consumer. Moreover, t must be emphaszed that my typcal consumer s a partally optmzng 1 Consumers are often requred to repay 2%-3% of ther outstandng balances on credt cards, HEOCs or on any other loans. 2 Ths assumpton s often true for credt cards and more often for HEOCs and mortgage loans. 10

21 consumer, choosng only the desred level of nsurance coverage (q), as opposed to a fully optmzng consumer, choosng both the nsurance coverage and the levels of wealth (W t ). A borrowng nstrument s commonly used by consumers for smoothng out consumpton across tme perods. Any loan, ncludng a lne of credt, can be used by consumers to serve the purpose of consumpton smoothng. Snce I am tryng to solate a purpose for lne of credt borrowng that a standard loan nstrument cannot capture, I consder a partally optmzng consumer nstead of a fully optmzng consumer. Another motvaton for consderng ths partally optmzng consumer behavor wll be the fact that abysmally low market rates of return are nducng almost the entre set of consumers (rrespectve of ther dscount rates) to take out some sort of loans, such as, student loans, car loans or home loans. Therefore, under the envronment of extremely low market rates of return, the queston as to why consumers borrow s almost trval. A more nterestng queston that has not been answered very satsfactorly n the lterature s that among all the varous borrowng nstruments that consumers have access to, what purpose do borrowngs on lnes of credt specally serve? So my assumpton that the consumer has already chosen the perodc wealth levels, W 0 and W 1, n a way that there s no gan n utlty from transferrng wealth from one perod to another, helps me focus on the more nterestng aspect of lne of credt borrowng, over and above t s use as a nstrument for smoothng consumpton across tme perods. 11

22 1.2.1 The choce to borrow n the presence of credt card only et me suppose that the consumer has only CC to borrow on. The consumer pays a premum pq n perod 0, rrespectve of the state of the world. Hs/her dscounted expected lfetme utlty s gven by, V C = V C C 0 + δv 1 where V C 0 = (1 - p ) U(W 0 - pq ) + p U(W 0 - pq - α ( q) ) and V C 1 = (1 - p ) U(W 1 ) + p U(W 1-1 α )( q)(1 + r ) ). ( C Havng only CC to borrow on, the consumer now faces the followng optmzaton problem: Maxmze V C w.r.t.q (1 - p ) U (W 0 - pq ) = (α - p ) U (W 0 - pq - ( q ) α ) + δ 1 α)(1 + r ) U (W 1 - (1 α )( q )(1 + ) ) (1) ( C More compactly I have, (1 - p ) U ( C N ) = (α - p ) U ( C o ) + δ ( 1 α)(1 + r ) o C U ( C ) (2) 1 where the varable C represents consumpton, subscrpts N and ndcate no-loss j and loss states and subscrpts 0 and 1 represent the tme perods. Usng equaton (2), I have U ( C U ( C N0 0 ) U ( C ) 0 C < 1 δ < = δ. ) (1 + r ) U ( C ) Equaton (2) and concavty of the utlty functon gves me, δ < δ C C 1 12 r C

23 U ( C N ) < U ( C 0 ) 0 W 0 - pq > W 0 - pq - α ( q ) α ( q ) > 0 q < (3) Hence, f δ < δ C, then I have q <. In other words, f the repayment scheme n CC makes the cost of borrowng accrue at a rate lower than consumer s rate of dscount, the consumer wll then optmally want to under-nsure n perod 0 and borrow on CC. Should a loss occur, the savngs from not payng full nsurance premums and payng CC debt overtme wll outwegh the nterest cost for a consumer whose dscount factor s lower than δ C. The desred loss state contngent CC debt, defned as D, s D 0 = (1 α)( q ) n perod 0 and s D 1 = 0 n perod 1. If D 0 > 0, then the consumer optmally wants to use CC to fnance the unnsured loss. However, n the absence of a realzed loss, CC debt wll not be observed n perod 0 even f D s postve. Therefore, a reason for the unobserved debt among CC holders can be the non-occurrence of the projected losses. Ths can provde an explanaton for the observed lack of usage of CCs for borrowng or transacton purposes among CC holders. et D C be the optmal uncondtonal debt on CC (.e. the desred CC debt, rrespectve of the state of the world and the tme perod that the consumer s n). Therefore, D C s observed f t s nonnegatve. It s possble to fnd condtons under whch the consumer wll not purchase any nsurance coverage n perod 0. For any degree of rsk averson, there exst a crtcal 0 13

24 value for δ, say δ, such that f δ δ, then the consumer does not nsure at all n perod 0. From equaton (2), I get ( p α) U ( C ) (1 ) ( ) + p U C 0 N0 δ = (4) (1 α)(1 + r ) U ( C ) where the margnal utltes n equaton (4) are evaluated at C 1 q = The choce to borrow n the presence of HEOC only Now let me suppose that the consumer now has only HEOC to borrow on. Interest payments assocated wth HEOC debt are ncome tax-deductble along wth the fact that there are fxed costs (τ) and non-nterest varable costs, called the costs of collateralzaton of credt (C). The consumer s dscounted expected lfetme utlty s now gven by, V H = V H H 0 + δv 1 where V H 0 = (1 - p ) U(W 0 - pq - τ) + p U(W 0 - pq - τ - α ( q) - c( 1 α )( q) ) and V H 1 = (1 - p ) U(W 1 - τ) + p U(W 1 - τ - ( 1 α )( q)(1 + rh (1 t)) ). Havng only HEOC to borrow on, the consumer now faces the followng optmzaton problem: Maxmze V H w.r.t.q (1 - p ) U (W 0 - pq - τ) = (α + c( 1 α) - p ) U (W 0 - pq - τ - ( q ) α - c(1 α )( q ) ) + 14

25 δ(1 - α)(1 + r H ( 1 t) ) U (W 1 - τ - (1 α )( q )(1 + rh (1 t)) ) (5) More compactly I have, (1 - p ) U ( C N ) = ( α + c ( 1 α) - p ) U ( C o ) + o δ ( 1 α)(1 + r H (1 t)) U ( C ) (6) 1 where the varable C represents consumpton, subscrpts N and ndcate no-loss j and loss states and subscrpts 0 and 1 represent the tme perods. Usng equaton (6), I have U ( C U ( C N0 0 ) (1 c) U ( C ) 0 < 1 δ < = δ ) (1 + r (1 t)) U ( C ) Equaton (5) and concavty of the utlty functon gves me, δ < δ H U ( C N ) < U ( C o ) o H 1 H. W 0 - pq - τ > W 0 - pq - τ - ( q ) α - c(1 α )( q ) ( α + c(1 α))( q ) > 0 q < (7) Hence, f δ < δ H, then I have q <. In other words, f the repayment scheme n HEOC makes the cost of borrowng accrue at a rate lower than consumer s rate of dscount, the consumer wll then optmally want to under-nsure n perod 0 and borrow on HEOC. Should a loss occur, the savngs from not payng full nsurance premums and payng HEOC debt overtme wll outwegh the nterest cost for a consumer whose dscount factor s lower than δ H. The desred loss state contngent HEOC debt, defned as D, 15

26 s D = (1 α)( q ) n perod 0 and s 0 D 1 = 0 n perod 1. If D 0 > 0, then the consumer optmally wants to use HEOC to fnance the unnsured loss. However, n the absence of a realzed loss, HEOC debt wll not be observed n perod 0 even f D s postve. Hence, a reason for the observed lack of usage among HEOC holders can be 0 the non-occurrence of the projected losses. Smlarly, let D H be the optmal uncondtonal debt on HEOC (.e. the desred HEOC debt, rrespectve of the state of the world and the tme perod that the consumer s n). Therefore, D H s observed f t s non-negatve. It s agan possble to fnd condtons under whch the consumer wll not purchase any nsurance coverage n perod 0. For any degree of rsk averson, there exst a crtcal value for δ, say δ, such that f δ δ, then the consumer does not nsure at all n perod 0. From equaton (6), I get ( p α c(1 α)) U ( C ) (1 ) ( ) + p U C 0 N0 δ = (8) (1 α)(1 + r (1 t)) U ( C ) where the margnal utltes n equaton (8) are evaluated at H 1 q = The choce to borrow n the presence of credt card and HEOC et me fnally address the choce of ncurrng debt when the consumer has access to both CCs and HEOCs. The dscounted expected lfetme utlty from not obtanng a HEOC and potentally borrowng D 0 = (1 - α)( q) on CC s gven by V C = V C 0 + δv C 1. For D 0 = 0, I have V C = U(W 0 - p) + δu(w 1 ). 16

27 The dscounted expected lfetme utlty from potentally borrowng D 0 on HEOC only s gven by V H = V H 0 + δv H 1. For D 0 = 0, I have V H = U(W 0 - p - τ) + δu(w 1 - τ). Hence, τ > 0 and for D 0 = 0, I have, V H V C < 0. et me draw upon the followng condton that realstcally represents the stuaton for a consumer wth access to both types of lnes of credt: Condton 1: V H V C s a strctly ncreasng functon of D 0. Ths s equvalent to requrng the followng: ( α C C α H ) U ( C0 ) + δ (1 + rc ) U ( C1 ) > ( + c) U ( C0 ) + δ[1 + rh (1 t)] U ( C (1 α) (1 α) 1 where C C α 0 = W 0 - pq - D0, 1 α C C 1 = W 1 - D (1 + r )), 0 C H ), C H α 0 = W 0 - pq - τ - D0 1 α - cd 0, C H 1 = W 1 - τ - D (1 + rh (1 )). 0 t Now suppose that the consumer has both CC and HEOC at hs/her dsposal, then the new dscounted expected lfetme utlty from potentally borrowng D 0 s V B = V B B 0 + δv 1 where V B 0 = (1 - p ) U(W 0 - pq - τ) + 17

28 p U(W 0 - pq - τ - α ( 1 α) C D 0 - α ( 1 α) H D 0 - H cd 0 ) and V B C H 1 = (1 - p ) U(W 1 - τ) + p U(W 1 - τ - D (1 + r ) - D (1 + r (1 )) ) 0 C 0 H t where D C 0 s the CC debt, D H 0 s the HEOC debt and D C 0 + D H 0 = D 0. I now consder a typcal consumer s behavor under the scenaro where he/she has both CC and HEOC at hs/her dsposal. et D 0 H, such that, D D 0 H 0, I B B ( V ) ( V ) have 0. H C D D 0 0 In other words, for a consumer wth both CC and HEOC taken out and wth relatvely small desred HEOC debt, transferrng balances away from CC and nto HEOC does not reduce utlty. Moreover, let D H > D > D, I B B ( V ) ( V ) have < 0, whch means that for extremely large desred HEOC debt, the H C D D 0 0 rsk of losng the home and therefore the cost of collateralzaton of credt s so hgh that consumer loses, n terms of utlty, by consoldatng debt nto HEOC. The consumer behavor descrbed n ths paragraph can be summarzed by the followng condton: 0 Condton 2: ( V D B H 0 ) ( V D B C 0 ) s a strctly decreasng functon of D 0 H that ntersects the D H 0 -axs at D (> D ). Ths bols down to requrng the followng: ( α c + c) U ( C0 ) < δ[ rc rh (1 t)][1 + rh (1 t)] U ( C ), where (1 α) 1 C 0 = W 0 - pq - τ - α ( 1 α) C D 0 - α ( 1 α) H D 0 - H cd 0 and C H C 1 = W 1 - τ - D (1 + r ) - D (1 + r (1 )). 0 C 0 H t 18

29 From the foregong analyss of consumer s choce under the three dfferent scenaros, and gven my assumptons and condtons, I have the followng results: a. D 0 > 0, f δ < δ C, b. D > 0, such that V H V C = 0, c. For D 0 < D, I have V H V C < 0, d. For D 0 > D, I have V H V C > 0 and e. For D 0 > D > D, I have V B > C H D0 = D0 D, D0 = D V H. The consumer desres to under-nsure and borrow on lnes of credt n the frst place, f he/she s suffcently mpatent (.e. f δ < δ C ). For a consumer wth both CC and HEOC at hs/her dsposal and wth relatvely small desred debt (.e. D D ), balance transfer away from hgh-nterest CC and nto HEOC s benefcal. However, the costs of HEOC prevent the consumer from usng HEOC for very small amount of desred debt (.e. for D 0 < D ). Only f the desred debt level exceeds D, t makes sense for the consumer to want to borrow on a HEOC. Fnally, for extremely large desred debt level (.e. for D 0 > D > D ), the rsk of losng the home and therefore the cost of collateralzaton of credt s so hgh that debt consoldaton nto HEOC makes the consumer worse off and hence I fnd the consumer nduced to carry debt on both CC and HEOC. 0 19

30 1.3 Data The data used n ths study s a pooled sample of 1995 and 1998 U.S. Surveys of Consumer Fnances (SCF). SCF s a natonwde survey conducted by Natonal Opnon Research Center (NORC) on behalf of the Board of Governors of the Federal Reserve System of Unted States. These two recent waves of the SCF provde a large and rch data set on household assets, labltes, demographc characterstcs and a number of varables capturng household atttudes. In 1998, 4,305 famles were surveyed, whle n 1995 the number was 4,299. Together there were 8,604 famles n the pooled sample. The sample had 6,493 households wth at least one bank-type CC (whch was 75.46% of the total number of households n the sample) and 2,664 households carred outstandng balances on ther bank-type CC. There were 669 households wth HEOCs (whch was 7.78% of the total number of households) and 373 of these households carred outstandng balances on ther HEOCs. To adjust the asset and lablty varables to the 1998 dollars, a factor of was appled to the fgures for To adjust the famly ncome varables of 1995, I appled a factor of These are wdely used factors devsed to compare SCF fgures of 1995 and Snce my man focus n ths chapter s to model consumers choce of ncurrng debt when they have access to both CCs and HEOCs, I select a sample of 5,157 households wth postve equty n ther homes and wth at least one bank-type CC n ther possesson. As descrbed by Table 1.6, I have four types of sample members: 20

31 I. D C = D H = 0, where D C s the observed CC debt and D H s the observed HEOC debt. Accordng to the theoretcal model, I can observe ths set of data f the consumers have taken out HEOCs and yet are not carryng any debt on them ether because the losses have not occurred or because they have repad ther entre HEOC debt. I can also observe ths set of observatons f the consumers have only CCs to borrow on and they do not carry debt on them ether because the losses have not occurred or because they have repad ther entre CC debt. II. D C > 0 and D H = 0. I can observe ths set of observatons ether f the consumers only have CCs and are carryng debt on them or f they have both HEOCs and CCs and yet they are carryng debt only on ther CCs. Ths second scenaro can occur f some consumers have extremely large desred levels of debt, along wth the fact that losses have only partally realzed durng the data collecton perod. Snce the consumers are watng for the bg chunk of losses to arrve and snce at very hgh levels of desred debt consoldaton nto HEOCs are utlty reducng, I can fnd some consumers carryng balances on ther CCs despte havng zero balances on ther HEOCs. III. D C = 0 and D H > 0. I can observe ths set f the consumers are carryng debt only on ther preferred lne, the HEOCs. IV. D C > 0 and D H > 0. Ths can occur f some consumers have such extremely large levels of debt taken out on ther HEOCs that consoldatng further debt nto HEOCs s not benefcal and hence they are carryng debt on CCs and HEOCs. Table 1.7 shows that the average CC debt among households wth postve levels of CC debt s sgnfcantly less than the average HEOC debt (among HEOC debtors), mplyng that the consumers on average borrow substantal amounts on ther HEOCs. 21

32 Agan accordng to Table 1.8, an overwhelmng majorty of HEOC debtors have credt card utlzaton rates ( Debt Credt mt) to be strctly less than one, whch mples that the substantal borrowngs on HEOCs are not due the fact that consumers have reached ther CC borrowng lmts. Table 1.9 supports the fact that the average rate of nterest on the collateralzed HEOCs s less than that on the non-collateralzed CCs. Fnally, Tables 1.10 and 1.11 compare the average consumer profles of CC debtors, HEOC debtors and HEOC nondebtors. 1.4 The econometrc model The consumer s dscounted expected lfetme utlty from potentally carryng amount of CC debt n perod 0, s gven by where V C = V 0 C + δv 1 C D 0 V 0 C = (1 - p ) U(W 0 - pq ) + p U(W 0 - pq - α α (1 D0 ) and ) V 1 C = (1 - p ) U(W 1 ) + p U(W 1 - ( 1+ ) D ). r C 0 Hence, I have the desred perod 0 CC debt as, 22 D 0 = G (W 0, W 1, r C, α, p, δ), and also the optmal uncondtonal CC debt as, D C = g (W 0, W 1, r C, α, p, δ). et D C denote the optmal uncondtonal CC debt for household. Therefore I have, D C = g (W 0, W 1, r C, α, p, δ ). carryng Agan, the consumer s dscounted expected lfetme utlty from potentally D 0 amount of HEOC debt n perod 0, s gven by

33 V H = V 0 H + δv 1 H where V 0 H = (1 - p ) U(W 0 - pq - τ) + p U(W 0 - pq - τ - α α (1 D ) 0 - cd 0 ) and V 1 H = (1 - p ) U(W 1 - τ) + p U(W 1 - τ - ( 1+ r H (1 t)) D ). 0 Hence, I have the desred HEOC debt to be, D 0 = H (τ, c, t, r H, W 0, W 1, α, p, δ), and the optmal uncondtonal HEOC debt for household as, D H = h (τ, c, t, r H, W 0, W 1, α, p, δ ). At D 0 = D, I have V H V C = 0; therefore the cutoff debt level D s a functon of all the varables n the model,.e. D = f (τ, c, t, r H, W 0, W 1, α, p, δ, r C ). Smlarly, the cutoff level of debt for household s gven by D = f (τ, c, t, r H, W 0, W 1, α, p, δ, r C ). Implcatons from the Theoretcal Model 1. HEOC debt for household (D H ) s observed f t s greater than the cutoff level of debt D. 2. For household, the margnal gan from consoldatng debt away from credt cards and nto HEOCs s non-negatve for all debt combned levels less than D, that s I have, B C H B C H [ V ( D, D )] [ V ( D, D )] H C 0, & 0 D H C + D D D D. 23

34 Snce all the households n the sample have at least one bank-type CC, neglgble (ε) costs of obtanng CCs wll guarantee that for all households n the sample the desred perod 0 CC debt, D 0 > 0 and hence the optmal uncondtonal CC debt, D C 0. Hence wthn my sample, I have the observed CC debt, D C = D C. The motve to consoldate debt nto HEOCs s lkely to make the observed sample of CC debt to be non-random. Followng testable Implcaton 2, I expect the observed CC debt to be negatvely nfluenced by HEOC ndebtedness. Ths observatonal dfference must be captured by two dfferent CC debt equatons. The endogenous varable, D H, should defne whch of the two CC debt equatons s relevant for household. Therefore, debt consoldaton motve brngs n smultanety n consumer s choce of debt. I need to account for ths smultanety n my econometrc model. Moreover, followng testable Implcaton 1, I expect the household to decde to borrow on HEOCs f the desred HEOC debt (D H ) s greater than the threshold level D. Hence, my econometrc model has to ncorporate ths selecton process nto the estmaton as well. Fnally, owng to the cross-sectonal nature of my data set, I use the perod 0 wealth (W 0 ) and the perod 1 wealth level (W 1 ) nterchangeably for my estmaton purposes. et me assume that wthn my model the between household varaton n p s purely random. et me also assume that δ s captured by varables such as Age, Income, Household Sze, Race and Educaton evel of the household (jontly represented by vector S ). Hence δ = ϕ S + η. Among the HEOC debtors, I have the followng equaton for D C 24

35 D C = γd H + β 1 X 1 + u 1 (9) where D H s the observed HEOC debt and X 1 s a vector of exogenous varables affectng D C. C Among the HEOC non-debtors, I have yet another equaton for D D C = β 3 X 1 + u 3 (10) et me defne the followng vectors: W 0 : Equty n the Home, qud Assets, Non-House-Non-Fnancal Assets and Famly Assets (represented by the sze of the household); X 1 : W 0, r C, α, S and CC Borrowng mt F : Incdence of Mortgage Debt, Debt Repayment Frequency and Mortgage Rate of Interest The margnal cost of collateralzaton of credt, c, s consdered to be a functon of the ndvdual s rsk-type. I have the dummy defnng the ncdence of delnquency, the dummes capturng household s atttude towards rsk and α (jontly represented by vector Rsk ) explanng household s rsk-type. The dummy varable whch determnes whether household temzes taxdeductons or not, and household ncome (jontly represented by vector T ) capture the ncome-tax rates (t ). The fxed costs of obtanng HEOCs (τ ) have no varaton across households,.e. I have τ = τ. Therefore, the fxed costs go nto the constant terms of the HEOC and the reservaton debt equatons. Moreover, equty n the home (HOMEQUITY), the rsk-type (captured by vector Rsk ) and other household characterstcs (F ) descrbe r H. Thus I have 25

36 c = α 0 + α 1 Rsk + ε 1, t = α 2 + α 3 T + ε 2 and r H = α 4 + α 5 HOMEQUITY + α 6 Rsk + α 7 F + ε 3. Substtutng for c, t, τ, δ and r H nto D H ; usng W 0, α and mposng the assumpton of randomness on p, I have a reduced form equaton for D H D H = β 2 X 2 + u 2 (11) where X 2 s a vector of exogenous varables nfluencng D H. Wth smlar substtutons and assumpton of randomness mposed on p, I have yet another reduced form equaton for D D = β 4 X 4 + u 4 (12) where X 4 s a vector of all the exogenous varables n my model. The HEOC debt s observed f D H > for HEOC debt to be, I = D H - D = β 2 X 2 - β 4 X 4 + u 2 - u 4 D. Therefore, let me defne the choce functon = δ Z - u. (13) Therefore, my econometrc model s gven by D D C H = γd = D H H ' + β X 1 1 ' = β X u 1 + u 2 f I >0 D D H C = 0 ' = β X u 3 otherwse where u 1, u 2, u 3 and u follow Multvarate Normal wth means zero, varances σ 1 2, σ 2 2, σ 3 2 and 1 and correlaton coeffcents ρ 12, ρ 13, ρ 1u, ρ 23, ρ 2u and ρ 3u respectvely. If X 2 26

37 contans at least one varable that s not ncluded n X 1, then all the parameters of the model are dentfed. Snce HEOC s a secured borrowng nstrument and t has exclusve features such as tax-deductblty of nterest rates, the varables capturng these propertes, such as c and t, provde the necessary varables for dentfyng the parameters of my model. In order to correct for the endogenety present n the CC debt equaton of HEOC borrowers, I use the estmated HEOC debt Dˆ H as an nstrument. The above econometrc model s estmated by probt two-stage method. ee et al. (1980) descrbe the estmaton procedure. In my model, I s not observed. All I observe s I = 1 f household carres HEOC debt (.e. f I > 0) = 0 otherwse. et me assume that there are N 1 observatons for whch I = 1 and N 2 observatons for whch I = 0, so that the total sample sze s N = N 1 + N 2. et me defne φ = φ(δ Z ) and Φ = Φ(δ Z ), where = 1, 2..N, φ s the standard normal densty and Φ s the cumulatve normal. Snce E(u 2 I = 1) = - σ 2u φ, Φ I can wrte equaton (11) as D H = β 2 X 2 - σ 2u φ Φ + µ 2 where E(µ 2 ) = 0 and σ 2u = Cov(u 2, u). 27

38 I frst estmate δ by probt maxmum lkelhood (.e. I get δˆ ). Then I estmate D H = β 2 X 2 - σ 2u ˆ φ + µ 2 Φˆ by ordnary least squares. Here φˆ and Φˆ are φ and Φ wth δˆ substtuted for δ. I can smlarly estmate the reduced form parameters n equaton (10). I have D C = β 3 X 1 + σ 3u where σ 3u = Cov(u 3, u). ˆ φ 1 Φˆ + µ 3 The structural equaton correspondng to I = 1 s gven by Snce D C = γd H + β 1 X 1 + u 1. E(u 1 I = 1) = - σ 1u φ, Φ I can wrte equaton (9) as D C = γd H + β 1 X 1 - σ 1u φ Φ + µ 1 where E(µ 1 ) = 0 and σ 1u = Cov(u 1, u). I estmate, D C H φˆ = γ Dˆ + β 1 X 1 - σ 1u Φˆ + µ 1 by ordnary least squares, where ˆ H φ Dˆ = ˆβ 2 X 2 - ˆ σ 2 u. Φˆ 28

39 VARIABES TYPE EXPANATION DHI CONTINUOUS HEOC Debt HEOC Rate of Interest (Maxmum Interest rate RHI CONTINUOUS charged among the dfferent HEOCs taken out by the household) DCI CONTINUOUS CC Debt RCI CONTINUOUS CC Rate of Interest HOMEQUITY CONTINUOUS Equty n Home IQUIDASSET CONTINUOUS qud Assets NHNFINASSET CONTINUOUS Non-House-Non-Fnancal Assets 1 Itemze Income Tax Deductons ITEMIZE BINARY 0 Otherwse 1 Got behnd n payments by two months or more DEINQUENCY BINARY 0 Otherwse CREDITIMIT CONTINUOUS CC Borrowng mt INCOME CONTINUOUS Income APHAI The Requred Rate of Repayment (Fracton of CONTINUOUS HEOC and Mortgage Debt Repad) HOUSEHODSIZE CONTINUOUS Household Sze 1 Household Has Some Knd of Mortgage Debt MORTGAGE BINARY 0 Otherwse RISK1 1 Above Average Rsk-Taker BINARY 0 Otherwse 1 Average Rsk-Taker RISK2 BINARY 0 Otherwse 1 No Rsk-Taker RISK3 BINARY 0 Otherwse Mortgage Interest Rate (Maxmum Interest Rate MORTGAGERATE CONTINUOUS charged among the dfferent mortgage loans taken out by the household) AGE CONTINUOUS Age of the Household SCHOO CONTINUOUS Years of Schoolng of the Household 1 Race s Non-Whte NONWHITE BINARY 0 Otherwse 0 No or Flexble Repayment Requred 1 ess Frequent Than Monthly Repayment Requred 2 Monthly Repayment Requred REPAYMENTFREQ CATEGORICA 3 More Frequent Than Monthly Repayment Requred (Maxmum of the Repayment Frequency on HEOC and Mortgage Debt) Table 1.1: Varable st. Household s rsk-tolerance vared wthn a 1 to 4 scale. 29

40 Snce all the second stage estmatons use some sort of estmated varables as regressors, the asymptotc covarance matrces of the second stage ordnary least squares estmators requre some correctons. See ee et. al. (1980) for the dervatons of the asymptotc covarance matrces of probt two-stage estmators. 1.5 Results and dscusson Table 1.1 presents the defntons of the varables used n the econometrc analyses. Table 1.2 shows the results of a probt equaton explanng the decson to hold HEOC debt. The Equty n Home (HOMEQUITY) and the Household Sze varable (HOUSEHODSIZE) postvely nfluence the choce to hold HEOC debt. However, ncome of the household (INCOME), household s lqud asset (IQUIDASSET) and Non-House-Non-Fnancal Asset (NHNFINASSET) have a negatve mpact on the HEOC debt holdng decson because such households have less need to resort to borrowng n the face of an unnsured loss. I have some support for Mester s (1994) hypothess that relatvely low-default-rsk borrowers self-select themselves as HEOC debtors. The predcted sgn for the parameter correspondng to DEINQUENCY s negatve. However, the predcted sgn for the parameter correspondng to RISK1 varable s postve and that for RISK3 s negatve, whch mples that HEOC borrowng becomes less attractve as borrowers become more rsk averse. Further, the taxdeductblty ncentve plays some role as I fnd that the predcted sgn for ITEMIZE to be postve. The credt card borrowng lmt (CREDITIMIT) has a sgnfcant postve nfluence on the choce of holdng HEOC debt. The demographc varables such as 30

41 Varables Coeffcent S.E CONSTANT HOMEQUITY IQUIDASSET NHNFINASSET HOUSEHODSIZE RISK1 RISK3 DEINQUENCY INCOME ITEMIZE APHAI MORTGAGERATE REPAYMENTFREQ MORTGAGE RCI AGE NONWHITE SCHOO CREDITIMIT Table 1.2: Probt equaton explanng the decson to carry HEOC debt. 3 3 Refer to page 29 for the defntons of the varables used n the table. I have, - Sgnfcant at 1% evel; - Sgnfcant at 5% evel; - Sgnfcant at 10% evel. 31

42 Varables CONSTANT HOMEQUITY IQUIDASSET NHNFINASSET HOUSEHODSIZE RISK1 RISK3 DEINQUENCY INCOME ITEMIZE APHAI MORTGAGERATE REPAYMENTFREQ MORTGAGE AGE NONWHITE SCHOO AMBDA + OS Probt Two-Stage Coeffcent S.E. Coeffcent S.E R 2 = F-value =14.88 N = 346 R 2 = 0.39 F-value =13.97 σ 2 = N = 346 Table 1.3: OS and probt two-stage estmates of HEOC debt, DHI (DHI = 0 for 4811 obs.). 4 4 Refer to page 29 for the defntons of the varables used n the table. I have, - Sgnfcant at 1% evel; ˆ φ - Sgnfcant at 5% evel; - Sgnfcant at 10% evel; + AMBDA =. Φˆ 32

43 AGE and SCHOO also have sgnfcantly postve effect on the decson to borrow on HEOC. Fnally, the debt repayment frequency (REPAYMENTFREQ) has a sgnfcant postve nfluence, whle the exstence of mortgage debt (MORTGAGE) and the credt card nterest rate (RCI) have a sgnfcant negatve nfluence on HEOC debt-holdng decson. Table 1.3 presents the results for OS and probt two-stage regressons for HEOC debt. The OS equaton s gven only for the sake of comparson; t s not the correct procedure to use. The varables capturng household wealth all have postve mpact on the volume of HEOC debt carred by the household. Agan, among the set of HEOC debtors the relatvely rsk-lovng ones carry more debt. Ths s supported by the fact that the predcted sgn for RISK1 s postve. Household Income (INCOME) has a negatve estmated sgn n the HEOC debt equaton. The estmated value of σ 2u s However, snce the estmated value of σ 2u s not sgnfcantly dfferent from zero, I conclude that there s no emprcal evdence of sample selecton n the estmates of the HEOC debt equaton. Table 1.4 presents the 2SS (for comparson) and the probt two-stage estmates for the CC debt equaton for ndvduals wth HEOC debt. The household wealth varables have the usual postve predcted sgns. The CC rate of nterest has an nsgnfcant, but postve estmated nfluence on the volume of CC debt. An explanaton for ths unusual sgn s that for credt card debtors wth HEOC to borrow on, the debt consoldaton motve (captured by the HEOC debt) makes the effect of credt card nterest rate on household s credt card debt rrelevant. Household Income (INCOME) has the usual negatve coeffcent and among the demographc varable only the race 33

44 2SS Probt Two-Stage Varables Coeffcent S.E. Coeffcent S.E. CONSTANT HOMEQUITY IQUIDASSET NHNFINASSET HOUSEHODSIZE RCI APHAI INCOME AGE NONWHITE SCHOO CREDITIMIT DHI AMBDA og = N = 346 -og = σ 1 = N = 346 Table 1.4: 2SS and probt two-stage estmates of credt card debt equaton for households wth HEOC debt. 5 5 Refer to page 29 for the defntons of the varables used n the table. I have, - Sgnfcant at 1% evel; ˆ φ - Sgnfcant at 5% evel; - Sgnfcant at 10% evel; + AMBDA =. Φˆ 34