Credit card holding: A microeconomic perspective for the case of Italian households

Transcription

1 Credt card holdng: A mcroeconomc perspectve for the case of Italan households Angel Garca* Unversty of Sena PhD Programme n Economcs Mcroeconometrc Applcatons Abstract Ths paper provdes a smple mcroeconomc evaluaton of the determnants of credt card holdng n Italy. Usng a Probt model, the analyss mostly concentrates on the demand sde of the credt card market. Thus, the focus has been on dentfyng specfc ndvdual characterstcs of Italan households, whch show to be statstcally sgnfcant for determnng the probablty of possessng a credt card. The data has been entrely collected from the Survey of Italan households Income and Wealth Relevant expected results are derved from ths study. In the frst place, the probablty of holdng a credt card s shown to move up wth ncreases n average famly ncome perceptons, although further ncreases to hgher levels of ncome show weak dmnshng returns captured by a negatve quadratc assocaton ncluded n the estmaton. Secondly, the age of the head of household s also shown to be a postve determnant even though decreasng returns are as well sgnfcant when the age squared value s consdered. Addtonally, dscrete varables such as geographc locaton, precsely, not lvng n the south or slands of Italy, basc and unversty-level educaton, ownng a vehcle, beng marred and formally employed are postvely related to a hgher probablty of possessng a credt card. Unexpectedly, havng a fulltme job seems to be negatvely related to the same probablty. Regardng, gender not much can be formally stated snce even though the coeffcent shows a negatve relaton, t s statstcally nsgnfcant. Partcularly, at mean values of the sample dstrbuton, the probablty of holdng a credt card manly ncreases wth basc educaton n 17%, unversty level educaton n 38%, and ownershp of a vehcle n 11%. Equvalently, decreases assocated to dscrete varables are manly drven by southern household locaton n around <14>%, and, unexpectedly by, fulltme workng n <5>%. * emal: garca@uns.t

2 2 TABLE OF CONTENTS 1. INTRODUCTION CREDIT CARDS IN ITALY ON CREDIT AND BEHAVIOURAL SCORING DESCRIPTION OF SAMPLE DATA THE PROBIT MODEL A PROBIT MODEL ON CREDIT CARD HOLDING RESULTS CONCLUSION

3 3 1. INTRODUCTION Money and means of exchange have always evolved over tme. Startng from the most prmtve forms of money lke pearls, salt, cattle, gran, precous metals and others to the most sophstcated and modern forms such lke checks, credt and debt cards, e-chps, electronc payments, and others, the payment system has always been facng a contnuous process of transformatons whch have manly been culturally, governmentally, and technologcally-drven. Regardless of the nterests of the natonal states n the use of a legal tender, or natonal currency subject to segnorage, the prvate bankng ndustry worldwde has been ncreasngly profcent n offerng alternatve means of payment, although stll denomnated n natonal currences. Thus, a great number of modern nstruments of payment have ncreasngly been assocated wth prvate credt nstruments, that s, wth fnancal nstruments that not only serve as a means of payment, but also represent a form of credt or n-advance expendture. Precsely, two of the most popular nstruments of payment nowadays are credt and debt cards. Frst credt cards were ntroduced n 1951 by Dners Club, but were only wdely spread untl the standards for magnetc strps were establshed around year Smultaneously, durng the same perod, the concdence wth the end of the Bretton Woods system, the lberalsaton of captal accounts, the development of off-shore bank busnesses, the deregulaton of bankng systems, and the new generaton of technology whch allowed for the storage of monetary value on slcon chps, explan, to a great extent, the dssemnaton of credt and debt cards durng the last decades of the past mllennum. However, abstractng from macroeconomc and technologcal aspects, some of whch have been prevously mentoned, natonal and nternatonal credt card systems have been wdely growng also due to a varety of mcroeconomc reasons. From the vewpont of the bankng ndustry (suppler), t represents a proftable busness provded that banks obtan net revenues from both, ssung funds, chargng merchant dscount fees, annual fees to cardholders, and n the case of revolvng credt, by mposng an nterest rate on the monthly due amount 1. From the pont of vew of cardholders (consumers), a credt card allows for the purchase of all knds of goods n a growng number of establshments, wthout havng to mmedately debt bank accounts through the use of 1 Revolvng credt represents the case of cardholders who usually roll-over credt card balances over month to month wthout ever payng n full, or at least, durng a relatvely long perod of tme.

4 4 checks or cash wthdrawals. In the case of revolvng credt, credt cards also allow consumers to fnance ther expendtures over a medum-term horzon. In short, even though credt cards nvolve the addton of an ntermedary, they undoubtedly ncrease the effcency of exchange. Ths paper provdes a smple mcroeconomc evaluaton of the determnants of credt card holdng n Italy. Usng a Probt model, the analyss mostly concentrates on the demand sde of the credt card market. Thus, the focus has been on dentfyng specfc ndvdual characterstcs of Italan households, whch show to be statstcally sgnfcant for determnng the probablty of possessng a credt card. The data has been entrely collected from the Survey of Italan households Income and Wealth Relevant expected results are derved from ths study. Frst of all, the probablty of holdng a credt card s shown to move up wth ncreases above average famly ncome, although further ncreases to hgher levels of ncome show weak dmnshng returns captured by a negatve quadratc assocaton ncluded n the estmaton. Secondly, the age of the head of household s also shown to be a postve determnant even though decreasng returns are as well sgnfcant when the age squared value s consdered. Addtonally, varables such as geographc locaton, precsely not lvng n the south or slands of Italy, basc and unversty-level educaton, ownng a vehcle, beng marred and formally employed are postvely related to a hgher probablty of possessng a credt card. Unexpectedly, havng a full-tme job seems to be negatvely related to the prevously mentoned probablty. Regardng, gender not much can be formally stated snce even though the coeffcent shows a negatve relaton for the case of women such coeffcent s statstcally nsgnfcant. The paper s structured as follows. Next secton brefly descrbes the profle of the credt card busness n Italy. The thrd secton comments, n bref, on the lterature revew regardng credt and behavoural scorng. The fourth secton ponts out certan aspects about the management of the data. The ffth ntroduces the Probt model. The followng secton presents the results, and the fnal offers some conclusons. 2. CREDIT CARDS IN ITALY Ardzz (2003) ndcates that at least 590 mllon card payment operatons took place durng year 2000 n Italy, from whch 46% were made by credt cards. Card transactons average around 10 per capta n a year, whch s ndeed low n comparson to many other developed countres.

5 5 Table Nro 1 summarses the market power dstrbuton n the credt card busness n Italy at the begnnng of the new mllennum. It shows that CartaSì s the leadng credt card company n both the ssung market and the acqurng market 2. The table also shows that BankAmercard represents the second most spread credt card n both the ssung and acqurng busnesses, whle Amex, Topcard, Moneta, Dners and others control only a mnor part of both markets. In short, two credt card companes control over half of both the ssung and the acqurng market. Table Nro 1: Credt Card Market Share n Italy as of year 2000 CREDIT CARD Issuer ISSUING MARKET % of value transacted ACQUIRING MARKET % transactons at Pont of Sale termnals CartaSì BankAmercard Amex 9 13 TopCard 5 2 Moneta 6 9 Dners 3 5 Other cards Source: Bank of Italy. One major evdent observaton by Ardzz (2003) s the fact that the majorty of the credt cards ssued n Italy work as charge cards. That s, most of the credt card contracts n Italy are establshed under condtons whch allow, at most, for a one-month payment delay before the bank proceeds to debt the credt cardholder s bank account. Ths mples that most credt card agreements n Italy do not actually nvolve consumer credt operatons, at least for over 60-day perods. Indeed, most credt card contracts n Italy nclude a drect debt pre-authorzaton, and therefore, nvolve no nterest rate payment by the cardholder. Thus, the Italan credt card busness 2 A bank or a credt card company acts as an acqurer when t accepts and receves electronc funds from a dfferent credt card company (ssuer) through ts own termnals or Pont of Sale (POS) network avalable at dfferent commercal establshments.

6 6 seems to be concentrated n the proftablty from mposng merchant dscount fees, rather than n the expanson of credt, consumer lendng, or revolvng credt per se ON CREDIT AND BEHAVIOURAL SCORING Durand (1941) s the frst to mplement statstcal study technques to dscrmnate among good and bad loans. Hs orgnal research worked as a spark lght for the development of future prvate credt analyss n both, the area of fnancal behavoural and credt scorng. Precsely, regardng the notons of credt and behavoural scorng, Thomas (2000) refers to t as an applcaton of fnancal rsk forecastng to consumer lendng. He ponts out that adults n the UK or US are contnuously beng credt scored or behavour scored at least once a week as the annual reports of the credt bureaux of both countres reveal. Thomas ndcates that the fact that most people are unaware of ths does not dmnsh the relevance and mplcatons of theses practces 4. Precsely, credt scorng and behavour scorng are methods whch allow organsatons decde whether or not to grant a credt to consumers who ask for t. Specfcally, whle credt scorng refers to a technque whch allows lendng frms to decde whether or not to grant a credt to a new applcant, behavour scorng s a method whch allows organsatons to take decsons on how to deal wth exstng customers from the vewpont of credt lmt extensons, marketng, payment collecton, and others. In general, as Thomas (2000) ponts out, credt scorng s a way of dscrmnatng among dfferent groups n a gven populaton when t s not smple to see the characterstcs that separate groups but only the related ones. The Probt model estmaton carred out throughout ths paper attempts to contrbute wthn ths framework as t searches for statstcally sgnfcant assocatons of ndvdual characterstcs of Italan households wth the probablty of possessng a credt card. The followng secton brefly descrbes the data used for the estmaton. 3 Thus, contrarly to the experence of other developed countres, the fact that most credt card agreements n Italy do not mply medum-term consumer lendng restrcts the profts from the ssung busness to the benefts from chargng merchant dscount fees to commercal establshments. 4 Those readers nterested n the lterature on credt scorng and behavour scorng may consult Rosenberg & Glet (1994); Hand & Henley (1997); Thomas, 1992, 1998, 2000.

7 7 4. DESCRIPTION OF SAMPLE DATA The data, whch, as prevously mentoned, has been entrely obtaned from the Survey of Italan households Income and Wealth 2002 (SHIW) has been transformed to generate the desred varables for the Probt estmaton. The survey s electroncally avalable at the Bank of Italy s web page 5 and collects 8,011 households nvolvng 22,148 ndvduals from whom 13,536 are ncome-earners 6. Specfcally, the varables used n ths paper are the followng: CARTA, employed to generate a dummy varable renamed as CARD, takng the value of 1 for those households from whch at least one member possesses a credt card and 0 for others; Y, renamed as YFAMILY, standng for famly ncome; AREA3, correspondng to the geographcal area and transformed n order to dfferentate among those households whch belong to the SOUTH of Italy (value of 1) and those whch do not (value of 0); ANASC, whch s related to the year of brth of the famly members, and has been used to compute the AGE of the head of household 7 ; SEX, whch s self-explaned and has been renamed as SEXFEM takng the value of 1 for women and 0 for men. Addtonally the varable STUDIO, whch n the orgnal SHIW takes dfferent values accordng to the schoolng level of the head of household, has been used to generate two dummy varables: BASICSECEDU and UNIVEDU. The frst varable takes the value of 1 when the head of household has reached up to basc or hgh-school educaton, and the second one takes the value of 1 when undergraduate or postgraduate level-educaton has been completed. Fnally, both varables smultaneously take the value of 0 when the head of household has not completed even a basc schoolng level. Furthermore, the varable APQUAL, whch has been used as a reference for the work status of the head of household, and takes a varety of values for employees, self-employed and not employed ndvduals, has been compacted nto one dummy varable n order to account for beng EMPLOYED (value of 1) or not (value of 0). The varable PARTIME has also been used and renamed as FULLTIME evdently n order to capture when the head of household has a fulltme job (value of 1) and when not (value of 0) It s mportant to keep n mnd that provded the samplng structure s composed by dfferent stratum dvsons, the SHIW ncorporates a weghtng at household level n order to obtan unbased estmates. 7 In the SHIW, the head of household s defned as the major ncome earner.

8 8 Addtonally, the varable STACIV whch orgnally consders 4 dfferent cvl status, 1 for marred, 2 for sngle, 3 for separated/dvorced, and 4 wdow/wdower, has been compacted nto a sngle dummy, namely MARRIED, whch takes the value of 1 when the cvl status corresponds to marred, and 0 when not. Fnally, the varable JWDURAT1 whch represents an estmated monetary value of the means of transport possessed by the household, was used n order to generate a dummy varable, named VEHICLE, takng the value of 1 when JWDURAT1 s found to be postve (assumed to be when the household owns a means of transport), and 0 when not. As prevously mentoned n the Introducton, the squared values of the famly ncome and the age of the head of household have been computed (YFAMILYSQ and AGESQ) n order to account for probably sgnfcant dmnshng returns. Fnally, the justfcaton for workng at a household level, nstead of at the ndvdual level, s that the most relevant data, precsely that regardng the possesson of a credt card (CARTA), s assocated wth the household unt, nstead of wth a specfc member of t 8. Varable Table Nro 2: Man Descrptve Statstcs Number of Obs. Mean Value (% Yes) Std. Dev. Mn Value Max Value Answers Dd not answer Yes No CARD 6,853 28% ,911 4,942 1,158 YFAMILY 8,011 28,229 22, ,248 n/a n/a n/a YFAMILYSQ 8,011 unnterestng unnterestng 0 unnterestng n/a n/a n/a AGE 8, n/a n/a n/a AGESQ 8,011 unnterestng unnterestng 36 unnterestng n/a n/a n/a SOUTH 8,011 33% ,665 5,346 0 BASICSECEDU 8,011 56% ,511 3,500 0 UNIVEDU 8,011 9% ,277 0 EMPLOYED 8,011 54% ,362 3,649 0 FULLTIME 8,011 41% ,249 4,762 0 VEHICLE 8,011 32% ,558 5,453 0 MARRIED 8,011 62% ,989 3,022 0 SEXFEM 8,011 30% ,411 5,600 0 Source: SHIW Specfcally, the queston from the SHIW 2002 was as follows: In 2002 dd you or another member of your household possess at least one credt card for household expendture (whch can be used to make payments n hotels, restaurants and shops, etc.)?

9 9 Table Nro 2 summarses the man descrptve statstcs of the varables used for the estmaton. The total number of observatons s confned to the effectve number of affrmatve and negatve answers to the queston of possessng or not a credt card. Thus, the fnal effectve number of observatons, whch s subsequently referred to as the reduced sample, s 6,853. Dummy varables have been precsely defned to take the value of 1 when an event occurs and 0 when t does not. Ths allows for nterpretng ther mean values as the percentage of all households n the whole sample sharng n common a partcular characterstc. Thus, for nstance, Table Nro 2 shows that the percentage of cardholders n the reduced sample s 28%. Equvalently, but precsely, by samplng constructon, the percentage of households belongng to the South (and slands) of Italy s exactly 33%. Regardng the level of educaton, whle the percentage of households whose head has acheved at least basc or secondary-level educaton s 56%, the percentage of households whose head has reached up to unversty level, ncludng both undergraduate and graduate degrees, s only 9%. Addtonally, whle employed head of households account for 54%, ¾ of them, that s 41% of household heads work fulltme. Only 62% of households are marred, 32% own a vehcle, and just 30% of them are lead by a woman. Wth respect to the non-dummy varables, the average household ncome per year s 28,229, and the average age of the household head s 55 years old. Precsely, Table Nro 3 reflects the cumulatve dstrbuton of Italan households ncome. It shows that for year 2002, a bt more than 50% of the households earned less than 24,000 n year Equvalently, Table Nro 4 shows that only 42% of household heads are younger than 50 years old. Table Nro 3: Household Income Dstrbuton Varable Obs. Cum % Mean Std. Dev. Mn Max Lmt 1,315 16% 8,269 2, ,000 <=12,000 4,154 52% 14,688 5, ,000 <=24,000 YFAMILY 6,038 75% 19,301 8, ,990 <=36,000 7,052 88% 22,448 11, ,994 <=48,000 7,517 94% 24,348 13, ,990 <=60,000 8, % 28,229 22, ,248

10 10 Table Nro 4: Head of household s age Varable Obs Cum % Mean Std. Dev. Mn Max Lmt 500 6% <=30 1,785 22% <=40 AGE 3,333 42% <=50 4,850 61% <=60 6,268 78% <=70 8, % THE PROBIT MODEL Probt models are meant to model the choce between two dscrete alternatves. Generally, as Verbeek (2001) ndcates, ths type of models descrbes a bnary dependent varable whch takes the value of: y 1 = 0 The probablty of choosng an opton s taken to be a functon of explanatory varables: p = P[ y = 1/ x ] = F( x β ) = 1,..., n As F( ) equals a probablty t should le n the [0,1] nterval, so t s sensble to let F be some dstrbuton functon. Thus, n the case of the Probt model the standard normal dstrbuton s assumed. That s: x F( w) = Φ( w) = β 1 1 exp x β dx 2π 0 2 Thus, the margnal effect of a change n a contnuous ndependent varable s gven by the th dervatve of the probablty that y = 1wth respect to the k element of x. That s by: Φ( x β ) = φ( x β ) β k x k f certan event or characterstc s present. f not.

11 11 Ths s precsely the man dfference wth respect to lnear models, from whch a constant margnal effect s obtaned. One reason why lnearty has been dscarded s because lnear models do not guarantee probablty estmates lyng n the [0,1] nterval. Addtonally, there are reasons mostly related to the fact that the error term from lnear probablty models tends to be hghly non-normally dstrbuted and heteroskedastc, mplyng a volaton of two of the fundamental Gaussan assumptons of classcal lnear econometrcs. However, n the partcular case of a Probt model, the lkelhood contrbuton of observaton assocated to y = 1 s precsely the probablty P { y 1/ } = x whch depends on the unknown parameter β, and equvalently for y = 0. Thus, the lkelhood functon s gven by: L N y 1 ( β ) = P{ y = 1/ x ; β} P{ y = 0/ x ; β} = 1 y Substtutng { y = 1/ x ; β} = F( x β ), and for smplcty, takng logs, the expresson s reduced to: P N log L( β ) log F( x β} + (1 y )log(1 F( x β )) (*) = N y = 1 = 1 Maxmzaton wth respect toβ yelds orthogonalty of FOC s as follows: log L β = N y Φ φ = Φ Φ x 1 (1 ) = 0 where φ = φ( x β ) s the dervatve of the dstrbuton functon (or densty functon). The generalsed resdual of the model s gven by the expresson wthn the square brackets, takng the f for y = 1 and f ( x β ) /(1 F( x β )) for = 0 value of ( x β )/ F( β ) x y. SOC s are guaranteed under non-collnearty of the ndependent varables, yeldng a negatve defnte Hessan matrx of second order dervatves, and therefore, a globally concave loglkelhood functon. Precsely the Hessan matrx s gven by: 2 log L( β ) β β N = Λ( x β )(1 Λ( x β ) x x = 1

12 A PROBIT MODEL ON CREDIT CARD HOLDING Once the fundamental theoretcal ssues regardng the use of Probt models have been revewed, the defnton of the specfc Credt card holdng Probt model for the case of Italan households s presented as follows: CARD 1 = 0 f household possesses a credt card. f not. DEPENDENT VARIABLE YFAMILY = Household s ncome. YFAMILYSQ = Household s ncome squared. SOUTH 1 = 0 f the household belongs to the south or slands of Italy. f not. AGE = Head of household s age. AGESQ = Head of household s age squared. SEXFEM 1 = 0 f the head of household s a woman. f not. BASICSECED U 1 = 0 If HH has reached up to basc or hgh-school educaton. f not. UNIEDU 1 = 0 If HH has reached up to undergraduate or postgraduate level. f not. MARRIED 1 = 0 If the household s marred. f not.

13 13 EMPLOYED 1 = 0 If the head of household s employed. f not. FULLTIME VEHICLE 1 = 0 1 = 0 If the head of household works fulltme. f not. If the household owns a vehcle. f not. 5. THE RESULTS Table Nro 5 shows the results from the Probt model. It assocates the probablty of possessng a credt card to the ndvdual characterstcs of Italan households. However, notce that, from Table Nro 5 only the sgn and statstcal sgnfcance of the coeffcents s relevant, snce as prevously mentoned, such coeffcents are not equvalent to the total margnal effect 9. Thus, the total margnal effect of a change n a contnuous varable s computed as the value of the frst dervatve of the probablty functon wth respect to the specfc ndependent varable, when the dependent equals 1 (CARD=1) and all other ndependent varables, both dscrete and contnuous, are kept fxed at a gven value (eg. at ther mean values). In the case of dummy varables, the dscrete margnal effect s computed as the dfference between the total probablty when the specfc ndependent varable takes the value of 1, and when t takes the value of 0, keepng as well as n the contnuous case, all other ndependent varables (dscrete and contnuous) fxed at a gven value (eg. at ther mean values). Despte of the prevous observatons, Table Nro 5 s stll relevant as t ndcates the presence of sgnfcant assocatons between the dependent varable, namely the households probablty of havng a credt card, and all ndependent varables, but one. The unque statstcally nsgnfcant assocaton refers to the specfc gender of the head of household (SEXFEM) whch, even though s of negatve sgn as mght have been expected, seems not to be suffcently relevant n statstcal terms for the determnaton of household s credt card holdng n Italy. 9 Recall that n the Probt model, the total margnal effect of a change n a contnuous varable s gven by: Φ( x β ) = φ( x β ) β k x k

14 14 Moreover, Table Nro 5 reflects a postve assocaton between the households probablty of possessng a credt card and the level of ncome of the partcular household (YFAMILY). Addtonally, t shows a negatve dependence upon the squared value of the household s ncome (YFAMILYSQ), mplyng the presence of dmnshng returns. That s, startng from an average household ncome, an ncrease n famly ncome perceptons ncreases the probablty, but further ncreases n famly ncome weakens ths effect. In relaton to the contrbuton of the geographc locaton (SOUTH) to the probablty of households credt card possesson, the dependence s of negatve sgn, mplyng that beng from the south or slands of Italy reduces the probablty of holdng a credt card. Regardng the age of the head of household (AGE) there exsts a postve dependence, even though dmnshng returns are present and captured by the nverse contrbuton of the squared value of the head of household s age (see Graph Nro. 1 n the Appendx). Addtonally, n relaton to the level of schoolng both varables, basc and secondary level-educaton (BASICSECEDU), and undergraduate and graduate educaton (UNIVEDU), are postve contrbutors to a hgher probablty. Table Nro 5: Probt Model Number of obs = 6,853 LR ch2(12) = 2,046 Prob > ch2 = Log lkelhood = -3,033 Pseudo R2 = CARD COEF. STD. ERR. Z P>Z [95% CONF. INTERVAL] YFAMILY E YFAMILYSQ -4.57E E E-11 SOUTH AGE AGESQ SEXFEM BASICSECEDU UNIVEDU MARRIED EMPLOYED FULLTIME VEHICLE CONSTANT

15 15 Unexpectedly, havng a full-tme job s assocated wth a lower probablty of holdng a credt card; however, beng employed (EMPLOYED), marred (MARRIED), and ownng a vehcle (VEHICLE), are postve contrbutors. In relaton to the goodness of ft of the Probt model, the pseudo R 2 shows only a 25% of accuracy 10. However, contrarly to the case of lnear models, judgements about the goodness of ft of categorcal models mght as well be consdered by examnng the ablty to predct observed responses. The trace of the 2x2 (YES, NO; YES, NO) matrx from Table Nro 6 shows that the model correctly classfes 78.48% of the actual observatons (880+ 4,498)/ 6,853. However, t also shows that the model s more effcent at targetng NO answers (91.02%) than at targetng YES answers (46.05%) Error Type I -. Equvalently, Table Nro 6 ndcates that the model wrongly predcted YES answers n 33.53% and NO answers n18.65% Error Type II -. Table Nro 6: Classfcaton of predcted values Credt card holdng Observed Classfed YES NO Total Classfed as YES f predcted Pr(YES) >=50% YES ,324 NO 1,031 4,498 5,529 Total 1,911 4,942 6,853 Senstvty Pr( YES/ YES) 46.05% Specfcty Pr( NO/NO) 91.02% Postve predctve value Pr( YES) 66.47% Negatve predctve value Pr(NO) 81.35% False YES rate for true NO Pr(YES/NO) 8.98% False NO rate for true YES Pr(NO/YES) 53.95% False YES rate for classfed YES 1-Pr( YES) 33.53% False NO rate for classfed NO 1-Pr(NO) 18.65% Correctly classfed 78.48% 10 The pseudo R 2 s gven by: 2 1 where log L pseudor = 1 1 s the maxmum loglkelhood of the model, 1+ 2(log L log L ) / N 1 0 and log L 0 s the maxmum loglkelhood when all varables, but the ntercept are set to 0. An alternatve measure s the Mc Fadden R 2 whch s gven by: 2 log L1 wth McFaddenR = 1 log L log L p log L 0

16 16 If one judges the Probt model as a non-dscretonary rule for the ssuance of credt cards n accordance to certan specfc characterstcs of an ndvdual applcant (or household), t would be completely sensble from the pont of vew of credt card ssuers, to expect credt card holders and non-holders to be concentrated n hgh and low levels of qualfcaton. Once ths s accepted, then the dscrepances among actual card holdngs and predcted card holdngs for every specfc observaton mght as well be seen as an error commtted by the credt card ssuer. That s, for nstance, ssuers mght grant credt cards to low-qualfed ndvduals (households) Error Type I -, or as well, mght not offer them to hghly-qualfed ndvduals (households) Error Type II. CARD = Pr(card) (predct) Table Nro 7: Margnal Effects (at mean values) VARIABLE dcard/dx STD. ERR. Z P>Z P>Z [ 95% C.I. ] X (**) YFAMILY 5.97E E E-06 30,761.6 YFAMILYSQ -1.30E E E E+09 SOUTH* % AGE AGESQ , SEXFEM* % BASICS~U* % UNIVEDU* % MARRIED* % EMPLOYED* % FULLTIME* % VEHICLE* % (*) dcard/dx s for dscrete change of dummy varable from 0 to 1 (*) the mean value of the ndependent varable ts computed for the reduced sample data of 6,853 obs. Table Nro 7 corroborates the prevously obtaned results regardng the sgn and sgnfcance of the coeffcents assocated to the ndependent varables. However, contrarly to Table Nro 5, the nformaton dsplayed on Table Nro 7 s not msleadng n the sense that t allows for a clearer nterpretaton of the coeffcents. For nstance, n a locus close to the mean values of all ndependent varables, the coeffcent accompanyng the varable YFAMILY ndcates that every 10,000 of addtonal annual

17 17 household ncome ncreases the probablty of possessng a credt card n 6%. However, the coeffcent assocated to the varable YFAMILYSQ also ndcates that every 10,000 of addtonal annual household ncome has also the negatve effect of decreasng the probablty of possessng a credt card n < >%. Regardng the age of the head of the household, whle the varable AGE ndcates a postve margnal effect of 1.28% from beng one year older, the varable AGESQ reports a decreasng return on age of <0.02>%. Addtonally, n relaton to dscrete varables, and precsely n the case of geographc locaton, beng from the south or the slands of Italy mples a <13.55>% lower probablty of possessng a credt card. Wth respect to the level of schoolng both varables, basc and secondary level-educaton (BASICSECEDU), and undergraduate and graduate educaton (UNIVEDU), contrbute by ncreasng the probablty of holdng a credt card n 17.06% and 38.05% respectvely. Beng marred, employed, and ownng a vehcle have both a postve margnal effect of 3.47%, 5.65% and 11.09% respectvely. As prevously stressed, unexpectedly, havng a full-tme job margnally contrbutes n a negatve way by reducng the probablty n <5.04>%. 8. CONCLUSION Ths paper provded a smple mcroeconomc evaluaton of the determnants of credt card holdng n Italy. Usng a Probt model, the analyss focused on the demand sde of the credt card market. Thus, the attenton was placed on dentfyng specfc ndvdual characterstcs of Italan households, whch showed to be statstcally sgnfcant for determnng the probablty of possessng a credt card. Relevant expected results were derved from ths paper. Frstly, credt card holdng s shown to be hghly-postvely related wth famly ncome, although, modest dmnshng returns are also present when a quadratc form s allowed. Secondly, the age of the household s head s also shown to be a postve determnant even though decreasng returns exst when ts squared value s present n the estmaton. Addtonally, dscrete varables such as geographc locaton, precsely not lvng n the south or slands of Italy, basc and unversty-level educaton, ownng a vehcle, beng marred and formally employed are postvely related to a hgher probablty of possessng a credt card.

18 18 Unexpectedly, havng a full-tme job seems to be negatvely related to the same probablty. Regardng, gender not much can be formally stated snce even though the coeffcent shows a negatve relaton for the case of women such coeffcent s statstcally nsgnfcant. Partcularly, at mean values of the sample dstrbuton, the probablty of holdng a credt card manly ncreases wth basc educaton n 17%, unversty level educaton n 38%, and ownershp of a vehcle n 11%. Equvalently, decreases assocated to dscrete varables are manly drven by southern household locaton n around <14>%, and fulltme workng n <5>% Wth respect to the goodness of ft, the model correctly classfes 78.48% of the actual observatons (880+ 4,498)/ 6,853. However, t s also shown that the model s more effcent at targetng NO answers (91.02%) than at targetng YES answers (46.05%) Error Type I -. Equvalently, the model wrongly predcts YES answers n 33.53% and NO answers n18.65% Error Type II -. A possble explanaton to the abovementoned results suggests that, If one judges the Probt model as a non-dscretonary rule for the ssuance of credt cards n accordance to certan specfc characterstcs of an ndvdual applcant (or household), t would be completely sensble to assocate the dscrepances among actual card holdngs and predcted card holdngs for every specfc observaton as errors commtted by the credt card ssuer. That s, for nstance, ssuers mght grant credt cards to low-qualfed ndvduals (households) Error Type I -, or as well, mght not offer them to hghly-qualfed ndvduals (households) Error Type II. Many of the varables under consderaton were expected to have an nfluence n both the demand sde and the supply sde for the credt card market n Italy. However, further research, should explore the ncluson of addtonal varables whch mght stll be playng a relevant smultaneous role n both sdes of the market. Panel data analyss mght allow for the study of the mplcatons of credt cycles, and fnancal dstresses for the restructurng and modernzaton of the credt card market n Italy.

19 19 REFERENCES Ardzz, Guerno (2003). Cost effcency n the retal payment networks: frst evdence from the Italan credt card system. Tem d dscussone del Servzo Stud, Banca D Itala, Number June Durand, D. (1941). Rsk elements n consumer nstallment fnancng. NBER, New York. Hand, D. J., & Henley,W. E. (1997). Statstcal classfcaton n consumer credt. Journal of the Royal Statstcal Socety Seres A 160, Rosenberg, E., & Glet, A. (1994). Quanttatve methods n credt management: a survey. Operatons research 42, Thomas Lyn (1992). Fnancal rsk management models. In: Ansell, J., & Wharton, F. (Eds.), Rsk analyss, assessment and management, Wley, Chchester. Thomas Lyn (1998). Methodologes for classfyng applcants for credt. In: Hand, D. J., & Jacka. S.D. (Eds.), Statstcs n fnance, Arnold, London, Thomas Lyn (2000). A survey of credt and behavoural scorng: forecastng fnancal rsk of lendng to consumers. Internatonal Journal of Forecastng 16, Verbeek, Marno (2001). A gude to Modern Econometrcs,

20 20 APPENDIX Table Nro 8: Credt Card holdng and the contnuous varables Reduced Sample N= 6,853 Credt card holdng Varable Range Obs. Mean Std. Dev. holders non-holders 0<=YFAMILY<12, ,835 2,417 6% 94% 12,000<=YFAMILY<24,000 2,409 17,900 3,447 14% 86% YFAMILY 24,000<=YFAMILY<36,000 1,808 29,469 3,432 27% 73% 36,000<=YFAMILY<48, ,225 3,433 45% 55% 48,000<=YFAMILY<60, ,177 3,409 57% 43% 60,000<=YFAMILY ,395 41,525 71% 29% Reduced Sample N= 6,853 Credt card holdng Varable Range Obs. Mean Std. Dev. holders non-holders 0<=AGE<= % 100% 20<=AGE<= % 72% AGE 30<=AGE<=40 1, % 61% 40<=AGE<=50 1, % 57% 50<=AGE<=60 1, % 66% 60<=AGE 2, % 88% Graph Nro. 1. Age of head of household and the Percentage of Credt card holders n Italy 50% 45% Percentage of Credt card holders 40% 35% 30% 25% 20% 15% 10% 5% 0% 0<=age<=20 20<=age<=30 30<=age<=40 40<=age<=50 50<=age<=60 60<=age Ranges of Age

21 Table Nro 9: Credt Card holdng and the dscrete varables 21 Varable SOUTH SEXFEM BASICSECEDU UNIVEDU MARRIED EMPLOYED FULLTIME VEHICLE Reduced Sample N= 6,853 Percentage of those who hold a credt card Characterstc Obs. n reduced sample holders non-holders From south and slands 1,827 16% 84% From other locatons 5,026 32% 68% Women 1,950 21% 79% Men 4,903 31% 69% Wthout basc educaton 2,024 6% 94% Wth secondary or basc educaton 4,111 34% 66% Wth postgrad. or undergrad. educaton % 43% Marred 4,409 32% 68% Not marred 2,444 20% 80% Employed 3,982 39% 61% Not employed 2,871 13% 87% Wth fulltme job 2,956 36% 64% Wthout fulltme job 3,897 22% 78% Wth vehcle 2,469 48% 52% Wthout vehcle 4,384 17% 83% Graph Nro. 2: Percentage of Credt card holders n the dfferent geographc locatons of Italy 40% Percentage of Credt Card holders 32% 24% 16% 8% 0% PERCENTAGE IN SOUTH AND ISLANDS Geographc Locaton PERCENTAGE IN OTHER LOCATIONS

22 22 Graph Nro. 3: Gender and the Percentage of Credt card holders n Italy 40% Percentage of Credt Card holders 32% 24% 16% 8% 0% PERCENTAGE OF WOMEN Gender PERCENTAGE OF MEN Graph Nro. 4: Educaton and the Percentage of Credt card holders n Italy 64% Percentage of Credt Card holders 56% 48% 40% 32% 24% 16% 8% 0% PERCENTAGE OF THOSE WITHOUT EVEN BASIC EDUCATION PERCENTAGE OF THOSE WITH SECONDARY OR BASIC EDUCATION Degree of Educaton PERCENTAGE OF THOSE WITH POSTGRAD. OR UNDERGRADUATE EDUCATION

23 23 Graph Nro. 5: Cvl Status and the Percentage of Credt card holders n Italy 40% Percentage of Credt Card holders 32% 24% 16% 8% 0% PERCENTAGE OF THOSE MARRIED Cvl Status PERCENTAGE OF THOSE NOT MARRIED Graph Nro. 6: Employment and the Percentage of Credt card holders n Italy 48% Percentage of Credt Card holders 40% 32% 24% 16% 8% 0% PERCENTAGE OF THOSE EMPLOYED Employment PERCENTAGE OF THOSE NOT EMPLOYED

24 24 Graph Nro. 7: Fulltme Jobs and the Percentage of Credt card holders n Italy 40% Percentage of Credt Card holders 32% 24% 16% 8% 0% PERCENTAGE OF THOSE W. FULLTIME JOB Fulltme Jobs PERCENTAGE OF THOSE W/O FULLTIME JOB Graph Nro. 8: Vehcle ownershp and the Percentage of Credt card holders n Italy 56% Percentage of Credt Card holders 48% 40% 32% 24% 16% 8% 0% PERCENTAGE OF THOSE WITH VEHICLE Vehcle Ownershp PERCENTAGE OF THOSE WITHOUT VEHICLE

25 Table Nro 10: Varance-Covarance Matrx YFAMILY YFAMILSQ SOUTH AGE AGESQ SEXFEM BASICSECEDU UNIVEDU MARRIED EMPLOYED FULLTIME VEHICLE CONS YFAMILY YFAMILYSQ SOUTH AGE AGESQ SEXFEM BASICEDU GRADUATEDU MARRIED EMPLOYED FULLTIME VEHICLE CONS