A Multistage Model of Loans and the Role of Relationships

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1 A Multstage Model of Loans and the Role of Relatonshps Sugato Chakravarty, Purdue Unversty, and Tansel Ylmazer, Purdue Unversty Abstract The goal of ths paper s to further our understandng of how relatonshps work n the borrower-lender nteracton for a loan. A practcal mplcaton emergng from classcal studes s that lenders overcome the problem of nformaton asymmetry by collectng nformaton about the borrowers through close relatonshps and usng ths nformaton n credt approval and loan rate decsons. We test ths mplcaton n our paper usng a robust sample selecton methodology and data from the 998 Survey of Small Busness Fnances. Our emprcal model accounts for the entre fabrc of the loan grantng process wthn a unfed framework, ncludng () a borrower s decson to apply to a fnancal nsttuton for a loan, () the fnancal nsttuton s decson to approve the applcaton for a loan, and (3) the loan rate the fnancal nsttuton chooses for the borrower condtonal on approvng the loan. Our model also eplctly ncludes the analyss of dscouraged borrowers (.e., those that do not apply for loans because they beleve they wll be rejected). We fnd that relatonshps matter only n a borrower s decson whether to apply for a loan and n the loan approval/rejecton decson by the fnancal nsttuton. Relatonshps, however, are not mportant n determnng the loan rate assocated wth the approved loan once the sample selecton bas n the loan process s approprately accounted for. Our conclusons reman robust to both relatonshp-drven loans and to the relatve sze of the busness. JEL: G Keywords: Credt Ratonng, Relatonshps, Lender, Borrower, Small Busness Loans, Sample Selecton Ths verson: May, 007 Acknowledgments: We thank the semnar partcpants at the Oho State Unversty; Purdue Unversty; Boğazç Unversty n Istanbul, Turkey; the 005 Mdwest Economc Assocaton meetngs; the 005 Federal Reserve System s fourth annual communty affars research conference (enttled Promses and Ptfalls ) n Washngton, D.C; and the 004 conference on the Mcro Foundatons of Credt Contracts n Florence, Italy; as well as Carol Bertaut, Jonathan Crook, Jonathan Fsher, Mary Gtzen, Adam Hagen, Rck Lang, Toshhko Mukoyama, Ed Nosal, George Pennacch, Mtch Petersen, Raghuram Rajan, Ayşeğül Şahn, Avandhar Subrahmanyam and Rck Wddows, for helpful comments and suggestons at varous stages n the evoluton of the paper. Patryk Babarz provded eceptonal research assstance. A prevous verson of ths paper was enttled A Reeamnaton of the Role of Relatonshps n the Loan Grantng Process. The usual dsclamer holds. 8 W. State Street, West Lafayette, IN , phone: , fa: , emal: 8 W. State Street, West Lafayette, IN , phone: , fa: , emal:

2 A Multstage Model of Loans and the Role of Relatonshps Abstract The goal of ths paper s to further our understandng of how relatonshps work n the borrower-lender nteracton for a loan. A practcal mplcaton emergng from classcal studes s that lenders overcome the problem of nformaton asymmetry by collectng nformaton about the borrowers through close relatonshps and usng ths nformaton n credt approval and loan rate decsons. We test ths mplcaton n our paper usng a robust sample selecton methodology and data from the 998 Survey of Small Busness Fnances. Our emprcal model accounts for the entre fabrc of the loan grantng process wthn a unfed framework, ncludng () a borrower s decson to apply to a fnancal nsttuton for a loan, () the fnancal nsttuton s decson to approve the applcaton for a loan, and (3) the loan rate the fnancal nsttuton chooses for the borrower condtonal on approvng the loan. Our model also eplctly ncludes the analyss of dscouraged borrowers (.e., those that do not apply for loans because they beleve they wll be rejected). We fnd that relatonshps matter only n a borrower s decson whether to apply for a loan and n the loan approval/rejecton decson by the fnancal nsttuton. Relatonshps, however, are not mportant n determnng the loan rate assocated wth the approved loan once the sample selecton bas n the loan process s approprately accounted for. Our conclusons reman robust to both relatonshp-drven loans and to the relatve sze of the busness. JEL: G Keywords: Credt Ratonng, Relatonshps, Lender, Borrower, Small Busness Loans, Sample Selecton

3 A Multstage Model of Loans and the Role of Relatonshps Fnally, you have the most sophstcated of all marketng tools: Person-to-person relatonshps.you know your customers personally by takng care of a varety of bankng transactons for them on a daly or weekly bass and, for many, you know them through communty actvtes as well. More than lkely, you know when they get marred, when they move, when they are havng chldren, when ther chldren are ready for college, when ther kds graduate and when retrement s around the corner. No computer model has been developed that can compete wth ths knd of knowledge. Communty Banker, June 00. Introducton The goal of ths paper s to test a smple premse: Do relatonshps between a borrower and a (potental) lender n fact matter equally through all stages of a loan applcaton/approval process? The bass to ths queston les n two seemngly counter actng ntutons, one emergng from the lterature and the other emergng from stylzed facts from the bankng ndustry and bank loan offcers. Specfcally, the current lterature on the role of relatonshps on lendng suggests that relatonshps wll mprove the loan effcency by cuttng down loan delnquences and defaults and enable loans to be made at lower rates. The counter to ths ntuton comes from the practtoners who suggest that whle the credt approval decsons mght be relatvely fleble, the actual loan rates are strctly bound around the current prme lendng rate, or the LIBOR, and there s very lttle room for adjustment. The mplcaton would be that loan rates should be drven by observables lke the credt hstory of the borrower and not be drven by soft nformaton metrcs lke relatonshps. To answer the above queston, we formally decompose the overall loan grantng process nto the followng (sequental) decson stages n order to closely eamne the effect of relatonshps on each stage of ths process: [The Applcaton Decson] a borrower s decson whether to apply to a lender for a loan (or not), See, for eample, Petersen and Rajan (994), Berger and Udell (995), Cole (998) and Chakravarty and Scott (999). The s C s for gettng a small busness loan approved nclude Character, Capacty of pay, Captal, Collateral, Condtons and Confdence (See, for eample, Recently, practtoners have added another C to ther recommendatons to small busnesses, whch s Communcaton. See for eample, Get your Bank Manager on your sde wth these smple strateges on

4 [The Credt Approval Decson] whether the lender approves the applcaton for a loan (or not), and [The Loan Rate Settng Decson] the loan rate the lender chooses for the borrower. We further assume that these stages are endogenously determned. Our analyss allows for the nherently dstnct role possbly played by relatonshps n the dfferent areas of the loan process and s based on the ntuton that, collectvely, relatonshps act as a sortng mechansm n ether voluntarly self-ratonng busnesses out of the loan markets altogether or encouragng them to formally apply for a loan wth a fnancal nsttuton wth whom they mght enjoy a certan level of relatonshps. We hypothesze that, below a crtcal relatonshp value, frms wll self-select nto stayng out of the loan markets (even though they need credt) and, above ths crtcal value, they wll apply for a loan. The bank may then evaluate the applcaton based on ts own (prvate) data about the frm, whch ncludes nformaton gleaned through relatonshps wth the applcant. Subject to the frm meetng the bank s proft mamzng condtons, the bank ether approve or reject the loan applcaton. Consequently, a sngle equaton ordnary least squares estmaton of loan rates on the effect of relatonshps wth ths non-randomly selected sample data wll gve us estmates for well-developed relatonshps (relatonshps above a crtcal value) for the selected group of those frms that were approved for a loan, and wll lkely overestmate the true effect of relatonshps on loan rates. 3 To eamne the queston n ts fullest sense requres the ncluson of those potental borrowers who would want a loan for ther busnesses but do not choose to formally apply because they are sure to be turned down by the bank. We term these borrowers as dscouraged borrowers. Whle the current body of relatonshp lendng research, eemplfed by the ctatons n footnote, have not ncluded dscouraged borrowers n ther analyss, there s now a growng body of evdence that appears to suggest that owners of small busnesses from certan demographc groups are dscouraged from applyng for a loan (see, for eample, Blanchflower, Levne and Zmmerman, 003 and Cavalluzzo, Cavalluzzo and Wolken, 00). 4 Gven the sgnfcant numbers of dscouraged borrowers n the populaton, they 3 The noton of relatonshps, such as the one we analyze n ths paper, can concevably comprse of two components: a mechancal sortng by whch lke-mnded frms and banks are attracted to one another and develop a long tenure wth each other smply because they are good fts; and a component that captures the real tme productvty ncreases over tme that lead to loan effcences and resultng lower loan rates. Ideally, t s the latter we want to capture through our relatonshp proes. Unfortunately, the (cross-sectonal) data does not permt us to dsentangle the two effects. To the etent that the former s present, t wll dlute the effect of (current) loan effcences on (future) loan rates. We dscuss ths ssue n detal n Secton. 4 The number of dscouraged and credt-constraned borrowers s not neglgble. Accordng to Cavalluzzo et al. (00), almost half of the small busnesses n the993 Natonal Survey of Small Busness Fnances (used by these authors n ther analyss) that desred credt dd not apply for a loan because they feared that the loan applcaton would be turned down due to poor credt hstory, prejudce, or for some other reason. Smlarly, almost 30 percent of the busnesses that appled for a loan were dened credt. These numbers suggest that dscouraged and credt-

5 cannot be thought to be mere random samples, and the unobserved characterstcs of the frms, such as the manager s ablty to develop good relatonshps and transmt the credt qualty of the frm to the lenders, through the development and the nurturng of relatonshps, are lkely to be correlated across the dscouraged, credt-constraned, and non-constraned, borrowers. One may also argue that the dscouraged, and the dened, have no pre-estng relatonshps wth banks. Therefore, ecludng them from the sample would not bas the parameter estmates of the relatonshp varables. However, n the 998 Survey of Small Busness Fnances (used n ths paper), over 98 percent of small busnesses reported havng a prmary nsttuton that they do busness wth that s, they have a pre-estng relatonshp wth at least one bank. Furthermore, the length of relatonshp wth the prmary nsttuton of the dscouraged and credt-constraned borrowers s comparable to the length of relatonshp of those that were approved for a loan. 5 We employ a robust sample selecton approach (dscussed n detal later) that accounts for the double selectvty n the loan process. 6 We use data from the 998 Survey of Small Busness Fnances (SSBF) to eamne the (possbly) dstnct role possbly played by relatonshps n dfferent areas of the loan process. Upon estmatng our model, we fnd that relatonshp measures are most mportant n ncreasng the probablty of applyng for a loan and lowerng the probablty of beng rejected for a loan. Among relatonshp varables, we fnd that measures capturng the estence of pre-estng relatonshps and pre-estng loan accounts, and the number of credt sources that the frm has assocaton wth, play mportant roles. Apart from relatonshp effects, we fnd that the fnancal characterstcs of small busnesses, such as the number of years under current management, total assets, and total labltes, also have a powerful effect n eplanng dscouraged and/or credt-constraned borrowers. constraned borrowers cannot, and should not, be ecluded from any formal analyss of determnants of avalablty and/or cost of credt. 5 For eample, almost 96 percent of the dscouraged and a 00 percent of the credt-constraned busnesses reported havng a prmary nsttuton that they do busness wth. The mean length of relatonshp wth the prmary nsttuton for dscouraged and credt-constraned borrowers s 6.5 and 5.56 years, respectvely, whle the mean length of relatonshp for those that were approved for a loan s 7.03 years. In addton, among the dscouraged (credt-constraned) borrowers, 4(5) percent have a relatonshp wth a sngle nsttuton, 3(33) percent have a relatonshp wth two nsttutons, 5 (4) percent have a relatonshp wth three nsttutons, and the remanng 3 (7) percent have a relatonshp wth four or more nsttutons. The correspondng numbers for those busnesses that were approved for a loan are as follows: 6 percent have a relatonshp wth a sngle nsttuton, 6 percent have a relatonshp wth two nsttutons, 7 percent have a relatonshp wth three nsttutons, and 3 percent have a relatonshp wth four or more nsttutons. 6 Double selectvty refers to the fact that the fnancal nsttuton s credt approval decson s usually observable only f the borrower decdes to apply for a loan, whle the loan rate s usually observable only f the borrower decdes to apply for a loan and the fnancal nsttuton approves the loan applcaton. 3

6 Havng dentfed that relatonshp measures, overall, play an mportant role n the loan applcaton and approval/denal processes, we go a step further n determnng the role of relatonshps n loan rate decsons. Intally, consderng only those small busnesses n our data that had outstandng loans (.e., wthout accountng for the sample selecton bas) we fnd that relatonshp measures, specfcally, the length of relatonshp wth the lender and the number of credt sources that the borrower has assocaton wth, do ndeed have sgnfcant power n eplanng loan rates as has been reported n the lterature. However, the statstcal sgnfcance of the length of relatonshp and the number of credt sources dsappears when the selecton bas s approprately corrected for. That s, relatonshp measures have no power n eplanng the loan rate once the nterest rate equaton s analyzed as part of the overall loan process (or, the loan rate estmaton model s statstcally lnked wth the applcaton and credt approval stages of our loan model). Stll, other characterstcs of small busness borrowers, such as the number of years under current management, total assets, and labltes, contnue to be sgnfcantly correlated wth the loan rate. Our estmaton results also show that among relatonshp varables, the number of credt sources that the frm has assocaton wth has a varyng effect on the dfferent stages of a loan grantng process. Whle the estence of multple relatonshps plays a postve role n the decson to apply for credt, t plays a negatve role n the decson to be approved for credt. Fnally, wthout accountng for the sample selecton bas, we fnd that the number of credt sources s postvely assocated wth the loan rate. Ths fndng s consstent wth the lterature that those who mantan multple relatonshps are perceved by potental lenders as fnancally stressed and, therefore, face hgher loan rates (see, for eample, Petersen and Rajan, 994 and Shkm, 005). When the selecton bas s approprately corrected for, the postve correlaton between the number of credt sources and the loan rates dsappears. We argue that ths s due to the fact that those frms that are more lkely to apply for credt also have assocatons wth a larger number of credt sources. Consequently, the effect of competton among varous fnancal sources reduces ther loan rate wth a gven lender. To ensure the robustness of our fndngs, we eamne two dstnct parttons of the data. Frst, we focus only on the smallest frms n our data as defned usng a smlar asset cut-off level to Berger and Udell (995). Second, we focus on only those frms wth estng lnes of credt under the assumpton that lnes of credt are relatonshp-drven loans dstnct from mortgage loans (say), whch are transactonal loans where the effect of relatonshps may not play a central role to begn wth (see, for eample, Berger and Udell, 995). Our man fndng, that relatonshps do not mpact loan rates once the sample selecton bas s approprately controlled for survves both parttons. That s, we fnd that relatonshps play no sgnfcant role n the loan rate determnaton stage. 4

7 The remander of ths paper s structured as follows. Secton revews the theoretcal and emprcal lterature and compares our fndngs wth the prevous lterature. Secton 3 constructs the emprcal framework. Secton 4 descrbes the data and defnes the varables used n the analyss. Secton 5 presents the fndngs of our emprcal analyss for small busnesses loans. Secton 6 presents the results of our robustness tests where we apply our emprcal analyss to loans etended to the smallest of small busnesses and to the lnes of credt etended to small busnesses. Fnally, Secton 7 concludes.. Background The lterature on relatonshp bankng has shown that lenders can overcome the problems of asymmetrc nformaton by developng close relatonshps wth borrowers. Development of long-term relatonshps wth the borrower can produce valuable nformaton about the prospects and credtworthness of the borrower that can be used n (future) credt approval and loan rate decsons. The effects of relatonshp bankng on the avalablty and the cost of funds for small busnesses have been nvestgated n an mpressve body of theoretcal and emprcal research. The fndngs of the prevous lterature demonstrate that two measures n partcular, the length of relatonshp and sngle versus multple bankng relatonshps, can have sgnfcant benefts, as well as costs, for borrowers. The theoretcal papers on bankng relatonshps have focused on how the duraton of a fnancal relatonshp nfluences the prce of a loan. Boot and Thakor (994) show that as the relatonshp duraton ncreases, borrowers obtan loans at lower rates because nformaton asymmetres are overcome more effcently and these effcency gans are passed along to the frm. However, Sharpe (990) suggests that nterest rates ncrease as relatonshps mature, snce the proprety nformaton about the borrower that the bank obtans may provde the bank wth an nformatonal monopoly and create a swtchng cost for the borrower (defned as a lock-n problem). The cost of ths lock-n problem for the borrower s also dscussed n Rajan (99), who notes that the nformed lender has the power to prevent the frm from contnung a project that has a negatve net present value. Whle the emprcal evdence supports the hypothess that relatonshps ncrease the avalablty of credt (Cole, 998), the hypothess that the length of the relatonshp reduces the loan rate has been both supported and rejected. For eample, usng U.S. small busness data, Petersen and Rajan (994) have found no sgnfcant correlaton between the relatonshp length and the loan rates whle Berger and Udell (995) have reported a sgnfcantly negatve correlaton between relatonshp length and the loan rates on relatonshp-drven loans. The ambguty carres over n the nternatonal front as well. Here, usng bank loans to Belgan small busnesses, Degryse and Cayseele (000) have reported a postve 5

8 correlaton between relatonshp length and loan nterest rates, whle, usng data from small busnesses n Germany, Harhoff and Kortng (998) have reported a negatve correlaton. Multple bankng relatonshps may reduce the lock-n problem. By havng a relatonshp wth more than one lender, a frm can reduce the possblty for ts ncumbent bank to eplot a monopolstc poston. 7 Evdence on the mpact of multple relatonshps on credt avalablty and loan rates s also med. Petersen and Rajan (994) fnd the frms that have multple relatonshps obtan credt at hgher rates and are more credt-constraned than frms wth a sngle bankng relatonshp. Smlarly, Cole (998) fnds that multple relatonshps reduce credt avalablty. But, D Aura, Fogla and Reedtz (999) fnd that frms wth multple relatonshps have slghtly lower nterest rates. In addton, Shkm (005) fnds that whle the ncdence of multple relatonshps ncreases the cost of credt, t also ncreases the avalablty of credt for fnancally stressed frms. Our analyss provdes a generalzed modelng framework of the entre loan grantng process, whch encompasses, and bulds on, among others, the research of Petersen and Rajan (994), Berger and Udell (995), and Cole (998). Usng a sample of small busness loans (that ncludes lnes of credt as well as other types of small busness loans) from the 987 verson of the Natonal Survey of Small Busness Fnances data set, Petersen and Rajan (994) show no sgnfcant effect of relatonshps on the loan rates charged by lenders. They obtan ths result by regressng the nterest rate quoted on a frm s most recent loan on proes capturng the underlyng cost of captal, as well as loan- and frm-specfc characterstcs and, most mportantly, relatonshp measures. They also separately eamne the role of relatonshps on the avalablty of credt and fnd stronger effects of relatonshps on ther proy for credt avalablty. In sprt, ths fndng s smlar to what we uncover usng data on small busness loans. However, there are several mportant dfferences between ther approach and ours. Frst, unlke our data, Petersen and Rajan s data do not allow them to observe credt avalablty drectly. The authors are therefore forced to fnd ndrect proes (.e. the percentage of trade credts repad late n Petersen and Rajan, 994, and the percentage of offered early payment dscounts taken by the frm n Petersen and Rajan, 995). In our data, we drectly observe whether or not the frm was dscouraged or whether or not t s dened a loan, and use these drect measures as proes for credt avalablty. Second, Petersen and Rajan separately estmate the role of relatonshps on loan rate and credt avalablty. However, conversatons wth bank offcals and other theoretcal consderatons pont unambguously to the fact that the two decsons, credt avalablty and the determnaton of the 7 Competton among banks may actually harm a borrower f the competton mposes constrants on the ablty of borrowers and lenders to share surpluses. Petersen and Rajan (995) show that hgh competton makes t more dffcult for banks to subsdze borrowers n earler perods n return for a share of the rents n the future and ths may dscourage banks from lendng to young frms. 6

9 loan rate, are netrcably woven together as part of the same loan process and should not be consdered as dstnct. In the current research, we provde such a unfed analyss. Berger and Udell (995) use the same 987 verson of Natonal Survey of Small Busness Fnances data set used by Petersen and Rajan (994), and the same sngle equaton regresson format, wth one mportant dfference. Focusng solely on small busness lnes of credt (as a subset of the loans eamned by Petersen and Rajan (994) from the same data set), they regress the loan rate premum over the bank s prme rate on the length of relatonshp, characterstcs of the loan contract and also fnancal, governance, and ndustry characterstcs of the frm. They fnd a negatve and sgnfcant correlaton between relatonshp length and loan rates. That s, the longer the bankng relatonshp, the lower s the rate on the loan. Ths fndng, they argue, contrasts sharply wth those of Petersen and Rajan (994) who report a statstcally nsgnfcant effect of relatonshp length on loan rates. 8 We are able to replcate the fndngs of Berger and Udell (995) wth the 998 SSBF data as long as we estmate the approprate regressons n solaton wthout controllng for the selecton bases across the varous stages of the entre loan grantng process. Subsequently, we are able to demonstrate our result of the rrelevance of relatonshp measures on loan rates once we approprately control for the sample selecton bas. Cole (998) nvestgates the role of pre-estng relatonshps on the avalablty of credt for small busnesses. Unlke our study, Cole (998) does not eamne the self-ratoned busnesses and, nstead, focuses only on those busnesses that appled for credt. 9 He reports that the length of the relatonshp s unmportant n determnng a potental lender s decson whether or not to approve the credt applcaton and fnds that a potental lender s more lkely to etend credt to a frm wth whch t has a pre-estng relatonshp. When we estmate the decson to apply (or not) for credt and the decson to approve (or reject) credt together, our results show that, consstent wth Cole, pre-estng relatonshps do play a sgnfcant role on beng approved for credt, whle the length of relatonshp does not. Addtonally, Cole (998) fnds that multple relatonshps reduce credt avalablty. Our estmaton results show that t s n the decson to apply for credt where multple relatonshps play a postve role, and t s n the 8 Blackwell and Wnters (997) use a sngle equaton ordnary least squares estmaton smlar to those used by Petersen and Rajan (994) and Berger and Udell (995) to eamne the effects of bankng relatonshps and montorng on loan nterest rates. The authors, usng a small sample of actve lnes of credt obtaned from banks, fnd that frms wth longer relatonshps are montored less frequently by banks, and that less frequently montored frms pay lower nterest rates on average. Blackwell and Wnters also nfer from ther results that, upon holdng the bank s montorng effort constant, the duraton of the bankng relatonshp has no drect effect on prcng the lnes of credt. 9 Usng the 998 SSBF data, we are able to replcate Cole s fndngs when we analyze only the lender s decson of whether or not to approve the (small busness) credt applcaton. 7

10 credt approval stage where multple bankng relatonshps appear to play a negatve role. Busnesses that have assocatons wth a larger number of lenders are lkely to have appled for credt n the past and are more lkely to apply n the future. Controllng for that effect, our results show that busnesses that have a sngle bankng relatonshp are more lkely to be approved for a loan compared to those that have multple bankng relatonshps. Among those that have multple relatonshps, credt approval does not sgnfcantly reduce wth the number of credt sources that the busness has assocaton. Fnally, an mportant econometrc ssue n the analyss of credt avalablty and cost of credt needs to be addressed. If there are omtted borrower-lender-specfc unobservable effects n the estmaton of the determnants of the cost of credt, correlatons between these and the bankng relatonshp proes can ether result n an upward, or a downward, bas n the estmate of the length of relatonshps (say). A good match between frms and banks mples a longer length of relatonshp snce borrowers are less lkely to approach other sources for credt. Ths wll result n an observed negatve correlaton between the length of relatonshp and the loan rate. On the other hand, busnesses that have a shorter length of relatonshp are busnesses that approach a new lender n order to obtan a better match. Ths wll result n a postve correlaton between the length of relatonshp and the loan rate. In the same ven, the labor lterature on the connecton between earnngs and job tenure (and eperence) has recognzed that the correlaton between omtted ndvduals job-specfc unobservable characterstcs and ther tenure varables can result n an upwardly-based estmate (Altonj and Shakotko, 987 and Abraham and Farber, 987) or n a downwardly-based estmate (Topel, 99). Unfortunately, n the contet of bankng relatonshps, ths s a very dffcult ssue to resolve wthout a rch data set wth nformaton on a frm s full relatonshp wth credt sources, loan applcaton/approval and assocated loan rates, and strong assumptons regardng the nature of the correlatons Model In the ntroducton, we dscussed the ntuton that a borrower can be dscouraged from applyng for a loan f she beleves that her relatonshps wth the potental lender are not developed enough. We also llustrated how the applcant for a loan may be rejected f her relatonshps (from the lender s pont of vew) are not developed enough. Therefore, a sngle equaton model wth a non-randomly selected sample could easly lead to coeffcent estmates that essentally confound the effects of varous stages 0 In the labor lterature, a dscouraged worker defned as a person who wants a job and s avalable for work but who s not lookng for work because she beleves she could not fnd t. Specfcally, the group of dscouraged workers have receved attenton n the studes of labor supply n terms of (a) ther smlartes and dssmlartes to the unemployed and to those who are not n the labor force (see, for eample, Kodrzyck, 000 and Benat, 00), and (b) on how they are affected from the fluctuatons n the economc condtons (Fnegan, 98). 8

11 and thereby ether enhance, or attenuate, the true effect of the ndependent varables on the partcular dependent varable. In ths secton, we present an emprcal model of relatonshps as t pertans to the overall lendng process. In so dong, we assume that the lendng process s comprsed of a three-stage decson. Frst, the borrower decdes whether or not to apply for a loan. Second, the bank employs a screenng process by whch the loan applcant s ether rejected or approved for the loan. Fnally, condtonal on approvng the loan, the lender sets the loan nterest rate. Snce the credt approval decson s observable only f the borrower decdes to apply for a loan, and the loan nterest rate s observable only when the applcant decdes to apply for a loan and the lender approves the applcaton, we have a double selectvty model descrbed by the followng three equatons: Assume a borrower s not dscouraged from applyng for a loan f The Applcaton Equaton y * = > + ε 0, () and s not credt-constraned f The Credt Approval Equaton y * = > + ε 0, () * where y and y * are latent varables representng the borrower s decson to apply to the lender for a loan and the lender s decson to approve the loan, respectvely; and are vectors of ndependent varables; and are vectors of parameters; ε and ε are normally dstrbuted error terms wth standard devatons σ and σ, respectvely and, wthout loss of generalty, σ =σ =. The borrower * apples for a loan ( y ) f y 0, and does not apply for a loan ( y 0 ), otherwse. Also, the = > * borrower s not credt-constraned ( y ) f y 0, and s refused a loan or credt-constraned = > ( y = 0 ), otherwse. Essentally, we observe y only f y =. That s, f the borrower decdes not to apply for a loan ( y 0 ), we do not, n fact, observe whether she s, or sn t, approved for a loan. = = The loan rate for borrower s represented by the followng equaton: The Loan Rate Equaton where y = + ε, (3) y 3 s the observable loan rate; 3 s a vector of ndependent varables; 3 a vector of parameters; and ε 3 s an error term wth the standard devatonσ 3. Recall that the loan rate s 9

12 0 observed only when the borrower s not dscouraged from applyng for a loan and s approved for a loan condtonal on applyng:.e., = = y y. The error terms are assumed to be ndependently and dentcally dstrbuted across the sample wth a jont normal dstrbuton: , ~ σ σ σ ρ ε ε ε N. (4) where ρ s the correlaton between ε and ε. We employ a two-stage selecton estmator to obtan the consstent estmates of the Loan Rate Equaton (Ham, 98 and Tunal, 986). The crucal ssue n correctng for bas wth the double selecton rule s the epectaton of the loan rate condtonal on 0 * > y and 0 * > y. Ths condtonal epectaton can be epressed as ), ( 0) 0, ( * * 3 ε ε ε E y y y E > > + = > > λ σ λ σ + + = (5) where ),, ( ) ) ( ( ) ( / ρ ρ ρ φ λ F Φ = and ),, ( ) ) ( ( ) ( / ρ ρ ρ φ λ F Φ = (6) and φ (.) and Ф(.) are the unvarate standard normal densty and the dstrbuton functons, respectvely, and F(.) s the bvarate standard normal dstrbuton functon. If 3 σ and 3 σ are not both equal to zero, the epectaton n Equaton (5) s not equal to 3 3 and the resultant least squares estmaton of Equaton (5) on the censored sample wll lead to the same sort of specfcaton error bas that Heckman (976) descrbed n hs sngle selecton rule case. We follow the same estmaton procedure as Heckman (976). That s, we frst estmate the parameters of the selecton Equatons () and () by mamzng the followng lkelhood functon: )}, ( ln{ )},, ( ln{ )},, ( ln{ 0 0 ρ ρ y y y y y F F L = = = = = Φ + + = (7) Etant research has shown that the estmated parameters may be senstve to the dstrbutonal assumptons made n the selecton models. It has been suggested that approaches based on semparametrc and nonparametrc estmators may be more approprate. However, t s almost mpossble to apply these methods to our specfc queston. See Greene (003, p. 789) for a dscusson of these methods and the nherent dffcultes n estmatng them.

13 where the frst term on the rght hand sde of Equaton (7) denotes the lkelhood of a borrower applyng and beng approved for the loan, the second term denotes the lkelhood of a borrower applyng and beng rejected for a loan, and the thrd term denotes a borrower not applyng for a loan (.e., selfratonng). We then use the parameter estmates of, and ρ to form consstent estmates ^ λ and λ of λ and λ n Equaton (6). A least squares estmaton of Equaton (5) provdes consstent estmators of parameters 3, σ 3 andσ 3 ^ 3. The least square estmaton does not account for the fact that λ and λ are estmators of λ and λ and ncludes some of the same varables n 3. Therefore, the standard errors of the parameter estmates may be nconsstent. We therefore use a bootstrappng method to obtan consstent standard errors. 4 ^ ^ 4. Data We use the 998 verson of the SSBF dataset, sponsored by the Federal Reserve Board. In partcular, the SSBF survey ncludes a natonally representatve sample of 3,56 small busnesses operatng n the U.S. The survey provdes detaled nformaton on each frm s credt hstory ncludng the frm s most recent borrowng eperence, ncome statement and balance sheet, frm characterstcs ncludng organzatonal form, and characterstcs of the frm s prmary owner. Whle the 998 SSBF s unquely suted to the study of credt ratonng because dscouraged and credt-constraned borrowers are dentfed drectly, t has ts own lmtatons. For eample, the 998 survey only ncludes nformaton on the most recent new loan applcaton eperence. Therefore, our Also, see Van de Ven and Van Praag (98) and Meng and Schmdt (985) for the lkelhood functon of a bvarate probt model when one of the dependent varables n the second stage s only partally observed. 3 Problems of double selectvty have been addressed n other areas of economcs. For eample, Co and Jappell (993) estmate the demand for consumer labltes condtonal on beng unconstraned n the credt markets and holdng postve debt. Ham (98) estmates labor supply n the presence of unemployed and underemployed workers. Tunal (986) apples the double-selecton framework to mgraton and earnngs decsons. We follow the same estmaton technques utlzed n these papers. 4 Specfcally, we generate 50 random samples wth replacement from the orgnal sample. For each of these random samples, we estmate Equaton (7) and use the estmates of, and ρ to calculate ˆ λ and ˆ λ. We then use ˆ λ and ˆ λ as ndependent varables n Equaton (5) to estmate the remanng unknown coeffcent, 3, as well as the sample selecton coeffcents, σ3 and σ 3. We repeat ths process 50 tmes, compute the standard devatons of these coeffcents for each of those cases, and report them as the correspondng standard errors of the coeffcents n Model 4 n Tables IV, V and VI.

14 model only focuses on new loans and does not nvestgate the role of relatonshps on the renewal of prevous credt wth the man lendng nsttuton, whch could be drven by dfferent relatonshp dynamcs. The followng two questons were used to defne a dscouraged borrower: () Durng the last three years, were there tmes when the frm needed credt but dd not apply because t thought the applcaton would be turned down? and () How many tmes dd the frm apply for new loan n the past three years? Based on these questons, we defne a dscouraged small busness borrower as one who answered yes to () and zero-tmes to (). We have 406 dscouraged borrowers who were dscouraged from applyng for a loan. We have 808 small busness borrowers who answered no to () and once or more to () and thus are defned as not dscouraged from applyng. 5, 6 Net, a credtconstraned small busness borrower s defned as one who appled for a new loan (.e., answered once or more to ()) and whose applcaton was dened. Fnally, a non-constraned small busness borrower s defned as one who appled for a new loan and whose applcaton was approved. Of the 808 borrowers who were not dscouraged from applyng, 39 were turned down and, therefore, were credtconstraned. The remanng 669 were approved for a loan. These were the non credt-constraned busnesses. 4. Defnng relatonshp factors Our choce of relatonshp varables s guded by the etant lterature related to small busnesses (see, for eample, Petersen and Rajan, 994; Berger and Udell, 995 and Cole, 998). Specfcally, the relatonshp varables ncluded are as follows: LENGTH s defned as the duraton (n years) that the frm has conducted busness wth the potental lender. ZERO_LENGTH s defned as a dummy varable capturng a zero length of relatonshp wth the potental lender. CHECK and SAVE are defned as dummy varables capturng f the frm has a checkng and savngs account wth the potental lender, respectvely; and PRELOAN s defned as a dummy varable capturng whether there were pre-estng loans wth the potental lender. Fnally, NUMBER_SOURCE s defned as the number of credt sources that the small busness has assocatons wth. Collectvely, our relatonshp varables -- LENGTH, ZERO_LENGTH, CHECK, SAVE and PRELOAN-- measure the strength of relatonshp wth the man credt source. A longer relatonshp 5 Small busnesses that answered no to (), but dd not apply for a loan n the past three years, are ecluded from the sample because they dd not need credt. 6 There are 5 small busnesses that answered yes to () and stll reported that they appled for a loan n the past three years. Out of these 5 small busnesses, 36 appled and approved for a loan and are ncluded n the non-constraned group. The remanng 6 small busnesses that appled, and were not etended a loan, are ncluded n the credt-constraned group.

15 (LENGTH and ZERO_LENGTH) should provde the fnancal nsttuton wth more (and precse) prvate nformaton about the borrower. Smlarly, CHECK and SAVE should also provde more nformaton about the borrower snce the lendng nsttuton can montor the cash flow of the small busness through these accounts. Whle PRELOAN ncreases the leverage of the frm, t also provdes valuable nformaton (through the servcng of that loan) to the bank about the character of the correspondng busness owner and hs credt qualty. We would epect that -- wthn our unfed framework of eamnng loan applcaton, loan approval and loan rate settng -- these relatonshp proes are assocated wth hgher probabltes of beng approved for a loan and negatvely assocated wth loan rates. 7 The epected correlaton between NUMBER_SOURCE and the probablty to apply for a loan s postve, snce the busnesses that have assocatons wth a larger number of lenders are lkely to have appled for credt n the past and are more lkely to apply n the future. In our unfed framework, the epected correlaton between NUMBER_SOURCE and loan approval s negatve. Havng multple credt sources may proy for a poor credt qualty of the frm, and frms may not start multple relatonshps as long as ther loan needs are met by ther prmary lenders. We also nclude SOURCE_ to the Loan Approval Equaton defned as a dummy varable capturng a sngle bankng relatonshp (versus multple relatonshps) to measure how sngle versus multple relatonshps are related to loan approval. The nfluence of NUMBER_SOURCE on the loan rate s ambguous. Whle havng multple credt sources mtgates the lock-n problem, a frm assocated wth multple credt sources could also sgnal fnancal stress. 4. Other factors affectng loan applcaton, loan approval and loan rate Berger and Udell (995) and Cole (998) have argued about the mportance of accountng for the potentally confoundng effect of frm age, whch prevous studes have shown to be hghly correlated wth the relatonshp-length varable dscussed above. Addtonally, Damond (99) argues that the age of a frm should nfluence whether t receves credt, smply because a frm that has been n busness for a longer perod of tme has generated enough reputatonal captal through ts ablty to survve the crtcal start-up perod. We, therefore, nclude AGE, defned as the number of years that the current owners have owned the busness, as a publc nformaton proy. We control for borrower rskness wth the tradtonal borrower-specfc measures of rskness that nclude sze, credtworthness and leverage. We proy for sze and credtworthness wth total busness assets (ASSETS), preta proft margn (PROFMARG), accounts recevable turnover (ARTURN), and 7 The fve relatonshp varables also capture the pre-estng relatonshps wth the credt source (the nsttuton the frm appled for a loan). By the same token, busnesses do not report ther pre-estng relatonshp wth the fnancal nsttutons they dd not apply to. 3

16 nventory turnover (INVTURN). We epect to fnd that as credt avalablty ncreases, the loan rate decreases wth the sze and credtworthness of the frm. We proy for leverage wth busness lablty (DEBT) and accounts payable turnover (APTURN). We epect to fnd that leverage s negatvely related to credt avalablty and postvely related to the loan rate. We also nclude control varables that measure the governance and ndustry characterstcs of small busnesses. The legal form of the busness s reflected n the dummy varables for (non- Subchapter S) corporaton (CORP), Subchapter S Corporaton (SUBS), partnershp (PART), and propretorshp (PROP). We nclude a dummy varable ndcatng whether or not 50% or more of the busness s owned by a sngle famly (CONC50). The ndustry characterstcs are measured by dummy varables for constructon (CONSTR), servce (SERVICE), retal (RETAIL) and other ndustres (OTHERIND). 8 The governance and ndustry characterstcs are ncluded as a proy for credt rsk to the lenders. We nclude a dummy varable to measure the educaton level of the current owner for those wth college degrees (COLLEGE). Also, the characterstcs of the potental lender are measured by dummy varables for commercal banks (BANK), other fnancal nsttutons (FINANCIAL), and nonfnancal nsttutons (NONFINANCIAL). The characterstcs of the fnancal market are measured by Herfndahl nde for fnancal nsttutons (HHINDEX) and a dummy that ndcates whether the frm s located n a Metropoltan Statstcal Area (MSA). 9 We control for the market nterest rate by PRIME RATE at the tme the loan was approved, and also by TERM STRUCTURE SPREAD and DEFAULT SPREAD. TERM STRUCTURE SPREAD s based on the maturty of the loan, and s the dfference between the yeld on government bonds of the same maturty as the loan and the yeld on treasury blls at the tme the loan was approved. DEFAULT SPREAD s defned as the dfference between the yeld on corporate bonds rated BAA and the yeld on the ten-year government bonds at the tme loan was approved. 0 Fnally, we control for loan contract characterstcs by dummy varables as to whether the loan s secured by accounts recevable or nventory (ARINV), by a securty other than accounts recevable and nventory (OTHERSEC), whether the loan s guaranteed (GUAR) and whether the loan has a floatng 8 Note that the governance proes (CORP, SUBS, PART, PROP and CONC50), and the ndustry characterstcs (CONSTR, SERVICE, RETAIL and OTHERIND) are defned as n Burger and Udell (995). 9 Note that the characterstcs of the potental lender (BANK, FINANCIAL, and NONFINANCIAL) and fnancal market concentraton (HHINDEX) are defned as n Petersen and Rajan (994). 0 The cost of captal proes, PRIME RATE, TERM STRUCTURE and DEFAULT SPREAD, are defned as n Petersen and Rajan (994). 4

17 rate (FLOAT). Table I presents a formal descrpton of the varables used n the emprcal estmaton. 4.3 Comparng across dscouraged, credt-constraned and non-constraned small busnesses Table II presents summary statstcs for the varables ntroduced above for dscouraged, credtconstraned, and non-constraned small busnesses n the 998 SSBF data., 3 Frst, we compare the dscouraged small busnesses to those that were not dscouraged from applyng for a loan. The number of fnancal nsttutons that a dscouraged borrower has assocaton wth (NUMBER_SOURCE) s lower (.9 versus 3.). Also, whle 4.0% of the dscouraged frms have a sngle relatonshp (SOURCE_), only 5.4% of those that appled for a loan have a sngle bankng relatonshp. Total assets (ASSET), labltes (DEBT) and accounts recevable turnover (ARTURN) are lower for the dscouraged borrowers relatve to those that appled for a loan. Dscouraged busnesses are less lkely to be Subchapter corporatons (SUBS) and owned by college graduates (COLLEGE); they are more lkely to be sole propretorshps (PROP) and to be majorty owned by a sngle person or famly (CONC50), compared to those busnesses that appled for a loan. Fnally, dscouraged borrowers are located n areas of lower concentratons of banks (.e., lower HHINDEX) and are more lkely to be located n a MSA (MSA). Net, we compare the credt-constraned wth the non-constraned small busness borrowers. Compared to non-constraned borrowers, credt-constraned borrowers are more lkely to have no bankng relatonshps (ZERO_LENGTH) (4.4% versus 33.4%) and are less lkely to have pre-estng loans (PRELOAN) (.4% versus 7.5%) wth ther potental lender at the tme they appled for a loan. However, there appears to be no sgnfcant dfference n the number of credt sources (NUMBER_SOURCE ) between constraned and non-constraned small busnesses. Among the fnancal varables measurng borrower characterstcs, there are sgnfcant dfferences between the credt-constraned and non-constraned busnesses. For nstance, the number of years under the current management (AGE) s lower for credt-constraned busnesses. Also, the nventory turnover (INVTURN) and accounts payable turnover (APTURN) of credt-constraned busnesses are hgher than those of the non-constraned busnesses. Fnally, credt-constraned busnesses are less lkely to be Note that ARINV, OTHERSEC and GUAR are defned as n Burger and Udell (995), whle FLOAT s defned as n Petersen and Rajan (994). Busnesses that have relatonshps lastng longer than 30 years wth the current lender and those that were owned by the current owners longer than 30 years are ecluded from the sample. Those that were etended loans from Famly or Other Indvduals and Owner are also ecluded. 3 To mnmze the effect of outlers, those busnesses whose nterest rate on the latest approved loan was n the upper % of the loan rate dstrbuton (hgher than 0 percentage ponts) and those that have assocatons wth more than 0 fnancal nsttutons, were ecluded from the sample. 5

18 corporatons (CORP) and are more lkely to be sole propretorshps (PROP); they are more lkely to be majorty-owned by a sngle person or famly (CON50), compared to ther non-constraned counterparts. 4 Overall, there are sgnfcant dfferences n characterstcs between small busness borrowers that were dscouraged from applyng for a loan and those that were not. Furthermore, among those busnesses that appled for a loan, there are sgnfcant dfferences n characterstcs between those that appled for credt but were constraned (.e., turned down for the loan), and those that appled and receved the loan. 5. Multvarate Analyss 5. Estmatng the two-stage selecton: applyng and beng approved for a loan Whether or not a gven small busness borrower s credt-constraned s not observable f the borrower s dscouraged from applyng for a loan. We estmate the lkelhood of beng constraned, gven by Equaton (7), by approprately correctng for ths sample selecton bas. We also note that n ths secton we are testng for an overall valdaton of our hypothess n the realm of small busness loans. Therefore, we do not partton the loans on any dmensons (such as whether they were transacton-drven), nstead focusng on all vald small busness loans n the data. We, however, do separately eamne small busness lnes of credt n our robustness secton later n the paper. The results of our estmaton are presented n Table III. The ndependent varables, capturng borrower-lender relatonshps and borrower characterstcs, ncludng governance and ndustry characterstcs, have been dscussed n Secton 4. The margnal effects of the ndependent varables ncluded n Equaton (7) are also provded n Table III. The margnal effects of each ndependent varable are calculated whle holdng all other eplanatory varables at ther respectve sample means. 5 The role of relatonshps n applyng for a loan. The relatonshp wth the potental lender (LENGTH, ZERO_LENGTH, CHECK, SAVE and PRELOAN) and the characterstcs of the potental lender (BANK, FINANCIAL and NONFINANCIAL) are not observed f the small busness dd not formally apply for a loan, and therefore these varables are not ncluded n from the Applcaton equaton. Those that have relatonshps wth more credt sources (NUMBER_SOURCE) are more lkely to apply for a loan. An ncrease by one unt n the number of credt sources (NUMBER_SOURCE) ncreases the probablty of applyng for a loan by 7.9 percentage ponts. Younger busnesses (lower 4 For those small busnesses holdng a loan, the average nterest rate on ther most recent loan equals 9.34 percent. 5 We add one and take the natural logarthm of LENGTH and DEBT. For nstance, LENGTH s operatonalzed as ln(+length) to ensure we do not lose observatons wth zero length. At the same tme, we nclude ZERO_LENGTH n our estmaton. 6

19 AGE) and those wth larger assets (ASSETS), and those wth lower accounts recevable turnover (ARTURN) and nventory turnover (INVTURN), are more lkely to apply for a loan. In addton, those n constructon (CONSTR) are more lkely to apply for a loan. The fnancal market characterstcs (HHINDEX and MSA) sgnfcantly affect the probablty of applyng for a loan. Busnesses located n more compettve fnancal markets (hgher HHINDEX) are more lkely, and those that are located n MSAs are less lkely to apply for a loan. Fnally, the probablty of applyng for a loan ncreases wth the educaton of the busness owner (COLLEGE). The remanng governance characterstcs (CORP, SUBS, PART and CONC50) do not appear to affect the probablty of applyng for a loan. The role of relatonshps n beng approved for a loan. Among relatonshp varables, the coeffcents for LENGTH, ZERO_LENGTH, PRELOAN and SOURCE _ are sgnfcant. Busnesses that do not have a relatonshp wth the potental lender (ZERO_LENGTH) are 7.4 percentage ponts less lkely to be approved for a loan. Controllng for a zero length of relatonshp, busnesses that have longer relatonshps (LENGTH) wth the potental lender are less lkely to be approved for a loan. At the same tme, those that have a pre-estng loan (PRELOAN) wth the fnancal nsttuton are 6.7 percentage ponts more lkely to be approved for a loan. The coeffcent of a sngle credt source (SOURCE _) s sgnfcant and postve, showng that those that have a sngle bankng relatonshp are more lkely to be approved for a loan. However, among those that have multple bankng relatonshps, the number of credt sources (NUMBER_SOURCE) does not sgnfcantly affect loan approval. The probablty of beng approved for a loan ncreases wth the number of years under the current management (AGE) and total lablty (DEBT). The probablty of beng approved for a loan decreases wth account payable turnover (APTURN) and ncreases wth the educaton of the busness owner (COLLEGE). Small busnesses that appled to banks (BANK) (relatve to other types of fnancal nsttutons) were less lkely to be approved for a loan. Our fndng of a negatve correlaton between the length of relatonshp and loan approval s dfferent from the prevous lterature. Cole (998), for eample, fnds that the length of relatonshp s postvely correlated wth the lkelhood of beng approved for a loan. However, when zero length of relatonshp s ncluded n the estmaton, the coeffcent of the length of relatonshp n Cole s estmaton s nsgnfcant. We also nteract the length of relatonshp (LENGTH) wth the varable measurng whether there was a pre-estng loan wth the lender (PRELOAN) n order to nvestgate whether the length of relatonshp has a varyng effect for those busnesses that have a pre-estng loan. These estmaton results are reported n Table III (Model ). Our results show that for those that do not have a pre-estng loan (PRELOAN) wth the lendng nsttuton, the length of relatonshp (LENGTH) does not have a sgnfcant effect on loan approval. However, for those busnesses that have a preestng loan (PRELOAN) wth the lendng nsttuton, the mpact of pre-estng loans (PRELOAN) on 7

20 the lkelhood of beng approved for a new loan decreases as the length of relatonshp (LENGTH) ncreases. In other words, at the ntal stages of the relatonshp, beng approved for a new loan s postvely and sgnfcantly correlated wth a pre-estng loan (PRELOAN). In sum, the results of a two-stage selecton model show that relatonshp varables are sgnfcant predctors of beng dscouraged from applyng for a loan and of beng approved for a loan. We now turn to the role of relatonshps n determnng loan rates. 5. Estmatng the loan rate ^ ^ We frst calculate λ and λ n Equaton (6) usng the estmates of, and ρ. Then we estmate Equaton (5) usng the sample of those busnesses that obtaned a loan n the past three years. The estmaton results are gven n Table IV, whch also provdes estmaton results wthout correctng for selecton bas. Note that the loan rate s defned as the nterest rate on the latest loan. In Model, we nclude the fnancal varables, governance and ndustry characterstcs, and the length of relatonshps and the number of credt sources. The coeffcent of the length of relatonshp (LENGTH) at -0.4 suggests that a small busness wth an addtonal 5 years of relatonshp -- 6 years versus year -- pays 30.3 bass ponts less on ts most recent loan. 6 The coeffcent for the number of credt sources (NUMBER_SOURCE) s sgnfcant, suggestng that busnesses that mantan multple bankng relatonshps face hgher loan rates. When pre-estng accounts (CHECK, SAVE and PRELOAN) are added n the estmaton (Model ) to measure the effect of the nature of the relatonshp wth the lender, the length of relatonshp (LENGTH) and the number of credt sources (NUMBER_SOURCE) are stll sgnfcant whle the correspondng coeffcents for the nature of the relatonshp (CHECK, SAVE and PRELOAN) are not sgnfcant. Fnally, we nclude the zero length of relatonshp (ZERO_LENGTH) varable n our estmaton (Model 3). In ths estmaton, the length of relatonshp (LENGTH) becomes nsgnfcant and decreases from to -0.37, suggestng that, among busnesses that have a relatonshp wth the potental lender, the rate does not decrease wth the length of relatonshp. The coeffcent for the zero length of relatonshp (ZERO_LENGTH) varable s sgnfcant and negatve, suggestng that busnesses that have no relatonshp wth the lender, at the tme they apply for a loan, receve loans at rates that are about 5 bass ponts hgher. Model 4 corrects for the sample selecton bas dscussed prevously. Zero length of relatonshp (ZERO_LENGTH) becomes nsgnfcant as well as the number of credt sources (NUMBER_SOURCE). Among fnancal characterstcs, small busnesses wth hgher levels of years under the current management (AGE), total assets (ASSET) and labltes (DEBT) have lower rates. The coeffcent of the number of years under current management (AGE), -0.8, suggests that a small 6 Snce LENGTH s operatonalzed as ln(+length) and the estmated coeffcent of ln(+length) s - 0.4, the effect of 5-years of relatonshp -- 6 years versus year -- equals -0.4*(ln (+6)-ln (+)). 8

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