The Racal and Gender Interest Rate Gap n Small Busness Lendng: Improved Estmates Usng Matchng Methods* Yue Hu and Long Lu Department of Economcs Unversty of Texas at San Antono Jan Ondrch and John Ynger Center for Polcy Research and Department of Economcs Syracuse Unversty March 20 Correspondng Author: Jan Ondrch Center for Polcy Research 426 Eggers Hall Syracuse Unversty Syracuse, NY 3244 jondrch@maxwell.syr.edu * The authors gratefully acknowledge support from the Ewng Maron Kauffman Foundaton and thank Coady Wng and the partcpants at New York Camp Econometrcs 200 for helpful dscusson.
ABSTRACT Ths paper studes racal and gender nterest rate gaps n small busness credt markets usng the 993, 998 and 2003 waves of the Survey of Small Busness Fnances (SSBF). These gaps are estmated wth a semparametrc (kernel) propensty-score matchng method that uses a bandwdth selected by least-squares cross valdaton. Our fndngs ndcate that, on average, Black and Hspanc owned frms pay an nterest rate that s, respectvely, 0.79 and 0.486 percentage ponts hgher than the rate pad by comparable Whte owned frms. We fnd no evdence of that busnesses owned by Whte women pay dfferent nterest rates than comparable busnesses owned by Whte men. We also fnd that n several cases our estmatng method produces sgnfcantly dfferent estmates and even dfferent hypothess test results than the tradtonal Blnder-Oaxaca decomposton method, whch s based on more restrctve assumptons. Key Words: Small Busness Credt; Lendng Dscrmnaton; Blnder-Oaxaca Decomposton; Propensty-Score Matchng.
. Introducton About half of prvate-sector output s attrbutable to small busnesses, defned as nonfarm establshments wth fewer than 500 employees, and the share of these busnesses owned by people n mnorty groups and by women has been growng over tme (Olson 2005). Researchers fnd consstent evdence that busnesses owned by people n legally protected and hstorcally dsadvantaged classes (henceforth smply protected classes) are more lkely to be dened credt than are busnesses owned by those n the majorty class, even controllng for characterstcs related to credt worthness. 2 Evdence concernng dspartes n nterest rates s more mxed. Some studes fnd no evdence of nterest-rate gaps (Cavalluzzo and Cavalluzzo 998; Cavalluzzo et al. 2002; Blanchard et al. 2007), whle other studes fnd that mnorty and women busness owners pay hgher nterest rates than do comparable frms owned by Whte men (Blanchflower et al. 2003). Barsky et al. (2002) pont out that studes of nterest-rate gaps n small busness lendng frequently fal to address problems that arse when behavoral relatonshps are nonlnear and when the groups beng compared have lttle overlap n ther characterstcs. They show that these problems can be addressed usng semparametrc propensty-score matchng and other technques. Black et al. (2006) use semparametrc matchng technques to study wage dfferentals, but matchng technques have not yet appeared n the lterature on small busness credt. 3 Accordng to Frequently Asked Questons at the webste of the U.S. Small Busness Admnstraton (SBA), Offce of Advocacy, http://appl.sba.gov/faqs/faqindexall.cfm?aread=24. 2 Ths evdence s revewed n Blanchard et al. (2007). 3 There are modelng optons other than matchng. Hrano, Imbens and Rdder (2003) show that weghtng by the nverse of a nonparametrc estmate of the propensty score leads to an effcent estmate of the average treatment effect. Busso, DNardo, and McCrary (2009) provde a comparson of the fnte sample propertes of propenstyscore matchng and weghtng estmators. Khan and Tamer (2009) and Kahn and Nekpelov (2009) nvestgate the convergence rate of weghtng estmators n the absence of strong support condtons.
Falure to account for nonlnearty n the relatonshp between the nterest rate and ts determnants wll result n based estmates. Blanchflower et al. (2003) and Blanchard et al. (2007) provde a partal soluton to ths problem by splttng ther sample and runnng separate regressons for each part. Ths strategy, whch s equvalent to ntroducng a set of nteracton terms, s less general than the approach used n ths paper, whch estmates the nterest-rate equaton usng semparametrc methods. The exstng lterature on nterest-rate gaps also gnores the common support condton, that s, t gnores the problems that arse when observatons compared across classes are dssmlar. Prevous studes pont out that mnorty owned frms tend to dffer from Whte owned frms n credt relevant characterstcs and two studes, Blanchflower et al. (2003) and Blanchard et al. (2007), fnd that unequal treatment vares wth such characterstcs. Under these condtons, tradtonal regresson technques that do not requre a common support also yeld based results. In ths study we attempt to address these two emprcal problems usng semparametrc propensty-score matchng wth data from the 993, 998, and 2003 waves of the Survey of Small Busness Fnances (SSBF). Matchng allows us to examne the support condton n a straghtforward way. In addton, unlke prevous studes, the semparametrc matchng method that we employ does not mpose assumptons on the functonal form of the nterest-rate equaton. The study s organzed as follows. In secton 2 we examne the emprcal challenges by revewng the methodologes adopted n studyng the nterest rate gap n small busness lendng. In secton 3 we present the theory of the tradtonal Blnder-Oaxaca decomposton method and the semparametrc propensty-score matchng method. The data set used for ths study s descrbed n secton 4. The estmaton results are provded n secton 5. We fnd that mnorty owned frms pay systematcally hgher nterest rates on approved loans than do Whte owned frms. Unlke prevous studes, however, our results suggest that Whte female owners of small 2
busnesses are not lkely to be treated dfferently than ther male counterparts. Concludng remarks can be found n secton 6. 2. Prevous Lterature The dentfcaton of dsparate treatment n the settng of nterest rates requres the dentfcaton of the nterest rate that would have been offered to a mnorty owned (female owned) small busness f t had been owned nstead by a Whte (male). The task then s to create ths ceters parbus condton so that the systematc dfferences n the outcome are attrbutable to dsparate treatment. The mplcaton s that a dsparate treatment study should attempt to fnd pars of ndvduals, one from the majorty class and one from the protected class, wth otherwse dentcal characterstcs. Second, the study should construct parwse dfferences n loan outcomes, such as denal of the loan or the nterest rate obtaned. Thrd, the study should aggregate the nformaton n a meanngful way to make a determnaton about the possble presence of dsparate treatment. The goal of ths study s to employ matchng to approxmate a quas-experment to provde a provsonal, yet meanngful estmate of the extent of dsparate treatment n nterest rates on loans to small busness owners. Ths study also contrbutes to the lterature by poolng three dfferent Surveys of Small Busness Fnances to produce more precse estmates. The exstng research on the nterest rate gap n small busness lendng has used a regresson approach or a lmted dependent varable methods n whch nterest rates charged on a loan or credt denal are a functon of the owner s race and a set of credt-worthness assessment crtera that mght be used by fnancal nsttutons. The coeffcent on the owner's race, or more generally, an aggregate measure of the systematc dfferences n coeffcents captures dsparate treatment. For smplcty, many studes assume a lnear functonal form n the econometrc regresson model, although no theorem suggests ths s the case. Some studes, for example, 3
Blanchflower et al. (2003) and Blanchard et al. (2007), challenge ths lnearty assumpton by runnng separate regressons for subsamples defned by organzaton type, frm sze, frm age, the scope of the market n whch the frms operate, etc. The fndngs n Blanchflower et al. (2003) ndcate that apparent dsparate treatment s not the same under all crcumstances. For nstance, Black owners of frms that were recently establshed are 36 percentage ponts more lkely to be charged hgher nterest rate than Black owners of frms that have exsted for more than 2 years. Evdence concernng average dscrmnaton n the nterest rates charged to small busnesses s more mxed. Some studes fnd no evdence of dscrmnaton n settng nterest rates (Cavalluzzo and Cavalluzzo 998; Cavalluzzo et al. 2002; Blanchard et al. 2007), whle other studes fnd that mnorty and women busness owners pay hgher nterest rates than do comparable frms owned by Whte men (Blanchflower et al. 2003). The goal of ths study s to use semparametrc propensty-score matchng to estmate racal and gender nterest rate gaps for small busness owners and compare these estmates to those obtaned by the tradtonal Blnder-Oaxaca decomposton method. 3. Econometrc Methods 3.. The Blnder-Oaxaca Decomposton Method The frst of our two econometrc methods s the tradtonal Blnder-Oaxaca decomposton method. Ths method decomposes the dfference of two lnear regresson functons, one for a protected class and one for a majorty group, nto a dscrmnaton effect that estmates the nterest rate gap as unequal treatment at the average default-rsk component levels of the protected class and a resdual endowment effect. 4 4 Under the assumptons that lenders weghts on each credt characterstc accurately reflects ts mpact on the probablty of default and that no credt characterstcs observed by the lender are omtted from the regresson, ths dscrmnaton effect corresponds to the legal concept of dsparate-treatment dscrmnaton. See Ross and Ynger (2002). We return to ths ssue after dscussng our results. 4
The Blnder-Oaxaca decomposton method s a regresson-based method that assumes a lnear functonal form. Wrte the regresson model for the nterest rate charged to the majorty class as: Y ι X β ε, 0 0 0 0 0 E( ε ) 0; V( ε ) I, 2 0 0 0 () where Y 0 s the N0 x dependent varable vector of nterest rates charged on majorty class loans, ι s an N0 x vector of ones, α 0 s the ntercept for the majorty class, X 0 s the N0 x k regressor matrx of characterstcs of default rsk for the majorty class, and β 0 s the kx coeffcent vector. OLS s best lnear unbased and satsfes the followng equaton: Y a ˆ X βˆ, (2) 0 0 0 0 where Y 0 s the sample mean of the dependent varable, X 0 s the row vector of regressor means, and the hat sgnfes OLS estmator. Wrte the regresson model for the nterest rate charged to the protected class as: Y ια X β ε, E( ε ) 0; V( ε ) I, 2 (3) where Y s the N x dependent varable vector of protected class nterest rates, ι s an N x vector of ones, α s the ntercept for the protected class, X s the N x k regressor matrx of protected class characterstcs of default rsk, and β s kx. Agan, OLS s best lnear unbased and satsfes the followng equaton: Y αˆ X β ˆ (4) where Y s the sample mean of the dependent varable, and X s the row vector of regressor means. 5
Let Y Y Y0 denote the dfference n mean outcomes across classes, let X X X 0 denote the dfference n mean endowments, and let βˆ βˆ ˆ β 0 denote the dfferences n coeffcents. Then the dfference n mean outcomes can be decomposed as follows: Y αˆ αˆ X βˆ Xβ ˆ, (5) 0 0 where the sum of the frst three terms on the rght-hand sde of equaton (5) s the total effect of dsparate treatment. A smple method for obtanng the Blnder-Oaxaca dscrmnaton effect uses the followng pseudo-model. The nterest-rate equaton for the majorty class s wrtten as: Y Z β ε 0 0 0 E( ε ) 0; V( ε ) I, 2 0 0 0, (6) where Y 0 s N0 x, Z 0 s a N0 x ( k ) matrx that ncludes a constant term, and β s ( k ) x, whle the nterest-rate equaton for the protected class s wrtten as: Y ια Z β ε, E( ε ) 0; V( ε ) I, 2 (7) where Y s N x, ι s N x, α s a scalar, and Z s a N x ( k ) matrx that ncludes a constant term. By replacng the condtonal expectatons n equaton (3) wth ther correspondng fnte sample analog, an estmator for the dscrmnaton effect can be derved as ˆ, Y Z β (8) N I where I denotes the set of sample members of the protected class. It s obtaned by the followng two-step method. Frst, run an OLS estmaton of the model for the majorty class to get the estmated coeffcent vector ˆβ. Next, regress Y Zβ ˆ on constant vector ι to get an estmate of the Blnder-Oaxaca dscrmnaton effect. To see that ths gves the correct answer, note that the estmate of the ntercept s Y αˆ ˆ 0 Xβ 0. Substtutng for Y from equaton (4) and rearrangng gves αˆ αˆ ˆ ˆ 0 X( β β 0), whch s exactly the Blnder-Oaxaca dscrmnaton effect. 6
The most appealng feature of the Blnder-Oaxaca method s ts apparent smplcty, although ths smplcty s a by-product of a restrctve lnearty assumpton. Moreover, standard errors have to be adjusted to account for the two steps nvolved n the model. Ths s dscussed n the Appendx. 3.2. The Semparametrc Propensty-Score Matchng Method The more modern semparametrc propensty-score matchng method relaxes the lnearty assumpton n the Blnder-Oaxaca nterest-rate equatons. For a gven sample frm the semparametrc propensty score matchng model specfes. where Y ( X ), (9) D D s 0 () when the ndvdual s a member of the protected (majorty) class and s an d fnte-varance mean-zero error term wthn classes that s ndependent across classes. An evaluaton problem arses because, at any tme, a frm may be ether owned by a member of the majorty class or the protected class, but not both. The quantty of nterest s the nterest-rate gap, whch s the expected dfference n the nterest rates pad by otherwse equvalent members of the two classes. Ths s called the effect of treatment on the treated. Formally, let Y be the potental nterest rate pad by a protected class frm, and let Y 0 be the potental nterest rate f the frm had been owned by a member of the majorty class. The effect of treatment on the treated s defned as TT E Y Y X, D E Y X, D E Y X, D. (0) 0 0 The average effect of treatment on the treated, ATT, s the average value of TT across sample members of the protected class. The dffculty n estmatng ATT s that, whle an estmate of the mean protected class outcome, E Y X, D, can be obtaned usng data on protected class frms, a drect estmate of ts counterfactual mean, E Y X, D, s not avalable. 0 7
Matchng estmators rely on the assumpton that comparson (non-treatment) outcomes, Y 0, are ndependent of the treatment, condtonal on a set of observable characterstcs, D, whch ndcates ownershp by a protected class, X. Ths selecton on observables assumpton s also called the Condtonal Independence Assumpton (CIA) and s expressed as follows: Assumpton : Y0 D X. () In partcular, t mples that the potental nterest rate that a majorty class frm must pay s ndependent of the class of the frm owner condtonal on a relevant set of observable characterstcs. Ths assumpton produces a comparson group that resembles the control group n an experment n one key respect: condtonal on X the dstrbuton of Y 0 gven D s the same as the dstrbuton of Y 0 gven D 0. (It s worth notng that we do not observe Y 0 gven D.) In addton, t s also assumed that for all X there s a postve probablty of beng treated ( D ) and of not beng treated ( D 0 ), whch can be wrtten as follows: Assumpton 2: D X Pr for all X. (2) Ths s called the common support assumpton, and t s an mportant assumpton that the Blnder-Oaxaca decomposton method fals to address. The support condton mples that a match from the majorty group frms can be found for each and every protected class frm. If Assumptons and 2 are satsfed, then, after condtonng on X, the Y 0 dstrbuton observed for the matched frms owned by members of the majorty group can be substtuted for the mssng Y 0 dstrbuton for protected class frms. Matchng methods have been used wdely n the program-evaluaton lterature as a way to approxmate an experment wth non-expermental data (Heckman, Ichmura, and Todd 997, 998; Smth and Todd 200, 2005). Ths approach has the advantages that t s less expensve and less ntrusve than an experment. Conventonal matchng estmators match each program 8
partcpant wth an observably smlar nonpartcpant and derve the average dfference n ther outcomes to measure the effect of the program. Several consstent matchng methods have been developed. As the sample gets arbtrarly large, all matchng estmators are conductng exact cell matchng. In a fnte sample, the choce of a matchng estmator s more of a practcal ssue, n the sense that t not only depends on the data but also on the capablty of the partcular matchng estmator to deal wth specfc data ssues. The smplcty of the Blnder-Oaxaca decomposton method rests on a restrctve lnearty assumpton. In practce, the potental nonlnear functonal form problem mght be caused by hgh order terms of explanatory varables and nteractons among them. For example, Ross and Ynger (2002) pont out that varaton n underwrtng standards across lenders takes the form of nteractons between lender characterstcs and underwrtng varables. Instead of mposng a specfc functonal form on the relatonshp between the dependent varable and the regressors, we relax the lnearty assumpton by usng a kernel regresson technque that allows the data to speak for themselves. Unfortunately, f the dmenson of X s hgh, one may run nto the curse of dmensonalty problem, whch arses when some subset of observatons n the treatment group have no correspondng frm from the comparson group wth exactly the same values of X. Rosenbaum and Rubn (983) frst ntroduced the propensty score as a means of reducng the dmenson of the condtonng problem. by matchng on the probablty of treatment. They showed that the dstrbutons of X are the same n the treatment and comparson group condtonal on the probablty of treatment. Thus, propensty-score matchng combnes groups of frms wth potentally dfferent values of X but dentcal values of 9
X Pr D. Matchng on the scalar propensty score n ths way avods the curse of dmensonalty. As shown n Smth and Todd (200), under Assumptons and 2, the mean mpact of treatment (beng a member of a protected class) can be rewrtten as E, (3) Y Y D E Y D E E Y D, P where P Pr D X 0 P Y 0. The second term can be estmated from the mean outcomes of the matched (on P ) comparson group. Matchng estmators take the form N s I S p Y Eˆ Y D, P, 0 (4) where ˆ Y D, P W j E 0, Y0 j s the matched outcome. 0 I 0 sample majorty and protected class members respectvely, and N s s the number of ndvduals both n sets I and I and I denote the set of S p s the common support regon, S p (see Smth and Todd 2005). The match for each protected class member n the summaton of (4) s a weghted average over the outcomes of members of the majorty class, where the weghts W, j depend on the dstance between P and P j. In the kernel matchng method used by Heckman, Ichmura, and Todd (997, 998) and Heckman, Ichmura, Smth and Todd (998), the weghtng functon s P P P P W, j K / K, j k (5) h k I h 0 where K s a kernel functon wth bandwdth parameter h. 5 Ths semparametrc propenstyscore matchng method that we use nvolves two steps. The frst step s propensty-score estmaton usng a logt model (as dscussed above). The second step uses a kernel functon to 5 We use the second-order Epanechnkov kernel defned as K 4 3 2,, 0, otherwse. 0
estmate the average treatment effect of protected class ownershp on nterest rates. The semparametrc propensty-score matchng results provde a robustness check on the Blnder-Oaxaca method. The key advantage of the propensty-score matchng method s that t avods mposng the restrctve lnear functonal form assumpton. The optmal choce of bandwdth parameter h for the gven kernel functon K s crtcal, even n a large sample. As shown by L and Racne (2007) and Pagan and Ullah (999), the least-squares cross-valdaton procedure selects optmal bandwdth by mnmzng mean-squared error Y ˆ 0 Y0,- 2, where ˆ 0,- 0 I0 N Y s the leave-one-out estmator that omts the th observaton n the comparson group and uses the remanng comparson-group observatons to ˆ generate Y0,, the estmate of Y 0. Because the th observaton s not ncluded n the estmaton, ths out-of-sample forecast avods the overfttng problem at h 0. Black and Smth (2004), the frst to apply the least-squares cross-valdaton procedure to semparametrc propensty-score matchng, clam that ths leave-one-out estmator does a good job of replcatng the essental features of the estmaton problem. In comparson, the choce of bandwdth by other methods, such as Nearest Neghbor, s more arbtrary. In the SSBF data, we have substantally fewer observatons belongng to the protected classes than to the majorty classes (Whtes n the case of the nterest rate gap for Blacks and Hspancs, males n the case of the female nterest rate gap, and Whte males n the case of the nterest rate gap for Whte females.) In fact, there are only 30 Black owned frms and 59 Hspanc owned frms n the pooled SSBF data compared to over 3,266 frms owned by Whtes. The semparametrc propensty-score matchng estmator that we employ s more effcent n handlng ths asymmetrcally dstrbuted sample because t uses sample nformaton effcently.
Usng Monte Carlo analyss, Froelch (2004) shows that kernel matchng, or a varant called rdge matchng, consstently performs well on a mean-squared error crteron. 6 The semparametrc propensty-score matchng estmator s more computatonally ntensve than the Blnder-Oaxaca decomposton method, because t requres a choce of optmal bandwdth and bootstrapped standard errors. In addton, the speed of convergence s slower for the semparametrc matchng estmator than for the Blnder-Oaxaca estmator. However, the payoffs to usng the semparametrc matchng estmator are also consderable. Frst, the semparametrc matchng estmator relaxes the lnearty assumpton of the Blnder-Oaxaca decomposton method and s therefore not subject to the bases when ths assumpton s volated. Second, the semparametrc matchng estmator enables a straghtforward examnaton of the support condton that prevents the researcher from erroneously makng predctons outsde the support of the data. 7 Ths second advantage of semparametrc matchng wll be addressed n greater detal n secton 5. 4. The SSBF Data The prncpal data used n the econometrc analyss of ths study are the 993, 998, and 2003 waves of the Survey of Small Busness Fnance (SSBF) from. Ths aggregate repeated cross-sectonal data contans 4,93 nonfnancal, nonfarm small busnesses. The sample s natonally representatve, and contans rch nformaton regardng the frm, such as ts age, locaton, employment, and ndustry. In addton, the data set also ncludes the term and type of the most recent loan each frm obtaned. The survey sample was drawn from more than 7.5 6 An alternatve way of addressng the over-samplng ssue s to employ a varant of Nearest Neghbor calper matchng called radus matchng, whch tends to use all of the comparson members wthn the calper to construct the counterfactual. Abade and Imbens (2006) show that bootstrappng, the most readly avalable technque of calculatng standard errors for matchng methods, gves ncorrect results for Nearest Neghbor matchng because of lack of smoothness. Therefore, radus matchng s problematc. In addton, Froelch (2004) shows that Nearest Neghbor matchng performs undesrably over a wde range of possble data-generatng processes. 7 Estmatng the wealth gap between Black and Whte households, Barsky et al. (2002) show that support problems can exacerbate msspecfcaton of the parametrc model. 2
mllon frms each year. A frm would be unlkely to appear n two surveys and t would appear n all three surveys wth a probablty approachng zero. We take advantage of the large sample obtaned from poolng all three waves of the SSBF data allows us to use a larger sample n the estmaton and the larger sample n turn allows us to produce more precse estmates of the nterest rate gap n small busness lendng and to check the robustness of the model specfcaton under alternatve assumptons. In the analyss of the racal nterest rate gap the number of Black-owned frms n the data s 30 and the number of Hspanc-owned frms s 59, whle, n the analyss of the gender nterest rate gap the number of female-owned frms s a much larger 84 and the number of frms owned by Whte females s 702. Table 2 presents the descrptve statstcs from the pooled SSBF data for all frms that had an actve loan durng the survey years, by race/ethncty and gender. These statstcs are not weghted. On average frms owned by mnorty classes pay a hgher nterest rate than those owned by Whtes. In partcular, the nterest rates charged to Black owned frms are on average 2.5 percentage ponts hgher than those charged to Whte owned frms. The Hspanc-Whte dfference n nterest rates s.4 percentage ponts. Dfferences n nterest rates by gender are relatvely small. The nterest rates charged to frms owned by women are n fact 0.07 percentage ponts lower than those charged to male owned frms. Frms owned by mnorty classes also dffer from Whte owned frms n ther credtworthness characterstcs. For example, mnorty owned frms are generally younger and smaller. In terms of credt hstory, mnorty owned frms seem less credtworthy than ther Whte counterparts as measured by whether the owner had been delnquent for more than 60 days on personal oblgatons over the past three years, or had legal judgments aganst hm or her over the precedng three years. 3
5. Results 5.. Propensty-Score Estmaton Results A logt model can be used to estmate the propensty score of mnorty-ownershp status based on the SSBF data. Varable selecton for the propensty-score estmaton s based on two consderatons: theory and evdence about the varables related to treatment and to the outcome, as well as goodness-of-ft. The goal s to construct a model that estmates the probablty that a frm has an owner from the protected class based on all the frms characterstcs that a lender can legtmately consder when t makes a decson about the frm's credtworthness. The exstng lterature on dscrmnaton n small busness lendng (Cavalluzzo et al. 2002; Blanchflower et al. 2003; and Blanchard et al. 2007) suggests that varables n the followng categores should be used to predct a frm's credtworthness: the frm's credt hstory, the frm s characterstcs, and the features of the specfc loan. Wthn each category, the varables are chosen based on the crteron of goodness-of-ft, that s, whether the coeffcent of the ncluded varable s statstcally sgnfcant at conventonal levels and whether t ncreases the model's predcton power by a substantal amount (Heckman 998). We do not nclude the Dunn and Bradstreet credt score n our specfcaton because ths credt score s based on the frm s entre credt hstory, ncludng delnquent events on the loan under consderaton. Such nformaton postdates the nformaton avalable to the lender and s lkely to ntroduce bas. The propensty score estmaton results for frms owned by Blacks and Hspancs are presented n Table 3A, those for females and Whte females can be found n Table 3B. More hghly educated owners are less lkely to be Hspanc generally. When a frm receves a fxed nterest-rate loan, t s more lkely that ts owner s Black, Hspanc or a Whte female. The hstograms of the estmated propensty scores for each group are shown n Fgure through Fgure 4. In all but the last two groups, the left hstogram presents propensty scores for frms 4
owned by Whtes (the D 0 group), whle the rght hstogram presents the propensty scores for mnorty owned frms (the D group). For the last two groups, treatment refers to the frm beng (Whte) female owned; the comparson group conssts of (Whte) male-owned frms. The horzontal axs ndcates ntervals of the propensty score and the heght of each bar on the vertcal axs defnes the fracton of the correspondng sample wth scores n the correspondng nterval. The hstograms are mportant because they can be used to examne the support condton for the propensty score. Along the dmenson of race, the mean propensty score gven D s about 0.5, whle the mean propensty score for D 0 s about 0.06. In the case of gender, the mean propensty score gven D s about 0.27 whle the mean propensty score for D 0 s about 0.20. Ths dsproportonal concentraton of the propensty score at the lower tal (especally among the racal/ethnc groups) s not surprsng. The sample conssts of 289 mnorty owned frms and 3,266 frms owned by Whtes. As dscussed n greater detal below, the kernel estmaton technques that we use can handle ths oversamplng ssue. In addton to the hstograms regresson-based balancng tests are conducted to check whether the dstrbutons of the covarates are balanced, condtonal on the value of the propensty score. The basc ntutton behnd the balancng test s that after condtonng on the propensty score, addtonal condtonng on X should not provde new nformaton about D. If t does, ths suggests msspecfcaton n the model used to estmate the propensty score. The regresson-based balancng test tself s smple: t regresses each condtonng varable on a polynomal n the propensty score and an nteracton between the treatment dummy and the same polynomal. If balance has been acheved, then the coeffcents on all the nteractons 5
should equal zero. 8 Almost all of the covarates pass the balancng test. For reasons of parsmony, the results of the balancng tests are not presented, but are avalable from the authors upon request. 5.2. Blnder-Oaxaca Estmaton Results Frst-stage Blnder-Oaxaca estmaton results for Whtes, Blacks and Hspancs are presented n Table 4A, those for males and females are presented n Table 4B, and those for Whte males and Whte females are presented n Table 4C. Whle results vary across groups, pror personal delnquency generally ncreases the nterest rate charged and frms wth more hghly educated owners are generally charged lower nterest rates on busness loans. The results for varous racal groups usng the SSBF data are shown n Table 5. Panel A presents cross-group dfferences n nterest rates on approved loans usng the Blnder-Oaxaca decomposton, and Panel B shows estmates of these dfferences based on the semparametrc propensty-score matchng method. Under the assumpton that our extensve lst of credt varables adequately controls for cross-group dfferences n credtworthness that lenders can legtmately consder, these dfferences can be nterpreted as measures of dscrmnaton. As shown n Panel A of Table 5, we fnd busnesses owned by Blacks and Hspancs have to pay hgher nterest rates than busnesses owned by Whtes, controllng for credtworthness and other factors shown n Table. Black owned frms face the largest degree of dscrmnaton, as defned by ths decomposton method; the nterest rates these frms pay are.09 percentage ponts hgher than the rates pad by ther Whte counterparts. On average, frms owned by Hspancs pay nterest rates 0.453 percentage ponts hgher than frms owned by Whtes. These estmates are all statstcally sgnfcant at conventonal levels. 8 See Smth and Todd (2005) for a dscusson of other standard balancng tests. 6
5.3. Semparametrc Propensty-Score Matchng Estmaton Results The estmates n Panel B of Table 5 are based on bandwdths chosen usng leave-one-out cross-valdaton, and the standard errors are bootstrapped wth 2000 replcatons. Agan, the key dfference between regresson-based estmates, such as Blnder-Oaxaca, and propensty-score matchng s that propensty-score matchng does not depend on a lnear functonal form assumpton. The semparametrc propensty-score matchng estmates dffer from those of the Blnder-Oaxaca decomposton n the followng ways. For Hspanc-owned frms the cross-group dsparty s slghtly larger than that from the Blnder-Oaxaca decomposton. Hspanc owned frms pay on average 0.486 percentage ponts more nterest on approved loans than do comparable Whte owned frms. The estmate s statstcally sgnfcant at the percent level. In contrast the estmated treatment effect of Black-ownershp decreases from.09 to 0.79 usng propensty-score matchng. Ths estmate remans economcally sgnfcant as t represents more than a 0 percent ncrease n the nterest rate over the average charged to Whte owned frms. The results for gender-based nterest-rate dspartes can be found n Table 6. The data suggest that busnesses owned by women pay an nterest rate that s sgnfcantly lower than the rate pad by comparable male owned frms. The propensty-score matchng method produces a larger effect, 0.27, than does Blnder-Oaxaca, whch yelds 0.7. When the sample s lmted to Whtes, the dsparty declnes and becomes nsgnfcant, as shown n the second column of Table 6. Of the 84 female owned busnesses n our sample, only 2 are owned by mnortes, and we do not estmate a separate effect for mnorty females. Nevertheless, a comparson of the two columns n Table 6 suggests that there s a large and sgnfcant male-female dsparty n nterest rates among mnorty owned frms, f not among Whte owned frms. Overall, these results suggest, but do not defntvely prove, that our matchng methods, whch are preferable on conceptual grounds, produce sgnfcantly dfferent results from results based on more tradtonal regresson methods. The study wth the set of controls that are most 7
comparable to ours, namely, Blanchard et al. (2008), fnds nterest-rate gaps of 0.459 for Black owned frms compared to Whte owned frms, -0.69 for Hspanc owned frms compared to Whte owned frms, and -0.769 for frms owned by Whte women compared to frms owned by Whte men. 9 Only the last of these three estmates s statstcally sgnfcant. Thus, matchng appears to ncrease the magntude of the gap for Black owned frms (and to make ths gap sgnfcant), to reverse and make nsgnfcant the gap for Hspanc owned frms, and to reduce and make nsgnfcant the gap for frms owned by Whte women. We cannot rule out the possblty that these results dffer from ours because they refer to 998 nstead of 993-2003, but, because these results refer to the year n the mddle of our sample, t s unlkely that they dffer from ours because of a trend over ths perod. These results ndcate that Black owned and Hspanc owned frms pay hgher nterest rates than Whte owned frms after controllng for a wde range of factors that are lkely to affect a busness s credt qualfcatons. These results are therefore consstent wth dsparate treatment dscrmnaton n the settng of the nterest rates charged to small busnesses, but they also could be explaned by the omsson from our analyss of factors that nfluence frm credtworthness and are observed by lenders, but not by us. 6. Conclusons Ths study contrbutes to the lterature on cross-group nterest-rate dspartes n small busness lendng by usng semparametrc propensty-score matchng wth data from the Survey of Small Busness Fnances from 993, 998, and 2003. Matchng methods relax the lnear functonal form assumpton and address data support problems. These ssues have been largely 9 These estmates come from Blanchard et al. (2008, Table 6, row (9)). Blanchard et al. also nvestgate whether some of the controls for loan terms are endogenous. Correctons for endogenety have lttle mpact on ther estmates. Blanchflower et al. (2003) fnd sgnfcant nterest-rate dscrmnaton aganst Blacks and Hspancs n 998, but they do not use as extensve a set of control varables. 8
gnored n regresson-based estmaton. Unlke prevous studes, we also aggregate the data from the three surveys n order to produce more precse estmates. These methodologcal nnovatons lead to new fndngs. More specfcally we fnd that Black owned busnesses pay sgnfcantly hgher nterest rates on approved loans than do equally credtworthy frms owned by Whtes. However, we cannot reject the hypotheses that nterest rates n small busness lendng would be unaffected by a swtch n ownershp to Whte men from Whte women. 9
APPENDIX ON CORRECT STANDARD ERRORS FOR THE BLINDER-OAXACA MODEL The model n Equaton (5) and (6) can be rewrtten n matrx notaton as followng. For the unprotected class: Y X β ε 0 0 0 E( ε ) 0; V( ε ) I, 2 0 0 0, where Y 0 s N0 x, X 0 s N0 xk, and β s kx and the model for the protected class: Y ια Xβ ε, 2 E( ε ) 0; V( ε ) I, where Y 0 s N x, ι s N x, α s a scalar, X s N xk, and β s kx. OLS estmaton of the model for the unprotected class gves ˆβ, wth varance matrx ( X X ), whch s estmated 2 0 0 0 by s ( X X ). Now regress Y Xβ ˆ on ι to get an estmator of α. Then 2 0 0 0 Therefore, ιι ι Y Xβ ˆ αˆ ( ) ( ). ˆ var( αˆ ) ( ιι ) ιvy ( Xβιιι ) ( ) ι 2 VY ( ˆ ) XVβ ( ) X ι N 2 2 ι I 0X( X 0 X0) X ι. N 2 2 2 Ths matrx s estmated by s s 2 0 ( 0 0) N ι I X X X X ι. Now note that for any NxN matrx A, ι Aι gves the sum of the elements of A. Hence, to estmate var( α ˆ), add the elements of s X ( X X ) 2 0 0 0 X, dvde the sum by 2 N, and add the resultng rato to s / N. 2 2 20
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Cavalluzzo, K., L. Cavalluzzo, and J. Wolken. 2002. Competton, Small Busness Fnancng, and Dscrmnaton: Evdence from a New Survey, Journal of Busness 75, 64-80. Froelch, M. 2004. Fnte Sample Propertes of Propensty-Score Matchng and Weghtng Estmators, Revew of Economcs and Statstcs 86 (), 77-90. Galster, G., D. Wssoker, and W. Zmmerman. 200. Testng For Dscrmnaton n Home Insurance: Results from New York Cty and Phoenx, Urban Studes 38, 4-56. Heckman, J. 998. Detectng Dscrmnaton, Journal of Economc Perspectves 2, 0-6. Heckman, J., H. Ichmura, and P. Todd. 997. Matchng as an Econometrc Evaluaton Estmator: Evdence from Evaluatng a Job Tranng Program, Revew of Economc Studes 64, 605-54. Heckman, J., H. Ichmura, and P. Todd. 998. Matchng as an Econometrc Evaluaton Estmator, Revew of Economc Studes 65, 26-94. Heckman, J., H. Ichmura, J. Smth, and P. Todd. 998. Characterzng Selecton Bas Usng Expermental Data, Econometrca 66, 07-98. Hrano, K., G. Imbens, and G. Rdder. 2003. Effcent Estmaton of Average Treatment Effects Usng the Estmated Propensty Score, Econometrca 7, 6-89. L, Q., and J. Racne. 2007. Nonparametrc Econometrcs: Theory and Practce. Prnceton, N.J.: Prnceton Unversty Press. Olson, E., July 29, 2005. Mnorty-Owned Busnesses Are On The Rse, New York Tmes. Ondrch, J., S. Ross, and J. Ynger. 2000. How Common Is Housng Dscrmnaton? Improvng on Tradtonal Measures, Journal of Urban Economcs 47(2), 470-500. 22
Ondrch, J., S. Ross, and J. Ynger. 2003. Now You See It, Now You Don t: Why Do Real Estate Agents Wthhold Houses from Black Customers, Revew of Economcs and Statstcs 85(4), 854-73. Pagan, A., and A. Ullah. 999. Nonparametrc Econometrcs. Cambrdge, U.K.: Cambrdge Unversty Press. Rosenbaum, P., and D. Rubn. 983. The Central Role of the Propensty Score n Observatonal Studes for Causal Effects, Bometrka 70, 4-55. Ross, S., and M. Turner. 2005. Housng Dscrmnaton n Metropoltan Amercan: Explanng Changes between 989 and 2000, Socal Problems 52, 52-80. Ross, S., M. Turner, E. Godfrey, and R. Smth. 2005. Mortgage Lendng n Chcago and Los Angeles: A Pared Testng Study of the Pre-Applcaton Process, Workng Paper No. 2005C03, Department of Economcs, Unversty of Connectcut, Storrs, CT. Ross, S., and J. Ynger. 2002. The Color of Credt: Mortgage Lendng Dscrmnaton, Research Methodology, and Far-Lendng Enforcement. Cambrdge, MA: MIT Press. Ross, S., and J. Ynger. 2006. Detectng Dscrmnaton: A Comparson of Methods Used by Scholars and Cvl Rghts Enforcement Offcals, Amercan Law and Economcs Revew 8, 562-64. Smth, J., and P. Todd. 200. Reconclng Conflctng Evdence on the Performance of Propensty-Score Matchng Methods, Amercan Economc Revew 9(2), 2-8. Smth, J., and P. Todd. 2005. Does Matchng Overcome Lalonde s Crtque of Nonexpermental Methods? Journal of Econometrcs 25, 305-53. 23
Interest rate Credt Hstory Personal delnquency Judgments Table : Varable Defntons from the Pooled SSBF Data Interest rate on the most recent loan (percent) Indcator for whether the owner had delnquent personal oblgatons n the past three years Indcator for whether there was judgment aganst the frm owner Frm Characterstcs Sales Frm's sales of the fscal year n $000 Proft Frm's proft of the fscal year n $000 Net worth Frm's net worth of the fscal year n $000 Frm age The age of the frm n years Employment The number of employees and owners Owner Characterstcs Educaton Indcator for whether the owner's educaton level was hgh school dropout / hgh school/ graduate / some college / college / post-graduate degree Busness experence Owner's years of busness experence Loan Characterstcs Loan amount The amount of loan granted n $000 Purpose of loan Indcator for whether the loan was new lne of credt/ captal lease / mortgage / vehcle/ loan / equpment loan / other type of loan Fxed nterest-rate loan Indcator for whether the nterest rate was fxed Collateral requred Indcator for whether collateral were requred Guarantor requred Indcator for whether a guarantor s requred to co-sgn on the loan Ponts pad at closng The ponts (n nterest percentage terms) pad at closng Lender Characterstcs Type of lender Whether the lender was commercal bank, savng bank, loan assocaton or credt unon / fnance company / other type of nsttuton or source. Years frm has busness relatonshp wth lender Years the lender had busness relatonshp wth the borrower Geographc Varables Metropoltan area Indcator for whether the frm was n a Metropoltan Statstcal Area (MSA) Regon ndcator Indcator for whether the frm was located n Northeast / North Central / South / West Source: Survey of Small Busness Fnances of 993, 998, and 2003. 24
Table 2: Means and Standard Devatons for Pooled SSBF Data (standard devatons n parentheses) Whtes Blacks Hspancs Men Women Whte Men Whte Women Sample sze 3266 30 59 293 84 293 702 Dependent Varable Interest rate 7.23 9.73 8.62 7.39 7.49 7.39 7.32 (2.78) (3.68) (3.52) 2.90 (2.97) (2.90) (2.83) Credt Hstory Personal delnquency ndcator 0.6 0.52 0.32 0.8 0.9 0.8 0.6 (0.63) (.03) (0.89) (0.66) (0.67) (0.66) (0.6) Judgments 0.02 0.06 0.06 0.03 0.02 0.03 0.02 (0.4) (0.24) (0.23) (0.6) (0.5) (0.6) (0.3) Frm Characterstcs Sales 7790.90 2025.25 364.94 8355.59 3946.95 8355.59 4073.46 (8374.70) (4647.83) (864.30) (863.93) (3877.78) (863.93) (452.94) Proft 723.98 348.63 435.6 800.5 28.9498 800.5 283.48 (4396.4) (39.53) (2795.50) (4673.8) (239.30) (4673.8) (249.0) Net worth 367.96 89.2 477.0 45.45 652.86 45.45 720.34 (5260.08) (760.32) (733.07) (5362.68) (3464.3) (5362.68) (3705.36 ) Frm age 7.08 2.6 2.53 7.05 4.30 7.05 4.86 (3.08) (8.29) (9.75) (3.3) (.00) (3.3) (.20) Employment 5.0 33.82 3.49 53.95 3.52 53.95 3.99 (74.05) (72.07) (54.64) (77.27) (53.44) (77.27) (53.58) Owner Characterstcs Hgh school dropout ndcator 0.02 0.03 0.08 0.02 0.02 0.02 0.0 (0.4) (0.7) (0.26) (0.4) (0.5) (0.4) (0.2) Hgh school graduate ndcator 0.7 0.09 0.9 0.6 0.20 0.7 0.20 (0.38) (0.29) (0.40) (0.37) (0.40) (0.37) (0.40) Some college 0.28 0.30 0.3 0.25 0.37 0.25 0.38 (0.45) (0.46) (0.46) (0.43) (0.48) (0.43) (0.49) College degree 0.34 0.35 0.25 0.35 0.27 0.35 0.26 (0.47) (0.48) (0.44) (0.48) (0.44) (0.48) (0.44) Post-graduate degree 0.9 0.22 0.7 0.2 0.5 0.2 0.4 (0.39) (0.42) (0.38) (0.4) (0.35) (0.4) (0.35) Busness experence 2.87 5.6 7.42 22.02 8.28 22.02 8.74 (0.96) (8.69) (0.63) (0.86) (0.7) (0.86) (0.80) 25
Loan Characterstcs Table 2: Means and Standard Devatons for Pooled SSBF Data (standard devatons n parentheses) (cont d) Whtes Blacks Hspancs Men Women Whte Men Whte Women Loan amount 979.84 362.54 265.20 048.44 469.26 048.44 502.2 (4545.8) (787.3) (739.06) (4739.32) (977.63) (4739.32) (2.54) Loan was new lne of credt 0.52 0.55 0.52 0.53 0.5 0.53 0.50 ( 0.50) (0.50) (0.50) (0.50) (0.50) (0.50) (0.50) Percent Loan was captal lease 0.02 0.05 0.03 0.03 0.02 0.03 0.02 (0.5) (0.2) (0.8) (0.6) (0.5) (0.6) (0.4) Loan was mortgage 0. 0.05 0.08 0.0 0.2 0.0 0.2 (0.32) Loan was vehcle loan 0.2 0.08 0.4 0. 0.2 0. 0.3 (0.32) (0.28) (0.35) (0.32) (0.33) (0.32) (0.34) Loan was equpment loan 0.3 0.07 0.3 0.2 0.3 0.2 0.2 (0.33) (0.25) (0.33) (0.33) (0.33) (0.33) (0.33) Loan was other type 0.0 0.20 0. 0. 0.0 0. 0.0 (0.30) (0.40) (0.3) (0.3) (0.30) (0.3) (0.30) Fxed nterest-rate loan 0.70 0.62 0.49 0.58 0.49 0.58 (0.50) (0.46) (0.49) (0.50) (0.49) (0.50) (0.49) Collateral requred.60.98.60.62.62.62.60 (.83) (2.27) (.85) (.83) (.93) (.83) (.9) Guarantor requred 0.58 0.54 0.52 0.57 0.57 0.57 0.58 (0.49) (0.50) (0.50) (0.49) (0.49) (0.49) (0.49) Ponts pad at closng 0.25 0.58 0.40 0.26 0.33 0.26 0.30 (0.84) (.40) (.42) (0.86) (.4) (0.86) (.02) 26
Table 2: Means and Standard Devatons for Pooled SSBF Data (standard devatons n parentheses) (cont d) Lender Characterstcs Whtes Blacks Hspancs Men Women Whte Men Whte Women Lender was commercal bank 0.78 0.7 0.74 0.78 0.74 0.78 0.74 (0.4) (0.46) (0.44) (0.4) (0.44) (0.4) (0.44) Lender was savng bank, loan assocaton or credt unon 0.07 0.02 0.06 0.07 0.09 0.07 0.09 (0.26) (0.2) (0.23) (0.25) (0.28) (0.25) (0.29) Lender was fnance company 0.08 0.4 0.2 0.08 0.0 0.08 0.0 (0.27) (0.35) ( 0.33) (0.27) (0.30) (0.27) (0.30) Lender was other type of nsttuton 0.06 0.4 0.09 0.07 0.07 0.07 0.07 (0.24) (0.35) (0.28) (0.25) (0.26) (0.25) (0.25) Years frm has busness relaton wth lender 8.4 4.70 6.88 8.4 6.98 8.4 7.20 (9.47) (5.7) (7.67) (9.37) (8.53) (9.37) (8.77) Metropoltan area 0.75 0.92 0.89 0.77 0.74 0.77 0.72 (0.43) (0.28) (0.32) (0.42) (0.44) (0.42) (0.45) Northeast 0.7 0.5 0. 0.7 0.4 0.7 0.5 (0.37) (0.36) (0.3) (0.37) (0.35) (0.37) (0.36) North Central 0.28 0.9 0.3 0.27 0.24 0.27 0.25 (0.45) (0.40) (0.33) (0.44) (0.43) (0.44) (0.43) South 0.34 0.54 0.42 0.35 0.36 0.35 0.35 (0.47) (0.50) (0.50) (0.48) (0.48) (0.48) (0.48) West 0.2 0.2 0.35 0.22 0.26 0.22 0.25 (0.4) (0.32) (0.48) (0.4) (0.44) (0.4) (0.44) Source: Survey of Small Busness Fnances of 993, 998, and 2003. These statstcs do not reflect sample weghts. 27
Table 3A. Propensty Score Estmaton Results for Blacks and Hspancs Blacks* Hspancs** Coeffcent Standard Error Coeffcent Standard Error Credt Hstory Personal ldelnquency 0.234 0.02 0.60 0.02 Judgments 0.526 0.44 0.576 0.397 Frm Characterstcs Sales 0.000 0.000 0.000 0.000 Square of sales 0.000 0.000 Proft 0.000 0.000 0.000 0.000 Net worth -0.057 0.38-0.027 0.038 Square of net worth -0.033 0.033 Owner Characterstcs Frm age 0.085 0.075-0.026 0.09 Square of frm age -0.002 0.004 0.000 0.000 Cube of frm age years 0.000 0.000 Employment -0.002 0.004 0.000 0.002 Square of employment 0.000 0.000 Hgh school graduate -0.77 0.678 -.276 0.390 Some college 0.87 0.635 -.85 0.376 College degree 0.025 0.632 -.607 0.384 Postgraduate degree 0.099 0.642 -.538 0.402 Busness experence -0.053 0.04-0.022 0.0 Loan Characterstcs Loan amount granted 0.000 0.000 0.000 0.000 Loan was captal lease -0.657 0.5-0.375 0.59 Loan was mortgage -.642 0.463-0.363 0.344 Loan was vehcle loan -.56 0.374-0.30 0.287 Loan was equpment loan -.38 0.388-0.325 0.277 Loan was other type 0.038 0.269-0.222 0.29 Fxed nterest-rate loan 0.832 0.225 0.353 0.95 Ponts pad at closng 0.706 0.89 0.2 0.069 Square of ponts pad at closng -0.065 0.025 Collateral requred 0.080 0.050-0.00 0.050 Guarantor requred -0.264 0.20-0.90 0.75 Lender Characterstcs Lender was savng bank, loan assn. or credt unon -.608 0.733-0.274 0.368 Lender was fnance company 0.479 0.325 0.70 0.29 Lender was other type of nsttuton 0.398 0.326-0.083 0.324 Years frm has busness relaton wth lender -0.072 0.065 0.03 0.02 Square of years frm has busness relaton wth lender 0.002 0.005 Cube of years frm has busness relaton wth lender 0.000 0.000 Geographc Varables Metropoltan area.360 0.334.37 0.263 North Central -0.292 0.330-0.368 0.34 South 0.522 0.280 0.589 0.284 West -0.70 0.369 0.908 0.292 Others Survey year 998-0.062 0.235-0.73 0.220 Survey year 2003 -.26 0.265-0.609 0.202 Constant -3.523 0.865 -.936 0.547 * Note: Authors calculatons usng unweghted SSBF data. N = 3,396. A logt model s used to predct the probablty of beng a Black-owned frm. The sample s lmted to Whte-owned and Black-owned frms. **Note: Authors calculatons usng unweghted SSBF data. N = 3,425. A logt model s used to predct the probablty of beng a Hspancowned frm. The sample s lmted to Whte-owned and Hspanc-owned frms. 28
Table 3B. Propensty Score Estmaton Results for Females and Whte Females Females* Whte Females** Coeffcent Standard Error Coeffcent Standard Error Credt Hstory Personal delnquency -0.063 0.062-0.07 0.072 Judgments -0.235 0.278-0.368 0.337 Frm Characterstcs Sales 0.000 0.000 0.000 0.000 Square of sales 0.000 0.000 0.000 0.000 Cube of sales 0.000 0.000 0.000 0.000 Fourth power of sales 0.000 0.000 0.000 0.000 Proft 0.000 0.000 0.000 0.000 Square of proft 0.000 0.000 0.000 0.000 Cube of proft 0.000 0.000 0.000 0.000 Owner Characterstcs Net worth -0.002 0.06 0.004 0.06 Frm age years 0.05 0.00 0.02 0.0 Square of frm age years 0.000 0.000 0.000 0.000 Employment 0.000 0.00-0.00 0.00 Hgh school graduate 0.80 0.290 0.496 0.365 Some college 0.337 0.285 0.724 0.360 College degree -0.25 0.287 0.4 0.363 Postgraduate degree -0.427 0.295-0.039 0.37 Busness experence -0.070 0.04-0.079 0.05 Loan Characterstcs Square of busness experence 0.00 0.000 0.00 0.000 Loan amount granted 0.000 0.000 0.000 0.000 Loan was captal lease -0.349 0.290-0.409 0.329 Loan was mortgage 0.04 0.5 0.067 0.63 Loan was vehcle loan -0.56 0.46-0.53 0.57 Loan was equpment loan -0.053 0.36-0.88 0.49 Loan was other type -0.49 0.47-0.02 0.60 Fxed nterest-rate loan 0.55 0.094 0.206 0.03 Ponts pad at closng % 0.02 0.04 0.032 0.048 Collateral requred 0.003 0.025-0.005 0.027 Guarantor requred 0.039 0.086 0.020 0.094 Lender Characterstcs Lender was savng bank, loan assn. or credt unon 0.20 0.56 0.29 0.63 Lender was fnance company 0.79 0.53 0.260 0.69 Lender was other type of nsttuton 0.077 0.70 0.065 0.9 Years frm has busness relaton wth lender -0.009 0.006-0.00 0.006 Geographc Varables Metropoltan area -0.074 0.098-0.094 0.02 North Central 0.02 0.36-0.04 0.45 South 0.78 0.29 0.205 0.38 West 0.327 0.36 0.38 0.47 Others Survey year 998 0.06 0.20-0.089 0.33 Survey year 2003 0.272 0.099 0.92 0.06 Constant -0.462 0.347-0.660 0.47 *Note: Authors calculatons usng unweghted SSBF data. N = 3,727. A logt model s used to predct the probablty of beng a female-owned frm. **Note: Authors calculatons usng unweghted SSBF data. N = 3,266. A logt model s used to predct the probablty of beng a Whte femaleowned frm. The sample s lmted to Whte-owned frms. 29
Table 4A. Blnder-Oaxaca Estmaton Results for Whtes, Blacks and Hspancs (standard errors n parentheses) Coeffcent Whtes* Blacks** Hspancs*** Standard Error Coeffcent Standard Error Coeffcent Standard Error Credt Hstory Personal delnquency 0.34 0.063 0.603 0.295 0.084 0.324 Judgments 0.686 0.276 0.26.326 0.785.220 Frm Characterstcs Sales 0.000 0.000 0.000 0.000 0.000 0.000 Proft 0.000 0.000 0.000 0.000 0.000 0.000 Net worth -0.05 0.009 0.49 0.48-0.22 0.26 Frm age -0.004 0.004-0.038 0.057 0.052 0.047 Employment -0.003 0.00-0.005 0.005-0.009 0.008 Owner Characterstcs Hgh school graduate -0.888 0.297-2.993 2.055-0.34.67 Some college -0.855 0.293-2.58.937 0.522.00 College degree -.240 0.29-2.96.97-0.898.39 Postgraduate degree -.240 0.298-2.70.934-0.796.249 Busness experence -0.09 0.004-0.069 0.050-0.090 0.038 Loan Characterstcs Loan amount granted 0.000 0.000 0.000 0.000 0.000 0.00 Loan was captal lease 0.466 0.273 -.40.569 0.84.70 Loan was mortgage 0.097 0.48 0.764.580-0.664.42 Loan was vehcle loan -0.644 0.42.366.239-2.576.032 Loan was equpment loan -0.36 0.30 0.967.226 0.073 0.975 Loan was other type 0.356 0.40.834 0.856.485 0.93 Fxed nterest-rate loan 0.764 0.09 0.577 0.675 0.622 0.653 Ponts pad at closng 0.29 0.047 0.03 0.224-0.00 0.95 Collateral requred -0.026 0.024-0.233 0.45-0.82 0.6 Guarantor requred -0.045 0.082 0.73 0.639-0.288 0.594 Lender Characterstcs Lender was savng bank, loan assn. or credt unon -0.070 0.55-2.69 2.357.09.347 Lender was fnance company 0.247 0.53 3.548.04.54 0.968 Lender was other type of nsttuton 0.593 0.70.53.05-0.745.0 Years frm has busness relaton wth lender -0.003 0.005 0.087 0.06 0.036 0.046 Geographc Varables Metropoltan area -0.05 0.092 0.67.22-0.588 0.859 North Central -0.034 0.22 -.439.057-0.586.38 South -0.05 0.8 -.46 0.847.67 0.954 West 0.34 0.29 -.77.75.508 0.960 Others Survey year 998 0.87 0.4 0.658 0.735 0.803 0.764 Survey year 2003-2.640 0.093-2.880 0.877 -.543 0.690 Constant 9.849 0.329 2.998 2.579 9.990.954 *Note: Authors calculatons usng unweghted SSBF data. N = 3,266. The dependent varable s the nterest rate. The sample s lmted to Whte-owned frms. ** Note: Authors calculatons usng unweghted SSBF data. N = 30. The dependent varable s the nterest rate. The sample s lmted to Black-owned frms. *** Note: Authors calculatons usng unweghted SSBF data. N = 59. The dependent varable s the nterest rate. The sample s lmted to Hspanc-owned frms. 30
Table 4B. Blnder-Oaxaca Estmaton Results for Males and Females (standard errors n parentheses) Males* Females** Coeffcent Standard Error Coeffcent Standard Error Credt Hstory Personal delnquency 0.204 0.066 0.289 0.36 Judgments 0.529 0.274.528 0.66 Frm Characterstcs Sales 0.000 0.000 0.000 0.000 Proft 0.000 0.000 0.000 0.000 Net worth -0.06 0.009 0.000 0.000 Frm age (years) -0.003 0.004-0.02 0.0 Employment -0.003 0.00-0.002 0.002 Owner Characterstcs Hgh school graduate -0.858 0.33-0.92 0.634 Some college -0.733 0.307-0.786 0.62 College degree -.4 0.304 -.206 0.632 Postgraduate degree -.85 0.30 -.43 0.647 Busness experence -0.024 0.005-0.030 0.0 Loan Characterstcs Loan amount granted 0.000 0.000 0.000 0.000 Loan was captal lease 0.44 0.283-0.07 0.636 Loan was mortgage 0.05 0.63-0.270 0.322 Loan was vehcle loan -0.547 0.59 -.376 0.3 Loan was equpment loan -0.230 0.45-0.07 0.289 Loan was other type 0.474 0.5 0.268 0.38 Fxed nterest-rate loan 0.882 0.00 0.576 0.200 Ponts pad at closng 0.94 0.05 0.048 0.080 Collateral requred -0.053 0.026-0.036 0.053 Guarantor requred -0.089 0.090-0.048 0.86 Lender Characterstcs Lender was savng bank, loan assn. or credt unon -0.07 0.78-0.273 0.329 Lender was fnance company 0.572 0.67 0.62 0.326 Lender was other type of nsttuton 0.520 0.8 0.895 0.362 Years frm has busness relaton wth lender -0.003 0.005 0.009 0.02 Geographc Varable Metropoltan area 0.022 0.05-0.320 0.208 North Central -0. 0.34-0.6 0.30 South -0.060 0.29 0.063 0.284 West 0.308 0.40 0.330 0.295 Others Survey year 998 0.230 0.22 0.083 0.260 Survey year 2003-2.679 0.0-2.57 0.28 Constant 9.908 0.349 0.379 0.745 * Note: Authors calculatons usng unweghted SSBF data. N = 2,93. The dependent varable s the nterest rate. The sample s lmted to female-owned frms. ** Note: Authors calculatons usng unweghted SSBF data. N = 2,564. The dependent varable s the nterest rate. The sample s lmted to Whte female-owned frms. 3
Table 4C. Blnder-Oaxaca Estmaton Results for Whte Males and Whte Females (standard errors n parentheses) Whte Males* Whte Females** Coeffcent Standard Error Coeffcent Standard Error Credt Hstory Personal delnquency 0.204 0.066 0.289 0.36 Judgments 0.529 0.274.528 0.66 Frm Characterstcs Sales 0.000 0.000 0.000 0.000 Proft 0.000 0.000 0.000 0.000 Net worth -0.06 0.009 0.000 0.000 Frm age (years) -0.003 0.004-0.02 0.0 Employment -0.003 0.00-0.002 0.002 Owner Characterstcs Hgh school graduate -0.858 0.33-0.92 0.634 Some college -0.733 0.307-0.786 0.62 College degree -.4 0.304 -.206 0.632 Postgraduate degree -.85 0.30 -.43 0.647 Busness experence -0.024 0.005-0.030 0.0 Loan Characterstcs Loan amount granted 0.000 0.000 0.000 0.000 Loan was captal lease 0.44 0.283-0.07 0.636 Loan was mortgage 0.05 0.63-0.270 0.322 Loan was vehcle loan -0.547 0.59 -.376 0.3 Loan was equpment loan -0.230 0.45-0.07 0.289 Loan was other type 0.474 0.5 0.268 0.38 Fxed nterest-rate loan 0.882 0.00 0.576 0.200 Ponts pad at closng 0.94 0.05 0.048 0.080 Collateral requred -0.053 0.026-0.036 0.053 Guarantor requred -0.089 0.090-0.048 0.86 Lender Characterstcs Lender was savng bank, loan assn. or credt unon -0.07 0.78-0.273 0.329 Lender was fnance company 0.572 0.67 0.62 0.326 Lender was other type of nsttuton 0.520.8 0.895 0.362 Years frm has busness relaton wth lender -0.003 0.005 0.009 0.02 Geographc Varable n metropoltan area 0.022 0.05-0.320 0.208 North Central -0. 0.34-0.6 0.30 South -0.060 0.29 0.063 0.284 West 0.308 0.40 0.330 0.295 Others Survey year 998 0.230 0.22 0.083 0.260 Survey year 2003-2.679 0.0-2.57 0.28 Constant 9.908 0.349 0.379 0.745 * Note: Authors calculatons usng unweghted SSBF data. N = 2,564. The dependent varable s the nterest rate. The sample s lmted to Whte male-owned frms. ** Note: Authors calculatons usng unweghted SSBF data. N = 702. The dependent varable s the nterest rate. The sample s lmted to Whte female-owned frms. 32
Table 5: Estmates of Race Dscrmnaton n Interest Rates, SSBF Data Blacks Hspanc Panel A: Blnder Oaxaca Estmates Coeffcent.09 0.453 Standard Error (0.30) (0.260) N 3,396 3,425 Panel B: Propensty Score Matchng Estmates * Coeffcent 0.79 0.486 Standard Error (0.369) (0.273) Bandwdth 0.005 0.008 N 3,396 3,425 Source: Survey of Small Busness Fnances of 993, 998, and 2003. The omtted racal/ethnc group n both columns s Whte. The standard errors are corrected accordng to the procedure n the Appendx. *The standard errors are obtaned by bootstrappng based on 2,000 replcatons. 33
Table 6: Estmates of Gender Dscrmnaton n Interest Rates Females Whte Females Panel A: Blnder Oaxaca Estmates Coeffcent -0.74-0.32 Standard Error (0.0) (0.04) N 3,727 3,266 Panel B: Propensty Score Matchng Estmates Coeffcent -0.266-0.88 Standard Error (0.29) (0.35) Bandwdth 0.034 0.039 N 3,727 3,266 Source: Survey of Small Busness Fnances of 993, 998, and 2003. The reference gender group n column () s male, and the omtted group n column (2) s Whte males. The standard errors are corrected accordng to the procedure n the Appendx. *The standard errors n Panel B are obtaned by bootstrappng based on 2,000 replcatons. 34
Fgure : The Dstrbutons of the Propensty Scores for Blacks Comparson group Treatment group Frequency 0 200 400 600 800 000 Frequency 0 200 400 600 800 000 0.0 0.4 0.8 propensty score 0.0 0.4 0.8 propensty score Fgure 2: The Dstrbutons of the Propensty Scores for Hspancs Comparson group Treatment group Frequency 0 200 400 600 800 000 200 Frequency 0 200 400 600 800 000 200 0.0 0.4 0.8 propensty score 0.0 0.4 0.8 propensty score 35
Fgure 3: The Dstrbutons of the Propensty Scores for Females Comparson group Treatment group Comparson group Treatment group Frequency 0 200 400 600 800 Frequency 0 200 400 600 800 Frequency 0 200 400 600 800 Frequency 0 200 400 600 800 0.0 0.4 0.8 propensty score 0.0 0.4 0.8 propensty score Fgure 4: The Dstrbutons of the Propensty Scores 0.0 0.4 0.8 propensty score 0.0 0.4 0.8 propensty score 36