Chapter 8 Group-based Lending and Adverse Selection: A Study on Risk Behavior and Group Formation 1

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1 Chapter 8 Group-based Lendng and Adverse Selecton: A Study on Rsk Behavor and Group Formaton Introducton Ths chapter deals wth group formaton and the adverse selecton problem. In several theoretcal papers (e.g. Ghatak, 2000) t has been shown that a debt contract wth a jont lablty component wll lead to assortatve matchng (homogeneous matchng), mplyng that safe borrowers wll group wth safe borrowers. The rsky borrowers wll not be allowed to form a group wth safe borrowers and hence have to rely on stand-alone debt contracts. It can be shown that the assortatve matchng may mply that the choce for a jont lablty debt contract or a standalone debt contract gves the bank nformaton on the type of borrower. Ths may, under certan condtons, solve the adverse-selecton problem n stuatons of asymmetrc nformaton. In theory therefore, jont lablty debt contracts may help to solve the adverse selecton problem n stuatons of asymmetrc nformaton. However, as s so often the case, emprcal evdence on ths s laggng behnd. Ths chapter takes up the challenge to emprcally contrbute to the queston whether jont lablty lendng may reduce adverse selecton problems. Snce t s not possble to drectly test whether jont lablty lendng reduces adverse selecton problems, an ndrect approach s used. More specfcally, ths chapter examnes whether jont lablty lendng leads to assortatve matchng n group formaton. Snce jont lablty debt contracts only help to solve the adverse selecton problem f assortatve matchng holds, testng for assortatve matchng provdes an ndrect test of the possblty that jont lablty lendng may help to solve the adverse selecton problem. There s some lterature that argues that homogeneous matchng only holds n a frctonless world (see Sadoulet and Carpenter, 2001, and the 1 Ths chapter s based on Lensnk and Mehrteab (2003). 157

2 references theren). However, the real world s characterzed by frctons due to e.g. mperfect nformaton, the unavalablty of partners wth the same rsk characterstcs, the nablty to enforce contracts, and the nablty to fully screen and montor group members. The advocates of the matchng frctons theory argue that heterogeneous matchng mght take place, but that the heterogenety s entrely due to so-called matchng frctons. In other words, the matchng frctons theory suggests that there wll be homogeneous matchng n the case where the analyss controls for matchng frctons. If there are matchng frctons that lead to some heterogenety, the matchng s stll essentally homogeneous; heterogenety s smply due to frctons and therefore generates devatons from optmalty. Yet, emprcal evdence on the homogeneous matchng hypothess n general and the matchng frctons theory n partcular s scarce. One of the few exceptons s Sadoulet and Carpenter (2001) on mcrocredt groups n Guatemala. Ths chapter examnes the emprcal relevance of the homogeneous matchng hypothess for two MFIs n Ertrea. The data we use has been descrbed n chapter 5. Our data provdes nformaton that can be used to test the matchng frctons hypothess. Ths chapter s organzed as follows. Secton 8.2 provdes a survey of the lterature on rsk behavor and group formaton; secton 8.3 explans the methodology we use to test the matchng frctons hypothess; and secton 8.4 explans how rsk s measured, a varable that we need to test for homogeneous matchng. Secton 8.5 presents two groups of ndependent varables that are assumed to affect rsk behavour. Here factor analyss s appled to regroup these varables n a smaller number of factors. Rsk behavor s estmated n secton 8.6. The results of ths equaton are used n secton 8.7 to test whether homogeneous matchng holds f matchng frctons are accounted for. Fnally, secton 8.8 concludes. 8.2 Group formaton and homogeneous matchng: a lterature revew Most of the matchng lterature draws heavly from the work of Becker (1993), who has worked extensvely on marrage matchng theory. Ghatak 158

3 and Gunnane (1999) present a model ndcatng that the group selfselecton process leads to homogeneous matchng. Ther theoretcal framework wll be presented below albet n a shorter verson. h L It s assumed that output R takes two values: hgh ( R ) or low ( R ), where R h > R L 0. For smplcty, we normalze R L to be equal to zero. We have two types of borrowers and both borrowers are rsk-neutral; one s safe whle the other s rsky. Output s hgh wth probablty p (0, 1). p s and p r ndcate the lkelness of success by safe and rsky borrowers, respectvely. The rsky type fals more often than the safe one ( p s > p r ). Yet, the rsky borrower receves hgher returns f he succeeds. For smplcty, t s assumed that the expected net returns are equal for both safe and rsky types: E ( R ) = ps R s = pr R r = R (1) The best way for banks to separate the safe borrower from the rsky borrower s to ask borrowers to pledge collateral. Rsky borrowers are lkely to fal more often and lose ther collateral. If a bank offers two sets of contracts, one wth hgh nterest rate and lower collateral and the other wth lower nterest rate and hgher collateral, the rsky borrower wll choose the former and the safe borrower the later contract. On the bass of nterest rate and collateral the bank may be able to dstngush the rsky borrower from the safe one. But snce the poor n developng countres do not have any serous assets to offer as collateral, banks have no effectve way to dstngush between safe and rsky borrowers. Wth the help of the jont lablty mechansm the bank wll be able to dstngush the rsky from the safe borrower. In the end, the expected result s that the safe types select ther lkes and form a group n order to acqure loans from the bank, whle the rsky ones prefer ndvdual loans. As a consequence, the bank can screen borrowers by varyng the degree of jont lablty. Under a jont lablty contract each borrower pays nothng f hs/her project fals, and an amount r f hs/her project s successful. Here r s assumed to be exogenously determned. In addton, the successful borrower pays a jont-lablty payment c f the other member 159

4 of the group fals. The expected net return of a safe type teamed wth a rsky type s then: E( Π ) sr ( r, c) = p p ( h s r R - r ) + s = ps h R - { r h p (1- p r ) ( R - r - c ) (2) p s + p s (1- p r ) c } (3) Smlar calculatons could be performed for exclusvely safe and rsky groups. Snce safe types are always preferred as partners, the queston becomes: wll the rsky types be wllng to make a large enough transfer to the safe types so that both rsky and safe types do better together? The logc behnd ths transfer s that n case the rsky borrower defaults the safe member s gong to pay c to the bank. Therefore, the transfer of money from the rsky to the safe borrower s to compensate the safe borrower. The net expected gan of rsky borrower from havng a safe partner s E (Π) sr ( r, c) - E (Π) rr ( r, c) = p r ( p s - p r ) c (4) Smlarly, the net expected loss for a safe borrower of havng a rsk partner s E (Π) ss ( r, c) - E (Π) sr ( r, c) = p s ( p s - p r ) c (5) By comparng expected returns under alternatve scenaros, we can calculate that a safe type wll requre a transfer of at least ps ( ps pr ) c to agree to form a partnershp wth a rsky type. Wll the rsky type be wllng to pay that much? Hs expected net gan from jonng a safe type s as much as p r ( p s pr ) c. If c > 0 and snce p r < ps, the expected gans to a rsky type are always smaller than the expected losses to a safe type. Hence, a rsky borrower wll not fnd t proftable to have a safe partner. Whle every borrower wants to have a safe partner, safe borrowers value safe partners more than rsky borrowers value safe borrowers. Hence, a rsky borrower cannot cross-subsdze a safe borrower n order to be accepted as a partner, leadng to groups contanng partners wth smlar 160

5 rsk behavor. Group formaton wll dsplay postve assortatve matchng under jont lablty contract. Ghatak (2000) goes one step further. He shows that f banks can offer a contnuum of jont lablty and stand-alone debt contracts, ncentve compatble separatng equlbra may be the result. The safe types prefer a combnaton of a hgh jont lablty component and a low lendng rate, whereas the opposte wll hold for a rsky borrower. By choosng a jont lablty debt contract a borrower sgnals that he/she s a safe borrower. Ghatak (2000) shows that a jont lablty debt contract by solvng the adverse selecton problem can lead to a Pareto optmal soluton. 2 Xnhau Gu (2000) also deals wth the formaton of borrowng groups through the explotaton of local nformaton and jont lablty. He states that statc models mplctly assume a borrower to always be endowed wth acceptable (vable) projects. However, entrepreneurs usually have dffcultes fndng nvestment opportuntes, and dynamc search models are useful tools to address such problems. He examnes the mpact of uncertanty about nvestment opportuntes on the borrowers project search decson and on the rate of loan repayment. He shows that safe borrowers prefer to group wth safe borrowers snce the effectve cost of borrowng s postvely related to rsk takng by group members. Laffont (2000) shows the role of group lendng n dfferentatng between borrowers of dfferent types (adverse selecton). He states that grouplendng contracts offer a subtle method of dstngushng between borrowers. When colluson between borrowers under complete nformaton s allowed for, group lendng as an nstrument mproves dscrmnaton between entrepreneurs of dfferent types. So, smlar types group together. 2 For an extenson of ths model and other related models see Gangopadhyay and Lensnk (2001), Xnhau Gu (2000), and Laffont (2000). See also Gangopadhyay, Ghatak, and Lensnk (2005). 161

6 Sadoulet (1999) presents a model that challenges the commonly assumed homogeneous matchng hypothess. In hs model, group membershp s endogenous, and group performance depends on both members types and on the dstrbuton of those types. Accordng to Sadoulet, group members choose partners n a context of mssng nsurance markets. The pont he wants to make s that f nsurance markets are mssng, homogenety s not optmal anymore. Heterogenety emerges as a constraned frst-best choce. Sadoulet suggests that members set up nsurance arrangements wthn ther group, n whch partners wll cover each other s loans n case a project fals. The reason for nsurance s that borrowers lve and work n rsky envronments and hence need nsurance. If a member who s able to nsure a partner n need, refuses to pay for hm, together wth the other member he wll lose access to future loans from the program because of the jont lablty prncple. Alongsde these nsurance arrangements there are transfer payments between members when both members are successful to remunerate the safe one for coverng for the rsky one n tmes of need. Thus, ths nsurance arrangement s taken to be an mportant part of the group formaton process. To ths end, Sadoulet s model suggests a non-monotonc matchng pattern n whch safer borrowers wll always form groups heterogeneously wth partners rsker than themselves. Mddle-type borrowers match ether heterogeneously wth safer borrowers or homogeneously wth borrowers of ther type dependng on whether these are avalable. Fnally, the rsker borrowers match homogeneously. Note that the models by Ghatak (1999) and Sadoulet (1999) are smlar. Ghatak gets homogeneous matchng snce hs model s statc, whereas Sadoulet gets heterogeneous matchng snce hs model s repeated. Moreover, n the model by Ghatak the beneft of homogeneous matchng s that t mproves repayment rates and thus leads to lower nterest rates. The problem s that the decrease n the nterest rate cannot compensate the safe borrowers for havng to cover the rsky borrowers loans f they fal. So, safe and rsky borrowers wll not form groups. In the model by Sadoulet the beneft s not lower nterest rates but access to future loans, whch has a much hgher drect value. 162

7 Armendárz De Aghon and Goller (2000) state that n urban economes wth heterogeneous, anonymous, and relatvely moble borrowers, random (rather than assortatve) matchng s ncentve compatble for all types of borrowers. A partcular feature of ther paper s that they assume that borrowers do not know each other. They show that cross-subsdsaton among members provdes a knd of a collateral that reduces the negatve externaltes from rsky to safe borrowers. The man mplcaton of ther work s that, as we move away from vllage economes by allowng for mperfect nformaton, assortatve matchng no longer leads to an equlbrum stuaton, and yet group lendng can mprove effcency and enhance welfare. There are few emprcal studes avalable that have rgorously tested the homogeneous matchng hypothess. Most emprcal studes have smply assumed that homogeneous matchng takes place. Some studes, however, do provde some nsghts. For nstance, for groups belongng to BancoSol, Bolva, Van Tassel (2000) found that groups match heterogeneously n unobservable busness characterstcs. The only emprcal paper avalable that has rgorously tred to nvestgate the matchng of group members s the one by Sadoulet and Carpenter (2001). For credt groups n Guatemala they estmated the relatonshp between rsk and the level of rsk heterogenety n the ndvdual groups, explctly accountng for the endogenety of group formaton and of borrowers choce of project rsk. Ther results show that borrowers n Guatemala group heterogeneously, and that the heterogenety cannot be explaned by matchng frctons. In lne wth the theoretcal paper by Sadoulet (1999) they suggest that borrowers mght want to form heterogeneous groups n order to set up nsurance arrangements. 8.3 The methodology: the role of matchng frctons We follow the methodology set out by Sadoulet and Carpenter (2001). The reader s referred to ther paper for a detaled explanaton of the methodology. The man problem we have to deal wth s as follows. In a frctonless world, the assortatve matchng theory mples that all 163

8 borrowers wll choose ther frst-best rsk level, and wll match together wth partners wth the same (frst-best) rsk level. However, f there are matchng frctons, borrowers may be forced to match wth partners of a dfferent rsk level, even f they prefer to match wth borrowers of the same rsk type. The matchng frctons theory states that homogeneous matchng only holds n a frctonless world and that all heterogenety comes from matchng frctons. Ths mples that there should be no statstcally sgnfcant relatonshp between frst-best rsk (rsk n a frctonless world) and heterogenety. In order to test ths theory, we need ndcators for frstbest rsk and matchng frctons. The problem s that these varables are not observable. Sadoulet and Carpenter (2001) solve ths problem as follows. If there are matchng frctons, the level of rsk heterogenety of borrower (h ) depends on her frst-best rsk choce ( r * ) and on matchng frctons (f ) 3 h ( * Hr, f ) = (6) Snce wth matchng frctons a borrower may not be able to match wth hs/her preferred partners, he/she may decde to adjust hs/her own rsk choce. Ths mples that the rsk level a borrower chooses (the observed rsk, r ) s a functon of characterstcs that affect the frst-best rsk choce (X ) and the heterogenety he/she s faced wth,.e. r RX (, h ) = (7) If equaton (6) s substtuted n equaton (7) a reduced form expresson for the observed rsk level can be obtaned r k( X, f) = (8) 3 In fact f refers to a matrx of varables determnng the frcton level f. 164

9 The full system of equatons (the structural model) can now be specfed as: h = H r, f ) (9) ( * r k( X, f) = (10) * r = k(,0) (11) X If the matchng frctons hypothess holds, then 0. It may be useful to compare ths condton wth the condton for homogeneous matchng n a frctonless world. In a frctonless world wth homogeneous matchng h should be zero n all groups. So, heterogenety between all members wthn a group and hence group heterogenety wll then be zero. In ths stuaton, the test for homogeneous matchng could be based on a measure of group heterogenety. Smply testng whether ths measure s equal to zero would do. However, wth matchng frctons h does not need to be h r h r = * equal to zero. The correct test s 0, whch mples that homogeneous = * matchng cannot be confrmed or rejected by testng whether a measure for group heterogenety dffers from zero. In order to correctly test the matchng frctons theory, we need varables for rsk and heterogenety at the ndvdual level. The rsk level a borrower chooses depends on the heterogenety he/she s faced wth. Snce the heterogenety an ndvdual borrower s faced wth s greater, the more hs/her rsk level s away from the group mean, a group heterogenety measure, whch gves the same heterogenety level for all members n a group, cannot be used. In the next secton we wll explan how we measure rsk. Secton 8.7 wll explan how we measure heterogenety. But frst we need to complete the dscusson of the emprcal methodology. The trck s to frst estmate the actual rsk equaton, for whch we take, for reasons of convenence, a lnear specfcaton: r = X α + f β + ε (12) 165

10 From ths regresson, estmated values for frst-best rsk and matchng frctons can be obtaned: * r = X α (13) βf = f β (14) These estmated values are then substtuted n the equaton for heterogenety: h = * α + γ r + δ βf + ε (15) Homogeneous matchng wll be emprcally confrmed f γ = 0. It s expected that δ How to measure rsk The frst step n the analyss s to develop a measure for rsk, whch s needed to estmate the rsk equaton (equaton 12). Note that n the theoretcal models t s assumed that there s only one project avalable per ndvdual, whch mples that projects and borrowers are nterchangeable. Ths also mples that the theoretcal measure for rsk refers to both the rskness of the borrower and the project. However, emprcally there s no perfect measure for ths theoretcal rsk concept avalable. We proxy the theoretcal concept of rsk by developng a measure for the rsk of a borrower s repayment strategy. Even ths s not drectly measurable and therefore has to be proxed by an (admttedly mperfect) ndcator. In lne wth Sadoulet and Carpenter (2001), we proxy rsk ( r ) by: r P S =, for P S P and r = 0 for P < S where P s the loan payment due per month and S s the amount the borrower reports to have saved one week before the due date to cover the 166

11 loan payments. 4 The rsk ndcator vares between 0 and 1. The hgher the percentage amount saved a week before the repayment date, the lower the rsk of a borrower s repayment strategy. We consder loan payments due per month, snce for the two mcrofnance programs n Ertrea the nstall payments members are supposed to make are monthly. In the questonnare we asked the borrowers to specfy the agreed nstall payment per month (P ). We also asked borrowers to specfy the average cumulatve savngs untl one week before due date (S ). Table 8.1 gves nformaton on the rsk measure and on the varables used to construct ths measure. The table also provdes data on the credt amount. Table 8-1 Informaton on credt and rsk CREDIT SIZE P S r Mean Medan Maxmum Mnmum Std. Dev Skewness Kurtoss Jarque-Bera Observatons Note: all values (except for r) are n Nakfas. The Jarque-Bera statstc s a test for normalty. The statstc has a χ 2 dstrbuton wth 2 degrees of freedom under the null hypothess of normally dstrbuted errors. 4 Note that Sadoulet and Carpenter use the sum of expected sales n the last three days before the due date as the scalng factor, nstead of P. Our questonnare also contans a queston on the expected sales n the last days (one week n our case) before the due date. However, snce the answers to ths queston were totally unrelable we decded to scale by P. 167

12 The value of loans ranges from 750 Nakfas to 8500 Nakfas, wth mean and medan loan szes of 3961 and 3500 Nakfas, respectvely. Loan terms vary from 3 to 24 months. The mean of our rsk ndcator s about 0.17, wth an even lower medan (0.09). Of the 351 borrowers 105 are left censored on the rsk measure (r = 0), 10 are rght censored (r = 1) and 236 are uncensored (0 < r < 1). Snce r = 0 for a relatvely hgh percentage of the group of borrowers, many borrowers show a tendency to save enough to repay the full monthly amount by the thrd week. Thus, borrowers seem to show a hgh degree of punctualty and a great readness to save ahead of tme n order to be sure of future access to credt from the program. Note that none of the varables s dstrbuted normally. It should be noted that a possble caveat of our rsk measure s that a person who gets a fxed payment (more than P ) n the week before the payment can be very safe despte the fact that S = 0. However, we do not thnk that ths wll substantally affect our results snce n practce ths does not seem to happen that often. Related to ths problem, the valdty of our measure may depend on the tme profle for the dfferent projects. Our measure may ncorrectly gve a hgher rsk rankng to a borrower wth a project that yelds an uncertan amount of ncome n the frst week as compared to another borrower wth a project that yelds a certan amount of ncome n the fourth week. Snce t s mpossble to obtan detaled nformaton about the tme profle of returns for the dfferent projects the loans are used for, ths problem cannot be solved. But gven the fact that the bulk of loans by the two programs n Ertrea are forwarded for the same purposes (tradng) so that the tme profle of most of the projects the loans are used for are probably smlar, we are reasonably convnced about the valdty of our rsk proxy. 8.5 Varables proxyng for frst-best rsk and matchng frctons The next step n the analyss s to determne whch varables possbly affect rsk, whch of those varables are related to frst-best rsk and whch of them are related to matchng frctons. Hence, we need to determne a vector of varables X (frst-best) and f (matchng frctons). 168

13 8.5.1 Matchng frctons (f) Sadoulet and Carpenter (2001) argue that varables proxyng for matchng frctons nclude ndcators of the degree of asymmetrc nformaton among dfferent members of a group, proxes for the ablty to montor and screen the actvtes of the dfferent members n a group, and varables on the avalable borrowng optons. In lne wth Sadoulet and Carpenter (2001) we select from our data set the followng lst of varables related to montorng, screenng, the avalable nformaton on other members, and the possblty to obtan credt. - BOGROUP = a dummy varable wth a 1 f the borrower s born n the vllage or town where the survey s conducted; - CHGRDUM = a dummy varable wth a 1 f the group member has been a member of another group; - KNMEMDUM = a dummy varable wth a 1 f the borrower knew the members well before they formed the group; - INTEGRITY = a dummy varable wth a 1 f the borrower knew about the behavoral ntegrty of all hs/her fellow group members before the formaton of the group; - KNACTDUM = a dummy varable wth a 1 f the group member knows the economc actvtes of the other group members; - KNPURPDUM = a dummy varable wth a 1 f the borrower knows for what purpose the other group members acqured ther latest loans; - KNSELDUM = a dummy varable wth a 1 f the borrower knows the monthly sales of the other group members; - LDIST = the logarthm of the average dstance of the busness of the group member from that of the other group members; - VISTDUM = a dummy varable wth a 1 f the group member vsts other group members; - ARREAR = a dummy varable wth a 1 f the borrower has had problems repayng hs/her debt n the current loan cycle; - OTHCREDIT = a dummy varable wth a 1 f the borrower has other sources of credt; - ACORDUM = a dummy varable wth a 1 f the group belongs to the SZSCS; 169

14 - NOMEM = the number of members n a group. From ths lst of varables, BOGROUP, CHGRDUM, KNMEMDUM, INTEGRITY prmarly refer to socal tes and peer screenng varables. These are varables that ndcate the amount of nformaton members have on each other. These varables, wth the excepton of CHGRDUM, deal n partcular wth the avalable nformaton before formng the group. An ncrease n the value of one of these ndcators mples more nformaton about each other that mght ncrease the probablty of better peer screenng and stronger socal tes. KNACTDUM, KNPURPDUM and KNSELDUM, LDIST and VISTDUM have to do wth the (possblty of) peer montorng. More vsts among members and a shorter dstance between members ncrease peer montorng. More group members tend to ncrease montorng efforts, but there s also more scope for free rdng. ARREAR and OTHCREDIT refer to possbltes to obtan credt from other sources; OTHCREDIT drectly measures whether a borrower has been able to rase funds from other sources than the mcrofnance nsttuton, and ARREAR measures repayment problems and may ndcate future possbltes to rase credt. ACORDUM and NOMEM are not drectly related to the ssues dscussed so far but as wll become clear later on they have been ncluded snce they are hghly correlated to each other Frst-best rsk We assume that frst-best rsk can be pcked up by varables that are drectly related to the soco-economc stuaton of the borrower. We consder the followng varables: - LINC: the logarthm of total monthly ncome; - AGE: the age of a borrower; - GENDUM: a dummy wth a 1 for a male, and a 0 for a female; - ILLIT: a dummy wth a 1 f the borrower s llterate; - PRIM: a dummy wth a 1 f the borrower has had any prmary educaton; 170

15 - SEC: a dummy wth a 1 f the borrower has had any secondary educaton; - GLEADER: a dummy wth a 1 f the borrower s a group leader; - MOSLDUM: a dummy wth a 1 f the borrower s a Muslm. The concepts matchng frctons and frst-best rsk are latent varables, whch cannot be observed drectly. Above, we have selected a group of varables that s assumed to be related to matchng frctons, and a group of varables that s assumed to be related to frst-best rsk. In order to better account for the hgh collnearty between some of the varables wthn the two groups, and n order to test whether we can reduce the number of ndependent varables by constructng a smaller amount of new composte varables, we performed a multple factor analyss (MFA). We started by applyng a factor analyss to the ndcators of the group of varables related to matchng frctons. The analyss suggests that eleven ndcators n ths group can be dvded nto three underlyng factors. The two remanng ndcators (ARREAR and OTHCREDIT) are left out of ths analyss snce they have very low factor loadngs, even f more underlyng factors are allowed for. The factor loadngs of the analyss are gven n table 8-2. The frst factor manly has to do wth KNMEMDUM and INTEGRITY, suggestng that the underlyng factor n ths case relates to nformaton members have about each other before they formed a group. ACORDUM and NOMEM manly determne the second factor. NOMEM has a negatve factor loadng, whch suggests that wth respect to our sample the average number of members n credt groups from the SCSZS s lower than n groups from the SMCP. A closer look at the data set confrms ths: the average number of members n credt groups from the SMCP s 5.2, whereas t s 3.6 for the SCSZS. The postve factor loadng on VISTDUM suggests that members of credt groups from the SCSZS vst each other more regularly than those of the SMCP system. The thrd factor manly has to do wth KNPURPDUM and to a lesser extent wth KNACTDUM. Ths may suggest that n ths case the underlyng factor 171

16 relates to nformaton members have about each other s busness, after the group has been formed. Table 8-2 Factor loadngs for factor analyss on matchng frctons varables FACTOR1 FACTOR2 FACTOR3 ACORDUM BOGROUP CHGRDUM KNMEMDUM INTEGRITY LDIST KNACTDUM KNPURPDUM KNSELDUM VISTDUM NOMEM Ch square Statstc: 24. 7; 25 Df; p-value: 0.479; CUMVAR=0.394 Note: factor loadngs smaller than 0.01 are not reported. Df denotes the degrees of freedom. CUMVAR gves the cumulatve varance explaned by the factors taken nto account. The factor analyss s done on 323 observatons (the common sample of all ndcators; observatons refer to members of both MFIs). The Ch square Statstc s a test of the hypothess that three factors are suffcent versus the alternatve that more are requred. The P-value s the probablty of beng wrong when the null hypothess s rejected (the plausblty of the null hypothess. So, the smaller s the P-value, the less plausble s the null hypothess). In the remander of the analyss we wll use the three factors, nstead of the eleven orgnal ndcators. We nterpret FACTOR1 and FACTOR3 as factors that prmarly have to do wth the asymmetry of nformaton among group members. FACTOR1 pcks up nformaton before formng the group; FACTOR3 pcks up nformaton after the group has been formed; and FACTOR2 prmarly relates to beng a member of a credt group wthn the SCSZS and the number of members wthn a group. The latter varable s mportant for rsk takng snce t gves nformaton on a possble peer montorng effort. Armendárz De Aghon (1999, proposton 3, p.95) states that a larger group sze tends to ncrease peer 172

17 montorng effort, due to a jont-responsblty, a cost-sharng, and a commtment effect. However, a larger group sze (also) ncreases the scope for free rdng n debt-repayment decsons. 5 Next, we perform a factor analyss on the ndcators for frst-best rsk. However, here the factor analyss showed that t s not possble to combne the ndcators nto a smaller group of underlyng factors. The number of factors that has to be taken nto account to accept the null hypothess of suffcent factors s almost equal to the orgnal amount of ndcators. Therefore, we decded to proceed wth the ndvdual frst-best ndcators n the remander of the analyss. 8.6 Estmatng rsk The next step n the analyss s to examne the possble emprcal relevance of our matchng frctons and frst-best rsk varables for explanng rsk of a borrower's lqudty strategy. In other words, the next step s the estmaton of equaton (12). The dependent varable s the proxy for rsk, r, whch we have constructed. The ndependent varables are the eght frst-best rsk ndcators, the three factors related to matchng frctons, and the remanng two varables (ARREAR and OTHCREDIT), whch are also related to matchng frctons. To examne non-lnear effects we also tred quadratc terms, but except for the quadratc term of LINC (LINC2) none of these appeared to be sgnfcant. Hence, they were left out of the analyss. The constructed dependent varable s censored between 0 and 1. Therefore, we estmate wth the Tobt estmaton technque wth left and rght censorng (usng normal dstrbuton of error terms). We also present ordnary least squares (OLS) estmates to test for dfferences n outcome 5 Note that n Armendárz De Aghon (1999) groups are exogenously gven. In practce, there s a tradeoff between the cost of group sze (montorng effort) and benefts of sze (dversfcaton, easer to cover one defaultng partner). Group sze s thus endogenous. We gnore ths problem n our analyss. 173

18 due to dfferent estmaton technques. The estmaton results are presented n table 8-3. Equatons 1A and 1B n table 8-3 show that LINC, LINC2, GLEADER, SEC, ARREAR and FACTOR2 sgnfcantly affect rsk behavor. Snce LINC has a sgnfcantly negatve coeffcent and LINC2 a sgnfcantly postve coeffcent, there seems to be a non-lnear relatonshp between the ncome of a borrower and hs/her rsk behavor. For low-ncome levels, an ncrease n ncome reduces rsk, whereas t ncreases rsk after a certan threshold level of ncome has been passed. Postve sgnfcant coeffcents for GLEADER, SEC and ARREAR suggest that a group leader takes more chances than a normal group member, that members who are more educated take more rsks, and that members who have had repayment problems n the past also take more chances. The negatve coeffcent for FACTOR2 mples that borrowers n a borrowng group belongng to the SZSCS take less rsks. The underlyng reason probably s that the numbers of members n credt groups belongng to the SZSCS are lower. Larger groups may lead to more rsk takng of the ndvdual members, possbly due to a better scope for freerdng. These results hold for both the OLS and Tobt estmates. In equatons 2A and 2B the regressons are repeated by gnorng the nsgnfcant terms. These regressons confrm the results suggested by equatons 1A and 1B. Fnally, we re-estmate the equatons by replacng ARREAR wth AMARREAR (equatons 3A and 3B). AMARREAR measures the amount of money that was nvolved when the borrower had problems repayng the debt, as a percentage of the loan sze n the prevous loan cycle. Ths ndcator serves as an alternatve ndcator for ARREAR. The results of these regressons agan confrm the basc message of equatons 1A and 1B. 174

19 Table 8-3 Estmatng results on rsk 1A 1B 2A 2B 3A 3B Method OLS Tobt OLS Tobt OLS Tobt LINC *** (-2.93) *** (-3.48) *** (-3.05) *** (-3.63) *** (-2.19) *** (-2.77) LINC *** (2.73) 0.078**** (3.31) 0.056*** (2.86) 0.080*** (3.48) 0.029*** (1.93) 0.048*** (2.51) AGE (0.22) (0.21) GENDUM (-0.63) (-0.84) ILLIT (-0.96) (-0.91) PRIM (0.16) (0.06) SEC 0.111*** (2.40) 0.149*** (2.39) 0.116*** (2.78) 0.157*** (2.72) 0.116*** (2.85) 0.148*** (2.59) GLEADER *** (2.70) 0.073*** (2.46) 0.060*** (3.00) 0.074*** (2.62) 0.042*** (2.25) 0.049** (1.91) MOSDUM (0.40) (0.47) ARREAR 0.320*** (8.35) 0.386*** (8.38) 0.321*** (8.53) 0.386*** (8.47) AMARREAR 0.399*** (6.72) 0.540*** (7.61) OTHCREDIT (0.06) (-0.08) FACTOR (-0.07) (0.50) FACTOR *** (-2.07) *** (-3.16) *** (-2.13) *** (-3.25) *** (-1.73) *** (-2.74) FACTOR (-0.47) (-0.68) CONSTANT 3.443*** (3.18) 4.734*** (3.64) 3.480*** (3.28) 4.846*** (3.78) 2.092*** (2.54) 3.188*** (3.03) adj. R Note: the amount of observatons s 323 for all regressons. That s, although we have 351 members n our data sets, the number of members who belong to the 102 groups s just 323. t- values (z-values for Tobt) based on whte Heteroskedastcty-consstent standard errors (for the OLS regressons) and QML (Huber/Whte) standard errors between parentheses. The Tobt estmates are done wth left (0) and rght (1) censorng; there are 94 left censured observatons and 10 rght censured observatons. 175

20 Snce FACTOR2 manly has to do wth three ndcators ACORDUM, VISTDUM and NOMEM we also perform OLS and Tobt regressons n whch FACTOR2 s replaced by one of these ndvdual ndcators. The regresson results show that each of these ndvdual terms, wth the excepton of the OLS estmate for NOMEM, s sgnfcant. Beng a borrower from a credt group assocated wth the SZSCS has a negatve effect on rsk takng. The same holds for more vsts among members of a credt group. An ncrease n the number of members of a credt group enhances rsk-takng behavor of an ndvdual borrower. The results are presented n table 8-4. * We are now able to come up wth an estmate of r = X α and βf = fβ (equatons 13 and 14, secton 8.3). To ths end we use the estmaton results of equaton 2B (the Tobt estmates) presented n table 8-3. As we explaned before, we argue that the varables that are related to the socoeconomc stuaton (.e. LINC, LINC2, SEC and GLEADER) determne the rsk choce n a frctonless world. The other varables (ARREAR and FACTOR2) are prmarly related to matchng frctons. By usng the estmated coeffcents of equaton 2B (table 8-3) we can now come up wth an estmate of r *, whch we name FIRSTBEST, and β f, whch we name FRICTION. 6 6 We assume that the condtonal mean (E[y ]) of the Tobt regresson equaton y = β x + ε equals Κ x. If all ndependent varables are taken nto account, ths predcts the so-called expected latent varable. 176

21 Table 8-4 Estmatng rsk by replacng FACTOR2 wth ACORDUM, VISTDUM and NOMEM 1A 1B 2A 2B 3A 3B Method OLS Tobt OLS Tobt OLS Tobt LINC *** (-2.95) *** (-3.49) *** (-2.87) *** (-3.25) *** (-2.89) LINC *** 0.076*** 0.051*** 0.068*** 0.053*** (2.77) (3.35) (2.68) (3.07) (2.69) SEC 0.085*** 0.114*** 0.078*** 0.092*** 0.109*** (2.25) (2.04) (2.12) (1.70) (2.64) GLEADER 0.060*** 0.075*** 0.057*** 0.071*** 0.060*** (3.10) (2.74) (3.02) (2.65) (3.00) ARREAR 0.324*** 0.392*** 0.316*** 0.373*** 0.318*** (8.74) (8.73) (8.66) (8.54) (8.50) ACORDUM *** *** (-2.31) (-3.48) VISTDUM *** *** (-2.37) (-2.79) NOMEM (1.43) CONSTANT 3.310*** 4.578*** 3.224*** 4.246*** 3.301*** (3.21) (3.68) (3.17) (3.48) (3.08) *** (-3.35) 0.074*** (3.18) 0.139*** (2.47) 0.074*** (2.64) 0.379*** (8.39) 0.023*** (2.40) 4.422*** (3.43) adj. R See the note to table Heterogenety The fnal step n the analyss s to estmate the heterogenety equaton. Therefore, we frst need to develop a measure of rsk heterogenety The measure for rsk heterogenety In lne wth Sadoulet and Carpenter (2001) we measure rsk heterogenety (h ) by: 177

22 group G ( r r ) j h = r G sgn( r r ) j, where ( N 1) r s the mean rsk n s Ths proxy measures the average Eucldean dstance between the rsk of a borrower and all of hs/her group partners. Note that our measure for heterogenety s ndvdual rather than group specfc, as t should be. Moreover, the heterogenety proxy gves hgher degrees of heterogenety for borrowers wth a rsk level that s further away from the mean rsk level n the group ths s also n lne wth theory. We sgn the average Eucldean dstance n order to allow for possble dfferences n behavour for the relatve safe and relatve rsky borrowers n a group (whch s n lne wth theores that examne group formaton n the context of mssng nsurance markets). However, we also used a measure for heterogenety that s not adjusted for havng a rsk above or below the mean rsk. Ths gave qualtatvely the same results. Snce our space s lmted, we have not presented these results. Table 8.5 gves descrptve statstcs of h. Table 8.5 Heterogenety h Mean Medan -2.78E-17 Maxmum 1.00 Mnmum Std. Dev Skewness Kurtoss Jarque-Bera Next, we wll examne whether or not heterogenety s caused by matchng frctons. We wll do ths by estmatng equaton

23 8.7.2 Estmaton results The estmates of the heterogenety equaton are presented n table Agan we use the OLS as well as the Tobt estmaton technque. The dependent varable n the regressons s our proxy for heterogenety (h). It seems that the coeffcent for FIRSTBEST s sgnfcantly dfferent from zero at the 99 per cent level, whch strongly suggests that homogeneous matchng wll not occur, even f the estmates are controlled for matchng frctons. Table 8.6 Estmatng heterogenety 1 2 METHOD Tobt OLS FIRSTBEST ( r * ) (3.20) (3.19) FRICTION ( β f ) (5.54) CONSTANT (3.13) (5.52) (3.13) adj R Note: the amount of observatons s 323 for all regressons. t-values (z-values) for OLS (for Tobt) between parenthess (based on Whte Heteroskedastcty-Consstent Standard Errors and Covarances and Huber/Whte robust standard errors and covarances, respectvely). In equaton 1 there s one rght and one left censored observaton. A possble caveat of our analyss may be that we have not ncluded all relevant varables n the equaton for rsk and that ths affects our estmates. There may be some relevant matchng frctons or frst-best varables mssng. Ths s for example suggested by the fact that there are 7 It should be noted that the varables FIRSTBEST and FRICTIONS are measured wth errors. OLS (and Tobt) estmates of the heterogenety equaton may therefore be based. A possble soluton, used by Sadoulet and Carpenter (2001), s to estmate the heterogenety equaton wth nstrumental varables. However, due to a lack of canddates for nstruments n our sample we decded to rely on the OLS estmates. 179

24 only a few varables for matchng frctons sgnfcantly. Ths may then lead to an omtted varable bas. The problem wth omtted varable bas s that t may lead to a correlaton between the dsturbance term and one of the rght-hand sde varables. Ths may bas the estmates of the coeffcent and standard error of X and f, whch may consequently affect our estmates of the heterogenety equaton. However, note that we are not drectly nterested n the parameters n equaton (12). We only use the ftted varables for frst-best rsk and matchng frctons. It s easy to show that the predcted values are consstent estmators, so that we can be reasonably sure that our result wth respect to FIRSTBEST and hence our concluson that homogeneous matchng does not hold s not affected by omtted varable bas because of a msspecfcaton of the rsk equaton. Our approach of obtanng FIRSTBEST and FRICTION s somewhat comparable to an nstrumental varable (IV) technque. As s well-known IV estmaton s desgned to overcome problems caused by correlaton between the dsturbance term and the rght-hand sde varables. 8.8 Conclusons Ths chapter ams to provde new nsghts nto the emprcal relevance of the homogeneous matchng hypothess for mcrofnance groups n Ertrea. A better nsght nto group formaton and whether these groups are homogeneous s extremely mportant for our understandng of the workng of mcrofnance programs. The result of our analyss can be used as an nput for the analyss of repayment performance of jont lablty schemes versus ndvdual lablty debt contracts. It also provdes ndrect evdence on the relablty of the hypothess that group lendng by means of jont lablty lendng can reduce adverse selecton problems. The estmates wth respect to rsk behavor suggest that among the borrowers from the mcrofnance programs n Ertrea, there s a non-lnear relatonshp between the ncome and rsk takng. Below a certan threshold level of ncome, an ncrease n ncome wll lead to less rsk takng, whereas an ncrease n ncome above a certan level wll ncrease rsk takng. We also fnd that group leaders take more rsk than regular group members, that better educated borrowers take more rsk, and that 180

25 borrowers who have had repayment problems n the past wll take more rsk. Moreover, we fnd some evdence that borrowers n larger groups wll take more rsk than borrowers n smaller groups. Concernng the homogeneous matchng hypothess, our results strongly ndcate that groups are formed heterogeneously. Most mportantly, we do not fnd support for the matchng frctons hypothess, n the sense that even f we control for matchng frctons, credt groups n Ertrea do not seem to consst of borrowers of a smlar rsk type. The mplcaton of ths fndng for repayment behavor s not clear beforehand. However, our result seems to be bad news for those who argue that group-based lendng may reduce problems of adverse selecton. In some theoretcal papers t has been argued that ncentve compatble separatng equlbra wll result f a lender offers dfferent types of debt contracts, wth varyng components for jont lablty. By choosng a partcular debt contract, the borrower wll reveal hs/her type and hence the asymmetrc nformaton and consequently the adverse selecton problem wll be solved. However, ths result s based on the homogeneous matchng hypothess. Of course, some reservatons wth respect to our man conclusons can be made. For nstance, the classfcaton of varables n a group that prmarly deals wth matchng frctons, and a group of varables dealng wth frstbest rsk determnants may be crtczed. In addton, our varables FIRSTBEST and FRICTION are constructed varables, and therefore are measured wth error. Ths may bas the estmates of the coeffcents. Moreover, the measure of rsk we use may not be the most accurate measure for rsk takng. There may exst other measures of rsk that are better proxes. It may then be the case that usng another measure for rsk wll lead to homogeneous matchng, nstead of the heterogeneous matchng we found by usng our measure for rsk. More research on these ssues s needed. Nevertheless, gven the data we have, and takng nto account all possble drawbacks of the methodology used, we thnk that our analyss, at the least, suggests that the commonly held assumpton of homogeneous matchng can not be confrmed for the case of Ertrea. If one accepts that groups are formed heterogeneously, an mportant ssue s then to examne why ths s so. A possble reason brought forward n 181

26 some recent papers s the nsurance that rsky and safe borrowers may provde. The models behnd the homogeneous matchng hypothess assume that borrowers are rsk neutral and that project returns do not covary. Ths mples that n these models there s no possblty to gan from economes of rsk poolng. However, f borrowers are rsk averse and project returns are not ndependent, a borrower may proft from groupng wth another borrower f the project returns of the two borrowers are negatvely correlated. Ths may then mply that heterogeneous matchng s the optmal outcome. 182

27 APPENDIX: Lst of varables used n the analyss wth expected sgns 183

28 Table 8-A1 Lst of varables wth ther expected sgns INDEPENDENT VARIABLES EXPECTED SIGNS PEER MONITORING KNACTDUM - KNPURPDUM - KNSELDUM - LDIST + VISITDUM - SOCIAL TIES BOGROUP - KNMEMDUM - INTEGRITY - CHGRDUM + PERSONAL CHARACTERISTICS AGE +/- GENDUM +/- ILLIT +/- PRIM +/- SEC +/- MOSLDUM +/- LINC +/- OTHER VARIABLES OTHERCREDIT - GLEADER +/- AREAR + NOMEM +/- ACORDUM +/- 184

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