Entry of Profit-Motivated Microfinance Institutions and Borrower Welfare

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1 INDIAN INSTITUTE OF MANAGEMENT AHMEDABAD INDIA Etry of Profit-Motivated Microfiace Istitutios ad Borrower Welfare Ratul Lahkar ad Viswaath Pigali W.P. No September 2012 The mai objective of the workig paper series of the IIMA is to help faculty members, research staff ad doctoral studets to speedily share their research fidigs with professioal colleagues ad test their research fidigs at the pre-publicatio stage. IIMA is committed to maitai academic freedom. The opiios, views ad coclusios expressed i the workig paper are those of the authors ad ot that of IIMA. INDIAN INSTITUTE OF MANAGEMENT AHMEDABAD INDIA

2 Etry of Profit-Motivated Microfiace Istitutios ad Borrower Welfare 1 Ratul Lahkar 2 ad Viswaath Pigali 3 Abstract I this paper, we model welfare implicatios of etry of commercial microfiace istitutios MFIs. We iitially characterize equilibrium with a sole fud-costraied beevolet credit istitutio followed by equilibrium with oly profit-motivated MFIs. We show that etry of such MFIs ca lead to a icrease i iterest ad default ad a declie i screeig. However, it ca still represet a Pareto improvemet sice: all agets previously deied credit ca obtai loas, ad existig cliets have the optio of seekig loas from MFIs. Fially, we model multiple group formatio as a equilibrium mechaism, which allows more efficiet risk diversificatio. Keywords: Microfiace, Joit Liability, Risk Diversificatio. JEL classificatio: D04; D86; G21. 1 Itroductio Sice the early 2000s, there has bee rapid expasio of microfiace idustry i the developig world, both i terms of umber of borrowers as well as ledig istitutios, thereby makig the idustry competitive. Itesificatio of competitio has led to cocers of excessive borrowig ad higher default rates, ad a cosequet deterioratio of borrower welfare ad sustaiability of this sector. I this paper, we seek to uderstad this issue from a theoretical perspective. Usig a model of adverse selectio, we show that etry of ew firms i the idustry ca, ideed, raise iterest rates ad default rates. Nevertheless, we show that higher iterest ad default rates ca coceal a Pareto improvemet i borrower welfare. Aggregate welfare improves primarily due to the fact that higher competitio icreases the outreach i terms of umber of loas. We also show that the presece of multiple firms eables a borrower to egage i more efficiet risk-diversificatio by formig multiple groups. This has a further welfare ehacig effect o borrowers. Microfiace refers to the idea of providig access to fiacial services to low-icome households, who are typically defied o-bakable by the traditioal bakig system. 4 While there are some operatioal dissimilarities across coutries, the fudametal idea - collateral free ledig to a group 1 We thak TN Sriivasa, Bidu Aath, ad Lakshmi Kumar for commets ad discussios. 2 IFMR, 24, Kothari Road, Nugambakkam, Cheai, , Idia. r.lahkar@ifmr.ac.i. 3 Idia Istitute of Maagemet Ahmedabad, Vastrapur, Ahmedabad , Idia. viswaath@iimahd.eret.i 4 While all fiacial products like micro ledig, micro savigs, micro isurace, etc, fall uder the caopy of microfiace we oly cosider micro credit for this study. For the rest of the paper, the term microfiace oly refers to micro credit. W.P. No Page No. 2

3 joitly liable for the loa of each idividual member - remais the core idea behid microfiace. The istitutio of joit liability is expected to trigger of moitorig of idividual behaviour by other group members, thereby substitutig for the role that collateral covetioally plays i combatig adverse selectio ad moral hazard amog borrowers Ghatak, For example, i Idia, there are two types of players from the supply side that operate o the priciple of joit liability: self help groups SHG ad traditioal microfiace istitutios MFIs. Self Help Groups SHG have bee i existece sice the early 1990s Basal, The SHGs, typically, operate o a ot-for-profit basis with the objective of ehacig borrower welfare. But sice they receive their fudig primarily from door agecies ad/or microsavigs of their cliets, their scope to exted credit is limited. The SHGs also have striget participatio costraits like regular savigs, ad madatory traiig programs. O the other had, the traditioal MFIs have bee i operatio sice late 1990 s, but oly picked up mometum i early to mid 2000 s. 6. Ulike SHGs, several of these MFIs are commercial orgaizatios motivated by profit, ad typically ted to follow SHGs ito a particular market. 7 Recet data suggests that MFIs have bee growig at faster rate tha SHGs both i terms of the amout of loas disbursed ad the umber of borrowers served Chapters 2 ad 3, Sriivasa, This suggests that MFIs are replacig SHGs as the major source of credit i the microfiace sector. The Idia example is represetative of the patter of historical developmets i microfiace idustry that has bee observed i other coutries. Microfiace starts out as a beevolet idustry, before seeig etry, ad subsequet domiace, from commercially motivated MFIs. This chage i orietatio of idustry from beevolet objectives to commercial motives has led to several cocers. For example, it has bee foud that icrease i the umber of microfiace leders icreases the default rate. 8 Aother criticism is that with access to multiple sources of credit, there may be icrease i idebtedess due to idiscrimiate borrowig. 9. I this paper, we attempt to uderstad these cocers from a theoretical perspective. To this ed, we develop a model of adverse selectio wherei there are two types of agets: high risk ad low risk. 10 This categorizatio serves as a proxy for possible differeces i the quality of borrowers. We evisage a iitial situatio with a SHG beig the sole leder. The ledig capacity of the SHG is costraied ad it seeks to optimize the utilizatio of the limited umber of loas it ca make while breakig eve. I this situatio, we show that if the proportio of low risk borrowers is 5 Joit liability refers to the istitutio where potetial borrowers orgaize themselves ito groups based o certai criteria ad obtai loas as a group. While loas are give to idividual members, the group as a whole is resposible for repaymet of all the loas. 6 As of 2009, the total outstadig loa portfolio of Idia microfiace idustry stads at $ 4.3 billio with more tha 25 millio active borrowers across over 80 MFIs. It has also experieced pheomeal growth betwee 2004 ad 2009 with the idustry doublig itself o a average both i terms of amout ad umber of loas disbursed. Ivertig the Pyramid, Itellicap, 3rd editio, Discussios with Madura Microfiace ad Gramee Kootas, two leadig MFIs based out of South Idia have cofirmed that MFIs typically follow oce SHGs have established their presece. 8 McItosh et. al 2005 discuss the developmet of microfiace i Ugada. They also provide evidece about the icrease i default rates followig i the the umber of firms. 9 The popular press has reported several suicides amog Idia farmers. This tred has bee attributed to over idebtedess as a result of icrease i competitio i this sector. For example, see Also, see ad for similar cocers expressed about microfiace sectors i Africa ad Bagladesh respectively 10 For expositioal coveiece, i the rest of the paper, SHG refers to a beevolet fuds-costraied orgaizatio whereas MFI refers to the microfiace istitutio to a profit makig etity. W.P. No Page No. 3

4 sufficietly low, the SHG imposes certai participatio requiremets o borrowers to scree out the high risk borrowers. Sice ledig is thereby limited to low risk borrowers, iterest rates ad default rates are low. Sigificatly, SHGs are able to serve oly a limited umber of potetial borrowers due to their costraied ledig capacity. The umet demad attracts MFIs guided by the profit motive, makig the idustry more competitive. We assume that these MFIs do ot have ay costrait o their ledig capacity. Therefore, they led to borrowers of either type as log as the margial profit is positive. We characterize the equilibrium that emerges uder Bertrad competitio i the presece of multiple MFIs ad the sigle SHG. I equilibrium, uless the proportio of low-risk borrowers is exceptioally low, MFIs adopt a o-discrimiatory ledig policy i which they led to ay borrower who approaches them. This iterest rate eeds to accout for the possibility of a borrower beig of either type. Hece, it is higher tha the iterest rate charged by the SHG whe it leds to oly low risk types. Furthermore, sice MFIs led to borrowers of both types, the default rate is also higher. Sigificatly, i this case, the MFIs do ot impose ay participatio cost o borrowers. 11 Our model, therefore, does predict that with etry of commercial MFIs, iterest ad default may go up. 12. Despite this, the situatio ca still represet a Pareto improvemet over the situatio whe the SHG is the sole leder. First, borrowers of both types, earlier left out of the SHG, ca ow access loas from the MFI. Secod, cliets of the SHG ca choose to remai with the SHG uder the pre-existig cotract. They ow have the additioal choice to migrate to MFIs if the avoidace of the participatio cost more tha compesates for the higher iterest charged by the MFIs. Therefore, several cocers expressed about competitio i microfiace idustry ca be iterpreted as reactios to bad radom draw of a otherwise ex ate Pareto improvig outcome. 13 Our fial set of results focus o the implicatios of borrowig from multiple sources o borrower welfare. The joit liability mechaism is ecessitated by the iformatioal asymmetry betwee borrower ad leder. However, compared to idividual ledig i the first best case of o iformatioal asymmetry, joit liability reduces the welfare of a risk-averse borrower by imposig the risk of her parters default o her. With multiple MFIs, o the other had, borrowers may be members of differet groups with oe group membership providig oly a fractio of her total loa requiremet. Provided defaults are idepedet across idividuals, ad her parters i differet groups are ot the same, this mechaism eables a borrower to diversify the additioal risk icurred due to the chaces of her parters defaultig. Hece, our aalysis suggest that multiple group membership ad hece, multiple loas is a mechaism for borrowers to achieve more efficiet risk diversificatio, istead of it beig a meas to idulge i over-borrowig. The existig theoretical literature o competitio ad microfiace models the borrowers based o their ecoomic profile, i.e., the richer borrowers ad the poorer oes. However, the literature is ot clear o whether the icrease i competitio leads to wider access of loas from MFIs To this extet, our results are cosistet with theoretical studies o bakig idustry. See See Marquez This implicatio is cosistet with the empirical fidigs of McItosh et. al 2002 see footote 8 13 Pareto improvemet of borrowers welfare is uambiguously valid wheever SHG screes borrowers. Recet empirical evidece suggests that SHGs do scree borrowers Basal, If this coditio does ot hold, the implicatios o welfare are more qualified. See Sectio 4 for details. 14 The empirical evidece so far seems to be mixed as well. For example, see Kai 2009, Olivares - Polaco 2005 ad Rhye ad Christe 1999 for evidece of decreased, ad Nagaraja 2001 for the evidece o icreased outreach amog the poor. W.P. No Page No. 4

5 For example, McItosh ad Wydick 2005 show that the icrease i competitio causes poorer borrowers to be uambiguously worse-off. This is because with icreased competitio, MFIs lose their ability to cross-subsidize poorer borrowers by chargig higher iterest from richer cliets. O the other had, Guha ad Roy Chowdhury 2010 show that icreased competitio coupled with multiple borrowig leads MFIs to reach out to poorer sectios. A commo feature of the two studies is that the MFIs have complete kowledge of the icome of idividual cliets. It is debatable as to what extet this assumptio is valid. I cotrast, we make a weaker iformatioal assumptio. MFIs are oly aware of the overall distributio of the risk profile of their cliets, ad ot idividual characteristics. This assumptio implies that MFIs offer a meu of cotracts from which, the borrowers ca self-select. O the other had, the existig literature assumes that a cotract is thrust upo the borrower based o her ecoomic status. Aother assumptio commoly cosidered i the literature is that MFs are o-profit orgaizatio. However, we do ot make ay such restrictive assumptio o MFIs objectives. The roadmap for the rest of the paper is as follows. I the ext Sectio, we characterize the equilibrium with oly a SHG preset. Sectio 3 characterizes a competitive equilibrium i a alterative situatio where the microfiace sector cosists of oly commercial MFIs. I Sectio 4, we compare the equilibrium outcomes characterized i the previous two sectios. While the precedig sectios talk about idividual liability, Sectio 5 icorporates the cocept of joit liability ad characterizes multiple group formatio as a equilibrium outcome. Fially, Sectio 6 cocludes the paper with the discussio of the results. A appedix outliig the proofs of some of the propositios is also attached. 2 Model ad Equilibrium with SHG Cosider a rural commuity with N agets. Each aget has a ivestmet opportuity that requires $1 of fiacig. The ivestmet yields a gross retur of Y if it succeeds ad zero if it fails. Agets, however, differ i the probability with which they succeed i their ivestmet. Of the N agets, N G are of the low-risk type type G for good whose probability of success is p G. The remaiig N B = N N G are of the high risk type type B for bad who succeed with probability p B, p G > p B. We deote by π = N G N the proportio of agets of the good type i the populatio. We assume that 1 N G N 1. The two iequalities imply that there exists at least oe aget of each type i the village. To avoid trivial ad tedious cases, we assume N to be a sufficietly large umber. Agets do ot have ay fud of their ow for the ivestmet. Therefore, they eed to obtai a loa from a ledig agecy. Throughout the paper, we assume all leders are risk eutral. I this sectio, we assume that there is oly oe such agecy i the village which we call a self-help group SHG. We also assume that the SHG does ot have sufficiet fuds to led to the etire commuity. To simplify our aalysis, let the SHG have oly $1 to led. 15 We further assume that the SHG is a beevolet istitutio i the sese that it seeks to maximize the social surplus that its 15 For the rest of the aalysis, this assumptio is without loss of geerality as log as the umber of loas the SHG ca give is less tha N G. W.P. No Page No. 5

6 loa ca geerate. I particular, the SHG charges the break eve iterest rate. I other words, if it faces a ledig cost of ρ > 1 i providig the loa, it oly seeks a expected retur of ρ from the borrower. All agets are risk-averse with a stadard icreasig ad cocave utility fuctio o cosumptio uc. We assume u0 is defied ad ormalized to zero. Borrowers are protected by limited liability i the sese that they eed to repay oly whe their ivestmet is successful. The oly source of cosumptio for a borrower is the successful realizatio of her ivestmet. Hece, i both the evets of a aget ot obtaiig a loa or her ivestmet failig, her payoff is u0 = 0. The key operatig priciple of microfiace is the absece of collateral to secure a loa. Credit istitutios eed to rely etirely o the iterest they expect to receive from borrowers to cover the cost of credit. This ca create moral hazard i the form of wilful default by borrowers. Joit liability costitutes a mechaism to alleviate such moral hazard. 16 However, if we assume that firms face o such problem i securig repaymet, the microfiace ca operate eve uder the covetioal idividual liability mechaism. I this, ad the ext two sectios, we ideed make such a assumptio. This allows us cofie ourselves to the idividual liability settig which greatly simplifies our aalysis without compromisig the results o the impact of commercializatio. I ay case, these results ca be easily exteded to the joit liability settig. We elaborate o this further i Sectio 5, where we itroduce joit liability to cosider multiple group formatio. I a complete iformatio sceario, the SHG is able to distiguish betwee the two types of borrower. Sice the SHG caot impose ay collateral requiremet, it charges gross iterest rate R G = ρ p G if it leds to a low risk borrower ad R B = ρ p B from a high risk borrower. The payoff of a type T borrower, T {G, B}, is the U T = p T uy R T. 1 We assume that U B > 0, i.e. p B Y > ρ, so that both types have the icetive to participate i the market i this sceario. Sice U G > U B, the SHG oly leds to the good type. We call this the first best solutio. Our iterest is i characterizig equilibrium uder icomplete iformatio; i.e. whe the SHG is uable to distiguish betwee the two types but kows π. The first best solutio is, therefore, ot implemetable. Suppose the SHG seeks to charge iterest R T from type T. The, sice p B uy R G > U B = p B uy R B, the bad type has the icetive to to seek the loa claimig to be the good type. Implemetatio of the first-best solutio, therefore, leads to a loss for the SHG ad hece, is ot feasible. Oe optio for the SHG, is, the to provide the loa to ay idividual without seekig iformatio about its type. For such ledig to be feasible, the SHG eeds to charge the iterest rate Rπ = ρ πp G + 1 πp B There is the additioal type of moral hazard i the form or borrowers slackeig effort, or takig excessive risk. The structure of our model rules out such possibilities. W.P. No Page No. 6

7 With this iterest rate, the expected beefit that the $1 loa creates is Ūπ = π p G uy Rπ + 1 π p B uy Rπ. 3 Note that the objective of the SHG is to maximize the beefit that its loa yields. Equatio 3 defies this beefit whe the SHG charges Rπ. It is possible, however, that at some values of π, it is more beeficial for the SHG to iduce truthful type revelatio, ad led to oly a low-risk borrower. 17 This ecessities the SHG to istitute a screeig mechaism, wherei it charges a cost of acquirig credit such that a high-risk aget loses the icetive to preted to be a low-risk type. Defie c S = p B u Y R G, 4 ad Û G = U G c = p G p B uy R G > 0. 5 If c S were the screeig cost imposed by the SHG, oly a low risk aget seeks the loa at iterest rate R G whereas high risk agets have o icetive to approach the SHG. 18 I that case, 5 represets the payoff of the low risk aget who obtais the loa. The followig lemma establishes this result formally. Lemma 2.1 Suppose the SHG seeks to led oly to a low-risk type aget. It offers the cotract R G, c S where R G is the iterest rate it charges ad c S is the cost it imposes o the borrower. Give this cotract, oly a low-risk type aget approaches the SHG for the loa. The payoff of the borrower is the ÛG defied i 5. Proof. We eed to verify that at cost c S, a high-risk aget has o icetive to misreport type ad approach the SHG for a loa. This follows sice p B u Y R G c S = 0. We further eed to check that that at ay cost c < c S, the high-risk aget does misreport her type. If she truthfully reveals herself as beig high-risk, the she is deied the loa see footote 17 ad her payoff is the outside optio, zero. If she claims to be low-risk, her payoff is p B u Y R G c > p B u Y R G c S = 0. Hece, c S is the lowest cost that prevets a high-risk aget from approachig the SHG for a loa. We also eed to cofirm that a low-risk aget does ot misreport type. This follows trivially 17 Oce the SHG obtais iformatio about type, it is ever optimal to led to a bad type. Oce type is revealed, if the SHG leds to a bad type borrower, it charges iterest R B ad the borrower obtais payoff U B. But Ūπ U B for all π with equality holdig oly at π = 0. Ledig without seekig revelatio of type is, therefore, better tha ledig to a bad type followig type revelatio. Further, if more tha oe agets approach the SHG, the the SHG radomizes uiformly betwee them. 18 I defiig 5, we use the assumptio, stadard i all screeig models, that the et utility of the aget from cosumptio after payig ay screeig cost is additively separable i cosumptio ad cost. Formally, defie vp, x, y = pux c for cosumptio x ad cost c. The, Û G = v p G, Y R G, c S. Moreover, as is agai commo i screeig models, we iterpret the cost as ot a moetary trasfer from the aget to the pricipal but rather a wasteful expediture of time ad effort that the aget has to icur to covey her type. I the cotext of microfiace, this cost ca take the form of madatory group meetigs, compulsory savigs, or a traiig period before obtaiig the loa etc. W.P. No Page No. 7

8 by footote 17. Further, the SHG makes zero profit. This follows from the iterest rate R G ad the fact that the borrower is low-risk with certaity. The value of c S is determied by the fact that the SHG has oly oe loa to offer. Give its objective of maximizig the beefit that its loa yields, the purpose of its screeig cost is to esure that high-risk agets do ot approach it for the loa. If, however, the the SHG does have sufficiet fuds at its disposal to satisfy the etire demad for credit, the it ca scree borrowers with a lower cost. I that case, it would be able to offer two alterative cotracts; cost c M = p B u Y R G U B 6 alog with iterest rate R G or iterest rate of R B with zero cost. Ideed, i Lemma 3.1 i Sectio 3, we show that commercial MFIs adopt these cotracts while screeig borrowers hece the subscript M i the defiitio of c M. Borrowers the self-select with low-risk types adoptig the former cotract ad high-risk types the latter. However, the SHG has oly oe loa which it is uwillig to offer to ay aget who reveals herself as high-risk. Hece, if it imposes cost c M or ay cost less tha c S alog with R G, a high-risk aget opts for the cotract sice the alterative is to forego the loa ad have zero payoff. The SHG, therefore, has the choice of offerig two cotracts the cotract Rπ, 0 or the cotract R G, c S where the first term deotes the iterest rate charged ad the secod the screeig cost imposed. For coveiece, we refer to the former as the poolig cotract, ad the latter as the separatig or screeig equilibrium. Give π, the SHG offers the former cotract if Ūπ > ÛG 7 We ow distiguish betwee two cases. First, for ay π, the SHG offers the loa at Rπ. Secod, there exists a cutoff value π such that the SHG offers the former cotract if π > π ad the latter cotract if π < π. This distictio emerges from the parameter values Y, ρ, p G ad p B. While formally, this may be established i several ways, ituitively, it is most coveiet to first fix the values of Y, ρ ad p G ad coditio the distictio o the value of p B. I the followig lemma, we determie the rage of values of π over which 7 holds as a fuctio of the value of p B. Lemma 2.2 Suppose Y, ρ ad p G are give. The, 1. There exists p B = p B, ρ Y < p B < p G, such that ÛGp B = U B p B. 2. If p B > p B, the Ūπ > ÛG for all π. If p B < p B, the there exists π = π p B, 0 < π p B < 1, such that for π < π p B, Ūπ < ÛG ad for π > π p B, Ūπ > ÛG. Proof. 1. At p B = p G, Û G = 0 < U B. At p B = ρ Y, U B = 0 < ÛG. The first part the follows by the cotiuity of the two fuctios i p B ad the itermediate value theorem. W.P. No Page No. 8

9 2. For the secod part, ote that at π = 0, Ūπ = U B. By the first part of this lemma, ÛG = U B at p B = p B. Therefore, at π = 0, Ūπ = ÛG if p B = p B. But U B ad hece, Ūπ, is a icreasig fuctio of p B whereas ÛG is decliig i p B. So, for all p B > p B, Ū0 > ÛG at. Furthermore, Ū0 is icreasig i π whereas ÛG is ot affected by π. Therefore, for all π, Ūπ > ÛG if p B > p B. Now, let p B < p B. By reversig the argumet i the previous paragraph, Ūπ < ÛG at π = 0. But at π = 1, Ūπ = U G > ÛG. Cotiuity of Ūπ ad the itermediate value theorem the establishes the existece of π, 0 < π < 1, as desired. Lemma 2.2 implies that as p B p B, π p B 0. For p B > p B, Ūπ > ÛG for all π [0, 1]; so π is ot defied. Ituitively, if p B is sufficietly high so that p B > p B, the there is lesser distictio betwee the productivity of the two types. Hece, Ūπ is close to U G at ay π, whereas, Û G is close to zero. Therefore, 7 is satisfied for all π, which makes it optimal for the SHG to offer the poolig cotract at ay π. However, if p B < p B, the the decisio to offer a cotract depeds o the value of π. If π is sufficietly high, the the chaces of a reduced productive use of the loa are low; so low that the impositio of the cost c S is ot justified. The expected output from the loa is, therefore, best maximized by chargig the commo iterest Rπ. However, if π is low, the the radom selectio of a borrower is more likely to result i the less productive use of the loa. Therefore, the SHG fids it optimal to deliberately target the loa to the high productivity or the lower risk type eve though this ecessitates the impositio of the cost c S. We formalize this ituitio i the followig propositio. Propositio 2.3 Give p G, Y, ad ρ, let p B followig two cases. be as i 1 of Lemma 2.2. The, we have the 1. If p B > p B, the the SHG offers the poolig cotract Rπ, 0. Give π, the rate of default is 1 πp G + 1 πp B. 2. If p B < p B, the there exists a critical π, 0 < π < 1, such that if π > π, the SHG offers the poolig cotract Rπ, 0. However, if π < π, the SHG offers the screeig cotract R G, c S. Give π, the rate of default is 1 p G. Proof. 1. If p B > p B, the by Lemma 2.2, Ūπ > ÛG for all π. Therefore, the poolig cotract optimizes the SHGs objective fuctio. Sice a borrower of either type may receive the loa, the rate of success, ad repaymet, is πp G + 1 πp B. Hece, the default rate. 2. If p B < p B, the Lemma 2.2 establishes the existece of π, 0 < π < 1, such that Ūπ > ÛG oly if π > π. I this case, the SHG offers the poolig cotract. But if π < π, Ūπ < ÛG. The separatig cotract optimizes the utilizatio of the loa. The default rate follows because oly a low-risk borrower receives the loa. I Figure 1, we illustrate Propositio 2.3 usig a umerical example. W.P. No Page No. 9

10 Figure 1: Let uc = c ad {Y, ρ, p G } = {3, 1.1, 0.9}. I both paels, the horizotal lie is U ˆ G p B ad the upward slopig lie is Ūp B. Lemma 2.2, part 1 implies p B = I the left pael, p B = 0.55 > p B. Hece, by Lemma 2.2 1, Ūπ > ÛG for all π ad, therefore, π is ot defied. Propositio 2.3 1, the, implies that the SHG offers the poolig cotract for all π. I the right pael, p B = 0.44 < p B. From Lemma 2.22, π = , the poit of itersectio of the two lies. Propositio 2.3 2, the, implies that for π > π p B, the SHG offers the the poolig cotract whereas if π < π p B, the SHG offers the separatig cotract R G, c S = , Credit Cotracts i a Commercial MFI sector Sectio 2 cosiders the ledig behaviour of a credit-costraied SHG i equilibrium. I this sectio, we cosider a alterative sceario where the microfiace sector cosists of at least two profitmotivated microfiace istitutios MFIs ad o SHG. We assume that each MFI has access to a ulimited amout of fuds for providig loas. Our objective is to idetify the behaviour of the MFIs i a Bertrad equilibrium. As i the case with the SHG, we seek to characterize the coditios, which, decide whether MFIs offer a poolig cotract to all borrowers or seek to iduce self-selectio amog borrowers. Like i Sectio 2. we first determie the screeig cost that MFIs impose o a borrower, who seeks a loa at iterest R G. As usual, i equilibrium, the screeig cost is the miimum cost that iduces truthful revelatio from high-risk borrowers. Alteratively, MFIs may offer loas to all borrowers at rate Rπ. The differet payoffs that a low-risk borrower obtais from the two policies determies a critical value, π, such that, oly if π < π do MFIs implemet the screeig equilibrium. For the SHG, the chage from the commo iterest rate mechaism to the screeig mechaism is govered by the objective of optimizig the expected beefit from its loa. However, MFIs decide o which cotract to offer, based o profit makig opportuity. Uder the commo iterest rate, the payoff of a type T, T {G, B}, is Ū T π = p T uy R. 8 It is obvious that ŪBπ > U B, whereas, Ū G π < U G. The absece of iformatio, therefore, beefits the high-risk type while workig to the detrimet of the low-risk type. It is also clear that W.P. No Page No. 10

11 the low-risk type s disadvatage is greater at lower π. Cosequetly, if π is sufficietly low, a profit opportuity may ope up for MFIs, wherei they istitute a screeig mechaism that imposes a cost c o ay borrower who claims to be low-risk, but which iduces truthful revelatio. Compared to payig iterest Rπ, the low-risk type beefits despite icurrig the cost sice the type specific iterest rate declies to R G. High-risk types do ot icur ay cost, but pays the higher iterest R B. As before, let us deote a cotract by R, c where c is the cost the borrower eeds to icur to obtai the loa at iterest R. The, uder the screeig mechaism, the MFI itroduces two cotracts R G, c ad R B, 0. Our task is to determie the cost c that the MFI imposes o ay low-risk type claimat. I equilibrium, c is the miimum cost that ca iduce truthful revelatio of type. I our discussio followig Lemma 2.1, we argued that if sufficiet fuds are available to meet the etire demad for credit, the a competitive fiacial sector imposes the cost c = c M defied i 6 as the screeig cost. Sice by assumptio, MFIs ca meet the etire credit demad, they imposes this cost i a screeig equilibrium. We formalize this uderstadig i the followig lemma. Lemma 3.1 Suppose that i a competitive equilibrium, MFIs seek to iduce truthful revelatio of type amog agets. The it itroduces two cotracts R G, c M ad R B, 0 where c M = p B u Y R G U B. Low-risk agets opt for the cotract R G, c M ad high risk oes for R B, 0. Proof. We eed to check that c M is the miimum cost at which o aget of either type has the icetive to misreport their type. If a high risk aget reports truthfully, ad therefore, opts for R B, 0, the her utility is U B. If she misreports ad opt for R G, c M, her utility is p B u Y R G c M = U B. Hece, she has o icetive to misreport her type. However, if c < c M, the the high risk aget fids it optimal to claim to be low-risk. For a low-risk aget, truthful reportig leads to utility p G u Y R G c M = ÛG + U B where Û G is defied i 5. Misreportig leads to utility U B. Therefore, truthful reportig is strictly better. Therefore, c M is the miimum cost that ca iduce truthful revelatio from both types. We also eed to verify that MFIs ear zero profit. This follows from the iterest rate charged from the two types ad the fact that the screeig mechaism iduces truthful revelatio. We therefore coclude that i equilibrium, MFIs either offer a commo cotract with iterest rate Rπ to all agets or offer the meu of cotracts {R G, c M, R B, 0}. Guided by the profit motive, they adopt the former alterative if ŪGπ > U G c M. Clearly, the choice of cotracts is determied by the value of π. I the followig propositio, we establish the presece of a cut-off value of π, π, such that MFIs opt for the commo iterest cotract if π exceeds this critical value. Lemma 3.2 Suppose the parameters Y, ρ, p G, p B are give. Cosider ŪGπ ad U G c M. There exists π 0, 1 such that for π > π, ŪGπ > U G c M ad for π < π, ŪGπ < U G c M. Proof. Note that U G c M = p G p B uy R G +p B uy R B. At π = 0, ŪGπ = p G uy R B. Sice p G p B uy R B < p G p B uy R G, ŪGπ < U G c M at π = 0. W.P. No Page No. 11

12 Figure 2: Cosider the umerical example i Figure 1 with uc = c ad {Y, ρ, p G } = {3, 1.1, 0.9}. Here, i both paels, the horizotal lie is U G p B c M p B ad the upward slopig lie is ŪGp B. I the left pael, p B = 0.55 ad π = give by the itersectio of the two lies. I the right pael, p B = 0.4 ad π = I either case, by Propositio 3.3, MFIs implemet the poolig cotract if π > π ad the separatig cotract if π < π. At π = 1, Ū G π = p G uy R G = U G > U G c M sice c M > 0. Hece, at π = 1, Ū G π > U G c M. The existece of π follows from the itermediate value theorem. Clearly, if π > π, MFIs offer the same cotract to all borrowers whereas if π > π, it implemets the screeig equilibrium. We formalize this equilibrium behaviour of MFIs i the followig propositio. Propositio 3.3 Let π be as characterized i Lemma 3.2. For π > π, MFIs offer the cotract Rπ, 0 to all borrowers. For π < π, MFIs offer the meu of cotracts {R G, c M, R B, 0}. Borrowers self-select with low risk borrowers optig for the cotract R G, c M ad high-risk borrowers optig for R B, 0. I either case, the aggregate default rate is 1 πp G + 1 πp B. Proof. The choice of cotract follows readily from Lemma 3.2. The default rate follows from the fact that uder either cotract arragemet, all agets, irrespective of type, do receive a loa. As i Sectio 2, we refer to Rπ, 0 as the poolig cotract ad the meu {RG, c M, R B, 0} as the separatig or screeig cotract. We ote that the screeig cotract that the SHG offers differs from the oe that MFIs offer. Also, aalogous to Figure 1, we illustrate Propositio 3.3 i Figure 2. We may reiterpret Lemma 3.2 alog the lies of Lemma 2.2 by varyig p B while keepig {Y, ρ, p G } fixed. This reiterpretatio facilitates compariso of the two lemmas. We ote that, ulike SHG behaviour i equilibrium, where π p B does ot exist if p B > p B, π p B always exists. However, give Lemma 3.2, it is easy to verify that as p B p G, π p B 0. Ituitively, i this case, ŪGπ is sufficietly close to U G, ad therefore, higher tha U G c M. This is true if π is ot exceptioally low, i which case, the iflatioary impact o Rπ makes acceptace of c M the W.P. No Page No. 12

13 preferable optio of low-risk types. We may, therefore, coclude that closer is p B to p G, the larger is the rage of π over which MFIs offer the o-discrimiatory cotract. 4 Welfare, Credit Cotract ad Default: Chages followig MFI etry Our larger objective is ot just to characterize equilibrium behaviour i the two alterative scearios we have cosidered i Sectios 2 ad 3. Istead, we aim to evaluate the impact of the trasitio of the microfiace sector from a beevolet to a commercial orietatio o the overall welfare of borrowers. As a corollary, we also assess the chages i iterest ad default rates, as well as o the itesity of screeig, durig this trasitio. I this sectio, we adopt this historical perspective by assumig a temporal sequece where iitially, a beevolet SHG is the sole source of loas. Retaiig our assumptio that the SHG ca provide oly oe loa, we assess how borrowers welfare, terms of credititerest ad screeig, ad default rates chage as a profit-orieted competitive MFI sector emerges. I order to uderstad the impact of this trasitio, it is critical to appreciate that the SHG, by itself, is able to satisfy a limited part of the demad for loas i the village. Therefore, eve with beevolet itetios, the SHG has a miimal impact o ehacig aggregate welfare i the commuity, i which it operates. However, the MFI sector has ulimited fuds at its disposal; or at least sufficiet fuds to meet the etire loa demad i the commuity. Hece, the MFI sector has a direct impact o aggregate welfare. Therefore, the welfare of all agets who were deprived from credit from the SHG must improve. Furthermore, if the SHG were idulgig i screeig the borrowers -ledig oly to the good types the welfare of all the cocered parties ecessarily improves. By Propositio 2.3, the SHG ecessarily screes if π exists ad, π < π. I other words, if π is sufficietly low ad p G sufficietly differet from p B so that π exists by Lemma 2.2, the etry of commercial MFIs must ecessarily lead to Pareto improvemet situatio. This argumet is formalized i the propositio below. Propositio 4.1 Suppose the parameters Y, ρ, p G, p B be such that π exists ad determied as i Lemma 2.2. Let π be as determied i Lemma 3.2. If the fractio of safe borrowers is sufficietly low, i.e. if π < π, the etry of commercial MFI sector always leads to a strict Pareto improvemet i welfare. The default rate icreases ad the level of screeig declies. The SHG shuts dow followig MFI etry. Proof. For π < π, we distiguish the followig two cases. 1. π < π. Irrespective of the relatioship betwee π ad π, the SHG imposes the screeig cost c S ad leds oly to a low-risk borrower who obtais payoff ÛG. Upo etry, MFIs impose the lower screeig cost c M. The pre-existig cliet of the SHG shifts to a MFI icreasig her payoff to U G c M. The payoff of every other aget improves as they access credit from MFIs. W.P. No Page No. 13

14 Note that the SHG loses its cliet ad therefore shuts dow. The default rate icreases from 1 p G to 1 πp G + 1 πp B. The itesity of screeig declies from c S to c M. Istead of oe iterest rate R G, multiple rates become prevalet followig MFI etry; R G ad the higher rate R B. 2. π > π. I this case, the SHG, as the sole leder, imposes the screeig cost c S ad leds oly to a low-risk borrower. The borrower obtais utility U G c S. However, whe MFIs eter, they offer the poolig cotract at iterest Rπ. Sice π > π, Lemma 3.2 implies Ū G π > U G c M, ad sice c S > c M, U G c M > U G c S. The existig cliet of the SHG therefore obtais a higher payoff from MFIs ad shifts. Every other aget improves welfare by accessig credit from MFIs. The SHG,therefore, shuts dow. Further, iterest rate icreases to Rπ from R G ad default rate to 1 πp G + 1 πp B from 1 p G. The fial cosequece is that screeig is etirely elimiated as a ledig policy istrumet with the exit of the SHG. We ote that i Case 1, istead of oe iterest rate R G, multiple rates become prevalet followig MFI etry; R G ad the higher rate R B. I Case 2, the prevailig iterest rate icreases from R G 19 to Rπ. It is, therefore, iterestig to ote that Pareto improvemet is happeig despite the fact that iterest rates ad default rates icrease with the etry of commercial MFI sector. The ituitio behid this result is as follows: the risky oes, who were left out of the market uder the SHG regime, participate i the market uder competitive regime. The safer oes participate i the market uder both regimes, but pay lesser screeig cost uder the competitive regime. Sice the competitio eables risky borrowers to participate i the market, the iterest rates, ad the default rates icrease. Therefore, a icrease i iterest rates ad defaults ca be artifacts of a ex ate Pareto improved situatio. 20 The key factor that explais the chages followig the etry of MFIs is ot the differig objective fuctios of the beevolet SHG ad the profit motivated MFIs but that MFIs ca disburse a much higher umber of loas. Bertrad competitio erodes ay coflict betwee seekig profit ad maximizig welfare through margial cost pricig. Therefore, if the SHG also had ulimited fuds at its disposal, the eve with its beevolet objective, it would have behaved exactly like the competitive MFI sector i equilibrium. I that case, etry of profit motivated MFIs would have made o differece either to borrower welfare, or to the terms of the credit cotract ad default rates. 19 Strictly speakig, the fact that the populatio size N is fiite requires MFIs to follow a more uaced policy whe they follow a SHG to a market. Defie ρ R N = N p G 1 G N 1 + p B N. B N 1 This is the commo break-eve iterest rate for MFIs if they kow with certaity amog their potetial borrowers, oly N G 1 are low-risk type. It is easy to verify that R N > Rπ but R N Rπ as. Suppose U G c S > p G uy R N. I this case, the low-risk SHG cliet cotiues borrowig from the SHG. Therefore, MFIs kow after etry that of the remaiig borrowers, oly N G 1 are of low-type ad hece charge R N. I this case, the SHG remais i busiess with its existig cliet. However, we assume that N is large eough such that if U G c S < p G uy Rπ, the so is U G c S < p G uy R N. Ideed, our assumptio of N is large eough is meat precisely to rule out such tedious borderlie cases. 20 The recet happeigs i the Idia microfiace sector ca be explaied usig this result. As poited out earlier, the Reserve Bak of Idia RBI is blamig competitio amog MFIs as a reaso for icrease i defaults, ad hece suicides. Therefore, this result has importat regulatory sigificace. W.P. No Page No. 14

15 Propositio 4.1 is relevat whe π exists ad π < π. However, these coditio may ot be satisfied. I such cases, the SHG offers oly poolig cotracts which subsidizes a high risk borrower. The, if MFIs, upo etry, scree borrowers, the welfare of the SHG cliet declies if she is of high risk as she caot be cross-subsidized ay loger. Alteratively, there is aother case where the etry of SHG weakly improves welfare i that the existig SHG cliet retais her level of welfare, while every other aget beefits from icreased access to credit. We discuss these two cases ow. 1. Weak Pareto Improvemet π > π. This icludes two subcases: a Let π exist. The, irrespective of the relatioship betwee π ad π, both the SHG ad MFIs offer the poolig cotract. Hece, the existig cliet of the SHG is idifferet betwee remaiig with the SHG or shiftig to MFIs. Every other aget beefits from access to MFI credit. Whe the SHG is the sole leder, the iterest rate ad default rate are, respectively, Rπ ad 1 πp G + 1 πp B. Oce MFIs eter, all remaiig potetial borrowers receive loa o these same terms. Neither sector imposes ay screeig cost ad therefore, there is o chage i this aspect of the credit cotract as well. Therefore, either the credit cotract or the default rate chages followig MFI etry. The SHG, give its objective fuctio of maximizig welfare with its oe loa, is idifferet betwee cotiuig with its solitary cliet or shuttig dow with its cliet obtaiig the loa from a MFI o exactly similar terms. b Let π ot exist. I this case, both the SHG ad MFIs offer the poolig cotract. This case is, therefore, idetical to Case 1a discussed above. 2. Declie i Welfare of existig high-risk SHG cliet π < π. This also has two subcases: a Let π exist. The SHG offers the poolig cotract ad depedig upo type T, its borrower obtais payoff ŪT π defied i 8. MFIs implemet the screeig equilibrium i which low-risk borrowers obtai payoff U G c M > ŪGπ. Hece, if the existig SHG cliet is low-risk, she shifts to MFIs. Therefore, ay cliet that the SHG retais after MFI etry must be high-risk with probability 1. The iterest rate she eeds to pay icreases from R B to Rπ ad her welfare declied to U B from ŪBπ. Every other aget beefits through icreased access to credit. Default rate remais uchaged ad iterest chages from the uiform rate Rπ to R G ad R B. Screeig which was earlier abset from the SHG is ow itroduced followig MFI etry. The fate of the SHG is more difficult to pi dow. Sice U G c M > ŪGπ, the SHG caot retai a low-risk borrower. Therefore, if its pre-existig cliet is a lowrisk type, it loses the cliet ad shuts dow. Hece, if, followig MFI etry, the SHG retais its cliet, it updates its belief of that cliet beig high-risk from 1 π to 1 ad charges iterest R B. Give its objective fuctio, the SHG is the idifferet betwee cotiuig with its high-risk borrower or shuttig dow i which case, the borrower shifts to MFIs. b Let π ot exist. I this case, the SHG offers the poolig cotract whereas MFIs follow the policy of screeig. This case is therefore idetical to Case 2a above. W.P. No Page No. 15

16 It is iterestig to ote that i Case 2 above, where the welfare of the existig SHG cliet declies if she is of high-risk, is also the oly case, i which, the level of screeig uambiguously rises followig etry of MFIs. It is, of course, a empirical questio as to whether such screeig actually icreases or falls followig itesificatio of commercializatio. If, however, it does declie, the we may argue with reasoable cofidece that there is a Pareto improvemet i social welfare followig etry of MFIs. Furthermore, Lemmas 2.2 ad 3.2 imply that if p B is close to p G, π ad π are likely to be low ad ideed, π may ot eve exist. I this situatio, the likelihood of π beig higher tha both π ad π is high. Therefore, as discussed i Case 1 above, the chaces that MFI etry leads to chages i default, iterest or screeig are low. I other words, if agets are less heterogeeous, etry of profit motivated MFIs is ulikely to chage ay of these variables sigificatly. O the other had, suppose p B differs sigificatly from p G. The, this implies both π ad π are high as i Case 1 of Propositio 4.1. I that case, icreased competitio is more likely to icrease default ad iterest rates ad reduce screeig itesity. Irrespective of whichever case occurs, etry of MFIs always represet a Pareto improvemet over the situatio whe the SHG is the sole leder. 5 Group Ledig ad Multiple Group Membership Sectios 2 4 aalyze the microfiace sector i the settig of idividual ledig without collateral. Microfiace of course, i reality, operates o the priciple of joit liability, which is expected to act as a mechaism to cotrol adverse selectio ad moral hazard. Nevertheless, it is sufficiet to cosider the idividual liability settig to covey the mai implicatios of commercializatio of microfiace without itroducig the complicatios of joit liability ito the aalysis. However, the structure of joit liability is ecessary to address the pheomeo of multiple group membership, aother widely reported cosequece of the icrease i the umber of microfiace firms operatig i a certai area. Istead of obtaiig her etire loa requiremet through membership of a sigle group, a aget may split up her total credit requiremets amog differet groups. Each group is the liable for oly that portio of the total loa that is obtaied through that group. Iformal coversatios with MFIs i Idia reveal that multiple group membership is a commo pheomeo. Macitosh et. al 2005 also preset evidece suggestig that this is ideed the case i the Ugada microfiace market. The practice of multiple group membership has bee criticized o the grouds that this may lead to idiscrimiate borrowig as borrowers form ew groups to shift to ewer MFIs, thereby escapig their liabilities with a existig MFI. 21 If, ideed, MFIs are ot aware of the idetity of idividuals who adopt this practice of multiple borrowig, this may be a problem that threates the sustaiability of the microfiace sector. Yet, the same coversatios with MFIs reveal that they are well aware of this practice, ad do ot seem iclied to impose ay restrictios o it, sice overall repaymet rates remai high. This suggests that borrowers are ot idiscrimiately borrowig, but are makig optimal use of the loa they obtai. It is simply that, istead of obtaiig that loa through oe group, they might be obtaiig parts of it through membership i differet groups. 21 For example, see cited earlier i footote 9. W.P. No Page No. 16

17 We, therefore, view the icidece of multiple borrowig as a ratioal respose of borrowers to a icrease i the umber of MFIs. Our aalysis reveals that this respose, i tur, is motivated by the possibility of more improved risk diversificatio. Joit liability ivolves a aget bearig the risk of failure of her group parters. For a risk averse aget, this has a detrimetal effect of welfare. With multiple membership, the aggregate liability i moetary terms remai uchaged. However, sice the liability is spread out over differet groups ad therefore differet parters, there is a better distributio of risk. A aget eeds to hoour a substatial proportio of her liability of coverig for her parters failure oly if most of her parters fail simultaeously. As the umber of groups icreases, this evet becomes icreasigly rare. We cosider a competitive microfiace sector cosistig of a umber of profit-motivated MFIs. We assume there exists some factor, for example, the possibility of wilful default, that makes idividual liability ledig without collateral impossible. Therefore, MFIs oly led o the priciple of joit liability, i which all group members are liable for each other s loa. Borrowers are protected by limited liability so that they oly eed to repay, whether for themselves or their parter, oly whe their ivestmet is successful. For simplicity, we cosider a sceario where a group cosists of two members. Idividuals are allowed to be members of multiple groups. If a aget is a member of groups, she sources a loa of 1 through membership of each group, thereby obtaiig her total loa requiremet of $1. We retai the parameter specificatio {Y, ρ, p G, p B } established i Sectio 2 to defie the credit sceario. We make the additioal assumptio that success rates of the ivestmet project fiaced by a loa are idepedet across idividuals. This implies havig two groups with the same parter does ot lead to ay better risk sharig tha havig oe group with that parter ad obtaiig a loa of 2 through that group. The purpose of risk spreadig is best served whe the aget does ot have ay parter i commo i ay two groups she may be a member of. We, therefore, assume that if a aget is a member of two-member groups, the all her group parters are differet from each other. All groups that we refer to i this paper follow this structure that we have outlied here. We first show that i a eviromet of complete iformatio, as a idividual of either type forms more ad more groups with other agets of the same type, her payoff icreases ad coverges to the payoff uder idividual ledig defied i 1. Uder the weaker assumptio that oly agets kow each others type but ot MFIs, we exted the previous result to show that irrespective of whether MFIs offer a separatig cotract or a poolig cotract, welfare is improvig with the umber of groups. Fially, we characterize equilibrium i which borrowers form as may groups as possible, while MFIs offer either the separatig or the poolig cotract depedig o which cotract maximizes the payoff of low-risk agets. I the spirit of Sectio 4, we close the aalysis by makig a compariso of this equilibrium with the equilibrium that prevails whe a fuds costraied SHG is the sole borrower. 5.1 Group Ledig ad Screeig I this sub-sectio, we seek to characterize a separatig cotract that MFIs offer i equilibrium. We establish this mometarily uder the assumptio that all agets are members of two member W.P. No Page No. 17