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The Developing Economies 52, no. 2 (June 2014): 179–201

A COMPARISON BETWEEN FORMAL AND INFORMAL MUTUAL-CREDIT ARRANGEMENTS Francesco REITO1* and Salvatore SPAGANO2 1

Department of Economics and Business, University of Catania, Catania, Italy, and 2IUSS Pavia (Institute for Advanced Study of Pavia), Pavia, Italy

First version received February 2013; final version accepted March 2014 We analyze under what conditions a group of potential entrepreneurs prefer to form a Rotating Savings and Credit Association (ROSCA), or a mutual-guarantee association, which we interpret in a rotating scheme and call Rotating Savings and Collateral Association (ROSCoA). We argue that: (1) ROSCAs (ROSCoAs) are likely to be more developed in countries with high (low) bank concentration; (2) the individual flow of savings required to participate in a ROSCoA is generally lower than that needed in a ROSCA; (3) under the assumption that members share their project income at the end of each period, ROSCAs and ROsCoAs are sustainable even without the use of sanctioning mechanisms. Keywords: Collateral; Moral hazard; ROSCA; Mutual-guarantee association JEL classification: D81, D82, O16

I.

INTRODUCTION

T

his paper analyzes the behavior of a group of potential entrepreneurs who, owing to insufficient resources, decide to join a mutual-credit arrangement to undertake their projects. We consider that agents can choose between a Rotating Savings and Credit Association (ROSCA), or a mutual-guarantee association that, to ease the comparison, we consider in a rotating scheme and call Rotating Savings and Collateral Association (ROSCoA). In the model presented in this paper, there is a group of potential entrepreneurs, with similar projects, who can decide to form either a ROSCA or a ROSCoA. The two main results are: a) if the contributions to the pot in each period are not sufficient for the project start up, entrepreneurs can only form a ROSCoA, and ask for loans; b) if the contributions to the pot are high enough, i) risk-neutral

* Corresponding author: Francesco Reito, University of Catania, Department of Economics and Business, Corso Italia 55, 95100 Catania, Italy. Tel: +39-3-288242694; Fax: +39-0-957537710; Email: [email protected] This paper has benefited from the constructive and detailed comments made by two anonymous referees. © 2014 Institute of Developing Economies

doi: 10.1111/deve.12043

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the developing economies

entrepreneurs are indifferent between ROSCA and ROSCoAs, and ii) risk-averse entrepreneurs prefer to join a ROSCoA when the credit market is perfectly competitive. The intuition for this second result is as follows. If group members are risk-neutral, they will always receive their first-best payoff either under a ROSCA or a ROSCoA, irrespective of the level of concentration in the credit market. If, instead, members are risk-averse, they can benefit from the insurance coverage provided by lenders. The aim of this article is also to provide a possible theoretical interpretation of mutual-guarantee associations. Indeed, the existing theoretical literature has not devoted much attention to such associations. One of the few exceptions is Busetta and Zazzaro (2012), who focus on an adverse-selection environment where prospective entrepreneurs pool their savings to raise the collateral required by a monopolistic lender to screen different types. In our paper, however, the emphasis is on the incentive mechanism needed to solve the ex-ante moral hazard problem of each potential borrower, in the two polar assumptions of monopolistic and perfectly competitive credit markets. The structure of the model is similar to that of Stiglitz (1990), where group lending and peer monitoring can mitigate the incentive for risk-taking by borrowers and increase repayment rates. In contrast to his paper, we choose not to emphasize the potential effect of monitoring activity among borrowing groups, and analyze the role of collateral as an incentive device. Another interesting theoretical contribution on the subject is by Madajewicz (2011), who argues that, compared to individual lending, joint liability lending can lead to riskier behavior because group members do not bear the full cost of project failure. In our model, in the absence of peer pressure, group lending is always more advantageous for ROSCoA participants, because the collateral pot can be used to secure more loans if some of the projects do not fail, and this implies that the expected cost of failure is lower under group lending. In the present paper, we interpret ROSCAs and ROSCoAs as self-help groups, which also provide income-sharing arrangements. A number of empirical papers report that one of the reasons to be a member of ROSCAs is the mutual insurance and social support needed to face potential individual negative shocks, or particular events, during the rotation cycle (such as marriages, illness, death of farm animals, theft, and funerals). This kind of insurance system may operate through the exchange of cash, food, labor, and gifts among members. For example, in his research on Mexico, Vélez-Ibañez (1983) reports that ROSCA members have more access to social links and favors, such as personal assistance and monetary or gift transfers, which in many cases operate beyond the scope of the association. Dupas and Robinson (2009), in their field experiment in Kenya, show that many ROSCAs, in addition to the monetary pot, provide some important emergency insurance (cash and in-kind transfers) in case of negative events. Chua et al. (2000) © 2014 Institute of Developing Economies

MUTUAL CREDIT AND COLLATERAL ASSOCIATIONS

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find that, in Uganda, ROSCA participants contribute to one another’s weddings and funerals, patronize each other’s businesses, and exchange favors.1 Similarly for ROSCoAs, De Gobbi (2003) argues how the relationship among members of mutual-guarantee associations is in general based on reciprocal assistance and solidarity. A rationale for this type of behavior is that these credit schemes may also be used to reinforce the commitment to group cohesion, and establish lasting economic and cultural relationships. Through the assumptions of self-help and gifts exchange, we are able to circumvent the enforcement problems that are usually associated with these types of organizations. Armendáriz de Aghion (1999) and Chiteji (2002) posit that ROSCAs rely heavily on interpersonal networks and social collateral to solve the problems of free riding and contract enforcement among members. In their argument, preexisting relationships and repeated interactions allow the association to screen potential candidates, and impose social sanctions on defaulters. Along the same line, Anderson, Baland, and Moene (2009) show that, when members are exponential discounters, ROSCAs cannot be incentive compatible for all members without some form of sanctioning to deter that behavior. However, some empirical evidence reports that ROSCA participants are, in some cases, reluctant to use punishment strategies in the event of opportunistic behavior. A possible explanation is provided by Gugerty (2007) and Basu (2011), who assume hyperbolic time preferences for members, and show that ROSCAs can be sustainable even in the absence of precommitment and social pressure.2 In the model we assume that, at the end of each period, members share their project income, through transfers of money or gifts. Thus, whatever the order of rotation, each participant can do no better than wait until the final period to receive the corresponding contributions of all other members. In this case, ROSCAs can be considered sustainable even under the assumption of standard exponential discounters, and without introducing social norms or moral punishments. However, although in this model the reason to participate in a ROSCA stems from pure economic rationality, it is important to stress that the emergence of the precommitment to self-help of members can be explained by social norms, or the desire to strengthen social ties and increase long-term relationships. As 1

2

Evidence on mutual insurance and gift exchange is also reported in Kühn (2010) and Fafchamps and La Ferrara (2012). In their models, agents increase their savings as they get closer to the desired lumpy durables, so ROSCAs can be used as a commitment device since they encourage members to follow the required savings path. If a member leaves the ROSCA, it increases current consumption, but it will save slowly in future periods. If it does not leave, current consumption is reduced, but the discounted utility from future periods will be higher. The agent will stay in the ROSCA if the advantages induced by the association compensate, at least, the incentive for current consumption. For a theoretical and empirical discussion on time inconsistency, see Tanaka and Murooka (2012). © 2014 Institute of Developing Economies

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emphasized by Thorp, Stewart, and Heyer (2005), social value plays a central role in determining the efficiency of group-based economic activities, such as ROSCAs. The same argument can be applied to the analysis of ROSCoAs. The present paper has two main empirical predictions: a) if the flow of individual savings is low, potential entrepreneurs can only form a ROSCoA. This seems consistent with microfinance practices and, in part, is supported by the empirical literature. For example, Handa and Kirton (1999) argue how ROSCA participation, in some cases, increases with members’ income, i.e., “richer” poor are more likely to join a ROSCA; b) ROSCoAs should be more common in countries with a low bank concentration index. Indeed, although this is not intended to be empirical evidence, we know from the literature that ROSCoAs are more common in Europe and Eastern Asia where the bank concentration index is, in general, relatively low. To mention a few examples, the concentration index is 0.28 in Taiwan, 0.35 in Italy, 0.45 in Japan, 0.47 in Thailand, 0.58 in Indonesia, 0.58 in France, 0.65 in China, and 0.71 in Germany. We will argue that the higher indices for China and Germany may reflect the fact that local banks may take advantage of risk aversion and promote the formation of ROSCoAs. On the other hand, both ROSCAs and ROSCoAs (or other forms of collateral-backed group lending schemes) should be seen as substitute sources of credit in developing regions where, in many cases, the bank concentration index is very high.3 For example, the index is 0.62 in Ghana, 0.72 in Cameroon, 0.72 in Kenya, 0.83 in Ethiopia, 0.96 in Malawi, and 1 in Jamaica. A.

Background

ROSCAs are informal self-help financial groups formed by individuals who meet regularly to make contributions to a common fund—the pot—which is given to each member in turn and in a predetermined order.4 ROSCAs can be found in many areas of the world, in particular in developing countries, with different names5 and different structures and rules. In a ROSCoA, on the other hand, members collect the collateral needed by a traditional lender to finance each member’s investment. Mutual-guarantee systems are in general formed by potential borrowers who cannot offer, individually, enough collateral to secure a bank loan. These organizations are quite widespread 3

4

5

Data are taken from the paper by Beck, Demirgüç-Kunt, and Levine (2006), and from the up-todate file made available online by the authors. Besley, Coate, and Loury (1993) offer one of the first rigorous theoretical descriptions of how ROSCAs may ease the intertemporal allocation problem in the acquisition of indivisible goods. For instance, stovkel in South Africa, osusu or adashi in Nigeria and Liberia, ekub in Ethiopia, jangi in Cameroon, sanduk ou gameya in Sudan, tontine in Congo Kinshasa, arisan in Indonesia, hui in Vietnam, kye in Korea, bisi in Pakistan, kameti in Sri Lanka, and tandas in Latin America; see Bouman (1995), and Armendáriz de Aghion and Morduch (2007).

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in Eastern Asia (see, e.g., Boocock and Shariff 2005), North America (see Bradshaw 2002), and Europe. For the European case, Columba, Gambacorta, and Mistrulli (2010) report that more than 1.4 million small and medium enterprises are currently members of mutual-guarantee associations.6 They are more common in France, Germany, Spain, and in particular Italy, which accounts for nearly 40% of the volume of total European guarantees.7 Conversely, mutual-guarantee systems are not so widespread in less developed countries, though, as reported by De Gobbi (2003), there are successful examples of guarantee schemes in Africa, in particular in Senegal, Ivory Coast, Burkina Faso, Morocco, and Tunisia. As pointed out by Columba, Gambacorta, and Mistrulli (2010), these guarantee institutions may or may not be organized in a rotating scheme, and in many cases banks allow members to receive credit up to a multiple of the mutual fund (for the Italian case, the authors report an average ratio between loans and guarantees of about 3).8 The remainder of the paper is organized as follows. Section II introduces the main features and assumptions of the model. Section III shows what happens if a group of individuals decide to form a ROSCA. Section IV derives the equilibrium financial contracts under a ROSCoA. Section V compares these two types of associations. Section VI concludes the paper. II.

THE ENVIRONMENT

Consider an n-period village economy with n identical would-be firms/ entrepreneurs. As in the moral-hazard section of Stiglitz and Weiss (1981), each firm has a choice between two projects, high risk (h) and low risk (l); both projects require a fixed investment of L. The high-risk project succeeds with probability ph and yields a return of Rh, whereas the low-risk project succeeds with probability pl > ph and yields Rl < Rh. Both projects produce nothing with the complementary probabilities. A project is considered efficient if its expected net product is (weakly) positive. To restrict the analysis, unlike Stiglitz and Weiss (1981), we assume that only the low-risk project is efficient:

pl Rl ≥ L and ph Rh < L. 6

7

8

(A1)

See the data provided by the European Mutual Guarantee Association, available at: http:// www.aecm.eu/en/aecm-european-association-of-mutual-guarantee-societies.html?IDC=18&IDD =24 In some countries, these institutions can obtain funding and financial support from local governments, as documented in Beck, Klapper, and Mendoza (2010). Other than facilitating the access to credit, mutual-guarantee associations can have several other functions: they negotiate contract terms collectively with the banks, provide consultancy, technical assistance and, more importantly, they carry out initial screening of aspiring partners to alleviate the problems of information asymmetry between banks and firms. © 2014 Institute of Developing Economies

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Thus, the high-risk project outcome is not only a mean-reducing spread of the low-risk one as in de Meza and Webb (1987), but here the two projects also produce different returns in case of success.9 At the beginning of each period t,with t = 1, 2, . . . , n, agents receive a constant and exogenous income, w ∈ [0, L/n], which is earned in the absence of the project. Since w < L, to have the possibility to implement the project before they set aside the whole investment sum, agents decide to form either a ROSCA or a ROSCoA. In a ROSCA, members collect the sum needed to finance each member’s investment, while under a ROSCoA the money collected can be offered as collateral to secure a bank loan. As in Chiteji (2002), we consider that the pot is used for an entrepreneurial activity and not for the acquisition of durable goods, and that a cycle consists of as many meetings as the number of members, so that the perperiod pot equals the amount needed for either the investment or the collateral.10 We assume that members enter into an informal income-sharing arrangement where, at the end of each period, they decide to share the income produced by the firm that received the pot (e.g., through ex-post transfers of money or gifts). Thus, the intra-group contractual arrangement can be viewed as a sort of equity participation in each other’s project. For the sake of simplicity, we assume that the final product is equally shared among all group participants. Besides, we consider that agents discount future income by the common factor δt, with t = 1, 2, . . . , n, and that they consume, at the end of each period, either their shares of each firm’s output, or their endowments if they cannot form a ROSCA or a ROSCoA. Consider risk neutrality (risk aversion will be discussed in subsection V.A.), and a risk-free rate normalized to 0. III.

THE ROSCA

We focus on the case of a fixed ROSCA where, at the beginning of each period, members make a contribution of L/n, and one of them receives the pot. The order 9

10

This assumption is used by several authors (Minelli and Modica 2009). In the present paper, it allows the analysis to be limited to the low-risk project. As inferred from the data reported by Armendáriz de Aghion and Morduch (2007), and Columba, Gambacorta, and Mistrulli (2010), the average ROSCA membership size may be considerably lower than the average ROSCoA size (up to a few dozen in ROSCAs, and up to hundreds or even thousands in ROSCoAs). One of the reasons for this difference may be that, since ROSCA participants in general live close to one another, the group size is generally low to strengthen social ties and guarantee the sustainability and performance of the institution. On the other hand, mutual-guarantee associations are more developed in countries where banks and entrepreneurs are given a certain measure of protection by the formal legal systems. This reduces the enforcement costs and allows for a larger number of participants. The high participation in credit-guarantee schemes may also be explained by the fact that members are in some cases supported by public funds.



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of recipients is randomly determined at the first meeting date.11 Since the start-up investment is fixed, only agents with w = L/n can form a ROSCA. In equilibrium, each member will always choose the low-risk project, since the expected payoff is related to the fixed investment, and not to the individual contribution. Indeed, since members equally share each period’s profit, the individual incentive constraint:

( pl Rl − L ) n ≥ ( ph Rh − L ) n ,

(ICROSCA)

always holds for equation (A1). Given the income-sharing scheme, the present value of the profit obtained by firm i, with i = 1, 2, . . . , n, in period t, with t = 1, 2, . . . , n, is:

uti ( L n , L n)l = δ t [ w + ( pl Rl − L ) n ],

(1)

where each firm receives the nth share of each period’s income and where, for convenience, we do not simplify and keep the notation of the endowment level. The first and second argument of the utility function will become clear in the comparison between ROSCAs and ROSCoAs in section V.12 The expected gross payoff obtained in a ROSCA cycle, the discounted sum of all n payoffs, is:

uni ( L n , L n)l = δ [ w + ( pl Rl − L) n], for i = 1, 2, … , n,

(2)

where δ = δ (1 − δ n ) (1 − δ ). As a result, by forming a ROSCA, agents have the opportunity to run a project with a final individual contribution equal to L. The participation constraints of ROSCA participants are trivially satisfied under equation (A1). Through the assumption of profit sharing, we are able to state the following result. Lemma 1. If members share their final returns, no individual has the incentive to leave the ROSCA. Proof. If final returns are shared among members, every participant is forced to wait until the end of the last period to receive all other members’ shares of profits. Thus, each member is always better off by joining a ROSCA since: 11

12

We do not consider the case of bidding ROSCAs, where members receive the pot through an auction procedure; see, for a theoretical analysis, Klonner (2003). In Section V, we will point out that each ROSCA member, receiving the pot, is offered the hypothetical financial contract (D/n, C/n) = (L/n, L/n), where D/n = C/n = L/n is the amount repaid by the firm either in case of success or failure, i.e., in the amount needed to participate in a ROSCA. © 2014 Institute of Developing Economies

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δ [ w + ( pl Rl − L) n] > δ n [ n ⋅ w + ( pl Rl − L)], or

(δ + δ 2 + … + δ n )[ w + ( pl Rl − L) n] > (δ n + δ n + … + δ n )[ w + ( pl Rl − L) n],

where the left-hand side of the inequality is the expected payoff obtained at the end of the ROSCA cycle, and the right-hand side is the payoff received by saving alone, waiting until the end of the last period to undertake the project. Lemma 1 implies that all members are better off with respect to self-finance, and that the ROSCA structure can be considered sustainable even in the absence of any sanctioning mechanism. IV.

THE ROSCOA

If agents decide to form a ROSCoA, they will collect, in each period, the individual collateral needed to secure a loan from a formal financial institution. Given that the project choice of ROSCoA members is unobservable and not contractible, lenders will face a standard ex-ante moral-hazard problem. As in Besanko and Thakor (1987), we consider that the output is imperfectly observable in the sense that the bank can only verify whether the project is successful or not, but not the exact amount produced. Thus, ex post, the final output cannot be related with certainty to the project choice (e.g., they may conceal or invest elsewhere some of the final product), and in this case the optimal form of financing is the debt contract (see de Meza and Webb 1987). The information structure analyzed in this model is similar to that employed by Madajewicz (2011), who argues that the choice of project quality is information so accurate and detailed that it is typically hardly observable by banks. Instead, whether an investment project exists or not is a type of rough information that is readily accessible to lenders. We also assume that members’ flow of income is perfectly observable. This is a realistic assumption for developed countries, and can also be considered reasonable for developing or rural economies, where collateral can consist of tangible personal property and easily observable assets. In the model, if income were imperfectly observable, firms could strategically choose to hide part of the endowment and offer the lowest possible collateral level. In this case, firms would always get a share of the project surplus (see Reito 2011). We consider in subsection IV.A the case of a single, monopolistic lender/bank, and in subsection IV.B the case of perfectly competitive banks. A. Single Lender A monopolistic bank tries to design the financial contract in order to extract all possible rent from each prospective borrower. As a benchmark, sub-subsection © 2014 Institute of Developing Economies


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IV.A.1 analyzes a one-period relationship between the bank and an individual firm not belonging to the ROSCoA. Then, sub-subsection IV.A.2 analyzes the relationship between the bank and ROSCoA firms. 1.

Benchmark: Individual liability lending Under individual liability, the financial contract specifies: the loan advanced by the bank, L; the amount repaid by the firm if the project is successful, D; the collateral transferred to the bank if the project fails, C. Suppose the individual entrepreneur has an endowment w ∈ [0, L]. Under the contract, a firm’s (gross) expected payoff, if the project is of type j, with j = h, l, is:

u ( D, C ) j = δ [ w + p j ( R j − D ) − (1 − p j ) C ].

(3)

The bank’s expected payoff is:

π ( D, C ) j = p j D + (1 − p j ) C − L,

(4)

where, to save on notation, we consider a discount factor of 1 for the lender. Had we perfect information, the bank would always promote the low-risk project. Given the linear utility structure, there would be multiple combinations of D and C such that the bank would achieve the first-best profit, plRl − L, and firms would be held to their (discounted) reservation payoff, δ · w. An example is the contract (D, C) = (Rl, 0). Under imperfect information, the firm will choose the low-risk project only if the incentive constraint is satisfied, if u(D, C)l ≥ u(D, C)h, or:

D ≤ D ′ + C,

(IC)

where D′ = (plRl − phRh)/(pl − ph). The equilibrium payoffs will depend on whether the firm is encouraged to choose the high- or low-risk project. Under the high-risk project, the bank would obtain (at most) a payoff of π(D, C)h = phRh − L, so it will never promote this project choice.13 Under the low-risk project, the firm’s participation constraint is:

u ( D, C )l ≥ δ ⋅ w,

(PC)

where we assume that the reservation income is measured in end-of-period terms (as noted, if a financial contract is not signed, the endowment is either consumed or sold at the end of each period). 13

This does not necessarily imply that it is never beneficial for the firm to choose the high-risk project. © 2014 Institute of Developing Economies

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The bank’s maximization problem is to choose the pair (D, C) to maximize:

π ( D, C )l = pl D + (1 − pl ) C − L, subject to equations (IC) and (PC). In equilibrium, the monopolistic bank will set the repayment so that the equation (IC) is binding, D = D′ + C. Since the firm’s endowment is observable, the bank will require the highest possible collateral level. Note that, given D = D′ + C, C = pl(Rl − D′) is the level of collateral such that:

u ( D, C )l = δ [ w + pl ( Rl − D ′ − pl ( Rl − D ′ )) − (1 − pl ) pl ( Rl − D ′ )] = δ ⋅ w, i.e., such that equation (PC) is also binding. Remark 1. If C is large enough, it is possible for the bank to extract all the project’s surplus through the collateral requirement, so that equation (PC) will be binding and equation (IC) will be slack. However, in the paper, we assume that the bank chooses to set the interest rate such that equation (IC) is always binding in order to reduce the collateral required to be eligible for a loan.14 The final profits will depend on the size of the endowment, and we can distinguish between three cases: i) w < pl(Rl − D′); ii) w ∈ [pl(Rl − D′), L[; and iii) w = L. Case i): If w < pl(Rl − D′), the collateral required by the bank is C = w. In equilibrium, the firm receives a (gross) expected payoff of:

u ( D, C )l = δ [w + p j ( R j − D ′ − w) − (1 − p j ) w] = δ [ pl ( Rl − D ′ )],

(5)

and the bank obtains:

π ( D, C )l = pl ( D ′ + w) + (1 − pl ) w − L = pl D ′ + w − L.

(6)

Hence, when w < pl(Rl − D′), the entrepreneur obtains something above the outside option, and the monopolistic bank is not able to extract all the rent. Note that, given the endowment, the payoff in equation (6) can be positive or negative. To restrict the analysis, assume that:

pl D ′ − L ≤ 0.

(A2)

Under equation (A2), the firm is able to obtain a loan only if w ≥ L − plD′ = CPC. For the special case where w = CPC, the firm’s equilibrium payoff is:

u ( D, C )l = δ [ w + pl [ Rl − ( D ′ + C PC )] − (1 − pl ) C PC ] = δ ( w + pl Rl − L ) , (5′) 14

We are grateful to a referee for suggesting this possibility.


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the first-best profit, while the bank receives:

π ( D, C )l = pl ( D ′ + C PC ) + (1 − pl ) C PC − L = 0.

(6′)

Case ii): If w ∈ [pl(Rl − D′), L[, the bank can extract all the surplus from the project as in a full-information setting. For example, if C = pl(Rl − D′), the entrepreneur receives a gross payoff of:

u ( D, C )l = δ [ w + pl [ Rl − ( D ′ + pl Rl − pl D ′ )] − (1 − pl ) pl ( Rl − D ′ )] = δ ⋅ w,

(7)

which corresponds to the outside option payoff. The bank, instead, obtains:

π ( D, C )l = pl [ D ′ + pl ( Rl − D ′ )] + (1 − pl ) pl ( Rl − D ′ ) − L = pl Rl − L, (8) which is the full-information profit. Note that, in this subcase, the bank is not strictly interested in a collateral larger than pl(Rl − D′) since, in any case, it would obtain the highest possible payoff. Therefore, we assume that, when w ∈ [pl(Rl − D′), L[, the equilibrium collateral is C = pl(Rl − D′) = CM. Case iii): If w = L, under risk neutrality, the entrepreneur is indifferent between undertaking the project without financial intermediation, or asking for a full collateralized loan. In the latter case, the participation constraint must take into account the fact that, under self-financing, the firm can receive the first-best payoff:

u ( D, C )l ≥ pl Rl − L.

(PCL)

Therefore, whatever the combination (D, C) chosen by the lender, equation (PCL) will bind and the final payoffs are again given by equation (5′) for the firm, and equation (6′) for the bank. This means that richer borrowers can receive special treatment, and the bank can offer a contract with a collateral level different from the initial wealth. For all w ∈ (CPC, CM), the firm and the bank reach an intermediate situation where they share the surplus produced. 2.

Bank–ROSCoA relationship At the beginning of the ROSCoA cycle, members will collect the collateral pot, C. Under equation (A2), to receive a loan, the per-period individual endowment must be such that w ≥ CPC/n. Again, assume that members share the income produced by each firm in any given period. Under the contract, the discounted profit obtained by member i, in period t, if the project is of type j, with j = h, l, is: © 2014 Institute of Developing Economies

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uti ( D n , C n) j = δ t [ w + p j ( R j − D ) n − (1 − p j ) C n],

(9)

where the argument of the utility function, (D/n, C/n), represents the shares of contractual repayment, D, and collateral, C, charged to firm i. The incentive constraint of the entrepreneur who wins the pot is uti ( D n , C n)l ≥ uti ( D n , C n)h , which is equivalent to the one derived under the individual liability analysis of sub-subsection IV.A.1, D ≤ D′ + C. So, to reach the repayment sum required by the monopolistic bank, the other ROSCoA members act as guarantors, each with the collateral fraction C/n. This means that, in a given period t, the participation constraints of all ROSCoA participants must be satisfied:

uti ( D n , C n)l ≥ δ t ⋅ w, for i = 1, 2, … , n.

(PCROSCoA)

The equilibrium expected payoffs will depend on the size of the collateral pot. Following the analysis of subsection IV.A.1, if C = CM, members’ expected payoffs, in period t, are:

uti ( D n , C n)l = δ t ⋅ w, i = 1, 2, … , n,

(10)

and the bank receives the full-information profit:

π t ( D, C )l = pl Rl − L, t = 1, 2, … , n.

(11)

In this case, the expected payoff of member i at the end of the ROSCoA is:

uti ( D n , C n)l = δ ⋅ w, i = 1, 2, … , n.

(12)

In the special case where C = CPC, the expected payoffs in period t are:

uti ( D n , C n)l = δ t [ w + ( pl Rl − L ) n ], i = 1, 2, … , n,

(13)

the first-best level for ROSCoA members, and:

π t ( D, C )l = 0, t = 1, 2, … , n,

(14)

for the bank. The end-of-cycle expected payoff of each member is:

uti ( D n , C n)l = δ [ w + ( pl Rl − L ) n ], i = 1, 2, … , n.

(15)

If the loan is fully collateralized, C = L, the participation constraint for each ROSCoA project is equation (PCL), and the final payoffs are again given by equations (14) and (15). This is equivalent to saying that, when C = L, ROSCA © 2014 Institute of Developing Economies


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participation is available, and thus the bank must consider the payoff of ROSCA members, δ [ w + ( pl Rl − L ) n ], as the reservation income of ROSCoA borrowers. Again, if the per-period collateral pot is such that n · w ∈ (CPC, CM), the entrepreneur and the bank share the project rent. For the income-sharing feature, Lemma 1 can also be applied to the analysis of this subsection, so can be considered sustainable. B.

Perfectly Competitive Lenders

In a competitive credit market, in addition to the incentive and the participation constraints of ROSCoA members, the financial contract must satisfy the bank’s zero-profit condition. For equation (A1), the bank will again induce the firm to choose the low-risk project, so this condition can be written as:

π t ( D, C )l = pl D + (1 − pl ) C − L = 0, t = 1, 2, … , n.

(0πC)

In this model there is not an unequivocal definition of competitive equilibrium. Indeed, each firm’s incentive constraint is D ≤ D′ + C, so there can be infinite equilibrium combinations of C and D satisfying equation (0πC), and maximizing the expected payoff of the current firm. However, we know that, with perfectly competitive and risk-neutral banks, firms are able to achieve the first-best payoff for infinite combinations of repayment and collateral levels. For example, if we substitute the repayment sum D = D′ + C (which takes into account all members’ collateral shares) into equation (0πC), we obtain an equilibrium collateral equal to L − plD′ = CPC, which is (weakly) positive under equation (A2). At the end of a given period t, ROSCoA members achieve an expected payoff of:

uti ( D n , C n)l = δ t [ w + ( pl Rl − L ) n ], i = 1, 2, … , n,

(16)

and the competitive bank receives:

π t ( D, C )l = 0.

(17)

The end-of-cycle expected payoff of each ROSCoA participant is:

uti ( D n , C n)l = δ [ w + ( pl Rl − L ) n ], i = 1, 2, … , n,

(18)

which corresponds to the first-best level. V.

ROSCAS AND ROSCoAS COMPARED

This section shows under what conditions entrepreneurs may prefer to form a ROSCA or a ROSCoA. The following proposition summarizes the discussion of Sections III and IV. © 2014 Institute of Developing Economies

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Proposition 1. In a monopolistic or competitive credit market, risk-neutral entrepreneurs with (a) w < CPC/n cannot form either a ROSCA or a ROSCoA; (b) w ∈ [CPC/n, L/n[ can only form a ROSCoA; (c) w = L/n are indifferent between a ROSCA and a ROSCoA. From proposition 1, we derive that: a) very poor individuals, with w < CPC/n, are marginalized and not able to undertake their projects before period n; b) individuals with w ∈ [CPC/n, L/n[ cannot participate in ROSCAs, and must refer to other forms of group-based arrangements, such as ROSCoAs, to access credit services. This result is confirmed by some empirical studies (Handa and Kirton 1999; Kimuyu 1999), and can be explained by considering that ROSCA participation requires a minimum budget to contribute to the pot, especially in the case of start-up investments; c) richer individuals have the possibility to choose between ROSCAs and ROSCoAs, and are indifferent between the two types of organizations. This conclusion may explain the extensive use of both informal and formal financial institutions in developing countries, as reported, e.g., by Carpenter and Jensen (2002) in their field study in Pakistan. Indeed, the authors found that, as income increases, individuals have the opportunity to choose between both sources, and that it is not unusual for ROSCA members to simultaneously borrow from formal credit markets.15 The comparison between ROSCAs and ROSCoAs is depicted in Figure 1. Since |(1 − ph)/ph| > |(1 − pl)/pl|, the indifference lines of potential entrepreneurs under the high-risk project are steeper than under the low-risk project. The switch line can be defined as the locus of contracts such that a firm is indifferent between high- and low-risk projects. Under equation (A2), in a ROSCoA, it is D ≥ C since D = D′ + C and D′ > 0 (it is D = C if the bank offers the contract (D, C) = (L/n, L/n) to borrowers with w = L/n). So, the switch line is always located on or above the 45° line. ROSCA members obtain their first-best payoff, uni ( L n , L n)l = δ [ w + ( pl Rl − L) n], and reach the indifference line denoted by uFB. We can thus imagine that these firms receive the hypothetical financial contract (D/n, C/n) = (L/n, L/n) at point R. In a monopolistic credit market, the contract offered to ROSCoA members will depend on the extent of the observable per-period income. If w ∈ [CM, L[, members receive the contract M, and earn a zero expected payoff. If w = CPC, they receive the contract PC and maximize their expected payoff. If, instead, w = L, borrowers can receive one of the contracts on the segment between points PC and R, where again they obtain their first-best profit. For each other w ∈ 15

We recognize that the fact that members can simultaneously borrow from formal and informal institutions is only weak evidence that individuals are indifferent between the two credit sources.


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Fig. 1. Comparison between ROSCAs and ROSCoAs under Risk Neutrality

D

High-risk Indifference Lines

Ra Switch Line

L/p a

M PC

Low-risk Indifference Lines

π

R

L/n

u

FB

FB

(π = 0 )

45°

PC

M

C / n C /n L/n

C

(CPC, CM), ROSCoA participants receive a contract between PC and M, where the bank and borrowers share the contractual rent. In a competitive credit market, ROSCoA members receive the contract PC, and again maximize their payoff. Besides, note that the individual endowment required for the start-up, if all n projects fail, is equal to: L in a ROSCA; w ∈ [CPC, CM] in a ROSCoA under monopoly; CPC in a ROSCoA under perfect competition. Therefore, we have the following additional result. Lemma 2. It is CPC < CM < L, so firms have the opportunity to undertake the project with a lower exogenous flow of savings under a ROSCoA than under a ROSCA. Proof. It is L > CM since this reduces to plphRl + plL > plphRh + phL, and CM > C since this reduces to plRl > L. PC

Remark 2. In the paper, the two projects produce different returns in case of success. This assumption is mainly used to simplify the analysis and rule out the equilibrium where the high-risk project is undertaken. Nothing changes if we © 2014 Institute of Developing Economies

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assume, as in de Meza and Webb (1987), that Rl = Rh = R, and that the high-risk project is inefficient, phR < L (the ICROSCA would still hold). Instead, the model would be slightly more articulated if we assume that phR ≥ L. Indeed, in this case, we could not rule out the possibility to choose the high-risk project, and the equilibrium analysis would split into several subcases. If, instead, as in Stiglitz and Weiss (1981), ph Rh = pl Rl = R ≥ L , risk-neutral ROSCA members would be indifferent between the high- and low-risk project. In a ROSCoA, if the credit market is in monopoly, D′ = 0 and equation (IC) would be D ≤ C. The collateral level such that all the low-risk project’s rent is extracted by the bank is C = plRl. Thus, if w ≥ plRl, the bank has two alternative choices: the first is promoting the low-risk project under the contract (D, C) = (plRl, plRl); the second choice is promoting the high-risk project and extracting all the surplus, e.g., through the contract (D, C) = (Rh, 0). In any case, the bank would obtain the full-information profit, plRl − L = phRh − L. Instead, if w < plRl, the monopolistic bank would always prefer the high-risk project. A.

Risk-Averse Entrepreneurs16

The previous analysis is based on risk neutrality and fails to explain why, in some countries with a more competitive banking sector, potential entrepreneurs seem to prefer to form a ROSCoA and not a ROSCA (in Italy, France, and Japan). It is also unable to explain why in countries with a high bank concentration index there is a strong presence of ROSCoAs (in Germany and China). These issues are discussed in this subsection, which introduces risk aversion on the entrepreneurs’ side. In this case, ROSCAs and ROSCoAs also represent risk-pooling arrangements. Assume that potential firms are strictly risk-averse, u′(·) > 0 and u″(·) < 0, and that there is decreasing absolute risk aversion. The function is normalized such that u(0) = 0. Lenders are again considered risk-neutral. In each period t, member i’s gross expected profit under the contract, when the project chosen is j, with j = h, l, is:

E [uti (⋅)] j = δ t [ p j u ( x Sj ) + (1 − p j ) u ( x f )], where x Sj = xlS or x Sj = xhS are the end-of-period returns in case of success, while xf is the return in case of failure. In this subsection, we limit the discussion to individuals who can actually choose between the two associations, i.e., we consider that firms have a per-period income of w = L/n.

16

This subsection is based on Stiglitz and Weiss (1992).



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With risk aversion, the switch curve is the locus where:

E [uti (⋅)]l = pl u ( xlS ) + (1 − pl ) u ( x f ) = ph u ( xhS ) + (1 − ph ) u ( x f ) = E [uti (⋅)]h. In a ROSCA, it is xlS = L n + ( Rl − L ) n = Rl n, and xf = L/n − L/n = 0. Again, we can consider that ROSCA members receive the hypothetical contract (D/n, C/n) = (L/n, L/n) and obtain a per-period payoff of E [uti ( L n , L n)]l = δ t [ pl u ( Rl n)]. In a ROSCoA, it is xlS = L n + ( Rl − D ) n , and xf = (L − C)/n, and members obtain E [uti ( D n , C n)]l = δ t [ pl u ( L n + ( Rl − D ) n) + (1 − pl ) u (( L − C) n)]. Since the high-risk project is negative valued, the bank will again promote low risk, and its per-period profit is given again by πt(D, C) = plD + (1 − pl)C − L. The incentive and the participation constraints for ROSCoA firms can be written as:

E [uti ( D n , C n)]l ≥ E [uti ( D n , C n ]h , and E [uti ( D n , C n)]l ≥ E [uti ( L n , L n)]l , where, as in subsection IV.A, if w = L/n, the payoff that can be obtained in a ROSCA, E [uti ( L n , L n)]l , must be considered as the reservation utility of ROSCoA participants. The switch curve has a positive slope since:

dD dC

E [u ]l = E [u ]h

=

( pl − ph ) u ′ ( x f )

pl u ′ ( xlS ) − ph u ′ ( xhS )

> 0.

(19)

The firm’s indifference curves are always steeper than the bank’s indifference lines. For example, under the low-risk project, it is [(1− pl ) u ′ ( x f ) pl u ′ ( xlS )] > [(1 − pl ) pl ], since u ( xlS ) > u ( x f ) and u″(·) < 0. Under risk aversion, we cannot derive the exact repayment and collateral levels without specifying the form of the utility function. So, we will also make use of the graphical representation, and denote, as before, by CM the collateral such that members receive an expected utility of 0, and by CPC the collateral such that the bank’s zero-profit condition (0πC) holds. Again it is D ≥ C, thus if a ROSCoA equilibrium exists, the financial contract must be located on or above the 45° line. But, in this case, we cannot be sure that the switch curve is entirely above the 45° line because, for example, some individuals may have a very low degree of risk aversion and thus a flat combination of points where they switch between highand low-risk projects. To rule out these cases, in this section we assume that ROSCA members strictly prefer the low-risk project at the implicit contract (L/n, L/n): © 2014 Institute of Developing Economies

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the developing economies Fig. 2. Comparison between ROSCAs and ROSCoAs under Risk Aversion in the Monopolistic Credit Market

D Switch Curve

M

L/n

Max π R

π

M

0πC

u

L/n

ROSCA

=

u

ROSCoA

C

E [uti ( L n , L n)]l > E [uti ( L n , L n)]h.

(A3)

If equation (A3) holds, the incentive constraint of ROSCoA borrowers is slack at the contract (L/n, L/n). For example, Figure 2 shows that, under equation (A3), there will always be a segment of the bank’s zero-profit line above the 45° line, and between point R = (L/n, L/n) and the switch curve. For equation (19), the switch curve is increasing at the point where it intersects the (0πC) line, and so there will be at least a portion of the curve above the 45° line and above point R (the switch curve may or may not intersect the 45° line below point R). In other terms, we choose to focus our discussion on potential entrepreneurs with a relatively higher degree of risk aversion and a rather steep switch curve. Consider first a monopolistic credit market. We will restrict our attention to the set of contracts:

C = {( D, C ) : π t ( D, C )l ≥ 0, E [uti ( D n , C n)]l ≥ E [uti ( D n , C n)]h , E [uti ( D n , C n)]l ≥ E [uti ( L n , L n)]l } , © 2014 Institute of Developing Economies


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i.e., for each member i, with i = 1, 2, . . . , n, and period t, with t = 1, 2, . . . , n, the bank’s zero-profit condition and firm’s incentive and participation constraints are satisfied. The monopolistic lender will offer a contract such that the borrowers’ participation constraint is binding, E [uti ( D n , C n)]l = E [uti ( L n , L n)]l . Thus, we can state the following. Proposition 2. In a monopolistic credit market, under equation (A3), and if

( D, C ) ∈C , risk-averse entrepreneurs, with w = L/n, are indifferent between ROSCAs and ROSCoAs. Under equation (A3), it is always possible for the bank to design the contract such that the incentive constraint is also binding, E [uti ( D n , C n)]l = E [uti ( D n , C n)]h . This implies that, since ROSCoA members’ indifference curves are steeper than the lender’s iso-profit lines, the bank can achieve a payoff higher than the (0πC) level. In contrast to the case of risk neutrality, the monopolistic bank earns positive expected profits on borrowers with w = L/n, so the high presence of ROSCoAs in countries where the banking system is rather concentrated (such as in Germany and China) can be partly explained by the incentive of banks to promote the formation of mutual guarantee associations. In Figure 2, ROSCA members receive the (implicit) contract R and reach the indifference curve denoted by uROSCA (to ease the representation, we do not depict the high-risk project indifference curves). In a ROSCoA, borrowers receive the contract M, where both incentive and participation constraints are satisfied with equality, and reach the indifference curve uROSCoA = uROSCA. The bank’s indifference line is denoted by πM. In a competitive credit market, had we perfect information, risk-averse borrowers would maximize their profit by increasing as much as possible their payoff in case of failure. This argument implies that under asymmetric information, the ROSCoA equilibrium contract is the couple (D, C) such that the collateral level is the lowest possible given the bank’s zero-profit condition (0πC). The competitive pressure will force banks to increase D and decrease C until the firm’s incentive constraint is binding and, for equation (A3), such that participation constraint is slack, E [uti ( D n , C n)]l > E [uti ( L n , L n)]l . Therefore, we derive the following. Proposition 3. In a competitive credit market, under equation (A3), and if

( D, C ) ∈C , risk-averse potential entrepreneurs prefer to form a ROSCoA.

Proof. Under equation (A3), E [uti ( L n , L n)]l > E [uti ( L n , L n)]h , it is possible for lenders to design a contract (D, C), with D > L and C < L, such that © 2014 Institute of Developing Economies

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the developing economies Fig. 3. Comparison between ROSCAs and ROSCoAs under Risk Aversion

D Switch Curve

PC R

L/n

π

FB

0πC

u

ROSCoA

u

L/n

ROSCA

C

the participation constraint is slack, E [uti ( D n , C n)]l > E [uti ( L n , L n)]l , and such that the incentive constraint is satisfied at least with equality, E [uti ( D n , C n)]l ≥ E [uti ( D n , C n ]h . Given that borrowers’ indifference curves are steeper than the banks’ zero-profit line, the contract that maximizes the expected utility of ROSCoA members will be the couple (D, C) for which the incentive constraint is binding, E [uti ( D n , C n)]l = E [uti ( D n , C n ]h. With perfectly competitive banks, riskaverse borrowers are partially insured by risk-neutral lenders, and the payoff of ROSCoA members is always larger than that obtained in a ROSCA. In Figure 3, the ROSCoA equilibrium is point PC where uROSCoA > uROSCA, and where banks reach their (0πC) line. VI.

CONCLUSIONS

The aims of this paper were: first, to provide a theoretical description of a mutualguarantee association, which we interpret in a rotating scheme we call Rotating Savings and Collateral Association (ROSCoA); second, to compare ROSCoAs and © 2014 Institute of Developing Economies


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ROSCAs under different assumptions about entrepreneurs’ risk attitudes and bank concentration. We interpret the mechanism of these associations as an incomesharing arrangement where members redistribute each other’s project income. Thanks to this assumption, ROSCAs and ROSCoAs can be considered sustainable in the sense that no members have the incentive to leave, even without introducing social constraints. One of the conclusions that can be drawn from the paper is that the individual flow of savings required to be a member of a ROSCoA is in general lower than that needed for a ROSCA. This implies that ROSCoAs may be a more efficient and cost-effective tool to contrast poverty, so that these conclusions may have interesting policy implications for less developed countries (e.g., Beck, Klapper, and Mendoza [2010] report that the government support of such associations in developing countries is relatively lower compared to developed regions). The most immediate implication is to help fostering the development of mutual-guarantee schemes, e.g., through special guarantee funds established by public authorities to partially cover the amount of guarantees required by formal lenders. REFERENCES Anderson, Siwan; Jean-Marie Baland; and Karl O. Moene. 2009. “Enforcement in Informal Savings Groups.” Journal of Development Economics 90, no. 1: 14–23. Armendáriz de Aghion, Beatriz. 1999. “On the Design of a Credit Agreement with Peer Monitoring.” Journal of Development Economics 60, no. 1: 79–104. Armendáriz de Aghion, Beatriz, and Jonathan Morduch. 2007. The Economics of Microfinance. Cambridge, MA: MIT Press. Basu, Karna. 2011. “Hyperbolic Discounting and the Sustainability of Rotational Savings Arrangements.” American Economic Journal: Microeconomics 3, no. 4: 143–71. Beck, Thorsten; Asli Demirgüç-Kunt; and Ross Levine. 2006. “Bank Concentration, Competition and Crises: First Results.” Journal of Banking & Finance 30, no. 5: 1581–603. Beck, Thorsten; Leora F. Klapper; and Juan C. Mendoza. 2010. “The Typology of Partial Credit Guarantee Funds Around the World.” Journal of Financial Stability 6, no. 1: 10–25. Besanko, David, and Anjan V. Thakor. 1987. “Competitive Equilibrium in the Credit Market under Asymmetric Information.” Journal of Economic Theory 42, no. 1: 167– 82. Besley, Timothy; Stephen Coate; and Glenn Loury. 1993. “The Economics of Rotating Savings and Credit Associations.” American Economic Review 83, no. 4: 792–810. Boocock, Grahame, and Mohd Noor Mohd Shariff. 2005. “Measuring the Effectiveness of Credit Guarantee Schemes: Evidence from Malaysia.” International Small Business Journal 23, no. 4: 427–54. Bouman, Frits J. A. 1995. “Rotating and Accumulating Savings and Credit Associations: A Development Perspective.” World Development 23, no. 3: 371–84. Bradshaw, Ted K. 2002. “The Contribution of Small Business Loan Guarantees to Economic Development.” Economic Development Quarterly 16, no. 4: 360–69. © 2014 Institute of Developing Economies

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