Mutual loan-guarantee societies in monopolistic credit markets with adverse selection

Journal of Financial Stability 8 (2012) 15–24

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Mutual loan-guarantee societies in monopolistic credit markets with adverse selection Giovanni Busetta a , Alberto Zazzaro b,∗ a b

Department of Economics, Statistics, Mathematics and Sociology, Università di Messina, Italy Department of Economics, Università Politecnica delle Marche, Money and Finance Research Group (MoFiR), Piazzale Martelli 8, 60121 Ancona, Italy

a r t i c l e

i n f o

Article history: Received 24 June 2010 Received in revised form 17 February 2011 Accepted 17 February 2011 Available online 3 March 2011 JEL classification: D82 G21

a b s t r a c t In many countries, Mutual Loan-Guarantee Societies (MGSs) are assuming ever-increasing importance for small business lending. In this paper we provide a theory to rationalize the raison d’être of MGSs. The basic intuition is that the motivation for MGSs lies in the inefficiencies created by adverse selection, when borrowers do not have enough wealth to satisfy collateral requirements and induce self-selecting contracts. In this setting, we view MGSs as a wealth-pooling mechanism that allows otherwise inefficiently rationed borrowers to obtain credit. © 2011 Elsevier B.V. All rights reserved.

Keywords: Mutual Loan-Guarantee Society Group formation Small business lending Collateral

1. Introduction In the words of the European Commission (2005, p. 10), Mutual Loan-Guarantee Societies (from now on MGSs) are “collective initiatives of a number of independent businesses or their representative organizations. They commit to granting a collective guarantee to credits issued to their members, who in turn take part directly or indirectly in the formation of the equity and the management of the scheme”. Like other types of public and private partial guarantee schemes around the world, MGSs are assuming ever greater importance in small business lending (Beck et al., 2010). For example, according to the Association Européenne du Cautionnement Mutuel (see Fig. 1), in 2009 their member systems, represented by 34 federations of MGSs operating in 17 EU countries, granted 855,000 guarantees for 34 billion euros, reaching a total volume of guarantees in portfolio greater than 70 billion euros held with more than 1.8 million small firms. Moreover, the importance of MGSs is destined to further increase in the light of the Basel II (and III) Accords which state that the guarantees of such institutions could, if granted in compliance

∗ Corresponding author. Tel.: +39 071 2207086; fax: +39 071 2207102. E-mail address: [email protected] (A. Zazzaro). 1572-3089/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jfs.2011.02.004

with some requirements, allow banks to mitigate credit risk associated with small business lending and to save regulatory capital (Cardone-Riportella et al., 2008). Surprisingly, in spite of their real-world diffusion and the attention paid to MGSs in the policy arena, there has been no previous attempt to model the incentives behind their formation1 . In the present paper we provide a theory to rationalize the existence of MGSs based on the contractual features of loans granted through the intermediation of such institutions. While MGSs play other important roles like screening and monitoring their associates and conducting collective bargaining with banks, our theory focuses on their distinctive function, that is of providing collateral to associates. Its major contribution is to show that, abstracting from any alleged informational advantage of entrepreneurs about each other, an MGS acts as a wealth-pooling mechanism that makes it feasible to offer separating contracts and reduces the likelihood of credit rationing. Furthermore, we show that conventional personal loans and loans covered by the MGSs’ guarantees may coexist, given that the pros and cons of joining MGSs are not identical for safe and risky borrowers.

1 By contrast, there exists a fairly large theoretical literature on the use of public loan guarantee programs and their welfare properties (Gale, 1990a,b; Lacker, 1994; Williamson, 1994; Kasahara, 2009; Modica and Minelli, 2009; Arping et al., 2010).

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Fig. 1. Guarantee activity of AECM member federations: 2002–2009. Source: (AECM, 2010)

Going more into detail, we develop an adverse selection model where banks cannot distinguish among borrowers and the latter do not possess enough collateralizable wealth to make separating contracts feasible. We assume that the bank holds all the bargaining power within the lending relation, but the borrower gains nonobservable private benefits from accessing the credit market and conducting an entrepreneurial activity. Moreover, we assume that borrowers are uninformed about other potential entrepreneurs. When the pooling contract results in rationing safe borrowers, they have an incentive to pool their wealth in an MGS so as to have a positive probability of accessing the separating contract and gain the private benefit of becoming an entrepreneur. In turn, risky borrowers may also find it worth becoming members of an MGS, since by participating in an MGS they dilute the risk of losing the wealth pledged as collateral with the safe associates. However, this benefit comes at the expense of a positive probability of not obtaining the MGS’s guarantee and relinquishing the benefit of entrepreneurship. Where the latter benefit is sufficiently high, risky borrowers prefer to borrow individually and the MGS formation acts as a sorting device. Otherwise, MGSs can form with the participation of both risky and safe borrowers. The rest of the paper is organized as follows. In Section 2, we discuss the model motivations and related literature. In Sections 3 and 4, we present the basic model and derive the optimal individual loan contracts, respectively. The incentives to form an MGS and the condition under which the assortative matching property holds are described in Section 5. In Section 6, we discuss comparative static results and testable implications. In Section 7, we discuss some possible extensions of the model concerning public contributions and multi-period relationships between banks and firms. In Section 8 we conclude. 2. Model motivations and related literature 2.1. Role and functioning of MGSs Asymmetries of information between banks and borrowers lie at the root of significant misallocation in credit markets. Due to the lack of information on individual borrowers, banks can cause the interest rate to become inefficiently high such that worthy borrowers are driven out of the credit market (Stiglitz and Weiss, 1981). Alternatively, borrowers with negative net present value projects could obtain financial support in the credit market by taking advantage of cross-subsidisation of borrowers with worthy projects (Mankiw, 1986; De Meza and Webb, 1987). In both cases, the reason for market failure is that banks are unable to recognize

the actual riskiness of borrowers and are forced to offer the same contract to borrowers with a different probability of success. As is well described in the literature, when borrowers’ wealth is large enough, banks may bypass informational asymmetries by offering a menu of contracts with collateral requirements acting as a sorting device. In this case, risky borrowers will self-select by choosing contracts with high repayment and low collateral, while safe borrowers will choose contracts with high collateral and low repayment (Bester, 1985; Besanko and Thakor, 1987). Typically, informational problems are particularly severe for small and micro enterprises. Such firms have a short credit history, meet less rigorous reporting requirements and the availability of public information on them is scarce. On top of that, the difficulty of banks in assessing the creditworthiness of small borrowers often goes hand-in-hand with inadequate availability of collateralizable wealth from the latter. Lack of information and collateral are therefore universally seen as the main structural features explaining the reluctance of banks to lend to small enterprises, especially during economic downturns, with negative effects on industry dynamics, competitiveness and growth (Beck et al., 2005; Beck and Demirgüc¸Kunt, 2006). In this context, in many countries around the world various types of loan guarantee funds have been created to help small and micro enterprises to gain easier access to the credit market (Gonzàles et al., 2006; Beck et al., 2010; Cowling, 2010; Honohan, 2010). Frequently, these funds assume a mutual corporate structure in which artisans and other small entrepreneurs (or their associations of category) create a non-profit mutual society which acts as an intermediary with banks and provides associates with collateral, mobilizing their own contributions to the common fund. Ever since the cooperative banking movements in the 19th century (Guinanne, 1994, 2001), in Europe there has been a long tradition and a great diffusion of mutual guarantee associations (AECM, 2010). Apart from Europe, the system of MGSs is well developed in South and North America (Oehring, 1997; Riding and Haines, 2001), East Asia (Hatekayama et al., 1997) and North Africa (De Gobbi, 2003), and the techniques for mitigating the risk of default on small business lending included in Basel II have created further stimuli to its worldwide diffusion (Cardone-Riportella et al., 2008). Although MGSs operate in disparate ways within and across countries, there are some general common features which they share. MGSs are non-profit, cooperative institutions created by small and micro private enterprises which constitute a collective fund with the aim of meeting the guarantee requirements of banks. Typically, the contributions of associate firms to the guarantees fund is supplemented by public resources from local and

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national governments (Gonzàles et al., 2006; Beck et al., 2010). In addition, government institutions often provide forms of counterguarantees to the MGS’s first guarantee (Cardone-Riportella et al., 2008; Zecchini and Ventura, 2009; Beck et al., 2010). Firm associates first apply for the MGS’s guarantee, whose assignment is not compulsory. Once obtained, then firms apply for a loan from a bank with which their MGS has subscribed an agreement on the loan-contract terms. Applications of the associate firms and loans, however, are made on a personal basis. At each bank with which they sign an agreement, MGSs deposit a guarantee fund. In case of default of a borrowing associate, the bank is entitled to claim directly up to a share of the loan granted (usually, however, the actual availability of the collateral pledged by the MGS to the bank would occur only after the law enforcement procedure against the borrower is terminated). 2.2. Microfinance versus mutual guarantee schemes Economic research on MGSs has confined itself to giving an informal account of their role and empirical evidence on their functioning (Levitsky, 1993; De Gobbi, 2003; Beck et al., 2010; Columba et al., 2009, 2010; Honohan, 2010), while there has been no attempt to formally model the incentives behind their formation and the circumstances under which MGSs can improve the pool of borrowers and the efficiency of credit markets. The theoretical underpinning of the policy debate on MGSs is the literature on microfinance and group lending, which emphasizes the importance of local information and social embeddedness in reducing asymmetric information and the advantages of borrowers in screening and monitoring their peers2 . In this context, two mechanisms are usually mentioned to account for the good performance of loans guaranteed by MGSs in terms of repayment rate: peer selection, which mitigates adverse selection problems, and peer monitoring, which alleviates moral hazard and improves the enforcement of contracts. Both these mechanisms, however, can be reasonably supposed to lose effectiveness as we move away from the village economy and lending to very small groups of poor people analyzed by microfinance literature and consider large groups of small enterprises in urban economies of developed countries like France, Germany, Italy or Spain where the MGS system is firmly in action3 . It is hard to believe that, within groups made up by hundreds or thousands of associates, working in different sectors and dispersed over a wide area usually consisting of many municipalities, a single member could have informational advantages about partners over local banks or greater capacities to impose social sanctions on bad members. Apart from all else, if banks really thought that MGSs were good at screening and monitoring their associates, then we should observe them offering MGS associates zero (or low) collateral contracts, which is the opposite of what occurs in loan contracts intermediated by real-world MGSs4 . Indeed, there are several differences between loans granted through a typical microfinance program and loans intermediated

2 The first theoretical papers on microfinance were published in the 1990s on the wave of the successes obtained by Muhammad Yunus’s Grameen Bank in alleviating poverty in Bangladesh (Stiglitz, 1990; Varian, 1990). Since then, innumerable contributions in the literature have been devoted to study the ever-increasing number of microfinance schemes being set up in developing and developed countries to facilitate access to credit to groups of vulnerable people (Morduch, 1999; Armendariz and Morduch, 2005). 3 The importance of very small, geographically concentrated groups for the viability of microfinance programs was amply acknowledged from the first contributions to the literature (Stiglitz, 1990). 4 We wish to thank a referee of this Journal for having called our attention to this point.

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by MGSs. In the first case, banks provide very small loans to individuals organized into small and self-selected groups. Each group member is jointly liable for the repayment of loans granted to any other group member. Loans are made sequentially to the group member and the repayment is diluted in several installments. Lastly, the loan contract rarely provides for collateral. By contrast, as we already stated, loans guaranteed by an MGS are granted to small and micro enterprises through a standard debt contract which provides for collateral. No MGS member is liable for the repayment of loans granted to other members. He/she only shares the credit risk of the latter through his/her participation in the guarantee fund of the MGS. 2.3. Related literature Our analysis is clearly related to the literature on peer group formation with adverse selection (Ghatak, 1999, 2000; Van Tassel, 1999; Armendariz and Gollier, 2000; Laffont and N’Guessan, 2000; Ghatak and Kali, 2001; Laffont, 2003). The main feature distinguishing our model is the motivation behind the formation of the group. In the existing literature, groups are formed in order to access the group lending contract with joint liability offered by lenders. In our model, instead, MGSs are created with the purpose of pooling personal wealth and accessing the individual separating contract with collateral requirement. Consequently, while the existing literature on group formation assumes away the presence of collateralizable wealth, we explicitly admit that potential entrepreneurs possess a certain amount of it. Moreover, in our model the assortative matching property of the group is triggered by the different incentives to constitute an MGS of good and bad borrowers and not by the peer selection effect among borrowers who know each other perfectly. In this respect, our analysis is similar in spirit to Armendariz and Gollier (2000); Laffont and N’Guessan (2000) and Laffont (2003) who consider the case of potential entrepreneurs who do not know each other’s type. However, in these papers, taking away the informational advantages of peers, joint liability is no longer a feature which is sufficient to attain assortative matching in the formation of groups. In particular, considering the same mean-preservingspread project environment as that we propose, Armendariz and Gollier (2000) show that, in the presence of auditing costs, peer group formation may solve the inefficient credit rationing of safe borrowers by reducing the probability of audits. However, the prevailing equilibrium is of a pooling type, where all kinds of group compositions are equally probable. 3. The model set-up The wealth-pooling role of MGSs can be properly illustrated by building on the influential models of costly collateral by Bester (1985) and Besanko and Thakor (1987)5 . Consider a continuum of risk-neutral potential entrepreneurs of measure 1, each endowed with the technology to start up a one-period investment project and an end-of-period collateralizable wealth W. Starting up the project requires a beginning-of-period monetary investment I, such that entrepreneurs have to borrow from a bank I units of money.

5 In these models, borrowers and lenders take their decisions simultaneously rather than sequentially. Since the existence of the wealth-pooling mechanism which drives our rationalization of MGSs is independent of whether moves in the lending game are simultaneous or sequential, we prefer to maintain the simultaneous-move structure as in the basic models of collateral in the economic literature (Freixas and Rochet (1997) provide a simplified textbook version of this type of model).

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Project returns follow a two-point distribution. A fraction ␪ of potential entrepreneurs is ‘safe’, endowed with projects that yield a return Ys with probability ps and zero with probability (1 − ps ). A fraction (1 − ␪) is ‘risky’, endowed with projects yielding Yr with probability pr < ps and zero otherwise. All projects are positive net present value, but the expected return on safe borrowers is no lower than that on risky borrowers, ps Ys ≥ pr Yr > I. In addition to returns Y, borrowers obtain a private (either monetary or non-monetary) benefit B from being an entrepreneur, which is assumed to be non-observable and therefore noncontractible. The private benefit B can be understood, for example, in terms of social status, autonomy and self-esteem of being an entrepreneur, elements that may represent an important motivation to start up entrepreneurial projects, especially in low-employment regions where the alternative options to selfemployment are rather meagres. Also, it embodies rents from social (political) connections and all the elements of value that can accrue to the entrepreneur by virtue of its control on enterprises’s resources, like tax evasion or other forms of fund diversion6 . The assumption that the bank cannot observe the benefit B is crucial to our results, as otherwise the bank would also extract such a surplus. In this case, the utility for borrowers from lending would be zero, like under credit rationing, and they would have no incentive to pool their wealth in order to form an MGS7 . However, it seems quite realistic to assume that there are benefits that agents can obtain from starting an enterprise which can neither be observed nor approximately inferred by banks on the basis of their past lending experience; benefits that, hence, are not extractable by banks even if they act in the local market as quasi-monopolists8 . To simplify the analysis, we further assume that B is constant across individuals and normalize bank’s beliefs at zero9 . Risk-neutral banks cannot distinguish safe from risky entrepreneurs but know their proportion. Each bank collects deposits elastically at a zero interest rate and lends in a monopoly regime10 with standard loan contracts Lj = {Rj , Cj }, where Rj denotes the gross repayment and Cj ∈ [0, W] the collateral requirement, with j = r, s. When a borrower fails to honour the contract, banks can seize returns plus pledged collateral. As in Barro (1976); Bester (1985) and Besanko and Thakor (1987), we assume that, due to inefficiency in contract enforcement, the bank can recover only a fraction ˇ > 1 of the collateral face value11 .

6 The huge literature on the benefits of becoming and being an entrepreneur clearly suggests that they are much wider than the strict monetary profit earnable from the entrepreneurial activity and that they are strongly influenced by factors related to the social and economic environment where (potential) entrepreneurs live and operate (Malecki, 1994; Benz and Frey, 2008; Benz, 2009; Casson, 2010). Therefore, an interesting extension of the model, especially for its empirical testing, would be to endogenize B. However, since it is the level of B which matters for the establishment and nature of MGSs in our theory, for the sake of simplicity, we prefer to treat B as exogenously given. 7 See Eqs. (2) and (6) below. 8 At the same time, it is realistic to assume that the average quality of firms operating in the market (the parameter ␪) is approximately known to the bank on the basis of its past lending experience. 9 Diversely, we could assume that B distributes randomly across the population and banks only know its density function. This, however, would complicate the model considerably without adding further intuition to the analysis. 10 The monopoly assumption seems to be a good approximation for credit markets populated by small, wealth-constrained borrowers. 11 Apart from the efficiency of legal and judiciary systems, the value of collateral to the bank (i.e., the value of ˇ) depends on the type of collateral (real versus financial assets) and its liquidity. Disparity in collateral valuation between banks and borrowers (i.e., ˇ < 1) makes isoprofit lines less steep than borrower indifference curves in the plane (C, R) and ensures that the separating equilibrium is unique.

4. Debt contracts under individual lending 4.1. Separating contracts Banks might sort safe and risky borrowers by offering two contracts, Ls = Rs , Cs and Lr = Rr , Cr such that the former is selected by safe entrepreneurs and the latter by risky entrepreneurs, and on both contracts borrowers can gain non-negative profits. Formally, the bank’s maximization program is given by vb = [ps Rs + (1 − ps )ˇCs ] + (1 − )[pr Rr + (1 − pr )ˇCr ]

max Rs ,Rr ,Cs ,Cr

ps (Ys − Rs ) − (1 − ps )Cs ≥ 0 pr (Yr − Rr ) − (1 − pr )Cr ≥ 0 ps (Ys − Rs ) − (1 − ps )Cs ≥ ps (Ys − Rr ) − (1 − ps )Cr pr (Yr − Rr ) − (1 − pr )Cr ≥ pr (Yr − Rs ) − (1 − pr )Cs

s.t.

(PCs ) (PCr ) (ICs ) (ICr ).

Since collateral is costly for banks, borrowers are required to pledge collateral to the minimum extent necessary to make the separation feasible. Now consider the pair of contracts LsS and LrS , such that (PCs ), (PCr ) and (ICr ) are binding: LsS LrS



ps Ys − pr Yr + ps pr (Yr − Ys ) S ps pr (Yr − Ys ) ; Cs = ps − pr ps − pr = {RrS = Yr ; CrS = 0} =

RsS =



(1)

From (1), the repayment required by the bank with contract LsS is clearly feasible, that is RsS < Ys , and (ICs ) is also met. Moreover: Lemma 1. If  < ˆ = [(ps − pr )]/[(ps − pr ) + ps (1 − ps )(1 − ˇ)], the pair of contracts LsS and LrS in (1) is the optimal separating equilibrium. Proof. Let vSb be the bank’s expected profits from offering contracts LsS and LrS . The bank might reduce by RrS the interest charged to risky borrowers with a loss in expected profits equal to (1 − )pr RrS . In this way, the bank softens the incentive constraint for risky borrowers and could offer a new self-selecting safe-contract  LsS with lower collateral and higher interest rate. Substituting RsS obtained from (PCs ) into (ICr ), we easily find that, with respect to the  contract LsS , the new contract LsS provides an increase in interest rate −1 equal to pr (1 − ps )(ps − pr ) RrS and a reduction in the collateral to ps pr (ps − pr )−1 RrS . For the bank, these changes in the contract entail expected gains equal to ps pr (1 − ps )(1 − ˇ)(ps − pr )−1 RrS . ˆ the expected loss on risky contracts LS is always higher If  < , r   than the expected gain on safe contracts LsS , such that vSs < vSs for S any Rr < 0, hence proving Lemma 1.  The economic intuition of Lemma 1 is straightforward. When the share of safe borrowers is not very large, the bank maximizes its whole profit by maximizing revenues on loans to r-type and forgoing part of the profit realizable with a reduction in the collateral  requirement on s-type loans as in contract LsS . Since in equilibrium banks extract all the rent from both types of projects, borrowers’ net utility is simply the private benefit B: Us (LsS ) = Ur (LrS ) = B

(2)

4.2. Credit-rationing equilibrium Assume that borrowers are wealth-constrained and cannot apply for the separating safe-contract LsS , i.e., assume that W < CsS . In this case the bank maximizes its expected profit by offering either a pooling or a separating contract. Following the same logic as Lemma 1, if  < ˆ the optimal separating contract requires safe borrowers to pledge all their wealth as collateral: L˜ sS L˜ rS





1 − ps W ; CsS = W ps   ps − pr = RrS = Ys + W ; CrS = 0 ps pr =

RsS = Ys −

(3)

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The bank’s expected profit is



vb (L˜ sS ; L˜ rS ) = ps Ys −





1 − ps W ps

+ 1 −  pr



Ys +



differently than under individual lending. Moreover, absent any peer (selection or monitoring) effect, lending to a member of an MGS is for the bank equivalent to lending to an individual borrower. Therefore, we have:

+  (1 − ps ) ˇW

ps − pr W ps pr



−I

(4)

With regard to the pooling contract, we have three possible candidates. First, the bank could ask all borrowers to pledge their wealth as collateral and charge the interest rate that makes monetary profits of safe borrowers equal to zero, such that all potential entrepreneurs may ask for credit: L1P = {R1P = Ys − (1 − ps )/ps W ; C1P = W }. However, it can be shown that this contract is not profit-maximizing because vb (L1P ) < vb (L˜ sS ; L˜ rS ) for any ˇ < 1. Second, the bank could offer a contract with zero collateral and the interest rate that satisfies (PCs) as equality: L2P = {R2P = Ys ; C2P = 0}. Once again, this contract is not profit-maximizing since, when ˆ vb (LP ) < vb (L˜ S ; L˜ S ).  < , s r 2 Finally, the bank could offer a contract asking for zero collateral and an interest rate equal to the positive return on the risky project: LP = {RP = Yr ; C P = 0 = LrS }. In this case, safe borrowers are excluded from the credit market and the bank’s expected profit is

vb (LP ) = (1 − )(pr Yr − I)

(5)

ˆ pr (Yr − Ys )/(pr (Yr − Ys ) + ps Ys − I)], a Lemma 2. If  < min[, ¯ > 0 exists such that vb (LP ) < vb (L˜ sS ; L˜ rS ) holds for any wealth W ¯ ), and a credit-rationing equilibrium prevails. W ∈ (0, W Proof. By comparing Eqs. (4) and (5), it is easy to show ¯ = ps [(1 − )pr (Yr − Ys ) − (ps Ys − that vb (LP ) < vb (L˜ sS ; L˜ rS ) if W < W −1 ˆ the denominator I)][(1 − )(ps − pr ) − ps (1 − ps )(1 − ˇ)] . If  < , of such an expression is certainly positive, while its numerator is positive only if ␪ < pr (Yr − Ys )[pr (Yr − Ys ) + ps Ys − I]−1 .  Hence, if the available wealth is sufficiently lower than the collateral required on the separating contract LsS , the bank maximizes its expected profit by offering a pooling contract that ration safe borrowers by raising the interest rate to Yr . In a credit-rationing equilibrium, risky entrepreneurs obtain the private benefits B, while safe entrepreneurs are excluded from the credit market and gain zero utility: Us (LP ) = 0; Ur (LP ) = B

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(6)

5. Borrowing through mutual loan-guarantee societies Assume that investors can participate in an MGS by contributing with a part w ≤ W of their wealth to a collective fund. This fund will be employed to pledge the collateral required by the bank in favour of MGS members who thus become indirectly jointly liable for each other’s loan repayment. Also, assume that the MGS does not have any informational advantages over banks with regard to their members. Each member is entitled to apply for the loan guarantee of the MGS. If, like in the case of individual borrowing with separating contracts (1), we exclude the possibility of any MGS member making side payments in exchange for the right to use the wealth of another, the collateral pledged to the bank has to be the same for all members, whether safe or risky. In this case, MGSs can display alternatively assortative and non-assortative matching of investors, being composed by either safe entrepreneurs only, risky entrepreneurs only or by both types of entrepreneurs. Since banks do not observe the benefit B entrepreneurs can gain from accessing the credit market, they cannot anticipate what types of entrepreneurs find it profitable to form and participate in an MGS (see below, Proposition 1), and hence cannot design loan contracts

¯ , and let banks be monopolist Lemma 3. Let  < ˆ and W < W against MGS members. Then the optimal loan contracts offered by banks to MGSs is: LM = LsS . ¯ , the optimal Proof. The proof can run intuitively. Since W < W contract offered by banks to individual borrowers is the pooling contract LP , which is equivalent to the risky contract under separating equilibrium (see Lemma 2). Therefore, the value of B ˆ from Lemma 1 the profitbeing unobservable and given  < , maximizing loan contract offered by banks to MGS associates is the safe-separating contract, LM = LsS .  Since W < CsS , guarantees by the MGS can be granted only to a share q = w/CsS of the associates. Assume that those associates who are refused the loan guarantee cannot apply to the bank for individual lending in the same period12 . Let Ujz (LM ) be the net utility for a j-type investor of participating in an MGS with z-type members, with j, z = s, r. Given the separating contracts (1) and since q < 1, clearly Ujz (LM ) < Uj (LjS ) for any j and z. Therefore, in the absence of credit rationing, it would not be worthwhile for either s- or r-type borrowers to form an MGS. By contrast, under the pooling contract, safe borrowers are credit-rationed, their net utility is zero and they have incentives to establish an MGS and pool their wealth for applying for the MGS contract. In turn, r-type may find it worth joining the MGS with safe entrepreneurs. This is because under the MGS contract they can borrow at conditions that are equivalent to those required with the r-type separating individual contract (recall that for risky borrowers the incentive constraint is binding and LrS ∼LsS ), but they can still take advantage of the joint liability and reduce the probability of losing their wealth. Proposition 1. Suppose that investors cannot observe each other’s type, that banks cannot observe the private benefit of becoming entrepreneur B and that in the credit market a rationing equilibrium prevails. Then: Case I. When the private benefit of being an entrepreneur is −1 sufficiently high, i.e., when B ≥ B˜ = (ps − pr )WCsS (CsS − W ) , risky investors will prefer to borrow individually through the pooling contract LP , whereas safe investors will gain from forming an MGS. ˜ risky investors have an incenCase II. When B is lower than B, tive to join an MGS in which safe investors participate. In turn, safe investors have an incentive to join an MGS in which risky investors participate only if B ≥ Bˆ = (1 − )(ps − pr )CsS . In this case, a necessary condition for a non-assortative MGS to exist is (1 − ) < W/CsS .

Proof. Case I. In order for assortative matching to prevail either Urr (LM ) > Ur (LP ) and Usr (LM ) ≤ Us (LP ) or Uss (LM ) > Us (LP ) and Urs (LM ) ≤ Ur (LP ) have to hold, where

⎧ M S S ⎪ ⎨ Urr (LM ) = q[pr (Yr − RSs ) + B] − (1 − pr )qCSs Uss (L ) = q[ps (Ys − Rs ) + B] − (1 − ps )qCs

M S S ⎪ ⎩ Urs (L M ) = q[pr (Yr − RSs ) + B] − (1 − p )qCsS

Usr (L ) = q[ps (Ys − Rs ) + B] − (1 − p )qCs

with (1 − pj )qCsS being the expected guarantee losses per associate, and where  and  are the shares of safe and risky entrepreneurs

12 A weaker, maybe more realistic, assumption would be that applying for a loan is costly. In this case, the model should be sequential instead of simultaneous; the analytical derivation of the market equilibria would be more cumbersome, but the wealth-pooling role of MGSs would remain in action.

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that join the MGS. Recalling that q = w/CsS , p␪ = ␪ps + (1 − ␪)pr and that the pair RsS and CsS are such that the participation constraints for s- and r-investors as well as the incentive constraint for the r-type are all binding, the above expressions for the borrowers’ utility can be simplified and rewritten as:

Urr (LM ) = Uss (LM ) =

w CsS

B;

⎧ w M ⎪ ⎨ Urs (L ) = C S B + w(p − pr ) s

w ⎪ ⎩ Usr (LM ) = S B + w(p − ps )

(7)

Cs

Since the net utility of forming an MGS, Ujz (LM ) − Uj (LP ), is not decreasing with w for any j and z, investors find it optimal to participate in the MGS’s guarantee fund with all their wealth and maximize the probability of gaining access to the loan guarantee: w = W . From (7) and (6) clearly Urr (LM ) < Ur (LP ) always holds and the only possible assortative equilibrium is that with safe investors in the MGS and risky investors borrowing individually out of the MGS. Again, from (7) and (6), we have Uss (LM ) > Us (LP ). Moreover, since Urs and Usr are strictly increasing with  and  respectively, if we rule out problems of coordination, the utility of risky (safe) entrepreneurs is maximized when all of them participate in the MGS, regardless of the number of safe (risky) entrepreneurs already in the MGS. Therefore, we can substitute for  =  = 1 into p␪ and ˜ easily verify that Urs (LM ) ≤ Ur (LP ) only if B ≥ B. ˜ Urs (LM ) > Ur (LP ) and risky investors find Case II. When B < B, it profitable to join an MGS with safe investors. The latter, however, gain from participating in an MGS with risky investors only ˆ if Usr (LM ) > Us (LP ) = 0, that is, recalling that  =  = 1, only if B ≥ B. ˜ Therefore, a non-assortative equilibrium can exist only if Bˆ < B, that is if (1 − ) < W/CsS .



The economic intuition of Proposition 1 is the following. In a rationing equilibrium, safe entrepreneurs cannot individually apply for a loan and lose the private benefit B. By establishing an MGS they can obtain credit and the benefit B with probability q = W/CsS . For risky investors, instead, joining the MGS means accepting a positive probability of being rationed and incurring the loss of the benefit of becoming an entrepreneur but gaining the opportunity to share the risk of losing their wealth with the safe investors. When B is high, the expected loss of rationing outweighs the benefit of risk sharing and induces r-investors to borrow individually. In this case, an assortative equilibrium prevails with ˜ risky MGSs formed by only s-type associates (Fig. 2). When B < B, investors find it profitable to join an MGS with safe investors. However, in order for a non-assortative MGS to be formed, safe investors too must gain from participating in an MGS with risky partners.

This is the case if the incentive of having a positive probability of obtaining the private benefit of entrepreneurship is strong enough to outweigh the negative effects of sharing the credit risk with risky ˆ Obviously, the concurrent participation of partners B, i.e., if B ≥ B. risky and safe investors in an MGS is possible only if the threshold level of B which makes it profitable for safe investors to participate in a non-assortative MGS, is no higher than the threshold level of B which makes the participation of risky investors profitable (i.e., if B˜ ≥ Bˆ like in Fig. 2a). This condition is satisfied if the probability of obtaining the guarantee of the MGS, q = W/CsS , exceeds the share of risky partners in the MGS, (1 − ␪). ˜ if B˜ < B), ˆ r-type investors When B is less than Bˆ (or less than B, have an incentive to join an MGS in which safe investors participate, while s-type have no incentive to join an MGS with risky borrowers and thus the MGS cannot be formed (Fig. 2b). 6. Comparative statics and empirical implications Our theory suggests a number of empirical implications concerning the structure and performance of MGSs. First, loans that take advantage of the MSG’s guarantee exhibit, on average, a lower rate of default than individual loans. Proposition 2. Suppose that in the credit market a rationing equilibrium prevails and an MGS is established. The ratio of default on M = (1 − p )/(1 − p ) in MGS loans to default on individual loans is dss s r M the case of assortative matching and drs = (1 − p )/(1 − pr ) in the M < dM < 1. case of non-assortative matching with dss rs It is worth noting that the lower riskiness of firms belonging to an MGS is simply due to the fact that the guarantee society is joined by safe investors who would otherwise be excluded from the credit market, and not to the better screening and monitoring capacities of peers. Other implications can be figured out from the following com¯ , B˜ and Bˆ for the parative static results on the threshold values W existence of assortative and non-assortative MGSs. Lemma 4.

¯ ∂W ∂

< 0;

¯ ∂W ∂ˇ

< 0;

∂B˜ ∂

> 0;

∂B˜ ∂W

> 0;

∂Bˆ ∂

< 0.

Signs of partial derivatives reported in Lemma 4 have straight interpretations. First, the greater the share of safe entrepreneurs in the economy and the less costly it is for banks to recoup pledged collateral, the less likely it is that a credit-rationing equilibrium prevails and MGSs form. Second, where safe entrepreneurs are actually rationed, an increase in the share of safe entrepreneurs and in the collateralizable wealth (together with a reduction in collateral requirements), all make assortative MGSs less likely; however, the

Fig. 2. The space of equilibria.

G. Busetta, A. Zazzaro / Journal of Financial Stability 8 (2012) 15–24

greater the share of safe entrepreneurs in the economy, the greater is the likelihood of non-assortative MGSs being established. Now, if we reasonably assume that in backward regions ␪, ˇ and W are typically lower than in developed economies, whereas B are not lower13 , we can state the following testable proposition. Proposition 3. In backward regions: (1) the number of MGSs is relatively (with respect to the number of firms in the economy) higher than in developed regions; (2) MGSs usually have fewer associates than in developed economies; (3) the repayment rate of loans guaranteed by MGSs is relatively (with respect to the average riskiness of local borrowers) higher than in developed regions. In the light of Lemma 4, the economic intuition behind Proposition 3 is clear. First of all, in backward regions, where the average quality of entrepreneurs is lower, courts are less efficient and civil trials to recover collateral are longer and costlier, the inefficient credit rationing of safe borrowers is more likely and therefore the incentive to form MGSs is stronger and their number is greater than in well-developed regions. Second, since in backward regions the assortative matching equilibrium is more likely to prevail (recall that, from Lemma 4, in backward regions Bˆ is greater and B˜ is lower than in developed regions) with only safe investors having an interest to pool their wealth in a mutual society, in these regions MGSs usually have fewer associates and their loan-repayment rate is relatively much higher than that of other non-guaranteed local firms. Propositions 2 and 3 are broadly consistent with empirical evidence for Italy, where mutual loan guarantee schemes are widely in use and the differences in economic development between southern (the so-called Mezzogiorno) and centre-northern regions are very pronounced. For example, according to data reported in Columba et al. (2009, 2010), out of 1073 MGSs listed in the register of “Ufficio Italiano Cambi” (UIC – Italian Office of Exchanges) in 2004, 44% are located in southern, less developed regions, whereas the number of firms with fewer than 20 employees operating in the south amounts to only 27 of the national total. As a consequence, the number of MGSs per 10,000 firms is twice the number in centre-northern regions. If we focus on craft firms, we obtain similar figures: at the end of 2007, 47.4% of MGSs belonging to the Italian Federation of Craft Guarantee Societies (Fedart Fidi) were located in the South, while in these regions the number of firms listed in the official register of craft enterprises is only 25 percent of the total14 . Secondly, the average number of associated firms per MGS in the South of Italy is about one fourth of that prevailing in central and northern regions (Columba et al., 2009, 2010; Fedart Fidi, 2009). Similarly, the MGSs’ own funds and the outstanding guarantees in portfolio are far lower in southern MGSs than in those located elsewhere. Third, small firms guaranteed by an MGS have, on average, a rate of default that is about half that experienced by non-guaranteed small firms. However, even more interestingly, if compared with the average default rate on loans granted in the region, the rate of repayment is higher for southern MGS than for centre-northern MGSs. For example, according to Bank of Italy figures, the ratio of bad to total loans for craft enterprises is 4.8% in northern regions, 6.9 in central regions and 12.2 in southern regions. For craft firms

13 Once again, it is important to point out that in our model B reflects the private benefits that an agent would gain from being self-employed as an entrepreneur r elative to the expected benefits of being employed in alternative activities which can be very low in less developed regions, as is testified by the large latent desire expressed by people in these regions to start own businesses (Blanchflower et al., 2001; Zazzaro, 2002). 14 See Fedart Fidi (2009).

21

belonging to northern, central and southern MGSs the percentage of bad loans is 4, 2.7 and 4.2, respectively. Besides this descriptive evidence, the higher repayment rate of loans guaranteed by southern MGSs is also proved by the multivariate analysis presented in Columba et al. (2009), who analyze a large sample of 385,000 firms with less than 20 employees. Specifically, they estimate a probit model with fixed effect by sector of activity where the dependent variables analyzed are, alternatively, the probability that a firm is classified as non-performing by at least one lending bank and the probability that it is classified as non-performing between June 2004 and June 2005. They find that for firms guaranteed by an MGS the probability of default is 5% lower than for other firms, but for southern firms guaranteed by MGSs the decrease in the default probability is as high as 11%. 7. Model extensions 7.1. Public funding The model we have presented can be enriched in many directions by incorporating other elements that characterize real-world MGSs. An important extension concerns the role of public contributions to the guarantees fund of MGSs. Typically, the contributions of associate firms are only part of the MGSs’ capital, while the rest is provided by government institutions at the local and national level and by non-governmental organizations (Beck et al., 2010). For example, according to data reported by Gonzàles et al. (2006), in Europe 52% of the private loan-guarantee schemes benefit from public contributions and in half of these the majority of the guarantees funds is made up by public resources. With regard to MGSs, Columba et al. (2010) report that in Italy more than 10% of these societies receive direct contributions from the public sector, accounting for more than 50% of the total funds. In our model, the addition of public contributions to MGS capital has the effect of lowering the probability of an MGS member not receiving the guarantees and thus being credit-rationed. This makes it more worthwhile for risky borrowers to join MGSs, with effects on the nature of the equilibria which depend on the relative size of public and private contributions. Proposition 4. Let kp be the public contribution to the MGS guarantees fund. Assume that in order to obtain contributions from the public sector, MGS associates have to contribute a minimum wealth W < W and that associates and the public sector split the MGS losses according to their participation in the MGS guarantees fund −1 ˛ = w(w + kp ) and 1 − ˛, respectively. Case I: kp ≥ (CsS − W ). If W /CsS ≤ (1 − ps )/(1 − p ) safe and risky entrepreneurs always have incentives to form an MGS and a nonassortative equilibrium would prevail, for any B > 0; otherwise, if W /CsS > (1 − ps )/(1 − p ), safe entrepreneurs prefer to stay out ˆˆ and a non-assortative MGS from the credit market when B ∈ [0, B], with only risky borrowers may prevail. Case II: kp < (CsS − W ). If W/kp ≤ (1 − ps )(ps − p )−1 , then the  equilibrium is non-assortative for B ∈ [0, B˜˜ ] and assortative 

with only safe borrowers for B > B˜˜ . If Wna /CsS > [(1 − ps ) + q(ps − pr )][(ps − pr ) − q(ps − pr )]−1 ≥ W/kp > (1 − ps )(ps − p )−1 , then the equilibrium is assortative with only risky bor   rowers for B ∈ [0, Bˆˆ ], non-assortative for B ∈ [Bˆˆ , B˜˜ ] and 

assortative with only safe borrowers for B > B˜˜ Finally, if W/kp > [(1 − ps ) + q(ps − pr )][(ps − pr ) − q(ps − pr )]−1 the equilibˆ and rium is assortative with only risky borrowers for B ∈ [0, B] assortative with only safe borrowers for B ∈ [0, B∗ ], while no MGSs  are formed for B ∈ [B∗ B˜˜ ].

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Case III: (CsS − W ) ≤ kp < (CsS − W ). The space of equilibria will be those detected in cases I or II according to whether the optimal contribution of associates is such as to make q equal to or lower than 1. Proof. The proof proceeds as in Proposition 1, with the difference that the expected guarantee loss per associate is now (1 − pj )q˛CsS = (1 − pj )w and, hence, the utilities of joining the MGS are

⎧ M S ⎪ ⎨ Urr (LM ) = q[(1 − pr )CsS + B] − (1 − pr )w Uss (L ) = q[(1 − ps )Cs + B] − (1 − ps )w

M S ⎪ ⎩ Urs (L M ) = q[(1 − pr )CsS + B] − (1 − p )w

Usr (L ) = q[(1 − ps )Cs + B] − (1 − p )w

Case I. If the public contribution per associate is so high that all MGS associates have the opportunity to access the MGS guarantees fund regardless of their contribution (i.e., q = 1 for any w ≥ W ), associate firms will contribute the minimum wealth W. In this case, it is easy to verify that Urr (LM ) > Ur (LP ), Uss (LM ) > Us (LP ) and Urs (LM ) > Us (LP ) hold for any value of B, whereas Usr (LM ) > Us (LP ) only if B > Bˆ = (1 − p )W − (1 − ps )CsS . Case II. When kp < (CsS − W ), q < 1 for any w ≥ W . In this case, associate firms determine their optimal contribution to the MGS capital by trading off the effect on the probability to access to the MGS’s guarantee and the effect on the share of the MGS’s losses they bear. However, differentiating Uij with respect to w we have that Ur r, Us s and Ur s are non-decreasing with w and therefore the optimal private contribution in assortative equilibria with risky and safe borrowers is w = W . Therefore

⎧ q(1 − pr )CsS − (1 − pr )W ⎪ Urr (LM ) > Ur (LP ) iff B ≤ B∗ = ⎪ ⎪ 1−q ⎪ ⎪  ⎨ (1 − p )W ˆˆ S M P Usr (L ) ≶ Us (L ) iff

B≶B =

q

− (1 − ps )Cs

⎪ Uss (LM ) > Us (LP ) iff B ≥ 0 ⎪ ⎪ ⎪ ⎪ ⎩ U (LM ) ≶ U (LP ) iff B ≷ B˜˜  = q(1 − pr )CsS − (1 − p )W rs r 1−q

 By simple algebra, it is easy to show that B∗ < B˜˜ . Therefore, when substituting q(W + kp )/CsS in Usr , we have that when W/kp ≤ (1 − ps )(ps − p␪ )−1 safe entrepreneurs always have incentives to form an MGS, and equilibria are thus  either non-assortative, for B ≤ B˜˜ , or assortative with only

safe entrepreneurs participating in MGSs. By contrast, if W/kp > (1 − ps )(ps − p␪ )−1 , safe entrepreneurs have incentives   to form an MGS only when B ≥ Bˆˆ . In this case, if Bˆˆ < B˜˜ (i.e., if W/kp [(1 − ps ) + q(ps − pr )][(ps − p␪ ) − q(ps − pr )]−1 ), when B is less  than B˜˜ MGSs are formed exclusively by risky entrepreneurs, when

 B is greater than B˜˜ they are formed by safe entrepreneurs, while   when B ∈ [Bˆˆ , B˜˜ ] MGSs include both safe and risky entrepreneurs.   If Bˆˆ ≥ B˜˜ , MGSs include only risky borrowers for values of B lower 

than B∗ and only safe borrowers for B > B˜˜ ; when B is in the  interval [B∗ , B˜˜ ], risky borrowers have an incentive to participate in an MGS only if safe borrowers also participate, while the latter have no incentive to participate in an MGS with risky borrowers and therefore no MGSs can form. Case III. It follows straightforwardly from Case I and Case II.  Fig. 3 depicts the space of equilibria as B varies. The intuition is clear. Public contributions have the effect of reducing the expected losses for MGS associates, which can thus extract some rent, besides B, from borrowing through the MGS with the contract LM = LsS . When B is not very high, risky entrepreneurs may find it optimal to not borrow individually and participate in an MGS even if q < 1 (if

kp is great enough to make q = 1, the participation of risky borrowers in the MGS is always profitable). However, notwithstanding the additional benefits, safe borrowers may find it worth staying out of MGSs including risky borrowers. If the public contribution is a small part of the MGS guarantees fund, the negative effects of sharing the credit risk with risky partners may still outweigh the benefit of accessing the credit market and starting up an enterprise. On the whole, participation of the public sector in the MGS’s capital expands the space of non-assortative equilibria and opens the door to the formation of MGSs with only risky associates. An interesting, indirect confirmation of the negative impact of public contributions on the average riskiness of MGS member firms is provided by Columba et al. (2010), who document that in Italy firms affiliated to MGSs supported by local and national governments pay, ceteris paribus, interest rates 13 basis points higher than firms in non-publicly funded MGSs. 7.2. Other extensions The model of MGSs we have presented is static in nature, assuming that loan contracts and bank-firm relationships can only last one period. In fact, banks tend to develop repeated interactions with borrowing firms over time, by lending on a relational basis. In this way, they mitigate problems of asymmetric information, but also increase the risk of being locked into the relationship. The informational and lock-in effects of long-lasting relationships have the opposite influence on guarantee requirements: on the one hand, the longer the relationship the lower the borrower’s riskiness and the less the need to secure the loan; on the other, banks have incentives to increase collateral and personal guarantee requirements to relationship borrowers in order to increase the seniority of their loan, strengthen their bargaining power and soften the threat of being locked in15 . To the extent that the informational benefits dominate the lock-in effects, we might expect that over time safe associates would receive lower collateral contracts per se and tend to abandon participation in MGSs or that safe MGSs (i.e., those formed by safe associates) supplement the core function of guarantee provider with other functions. The empirical implications are that old associates would be riskier than their young counterparts – i.e., that the rate of loan repayment of old associates would be lower than that of young associates – and that MGSs with a higher rate of good loans (i.e., a higher solvency rate) would supply their associates with more services. Another important question in a multi-period context is collateral renegotiation. As we stated above, each MGS signs contractual agreements with a number of banks to which their associates may apply for a loan. This implies that each bank counts among its customers more than one associate belonging to the same MGS. The point is that the incentive for a bank to call in the MGS’s guarantee in the event of insolvency of one of its own borrower-associates may depend on the number of MGS associates who borrow from that bank. When such a number is large, the bank might be willing to forgo the acquisition of the guarantee and renegotiate the loan contract in order not to reduce the guarantees fund of the MGS and the opportunity to lend to good associate firms. In this case, the implication is that the greater the share of an MGS’s associates borrowing from the same bank, the lower would be the rate of guarantee payments for that MGS.

15 Empirical evidence mirrors the conflicting theoretical predictions: some studies document a negative association between collateral and the duration of the lending relationship (Berger and Udell, 1995; Jiménez et al., 2006; Bharath et al., 2009), others a positive association (Elsas and Krahnen, 2002; Ono and Uesugi, 2009) and others a mixed association depending on whether the guarantee is real or personal (Pozzolo, 2004; Steijvers et al., 2010).

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23

Fig. 3. The space of equilibria with public contributions.

8. Conclusions In many countries, an increasing number of small and micro enterprises are affiliated to MGSs and gain access to bank loans thanks to the collective guarantee granted by such institutions. The role of intermediary and development agent which MGSs play in the economy is especially important during downturns, such as the one we are currently experiencing (AECM, 2010). The MGSs play fundamental informative and bargaining functions in credit markets. First, MGSs screen and monitor associate members, helping banks to overcome information asymmetries at a lower cost. Second, MGSs provide associates with extra bargaining power against the bank. By offering banks the opportunity to operate with a large number of selected and guaranteed borrowers, MGSs are in the position to subscribe, on behalf of their associates, to loan agreements at more favourable conditions than those each single associate could obtain on the credit market by themselves. However, neither the informative nor bargaining functions form part of the typical activity of MGSs which consists of providing

guarantees to associate enterprises. Indeed, the former functions could be carried out by institutions other than MGSs, which do not grant collateral, like rating agencies, associations of category or chartered accountants. In this paper we advanced a theory to rationalize the existence of MGSs, focusing on their distinctive function of pledging collateral for loans granted to their members. The basic intuition is that the motivation for the existence of MGSs lies in the inefficiencies created by adverse selection, when borrowers do not have enough collateralizable wealth to satisfy collateral requirements and induce self-selecting contracts. In this setting, we view MGSs as a wealth-pooling mechanism that allows otherwise inefficiently rationed borrowers to obtain credit. Despite abstracting from any peer selection and peer monitoring mechanisms, we find that MGSs may be characterized by assortative matching with only safe borrowers, when the MGS is exclusively funded by their associates, or with only risky borrowers, when the public sector contributes to the guarantees fund.

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