Financial inclusion of vulnerable households through Savings and Borrowing Groups: Theory and experimental evidence from Uganda

Transcription

1 Financial inclusion of vulnerable households through Savings and Borrowing Groups: Theory and experimental evidence from Uganda Alfredo Burlando and Andrea Canidio PRELIMINARY AND INCOMPLETE. This version: March 2, Abstract Savings and borrowing groups (SBGs) are bringing nancial inclusion to millions of unbanked people in developing countries. However, their ability to meet the nancial needs of the poorest members of local communities remains unclear. In this paper, we rst develop a model of SBG. We use the model to describe individual behavior and individual welfare as a function of the ability to save and borrow of other groups' members. We argue that including a person with a low ability to save imposes a negative externality on the group when the funds available to the group are scarce, and a positive externality when funds are in excess of the demand for loans. We test the model using data from an evaluation of a nancial inclusion program in rural Uganda, where we exogenously changed the proportion of vulnerable participants with low ability to save in some newly created groups. We show that having members with a lower propensity to save depresses borrowings from other members of the group. This result suggests that groups are resource constrained, and that vulnerable members are more likely to be rationed out of loan relative to the rest of the group. JEL classication: O12, O16 Keywords: Savings and borrowing groups, Savings groups, Financial inclusion, Local nance, VSLA, Self-help groups. We are grateful to SCORE's chief of party Massimo Zucca, as well as to Patrick Walugembe, Noel Nakibuuka, John Paul Nyeko, Michael Muwairwa, Ramadhan Kirunda, and all the sta at FHI360, AVSI, CARE, and TPO for their support in the design of the intervention, implementation of the intervention, and data collection. We received outstanding research assistance from Derek Wolfson, Biraj Bisht, and Attila Gaspar, for which we are extremely thankful. We beneted from comments and suggestions received from the participants to the 2014 GDN Workshop in Prague and the 2014 Northwest Development Workshop. Finally, we acknowledge the nancial support of USAID (through project SCORE), CERGE-EI Foundation under a program of the Global Development Network (Regional Research Competition), Central European University (Research Support Scheme), and University of Oregon. All opinions expressed are those of the authors. Department of Economics, University of Oregon, Eugene, OR , USA, burlando@uoregon.edu. Department of Economics, Central European University, Nádor u. 9, 1051 Budapest, Hungary; canidioa@ceu.hu. 1

2 1 Introduction 2 1 Introduction To this day, lack of access to nancial services is a key roadblock for the socioeconomic development of poor rural households in large parts of the world. In this paper, we study the ability of savings and borrowing groups (SBGs) to ll this gap and bring nancial inclusion to poor vulnerable households who are usually not reached by traditional banking or micronance interventions. 1 SBGs are spreading extremely fast in sub-saharan Africa and elsewhere, partly because they can be set up and maintained with minimal outside intervention. In 2014, an estimated 10.5 millions households are members of SBGs, a tenfold increase relative to However, the ability of a SBG to provide nancial services to its memberand especially to those who would otherwise be unable to access formal savings and borrowingdepends crucially on the group composition. Well-functioning SBGs require a membership that is able to save, to borrow, to utilize the borrowed funds, and to repay the group. In addition, the composition that is better suited to provide nancial services to the most vulnerable members of a community may be very dierent from the composition preferred by the better-o part of the community. Understanding how the group composition aects savings, borrowing, and the welfare of the groups' members, is fundamental in understanding how and if SBGs can be an eective tool for nancial inclusion. In this paper, we study theoretically and empirically the eect of SBGs composition on its members behavior and welfare. The kind of group we are interested in modeling is commonly found in sub-saharan Africa. SBGs are typically composed of twenty to thirty members who save and borrow from the group. Individual savings are accumulated on a weekly basis in a common pool stored in a safe box, and lent out to requesting members over the group's operating cycle (usually one year). Loans are paid back to the group with interest, which is decided by the group at the beginning of the cycle. At the end of the operating period, all funds in the safe are shared among the group's member in proportion to the amount saved during the period of operation. To start, we build a theoretical model representing the functioning of a SBG. We use the model to study how the propensity to save and borrow of the group's members shape the individual saving and borrowing decisions, as well as the collective performance of the group. In line with how SBGs operate, we assume that the interest rate on loans is established by the group at the beginning of the cycle and is taken as given. The return on savings, instead, is determined ex-post (at share out) and is equal to the total interest-rate payments collected by the group divided by the total savings collected. The members of the group save and borrow from the group taking as given the return on savings, the cost of borrowing, the availability of funds within the group and 1 Dierent papers use dierent names to denote SBGs, partly because SBGs can have slightly dierent rules of operation. See Section 2 for more details. 2 Currently, 1.2 million people belong to SBGs in Uganda, where we conduct our intervention. These statistics are taken from the Savings-Led Working Group (SLWG) of SEEP. See

3 1 Introduction 3 the availability of investment opportunities outside of the group. The return on savings is then determined in equilibrium, butcruciallyit may fail to equate demand and supply for funds. As a consequence, within the group, funds may be in excess or may fall short of the demand for loans. The main result we derive is that savings and borrowing decisions by one member of the group impose an externality on other members of the group. Crucially, whether this externality is positive or negative depends on whether the demand for loans is rationed, that is, whether every person who wishes a loan of a certain size can get it. When there is no rationing, the supply of funds available exceeds the demand for loans, and every additional dollar saved reduces the return on savings for everyone else. This negative externality causes the other members of the group to reduce their savings. An agent who increases her borrowing from the group, on the other hand, causes an increase in the equilibrium return on savings, which in turn increases savings by everyone else. However, when the group does not generate enough funds to satisfy the demand for loans, the sign of the externalities generated by an increase in savings or borrowing are reversed. In this case, additional contributions to the group create a positive externality on potential borrowers, because rationing is eased and more people are able to meet their borrowing needs, while additional demands for funds create a negative externality as they worsen rationing. Our theory has important implications for the nancial inclusion of the very poor, as the model suggests that including vulnerable members in a savings group will aect the performance of the group and its ability to provide nancial services to its members. The sign of this eect depends on whether this extra member is a net borrower or net saver, and whether the group is rationed out of funds or has excess funds. In the context of the savings groups we analyze in Uganda, we nd that, compared with the average member of the group, vulnerable households have a lower ability to save but share the same demand for loans. Hence, the inclusion of a vulnerable household into a group will reduce the supply of funds. If this inclusion occurs in groups that would have been otherwise rationed, this inclusion is welfare decreasing. If instead the group is not rationed, then this inclusion is welfare increasing. We evaluate the theory using data from an RCT we conducted in Uganda. We exploit a preexisting program that actively enrolls the most vulnerable members of a community in SBGs. This program identies members of the community with signicantly lower socioeconomic characteristics, and organizes new savings groups that include those identied members with other, self-selected members of the population. To study the implications of this inclusion of vulnerable populations, in our experiment we randomly assigned some identied vulnerable participants to groups that had many other vulnerable members, while others were assigned to groups with few vulnerable members. In other words, we created exogenous variation in the vulnerability prole of peers for a random sample of vulnerable group members. The empirical evidence points to three main results. First, aggregate savings and borrowings

4 1 Introduction 4 are signicantly higher in groups with fewer vulnerable members compared to groups with a majority of vulnerable members. Total savings in the less vulnerable groups was, by the end of the rst cycle, 30% larger than the comparison. We nd no evidence that the intensity of use of resources diered between the two types of groups, suggesting that the returns on savings was similar across groups with dierent vulnerability proles. Second, the vulnerable themselves save and borrow less when placed in more vulnerable groups. Again, the magnitude of the dierence in savings and borrowing is signicant: the vulnerable enrolled in highly vulnerable groups save 20% less and borrow 45% less on average than those enrolled in less vulnerable groups. Since our vulnerable participants were randomly assigned to groups, this dierence in savings and borrowing is driven by the characteristics of their group. Third, savings and borrowing from other group participants does not vary signicantly with the treatment. That is, while vulnerable groups operate at a smaller scale, this seems to aect dierentially the vulnerable and the non-vulnerable. However, because there was no random assignment of non-vulnerable participants, it is hard to establish the extent to which this result is due to unobserved and systematic dierences in the demand to save or borrow for these members. The empirical results together with the theoretical predictions suggest that the groups we study are rationed of funds, and this rationing is less severe in groups with fewer vulnerable members. As a consequence, our model predicts that vulnerable households are better o when placed in groups with many non-vulnerable households. 3 Importantly, the penalty for being included in a vulnerable group does not seem to extend to the non-vulnerable population. This conclusion is relevant for the creation of SBG in areas where there is the possibility of including both vulnerable and non vulnerable households in the same SBG. It also suggests that SBGs created in areas in which the majority of the population is vulnerable may be more acutely unable to meet the demand for loans. The functioning of these groups can be improved by providing outside funds, as well as by changing the rules of functioning of the group so to encourage early savings (that can be lent out multiple times). The existing literature on savings and borrowing groups has largely focused on measuring the eect of SBG participation. For example, Beaman, Karlan, and Thuysbaert (2014) randomize at village level the creation of SBGs in Mali. They nd that treated villages have higher savings (+30%), borrowing, consumption smoothing, food security, livestock holding compared to control villages. They also report that the wealthiest member of each village tend to select into SBGs. Ksoll and Forskningsenhed (2013) nds similar results employing a similar research design. Bundervoet (2012) nds large eects of SBG participation on household welfare by randomizing the timing of the provision of the SBG training. Whereas these works establish that SBG participation is overall benecial to the households who choose to participate, our study is mainly concerned with the determinants of savings and borrowing behavior within the SBG. 3 We will be able to directly measure the welfare implications for the vulnerable once an in-depth endline data collection process is concluded.

5 2 Functioning of savings and borrowing groups 5 By investigating these incentives, we are able to show that the benet of SBG participation depends crucially in the composition of the groups. With this respect, we are close to Greaney, Kaboski, and Van Leemput (2013), who study theoretically and empirically the mechanism of group formation. Their main nding is that when the SBG training is paid by the group members rather than being provided for free, high-risk low-returns agents are driven out of the group, which improves the functioning of the SBG. Greaney, Kaboski, and Van Leemput (2013) abstract away from the specic rules determining the functioning of a SBG, and simply assume that the equilibrium return on savings is such that supply and demand for funds are equalized (i.e. an SBG is a local credit market with limited liability). Instead, we focus on the rules governing the functioning of an SBG, and on how these rules determine the return on funds, the behavior, and the payos of the group's members. At the same time, we abstract away from the determinants of group formation. More generally, our paper is related to the literature on nancial inclusion. Several existing papers demonstrate that mocroentrepreneurs benet from access to nance (see, for example, Banerjee, Duo, Glennerster, and Kinnan, 2013) and access to a safe way to store their money (see, for example, Dupas and Robinson, 2013). For other subpopulations, the evidence remains mixed, with some evidence of overindebtness from micronance in Bangladesh (Karim, 2011) but not in Mexico (Angelucci, Karlan, and Zinman, 2015). Finally, our paper also contributes to the literature on peer eects in nancial markets, as it quanties, in the particular context of savings groups, the importance of the peer group in generating nancial outcomes (Feigenberg et al, 2014). In our experiment, SBGs with dierent composition are dierentially able to satisfy the demand for loans of its members, but are equally able to provide a safe way to store funds. Therefore, vulnerable households enrolled in SBG with dierent vulnerability proles are dierentially able to access credit from the group. By comparing the welfare of vulnerable households enrolled in dierent types of SBGs, we can measure the eect of extending credit to vulnerable households, which are usually not reached by micronance interventions. The rest of the paper proceeds as follows. Section 2 provides some background on SBGs, and describes in details their rules of operation. Section 3 describes and solves a theoretical model of SBG, and derive a set of comparative statics that will be relevant for our empirical analysis (that we summarize at page 16). Section 4 describes our intervention. Section 5 presents our empirical results. Unless otherwise stated all mathematical proofs and all statistical tables are in appendix. 2 Functioning of savings and borrowing groups We dene SBGs as a formal association with limited membership (typically around participants) which provides a source of interest-bearing savings and self-generated credit to its members. There are many types of SBGs in operation, each following somewhat dierent rules.

6 2 Functioning of savings and borrowing groups 6 The most common type is the Village Savings and Loans Association (VSLA), which was rst introduced by CARE International in Niger in Other NGOs have introduced their version of savings and borrowing groups, such as Oxfam's Saving for Change groups and Catholic Relief Services' Savings and Internal Lending Communities. These models are similar to each other with respect of the basic functioning of the groups, but dier in how training is organized, how records are kept, the level of involvement of NGOs in the workings of the groups (see Ashe, 2009, Vanmeenen, 2010). The data used in this paper originated from VSLAs, but our theoretical and empirical contribution extends to the most common types of SBGs. Savings and borrowing groups generally operate in the following way. First, an association organizer recruits potential members within a community. 4 Participants attend weekly training meetings for a period of one month, during which the association is explained. Following the training period, the group agrees on the bylaws of the association, which include the maximum weekly savings allowed, the internal interest rate charged on loans and the length of the saving cycle. Savings contributions are measured in shares, and the participant can deposit in the account up to a multiple of the share value (in the groups we study, the multiple is ve). Savings are kept in a metal safe box, which is open only when the group is in session and is secured with multiple locks whose keys are given to dierent members of the group. Borrowing from the safe box takes place some time (typically three months) after the beginning of the savings period. Each participant is limited to borrowing up to three times the amount they saved until that point. Loans are extended only if the group agrees on the purpose of the loan, and subject to a resource constraint (the amount available in the safe box). Loans must be generally repaid within three months; the interest is calculated on the outstanding loan amount after one and two months from the date the loan was given out; no minimum weekly contributions are generally required. receive another loan. Once the loan is paid back, the borrower is eligible to Loan disbursements end some time before the end of the cycle, and all repayments must occur by the end of the cycle. The last meeting is devoted to the share out: the contents of the safe box are emptied and divided among the members of the group in a way that is proportional to the amount each person saved. A new cycle is eventually started. Between the end of the old cycle and the beginning of the new cycle the group composition may change and the rules governing the groups may be modied. 4 SBGs are often initiated by NGOs: there are xed costs that a group needs to pay (such as books required to register the transactions and the safe where the funds are kept), and the group requires intensive training. Once they are set up, SBGs can be sustained by members only, without the need of continuous NGO support.

7 3 The Economics of a Savings and Borrowing Group: a Theoretical Model 7 3 The Economics of a Savings and Borrowing Group: a Theoretical Model We start by developing a theoretical model of SBG functioning. We assume that the group is eective in generating sucient peer pressure and preventing both voluntary or involuntary defaults. We focus on how the rules governing a SBG shape the incentive to save and borrow of each member of the group. We show that, despite the absence of moral hazard or adverse selection, the rules governing a SBG can generate an inecient supply of funds, which can be in excess or fall short of the demand for loans. We then describe how each member's welfare changes when the composition of the group changes. Consider a group composed of n individuals. The timing of the game is the following: In period 0, the group meets and agrees on the interest rate that will be charged on loans r and on the maximum savings per period s. In periods 1 each member i: rst receives w i, which is a per-period wage (i.e. non-investment income generated outside of the group). then saves s i, then borrows b i, then invest y i in an outside project. then earns f i (y i ) from the funds invested outside of the group, where f i () is continuous and strictly concave. 5 nally repays (1 + r)b i to the group, saves a i 0 outside of the group, and consumes the rest. In period 2, the total money generated by the group is redistributed to the group members in proportion to the amount saved. We allow f i (y i ) to be stochastic, but we assume that the randomness is resolved at once after the investment level y i is set. Instead, we assume that w i is deterministic. 6 Note also that f i (0) can be nite and heterogeneous across agents, which implies that the decision to be a net borrower or net saver depends not only on the initial wealth level of the agent, but also on other characteristics which we do not model. We also assume that the length of the cycle is xed to 1 period, and therefore abstract away from issues related to the time prole of savings and borrowing (and 5 The assumption of concavity allows us to show the existence of the equilibrium of the game. The reason is that, if f i() is locally convex, then optimal savings and borrowing may be a non-convex correspondence, which would prevent us from invoking standard xed point theorems. However, unless otherwise mentioned in the text, all our resultsbeside existencehold true also when f i() is locally convex. 6 Under this assumption, in period 0 each agent can perfectly forecast the demand for loans in period 1, which will help us solve for the voting game.

8 3 The Economics of a Savings and Borrowing Group: a Theoretical Model 8 the possible ineciencies arising from it). Finally, by assuming that the return on the outside project f i (y i ) is independent on the group composition, we are eectively abstracting away from other relevant channels through which group composition may impact individual welfare, such as learning from peers, changes in the social network structure, and aspirations. Independently on the rules agreed upon in period 0, no member is allowed to borrow more than 3 times the total amount saved with the group up until that period, and therefore b i 3s i, (1) which we call leverage constraint. In addition, the agent can save with the group up s, so that s i min{w i, s}, (2) Note that the timing described above implies that y i b i + w i s i. (3) In other words, the resources available for investment are equal to the own funds minus the savings with the group, plus borrowing with the group. Finally, consumption at the end of each period is: c i = f i (y i ) y i rb i + w i a i s i, (4) which is the agent's budget constraint. We assume that consumption must be non-negative for every realization of f i (y i ). 3.1 Individual problem Under these assumptions, member i decides how much to save and borrow within the group by solving the following problem: m = (s i + s i )(1 + R) + a i s.t. b i C i equations 1 to 4 max b i,s i,y i,a i {E [u i (c i )] + β i m} aggregate resources constraint where β i 1 is an agent-specic discount factor, u(.) is a strictly increasing and concave function, and m is the amount of money available to the household at the end of the cycle. We assume that m enters linearly into the agent's utility function, and hence represents the

9 3 The Economics of a Savings and Borrowing Group: a Theoretical Model 9 continuation value corresponding to a given amount of money received at share out. 7 Finally, we implicitly assumed that the resources saved outside of the group do not generate any return. The term C i is the cash available to member i of the group at the beginning of each period, dened as C i = s j b j. j j i The term R is the implicit return on savings, and is given by the total amount of cash available to the group at the end of the cycle divided by the total amount saved within the group: R = r B S, where B = i b i and S = i s i are aggregate borrowing and savings for given borrowing and savings prole. Note that, by denition, R r. We conclude the description of the model by introducing our main assumption: Assumption 1. The return on savings at the end of the cycle R and the funds available to each member of the group in each period C i are taken as given by the group members but are determined in equilibrium. In other words, the group members fail to anticipate that by increasing the amount saved (or borrowed) they will aect the return on savings and the availability of funds for the entire group. As a consequence, we can treat the return on savings and the funds available to the group in each period as equilibrium quantities. 8 Call s i (R, C i ) the optimal savings and b i (R, C i ) optimal borrowings of agent i in period t. Lemma 1. s i (R, C i ) and b i (R, C i ) are upper hemicontinuous and convex valued for all R and C i. In addition, s i (R, C i ) is weakly increasing in R. If the aggregate resource constraint is binding b i (R, C i ) is weakly increasing in C i. If the aggregate resource constraint is not binding, s i (R, C i ) and b i (R, C i ) are independent on C i. Note that, whereas the supply for funds is increasing in R, the demand for loans may be somewhere increasing and somewhere decreasing in R. It may be increasing because an agent needs to save if she wishes to borrow, and therefore, conditional on being a net borrower, increasing the return on savings decreases the cost of borrowing. However, the demand for loans 7 Our results are unchanged if the utility of cash at share out is also curved, provided that it is less curved than a logarithmic function, so that s and R remain complements. 8 Given that the group is large, the incentives to inuence the return on savings and the resources available to the group by setting a specic s i or b i are likely to be negligible. Note also that all our results are robust to assuming that the aggregate resource constraint is b i αs i + C i, and C i = j i sj + (1 α)si j i bj, where α is the amount of an agent's own savings that this agent expects to be able to borrow back from the group. The parameter α should depend on the rationing mechanism employed by the group (see Section 3.2).

10 3 The Economics of a Savings and Borrowing Group: a Theoretical Model 10 may be somewhere decreasing if, as R increases, an agent switches from being a net borrower to being a net saver. Note also that, when the resource constraint is binding for one member of the group, it is also binding for all members of the group. However, as we discuss more in details in Section 3.2, the fact that the aggregate resource constraint is binding does not imply that all members cannot meet their demand for loans. It may be the case that some members can fully meet their demand for loans, while the burden of rationing falls disproportionately on some other members. We say that a member is rationed out if her demand for loans is strictly increasing in C i. Hence, if additional resources are introduced into the group, those who are rationed out increase their borrowing, while those who are not rationed out are unaected. Lemma 2. If b i (R, C i ) > 0 and R < r then constraint 1 is binding, so that b i (R, C i ) = 3s i,s (R, C i,s ). If b i (R, C i ) > 0 and R = r then b i (R, C i ) = 3s i,s (R, C i,s ) maximizes the agent's utility. When constraint 1 is not binding, it is always possible to decrease savings and borrowing by the same amount and maintain the scale of the outside investment y i unchanged. If R < r, decreasing simultaneously borrowing and savings increases the resource available to the agent. Hence, 1 cannot be binding at the optimum. If instead r = R, simultaneously saving and borrowing allows the agent to shift resources between period 1 to period 2 (i.e. borrowing at cost r in period 1 to receive R = r in period 2). However, the same can be achieved by setting an appropriate a i. Hence, the agent is indierent between shifting resources between period 1 and 2 within the group (by simultaneously saving and borrowing) or outside of the group (by setting an appropriate level of a i ). Finally, note that if the agent breaks this indierence by borrowing the minimum amount from the group, then Constraint 1 must be binding also when R = r. Assuming this tie breaking rule, Lemma 2 implies that every member who borrows maintain a 1-to-3 ratio between savings and borrowing. Corollary 1. If R < r, then both b i (R, C i ) and s i (R, C i ) are functions. Clearly, for every agent and every R, r, C i, there is a unique investment level y i that maximizes the agent's utility. The proof of Lemma 2 shows that, if an agent is a borrower and R < r, then there is a unique combination of s i and b i that achieves y i at the lowest cost. If, instead, the agent does not borrow from the group, again this agent cannot do better than invest in y i and save the remaining funds with the group. 3.2 Rationing mechanism. Before solving for the equilibrium of the model, we need to discuss how C i,s is determined. In this section, we assume that in each period, each person announces her demand for loans, and the group allocates the available funds according to a rationing mechanism.

11 3 The Economics of a Savings and Borrowing Group: a Theoretical Model 11 According to our direct observation (and in line with the empirical results discussed in section 5.3.5) the groups we study seem to give priority to individuals based on their cumulative savings with the group. Not only, the burden of rationing seems to be uneven, in the sense that some members may be able to fully satisfy their demand for funds while others are rationed out. It is important to note, however, that the rationing mechanism is not part of the ocial rules adopted by the group, nor it seems to be the outcome of an explicit choice. From the theoretical point of view, we will simply assume that the rationing mechanism adopted by the group satises some desirable properties. We then discuss whether and under what condition some well-known allocation rules satisfy our assumptions. For the remainder of the paper, we assume that the rationing mechanism adopted by the group is: Resource monotonic: for given r, s and R, increasing the funds available to the group weakly increases the amount borrowed by each member, Pareto ecient: the allocation of funds induced by the mechanism is never Pareto dominated by another feasible allocation, Strategy-proof: no member has an incentive to misreport her demand for funds. In general, whether a given rationing mechanism satises the above three properties depends on the member's preferences over the amount to borrow. For example, a large literature has investigated allocation mechanisms in the context of single peaked preferences, arguing the merits of the so-called uniform rule. This rule amounts to imposing an upper bound on the level of borrowing achievable by each member. If any member borrows less than the upper bound announced (because her peak is below the upper bound), the remaining resources are distributed among the other members using again the same mechanism. Kbrs (2003) consider an allocation problem with single peaked preferences and free disposal (i.e. not all resources need to be allocated), and shows that the uniform rule is the only strategy-proof mechanism that satises eciency, no-envy, and is resource monotonic. 9 It is easy to see that, in our context, preferences are single peaked (and the results in Kbrs (2003) apply) because the return on the outside investment f i (y i ) is strictly concave for all i. Remark 1. By a direct application of Kbrs (2003), the uniform rule is the only rationing mechanism that is resource monotonic, Pareto ecient and Strategy proof. Moreover the uniform rule is also envy free. It is interesting to note that, if we relax our assumption on f i (y i ) and allow some convexities in the outside investment, the uniform mechanism may fail to be either ecient or resource 9 A rationing rule satises no-envy if for every announcement prole, the allocation implemented by the mechanism is such that no group member wants to swap what she received with what some other group member received. For a review of this literature and the formal denition of these properties, see by Thomson (2014).

12 3 The Economics of a Savings and Borrowing Group: a Theoretical Model 12 monotonic. For example, suppose that all investment opportunities are discrete, in the sense that they require a xed investment level to deliver a given return. It follows that an agent's utility may have local maxima, which emerge whenever extra funds allocated to the agent are not sucient to start a new investment opportunity, but need nonetheless to be repaid with interest. When resources are scarce, an agent may borrow little and settle for a local maximum. As aggregate resources increase, some agents may discretely increase the amount borrowed with the group, potentially decreasing the resources available to other members of the group. A second widely-studied rule that can applied to our context is serial dictatorship, in which all agents are ordered and each of them can, in turn, choose how much to receive from the available funds. Serial dictatorship is appealing because it is ecient, strategy proof and satises resources monotonicity whenever two conditions are met: when indierent between multiple borrowing levels, members demand the lowest level. Consider the list of dictators, 1, 2,...k, where dictator 1 chooses before all other dictators (and so on). If the k th dictator borrows a positive amount, then all k 1 dictators fully meet their demand for loans. i.e. they would not borrow more even if more resources were available. To understand better the last point, suppose that an earlier dictator leaves funds to the following dictator, who then uses these funds. The above condition rules out situations in which an earlier dictator can only invest in projects requiring an upfront investment larger than the available funds (and therefore leaves funds on the table), while the later dictator can invest in projects that require an upfront investment lower than the available funds. This condition is always satised if the return on investment is continuous, smooth and concave. It is also satised if all investment opportunities faced by all agents have the same minimum investment level (but may deliver dierent returns). To summarize, the uniform rule has very appealing properties if all f i (y i ) are strictly concave. In the presence of convexities, serial dictatorship is resource monotonic, ecient and strategy proof provided that the these convexities satisfy a regularity condition. Most of the results we will present in the remainder of the paper simply rely on the rationing rule being resource monotonic and ecient. Hence, for the most part we will abstract away from the specic rationing rule. Finally, note that whereas under the uniform rule rationing operates exclusively through the intensive margin of borrowing, under sequential dictatorship rationing involves mostly the extensive margin. We will return to this dierence between the two rules when discussing the empirical evidence. SOMETHING ABOUT RATIONING AND VOTING

13 3 The Economics of a Savings and Borrowing Group: a Theoretical Model Equilibrium Despite being taken as given by the group's members, R and C i are determined in equilibrium. In particular, the equilibrium R = R solves: R S(R ) = rb(r ) (5) where S(R) and B(R) are the aggregate demand and supply of funds, which depend on R because the individual demand and supply depend on R. Note that, whereas the individual demand and supply for funds depend both on R and on C i, the aggregate demand and supply for funds only depend on R. The reason is that, in the individual maximization problem, C i matters only if the aggregate resource constraint is binding. Furthermore, the aggregate resource constraint is either binding for everybody or not binding for anybody. Therefore, when looking at the aggregate, we can simply distinguish between R for which the aggregate resource constraints is binding and R for which the aggregate resource constraint is not binding. Whenever the aggregate resource constraint is not binding, aggregate borrowing depends on aggregate savings only through the equilibrium R. Instead, in periods in which the aggregate resource constraint is binding, aggregate borrowing depends on aggregate savings directly because B(R) = S(R). Distinguishing between periods in which the aggregate resource constraint is binding or not will be relevant when performing our comparative static analyses. For example, assume that a member of the group drops out and is replaced by another person with a higher propensity to save at every R. 10 If the resource constraint is binding, we can solve for the new equilibrium simply by shifting upward S(R). If instead the aggregate resource constraint is binding, then aggregate borrowing will also respond to an increase in overall funds available to the group. Proposition 1. An equilibrium R always exists. If β i is suciently small for all i, then the equilibrium is unique. If the unique R is strictly smaller than r, then the LHS of equation 5 crosses the RHS of equation 5 from below. Note that β i determines the sensitivity of the borrowing decision on the return on savings. If this sensitivity is low the cost of borrowing is determined mostly by r and not by R. Hence, as β i decreases, the elasticity of aggregate borrowing with respect to R decreases, and multiple equilibria disappear. In what follows, we always assume that R is unique for all r and s. Finally, knowing how RHS and LHS of equation 5 intersect will be relevant when performing the comparative statics. 10 If the rules of the group are chosen by majority voting, then changing the composition of the group does not aect the rules adopted by the group as long as the "median" member of the group does not change (see Section 3.5). Hence, we can analyze changes in the demand and supply of funds due to a change in the group's composition keeping the rules adopted by the group constant.

14 3 The Economics of a Savings and Borrowing Group: a Theoretical Model Comparative statics for given rules adopted by the group. Increase in aggregate savings Suppose that the aggregate savings S(R) increases. This could be the case if, as discussed earlier, a member of the group who only saves drops out of the group and is replaced by another agent who also only saves but has a larger propensity to save at every R. Clearly, if the resource constraint is never binding, then, for given R, the increase in aggregate savings has no eect on aggregate borrowing. Hence, the behavioral responses of the group's members is driven by the fact that, by proposition 1, when S(R) shifts upward R decreases. Corollary 2. If the aggregate resource constraint is not binding, an increase in S(R) leads to lower R and lower individual savings. Everybody in the group is worse o. If instead the aggregate resources constraints is binding, adding resources to the group has also a direct eect on the borrowing levels that are possible within the group. Corollary 3. Suppose the aggregate resource constraint is binding, and that S(R) increases. Furthermore, suppose that the aggregate resource constraint is binding also at the new S(R). Each member's borrowing (weakly) increases and everybody in the group is (weakly) better o. The return on savings is xed at R = r. The above corollary follows from the fact that as long as the resource constraint is binding B(R) = S(R) and R = r. Hence, increasing S(R) has no eect on the incentive to save (and on the welfare of savers), but it allows borrowers who are rationed out to increase their level of savings. Corollary 4 and 3 illustrate one of the main results of the model: that exogenously increasing the funds available to the group (for example, by replacing one of the members of the group) will impose an externality on the other members of the group. The key determinant of the sign of this externality is whether the group is resource constrained. Quite intuitively, when the resources within the group are scarce, adding more resources is benecial to the other members of the group. More interestingly, when the group is not resources constrained, adding resources to the group hurts everybody else in the group because it decreases the return on savings. Increase in aggregate borrowing We can similarly analyze what happen when the group composition changes in a way that increases aggregate borrowing leaving unchanged aggregate savings. This would be the case if, for example, a net saver is replaced with a net borrower who saves the same amount at every R, but uses these savings to actually borrow funds from the group. If the aggregate resource constraint is not binding, by Proposition 1 the eect of an increase in aggregate borrowing is an increase in R, leading to the following corollary.

15 3 The Economics of a Savings and Borrowing Group: a Theoretical Model 15 Corollary 4. If the aggregate resource constraint is not binding, then an increase in aggregate borrowing leads to an increase in R, higher individual savings and borrowing. Everybody in the group is better o. If instead the aggregate resources constraints is binding, then the impact of an increase in aggregate borrowings depends on how the funds are rationed among borrowers. For example, if the new demand for funds goes completely unmet, then the existing members of the group are indierent to the increase in the demand for funds. If instead the addition of a borrower decreases the amount of funds available to the other borrowers, then the existing borrowers are made worse o by the increase in the demand for funds. Corollary 5. If the resource constraint is binding, an increase in the demand for loans has no eect on R. As a consequence, everybody in the group borrows (weakly) less and everybody is weakly worse o. Overall, increasing aggregate borrowing and increase savings have opposite eects on the group. When the aggregate resources constraint is binding, increasing savings makes the group better o while increasing borrowing makes the group (weakly) worse o. When the aggregate resource constraint is not binding, increasing savings makes the group worse o, while increasing borrowing makes the group better o. 3.5 Period 0: setting the rules of the group. In period 0, the choice of r and s is determined by two basic trade-os. For given R and given available funds, a higher r or a lower s will make everybody in the group weakly worse o. However, a higher r or a lower s may actually increase R, beneting everybody in the group. Furthermore, r and s have an additional eect on the availability of funds and on whether some borrowers will be rationed out. Crucially, each group member will solve these trade os dierently depending on their demand for funds and on the rationing mechanism. The period-0 voting game is problematic because, in general, preferences are not single peaked (neither over r nor over s) and a Condorcet winner may not exist. A group member may have a preferred r and s in case she is a borrower and a preferred r and s in case she is a pure saver (i.e. no borrowing). If a borrower, an agent is facing a trade o between availability of funds (which is increasing in r), and cost of borrowing. In general, an agent prefers the smallest r such that her demand for loans is fully met to any larger r (but may, in fact, prefer an even smaller one). If a pure saver, the agent prefers the r and s that maximizes R to any other r. Hence, an agent's utility may be rst decreasing and then increasing with r if the agent switches between being a borrower to being a saver. When preferences are not single peaked, the outcome depends on the details of the voting game being played, such as who can propose options for voting, how many voting rounds are

16 3 The Economics of a Savings and Borrowing Group: a Theoretical Model 16 allowed, how long can the voting period last, whether options that have previously been outvoted can be re-proposed, and so on. Because the voting procedure is not part of the model, each group is likely to have adopted a dierent voting game. We also note that, in our data, the strongest determinant of the rules adopted my the group is the identity of the organization forming the group, suggesting that most groups decided to adopt the default option proposed to them. Despite this diculties, we conclude the theoretical section by showing that, under some strong assumptions, the voting game has a unique Condorcet winner. Proposition 2. Suppose that, in period 0, each group member maximizes E [u i (c i )] subject to all the constraint presented in Section 3.1. There exists a Condorcet winner of the game, which is the r preferred by the member with the median peak over r, and the s maximizing the availability of funds for this r. It is reasonable to assume that, in period 0, all members of the group discount heavily the payo at share out relatively to the instantaneous payos earned while the group is operating, because the share-out date is suciently far in the future while the date at which each agent may borrow from the group is much closer. The proposition considers the limit case β i = 0 for all i, in which the utility at share out is completely ignored and the only determinant of the choice over r and s is the ability to borrow cheaply. Hence, for every r, everybody agrees that s should maximize the availability of funds. 11 When choosing over r, we have a standard voting game with single peaked preferences. 12 Empirical implications In our experiment, which we fully describe below, we exogenously varied the number of SBG members who belong to ultra-poor households (which we also call vulnerable households). The vulnerable dier from the non-vulnerable in a number of important characteristics, which will be described in greater detail in section However, for the purposes of our theory, the key observation is that vulnerable households save less than non-vulnerable households. Among other relevant dimensions, including demand for loans and likelihood to default on loans, the vulnerable and the non-vulnerable are statistically indistinguishable. Therefore, the more vulnerable households in a group the lower the supply of funds in that group. If the aggregate resource constraint is not binding, decreasing the funds saved with the group should lead to an increase in the return on savings, an increase in the level of savings, and higher overall welfare. If, on the other hand, the resource constraint is binding, the reduction in 11 Note the amount of cash available for borrowing may not be monotonic in s. For example, if the person saving the most is actually a net borrower, constraining this person in the amount she can save may generate more resources to the remaining members of the group. 12 Note that, in case an agent does not expect to borrow, she will be indierent over r and s. A Condorcet winner exists if agents who are indierent break their indierence appropriately.

17 4 The Intervention 17 savings exacerbates the scarcity of funds. Theoretically, we should expect borrowers to (weakly) decrease the amount borrowed. In addition, because of Lemma 2, those who decrease their level of borrowing should also decrease their level of savings. Interestingly, depending on the rationing mechanism, not everybody will be equally aected by the decrease in the available resources. In particular, we discussed the merit of two possible rationing mechanisms. Under a uniform rule, rationing occurs mostly through the intensive margin: for given r and s, everybody is able to borrow something if they wish to borrow. Alternatively, sequential dictatorship implies that rationing occurs mostly through the extensive margin, by determining who can borrow. Finally, we highlighted the diculty in reaching an agreement in period 0 over r and s. Because preferences are not single peaked, there is no simple way of aggregating the members preferences. Any outcome of the period-0 voting game depends crucially on how voting is conducted. 4 The Intervention 4.1 The context of the intervention: project SCORE Our research project is in partnership with three NGOs based in Uganda (AVSI, CARE, TPO) that provide services to 125,000 Vulnerable Children (VC) and their household in 35 districts across Uganda. Project SCORE (Sustainable COmprehensive REsponses for vulnerable children and their families) was launched in the fall of 2011 with a USD 9 million USAID grant. Project SCORE is a set of interventions implemented over a period of 5 years having the following goals: to identify vulnerable children and their families across communities in Uganda; to improve their socio-economic status, food security, and nutrition status; and to increase the availability and access to protective, legal and other critical services. A household is included into the program if identied as vulnerable, which is done using a short questionnaire about the socio-economic status and well-being of the household. Households identied as being vulnerable receive a number of interventions, including classes on advanced farming techniques, cooking, nutrition, business training and business development. The program oers no transfers to beneciary households, either in money or in kind. The most important intervention carried out under SCORE involves the enrollment of bene- ciaries into SCORE-created SBGs, which follow CARE's VLSA model. Such groups are formed by rst enrolling a core of SCORE recipients, and then enrolling other interested community residents. To ensure that vulnerable participants remain dominant in the group, SCORE requires that at least half the membership belongs to beneciary households. As a consequence, compared with SBGs supported by other organizations, SCORE groups are generally much more inclusive of vulnerable and marginal households, but have less freedom to self-select their members. Importantly, the three NGOs involved in program SCORE do not provide services directly.