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**The economics of lending with joint liability: theory and practice**

Maitreesh Ghatak , Timothy W. Guinnane

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**Some thought provoking facts………**

Given a concave production function lower capital implies higher MPK which implies higher r . So poor should get their start up capital. Among the poor are there exists most brilliant entrepreneurs of the world who can do wonders with very little amount of capital. The formal money lending institution says ‘no collateral, no business!’ Informal local moneylenders charge a very high interest for them and they still accept the loan.

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Getting into the model The poor don’t have any collateral and hence they have limited liability constraint. the amount of loan is very little and the administration cost is relatively very high for such small loans. Local moneylender has more information than the outside formal money lender (which from now we would call banks) about the borrower and he has to put a lot of effort to enforce agreement that increases the r. Without collateral the problems of Adverse Selection, Ex-ante and Ex-post Moral Hazard become more severe.

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Adverse Selection : Two types of borrower with two different success probabilities and different revenue: risky ( y , p ) and safe ( y , 1), where 0 p 1 and py = y . Borrowers need $1 for the project and project takes 1 month. The borrowers has no collateral so limited liability constraint applies. Gross cost of $1 for the bank is k>1 and y≥k Banks operative in a perfectly competitive framework and only break even. Bank knows that fraction q of total borrowers are risky but doesn’t know whether a borrower is safe or risky. Let Rb be the equilibrium gross interest rate. If q>0 then Rb >k , which implies there exists cross subsidization.

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Ex-ante Moral Hazard Again borrower has no collateral and require $1 for the project. Bank’s cost is k>1 and bank only breaks even. Borrowers cost of working is c and they can shirk. If they work probability of success is 1 else p(where p<1), return from a successful project is y, where y-c>k. The borrower works if ( y − R ) − c >p ( y− R) So at equilibrium R <y−(c/1−p). The efficient outcome is to lend when k< y− c. If y−c > k > y−(c/1−p) borrowers will shirk. Then bank wont lend at all.

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Ex-post Moral Hazard Borrowers need $1 for the project and the project is always successful yielding y. Borrower can pay R or can ‘run with the money’. If she runs, she gets y but forfeits her collateral w. Probability that the bank will verify the state is s. If the borrower pays then her net return is y − R. Instead if she runs then net return is ( 1− s)(y + w) + s.y . In case she doesn’t run R<s.w. Now if borrower has no collateral then R<s.0=0. Hence no lending will take place. To solve the problem one major breakthrough can be achieved by properly defining the property rights [De Moto (2000)].

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**The Model: Y takes two values, high and low and**

Output is high with probability Each project requires 1 unit of capital The lender needs to be paid back an amount r>1 per loan, principal +interest, on average. Borrowers will borrow only if their payoff exceeds the opportunity cost of their labor, The project returns of different borrowers are uncorrelated. All projects are socially profitable i.e. The borrower has no collateralizable wealth and there exists limited liability constraint.

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**There are four kinds of market inefficiency problem: Adverse Selection **

Individual liability A standard loan contract specifies a gross interest rate r which is the amount that the borrower must repay as the individual liability. Joint liability: If a borrower is willing and able to pay her loan but her partner is unwilling or unable to repay then the former must pay an additional amount c to the bank, where c can be interpreted as the net [resent discounted value of the cost of sacrificing present consumption in order to pay joint liability for a partner. If a group member defaults then the entire group will be denied future credit until the loan is repaid. There are four kinds of market inefficiency problem: Adverse Selection Moral Hazard Auditing Cost Enforcement

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Adverse Selection Borrowers are risk neutral and are of two types, safe (a) and risky (b) . Borrowers know each others type. With a project of type i ,output has two values and 0. The probability of high return is where, The expected payoff of a borrower of type i when her partner is type j from a joint liability Both types prefer safer borrower than riskier because For riskier borrowers > (1) And for safer borrowers > (2) as

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The safer borrowers dominant strategy is to thus make safer partner whereas for riskier borrower the safer borrower will charge compensation for the net expected loss of having riskier borrower but ;then < The riskier borrower will not go with a safer borrower. As a result group formation will show positive assortative matching under joint liability contract. By this property the bank can screen borrowers as the riskier would not accept an increase in the joint liability. If the bank offers two contracts, one with high joint liability and low interest rates and the other with low joint liability and high interest rate, safe borrowers will select the former contract and risky borrowers the latter.

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**Moral Hazard Individual liability:**

Output has two values YH with probability p and 0 otherwise and borrowers are risk neutral. Borrowers choose actions or level of efforts p [0,1] and they incur disutility cost 1/2γp2 which is unobservable to the bank. Social surplus pYH − 1/2γp2 is maximized at p=p*=YH/γ and assuming YH <γ we have interior solution. Hence with perfect information the bank charges r=ρ/p*(3) Individual liability: Under moral hazard the borrower takes r as given and chooses p to maximize her private profit, (4) The interest rate is like a tax on success hence p*= ,and p decreases with higher r.

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**Now substituting p=(YH −r)/γ from (4) in bank’s zero profit condition in (3) we get**

and taking the higher value of p,(as borrowers utility is higher for higher p and bank remains indifferent with the level of p) Joint liability: Under joint liability, when the borrower’s project fails her partner is liable for the amount c. If a borrower’s partner chooses an action p then the payoff function of a borrower who chooses an action p is and her best response function is Hence p and p are positively related.

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**Cooperative Joint probability:**

In case of non-cooperative decision making this will result in a symmetric Nash equilibrium, so p=p=(YH − r − c)/(γ − c). Now the bank’s zero profit condition becomes rp+cp(1−p)=ρ and substituting the value of r we get which is same as under individual liability. Cooperative Joint probability: If borrowers can contract p among themselves and can observe each others action perfectly and costlessly and choose project cooperatively then Substituting it in bank’s zero-profit condition we get And hence,

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Given the condition that YH<γ and as borrower cant pay more than his income so c<γ. This implies equilibrium value of p is higher under cooperative decision making than under individual liability. If monitoring is costly, then borrowers must be given incentives to monitor. Suppose that if a borrower chooses a level of monitoring a, then with probability a, she can observe the true action chosen by her partner, and with probability 1-a, she receives a completely uninformative signal. If the action undertaken by her partner is different from that agreed on, then she can impose a non-monetary punishment of S which stands for social sanctions. The cost of monitoring is given by the increasing and convex function M(a). Let pD (r,c) denote the individual best response of a borrower given that her partner chooses Then

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The borrowers incentive compatibility constraint to choose not deviate to pD given her partner chooses a monitoring level a and the agreed upon project choice be is given by, and as monitoring is costly this will held with equality. The borrowers incentive to undertake requisite level of monitoring given her partner chooses is or, equivalently, As long as social sanctions are effective enough i.e., S is large. or monitoring costs are low enough i.e is small., joint-liability lending will improve repayment rates through peer monitoring even when monitoring is costly.

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**Costly state verification**

All projects are identical and the only departure from the first-best is costly output verification. The outside lender has to pay γ to verify the return of each individual project. There are no problems of moral hazard, adverse selection or enforcement of contracts. The financial contract specifies three numbers: the transfer from the borrower to the bank when the project succeeds r , and the probabilities of an audit λH and λL,when output is high and low. Everyone is risk-neutral and there is a limited-liability constraint. The optimal contract then solves

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**Individual liabilty: The optimal contract then solves subject to**

1) [truth telling constraint]; 2) ρ p(r – λH γ) + (1 - p)(-λL γ) [bank’s break even constraint]; Since there is no risk haring in the optimal contract λH=0 and λL=λ, and borrowers pay r in case of high output. From the two constraints we get, now to ensure that λ1, we must have And hence, Finally optimal contract exists if

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Joint liability: The borrowers can write side-contracts with each other costlessly and that there is no cost for a borrower to observer her partner’s project returns. There are two relevant truth-telling constraints. The first one is The second one is if a borrowers own project yields high returns and her partner’s project yields low returns, she has the incentive to report this state truthfully and repay her own loan as well as joint liability for her partner. Only the second truth-telling constraint, will bind. The bank’s zero-profit condition is now: ;

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**Solving the truth-telling and the zero-profit constraints, we get:**

Hence the rate of interest is lower under joint liability so social welfare increases.

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Enforcement The borrowers are risk-averse and the only departure from the first-best is that borrowers can default intentionally even when they are capable of repaying. The punishment a bank can impose on a delinquent borrowers is limited and consists entirely of never lending to her again. If a borrower’s project yields output Y ≥ r so that she is able to repay, she will repay only if the benefit of defaulting, the interest cost, is less than the discounted net benefit of continued access to credit , (*) In this infinitely repeated games we are restricting attention to stationary equilibria of the super game between the borrower and the lender where cooperation is achieved by trigger strategies, namely, both parties revert to the worst subgame perfect equilibrium of the super game if one of the parties misbehave. If the borrower defaults once, the bank never lends to the borrower again, and the borrower never repays if she receives a loan again.

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**Joint-liability contract**

The bank does not pre-commit to future interest rates and hence is independent of the interest rate r. Even if it depends on r, the argument goes through: for a given r, there will be some critical Y(r) such that borrowers will repay if Y≥Y(r) . Let Y(r) be the income level that satisfies (*) with strict equality. If there is diminishing marginal utility of income, then for a given r, the borrower will repay only if Y≥Y(r). Joint-liability contract The group members are considered to be in default unless every loan is repaid and in the event of a default no one gets a loan in the future. A borrower will choose to repay even if her partner defaults given that she is able to repay, i.e., Y≥2r , if: If Y ≥ Y(2r) ,[and Y(2r) ≥ Y(r)] she will pay for both her own and partner’s liability. Assume for simplicity Y(r) ≥ 2r and that if both members have an income Y≥Y(r) , then they repay under joint liability.

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**There will be two distinct cases:**

One group member is unable or unwilling to repay i.e. has an income realization Y Y(r) and the other member is willing to repay both her own and her partner’s obligation i.e. has income Y ≥ Y(2r) . In this case, joint liability is beneficial compared to individual-liability lending. One member is unable or unwilling to repay her own debt i.e., Y < Y(r) and her partner is willing to repay her own debt but not both of their debts i.e. Y(r) Y Y(2r). Now individual liability is better than joint liability.

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**Hence social sanctions alter the effect of joint liability**

Hence social sanctions alter the effect of joint liability. Suppose a default by one borrower that hurts the other group member because she is cut off from loans in the future elicits some punishment from the community (‘social sanctions’). Social sanctions reduce the attractiveness of the payoff stream in the case when one party defaults intentionally r Y <Y(r) , and the other party was willing to repay her own loan but not her partner’s Y(r)<Y<Y(2r) . In this case, repayment would definitely be higher under joint-liability contracts. If repayment decisions are taken cooperatively, repayment behaviour under joint liability is identical to repayment behaviour with individual liability.

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**Problems with joint liability**

Group size and formation: If project returns are independent then increase in group size will reduce the risk of default and hence would reduce r. But with an increase in group size borrowers are less informed about each others type and there can free rider problem for activities like ‘monitoring’ or ‘auditing’, which have the public good property. Social ties: Joint liability framework works only when borrowers are informed about their group members. If the social ties among the group members are loose enough that may lead malfunctioning of the framework. In most of the cities the joint liability framework failed because of this reason.

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Dynamic incentives: The enforcement mechanism works through the dynamic incentives inherent in the lenders threat of cutting off the borrower from any future credit. But most of the lending institutions being pro poor institution in reality it is very hard to realize the threats which can possibly increase the default rate leading to a socially inefficient solution. In the next presentation Dyotonadi will present the issues regarding DYNAMIC INCENTIVES.

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