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The Problem of Moral Hazard - Pace University

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microfinanceand Moral hazard
P.V. Viswanath
The Problem of Moral Hazard
Moral Hazard refers to situations where the bank’s risk is tied to unobservable choices made by borrowers.Lenders cannot observe the borrower’s choices about how hard to work or which projects to choose or the realization of project returns.The bank might lend money on the assumption that the borrower will take a certain action, but the action that the borrower takes might increase the riskiness of the loan or reduce the cashflows from the project.The basic problem is that the objectives of the borrower are not the same as that of the lender.For example, the borrower wants, often, to minimize his/her effort. Similarly, given limited liability, increased cashflow volatility may increase the expected payoffs to the borrower, but reduce the value of the loan for the lender.
Shirking in Individual Loans
Consider the following example, which deals with potential borrower shirking:Each individual can invest $1 in a one-period project. She canA: either expend effort and make y with prob. 1 orB: shirk and make y with prob. p < 1.The costof effort =c; weassume y > k (i.e. the projects are desirable) and there’s limited liability, i.e. no collateral.Borrower’sproblem is to choose between two options:Expend effort: Return = (y-R) – cShirk: Return = p(y-R)The borrower will expend effort if (y-R) – c > p(y-R), i.e. if R < y - c/(1-p), i.e. if the interest rate is low enough to make the expenditure of effort worthwhile. This is called the incentive-compatibility constraint.If R is too high, then the bank won’t necessarily make more money because then borrowers are going to shirk.
Ex-Ante Moral Hazard and Inefficiency
Suppose borrowers shirk, then there might be circumstances when the bank will make money. For example, if the bank charges R = k/p, then on average, the bank will makep*(k/p) or k, which is break-even.If R=k/p < y, then, then the borrowers will borrow. So we might be in a situation where R= k/p <y, but R > y – c/(1-p), so all borrowers shirk and the bank still meets its costs.What is the problem, then?Well, if y > c + k, then thesocialoptimum is for borrowers to expend effort, but in this set-up, borrowers are _not_ going to expend effort. This means that there are inefficiencies.Let’s look at some numerical examples.
Efficient Expenditure of Effort
Suppose k=1.1,p=0.99, c=0.0005,and y=1.2. Then, the incentive compatibility constraint is for R <1.2-0.0005/(1-0.99)=1.15 (or 15%).Attheinterestrate of 15%,the borrowers will not shirk.At this rate, the bank will make excess profits. At an interest rate ofR=k/p= 1.1/0.99 =1.1111 (or 11.11%),the bank will break even.At this interest rate, the borrowers willnotshirk either,becausethe payoff would be1.2-1.1111-0.0005<0.08839 if they expendedeffort, while, if they shirked, it would be 0.95(1.2-1.1111) = 0.088 < 0.08839.It is also socially optimal for themnot toshirk, becausey(1-p) = 1.2(.01) = 0.012 > 0.0005 = c. And, furthermore,y-k-c=1.2-1.1-0.0005 >0.Soat the zero profit interest rate, the borrowersexpend effort, and this issocially optimal. No problem, here!This is not too surprising because the cost of putting out effort is pretty low. Shirking is likely to occur when effort is costly.
Efficient Shirking
Suppose k=1.1, p=0.95,c=0.11,andy=1.2. Then,the incentive compatibility constraint is for R <1.2-0.11/(1-0.95) =-1.0 (or -200%).At this interest rate, the borrowers will not shirk. However,at this rate, the bank will not make any money, because its profit will be-1-1.1< 0.Itcould set the interest rate at R=k/p = 1.1/0.95 =1.157895.Inthis case, it will be able to collectp=95%of the time and when it does, it will collect R=k/p. Its expected profit will be (k/p)*p – k = k-k = 0, so it breaks even. In our example the profit will be (1.157895)/(0.95) – 1.1 = 0, as explained above.At this interest rate, the borrowers will shirk, but it would be optimal for them to shirk because the payoff would be1.2-1.15789-0.11< 0 for them, if they expended effort.It is also socially optimal for them to shirk, because y-k-c = 1.2-1.1-0.11 < 0.Soat the zero profit interest rate, the borrowers shirk, which is socially optimal. No problem, here!In this case, effort is costly, so shirking occurs; and it’s so costly relative to the increase in return from 10% to 20%, that it’s socially not worthwhile.
Inefficient Shirking
Suppose weset k=1.1, p=0.95,c=0.008,andy=1.2.Theincentive compatibility constraint is for R <1.2-0.008/(1-0.95) =1.04 (4%). At this rate, borrowers will not shirk. Atthis rate,though, thebank will not make any money, because its profit will be1.04-1.1< 0.Itcould set the interest rate at R=k/p = 1.1/0.95 = 1.157895; in this case, it will be able to collectp=95%of the time and when it does, it will collect R=k/p. Its expected profit will be (k/p)*p – k = (1.157895)/(0.95) – 1.1 =0;so it breaks even.Atthis interest rate,borrowerswill shirk,because the shirking payoff is 1.2-1.1579 – 0.008 = 0.034 < the non-shirking payoff of 0.95(1.2-1.1579) = 0.04.Butthey shouldn’t shirk from a social optimum point of view becausey(1-p) = 1.2(0.05) = 0.06 > 0.008; and also y-k-c= 1.2-1.1-0.008> 0. Hence at the zero-profit interest rate, there will be inefficient shirking.This is an intermediate case, where effort is costly enough to make borrowers shirk from a private utility maximization point of view, but the increase in payoff from 10% to 20% is enough to make it socially optimal for borrowers not to shirk.
Causes of inefficient shirking
Whyis there inefficient shirking? Let’s first look at it from the point of view of the borrower.Becausethe cost of the effort, c, is paid by the borrower all the time if he expends effort.Onthe other hand, if heshirks,then hedoesn’t have to bear the cost of hiseffort all the time.p% of the time, this works out well for him, while (1-p)% of the time, his shirking leads to a loss of value of (y-R) for him. So shirking only affects him part of the time. So he is trading off (1-p)(y-R) against c.If he were putting up his own money, he’d lose the entire$y, (1-p)% of the time. Hence, his loss, if he shirked, would be$y, (1-p)% of the time. Hewould betrading off y(1-p) against c. Once the bankis lending himmoney,hiscalculation changes. He only loses $(y-R), (1-p)% of the time.Clearly, if the borrower used his own money, he would shirk a lot less, since y > y-R.Of course, even though expending effort could be better than shirking, it may be better not to undertake the project at all, even by expending effort. This would be true if y-k < c.Shirking represents a saving of effort and a loss ofvalue at the same time.The saving of effort is worth c, both for the borrower and for society – so there is no conflict between the borrower and society on this end. However, the problem is thatpart of the time (when the project doesn’t pay off), shirkingrepresents apartial lossof value to the borrower(only y-R), while, for society, shirkingrepresents a loss of value of y > y-R. Hence the borrower may find it optimal to shirk even when shirking is inefficient from a social point of view.
Borrower Shirking and Inefficiency
k=1.1, p=0.95, c=0.008, and y=1.2The graph shows the bank’s profit at different interest rates; the kink is at the point where the borrower finds it optimal to shirk ( an interest rate of 4%). In this example, shirking is inefficient,independentof the interest rate.y(1-p) = (1.2)(1-0.95) = 0.6 > c = 0.008; and y-k = 1.2-1.1 > c = 0.008
Shirking and Collateral
Even though shirking is possible with individual loans, the presence of collateral can help reduce the scope of the problem.This has to do with the likelihood of default. If the borrower stands to lose his collateral, he will think twice about defaulting. An incentive to shirk exists because of the limited liability characteristic of the loan.Mathematically, if w is the size of the collateral (per dollar of borrowing), it’s optimal for the borrower to shirk only if p(y-R) – w(1-p) > (y-R)-c, in contrast to the previous condition of p(y-R) >(y-R)-c. Obviously, the incentive to shirk is decreasing in the size of the collateral, w.
Ex-ante MoralHazard and Group Lending
What if loans are made to a group, instead of to an individual?We saw earlier that the borrower’strade-offis an expected loss of (1-p)(y-R)from shirking against a sure cost of c from not shirking.From this, it is clear that the lower p is, the less the borrower will want to shirk.At this point, we go back to the result in our analysis of adverse selection – group lending essentially is equivalent to cashflow diversification for the lender. If there are two borrowers, the probability of not paying the lender drops from p to p2. As a result, there will be less shirking.Another way of looking at it is that group lending reduces the gap between the public cost of shirking and the private cost of shirking.We assume, here, thatthe group can enforce the joint liability rule, through sanctions, etc. However, all we really need is that the enforcement rule is credible so that all borrowers actually expend effort. Since this is the equilibrium situation, the group will never actually have to forcesanctions in equilibrium.
Ex-post moral hazard
The term ex-post refers to difficulties that emerge after the loan is made and the borrower has invested and made his decision regarding effort. This is also termed the enforcement problem.What happens if, after the cashflows are generated, the borrower decides not to pay?If the cashflows are not observable or it is costly to verify them, the borrower may end up not paying back the loan.Note, also, that in developing countries, the legal system may not always be dependable.Furthermore, loan sizes are small and the cost of prosecuting may be too high.If, as before, w is the amount of collateral and s is the probability of the bank being able to seize the collateral, then the borrower gets y+w-R if he repays the loan; if he chooses not to repay, then her payoff is (1-s)(y+w) + sy. The decision simplifies to“payif R < sw.”Not surprisingly, if loan collection is probabilistic, the tradeoff is simply loan repayment versus expected loss of collateral.
Ex-post moral hazard and group monitoring
We now assume that ex-post moral hazard exists because of the difficulty of verifying project cashflows. Asbefore,wehave a two-person group. Each personobtainsy with probability1; however, the money can be collected only if the bank can prove objectively that there were sufficient revenues.Eachgroup member can, by incurring a monitoring cost k,check,ex post, the actual revenue realization of his partner and observe it with probability q. With probability (1-q), the monitoring isunsuccessful.Also,if a borrowertriesto divert duerepayments and he is successfully observed doing so, he has to pay a social sanction, d.Alternatively,we can think of this as the ability of aborrower,by incurring a cost of k, toget his recalcitrant partner to pay up his share. Furthermore, when the partner has to pay up, he has to pay what he owes plus a penaltyd for trying to get out of paying.The following table shows the payoff to a borrower trying to get out of paying in different cases, along with the probabilities.
From the table above,we can show thatifR denotes the gross interest rate set by the bank,aborrower will choose to repay if and only if: y-R-k > y-k - q2(d+R) - q(1-q)(d+y).This can be rewritten as R < y + [q(d+y) – y]/(1- q2). From this, we note:As q increases, the RHS increases and R can be larger.Similarly, as d increases, the RHS increases and R can be larger.Consequently, monitoring allows for higher interest rates, consistent with repayment. In the absence of group monitoring, with zero collateral, we saw that there would be no repayment, at all.
Ex-post moral hazard and group monitoring





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The Problem of Moral Hazard - Pace University