Moral Hazard

Report
MICROFINANCE
AND 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 can




The cost of effort = c; we assume y > k (i.e. the projects are desirable) and
there’s limited liability, i.e. no collateral.
Borrower’s problem is to choose between two options:




A: either expend effort and make y with prob. 1 or
B: shirk and make y with prob. p < 1.
Expend effort: Return = (y-R) – c
Shirk: 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 make
p*(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/(1p), so all borrowers shirk and the bank still meets its costs.
What is the problem, then?
Well, if y > c + k, then the social optimum 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%).
At the interest rate of 15%, the borrowers will not shirk. At this rate,
the bank will make excess profits. At an interest rate of R=k/p =
1.1/0.99 = 1.1111 (or 11.11%), the bank will break even.
At this interest rate, the borrowers will not shirk either, because the
payoff would be 1.2-1.1111-0.0005 < 0.08839 if they expended
effort, while, if they shirked, it would be 0.95(1.2-1.1111) = 0.088
< 0.08839.
It is also socially optimal for them not to shirk, because y(1-p) =
1.2(.01) = 0.012 > 0.0005 = c. And, furthermore, y-k-c = 1.2-1.10.0005 > 0. So at the zero profit interest rate, the borrowers
expend effort, and this is socially 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, and y=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.
It could set the interest rate at R=k/p = 1.1/0.95 = 1.157895.
In this case, it will be able to collect p=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 be 1.2-1.15789-0.11 < 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.
So at 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 we set k=1.1, p=0.95, c=0.008, and y=1.2.
The incentive compatibility constraint is for R < 1.2-0.008/(1-0.95) = 1.04
(4%). At this rate, borrowers will not shirk. At this rate, though, the bank will not
make any money, because its profit will be 1.04-1.1 < 0.
It could set the interest rate at R=k/p = 1.1/0.95 = 1.157895; in this case, it
will be able to collect p=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.
At this interest rate, borrowers will shirk, because the shirking payoff is 1.21.1579 – 0.008 = 0.034 < the non-shirking payoff of 0.95(1.2-1.1579) =
0.04.
But they shouldn’t shirk from a social optimum point of view because y(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






Why is there inefficient shirking? Let’s first look at it from the point of view of the borrower.
Because the cost of the effort, c, is paid by the borrower all the time if he expends effort.
On the other hand, if he shirks, then he doesn’t have to bear the cost of his effort 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. He would be trading off y(1-p)
against c. Once the bank is lending him money, his calculation changes. He only loses $(yR), (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 of value 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 that part of the time (when the
project doesn’t pay off), shirking represents a partial loss of value to the borrower (only yR), while, for society, shirking represents 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
Bank
profit
0.1
0.2
0.3
0.4
0.5
0.6
1
1.04
1.041
1.1
1.158
1.2
1.3
Shirk/don’t shirk
-1
Effort
-0.9
Effort
-0.8
Effort
-0.7
Effort
-0.6
Effort
-0.5
Effort
-0.1
Effort
-0.06
Effort
-0.11105
Shirk
-0.055
Shirk
0
Shirk
0.04
Shirk
0.135
Shirk
Bank Profit and the Interest rate
0.2
1.2
1.04
1.158
1
1.1
1.041
0
0
0.5
-0.2
Bank Profit
R
1.3
1.5
-0.4
0.6
-0.6
0.5
0.4
-0.8
0.3
0.2
-1
0.1
-1.2
Gross Interest Rate
k=1.1, p=0.95, c=0.008, and y=1.2
The graph shows the bank’s profit at different interest rates; the kink is at the
point where the borrower finds it optimal to shirk (i.e at an interest rate of 4%).
In this example, shirking is inefficient, independent of 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 Moral Hazard and Group Lending






What if loans are made to a group, instead of to an individual?
We saw earlier that the borrower’s trade-off is an expected loss of (1p)(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, that the 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 force sanctions 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 “pay if 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. As before, we have a twoperson group. Each person obtains y with probability 1; however, the
money can be collected only if the bank can prove objectively that
there were sufficient revenues.
Each group 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 is unsuccessful.
Also, if a borrower tries to divert due repayments 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 a borrower, by
incurring a cost of k, to get 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 penalty d 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.
Ex-post moral hazard and group monitoring
Payoff to first borrower from
attempting to default
q2
y-k
monitors unsuccessfully
monitors unsuccessfully
(1-q)2
y-k-(d+y)
monitors unsuccessfully
monitors successfully
q(1-q)
monitors successfully
monitors unsuccessfully
q(1-q)
From the table above, we can show that if R denotes the gross interest rate set
by the bank, a borrower 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:



Probability
monitors successfully
y-k

Second monitoring
Borrower
monitors successfully
y-k-(d+R)

First monitoring borrower
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.

similar documents