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Why Is There Debt?
Jeficy M.

The striking feature of debt contracts is that over
a wide range of circumstances the payment is fixed
and invariant, although occasionally, as in a default,
less than the full payment is made. In this article I
offer a simple explanation for why such arrangements
are widely observed. The explanation relies on recent advances in the theory of financial arrangements
under imperfect information. I will argue that the
opportunity
for borrowers to hide their future
resources sharply constrains the degree to which loan
repayment can be made contingent on the borrower’
s
future resources.
From one point of view it is not obvious that the
ubiquity of debt contracts is a puzzle. A borrower
acquires a sum of money today that will be repaid
in the future, along with an additional payment, called
interest. The interest rate is the price for the temporary use of resources. It seems perfectly natural
that this amount is predetermined.
Modern economic theory has taught us to view
matters differently. When a loan is made, the lender
acquires a contingent claim, a promise by the
borrower to pay an amount that can depend in any
arbitrary, prespecified way on future events. l Many
familiar contracts actually do involve future payments
that are contingent in significant ways. Insurance contracts are promises to make a payment contingent
on some particular future loss. Partnership agreements and profit-sharing arrangements make future
payments contingent on the uncertain profits of
the firm. Traded securities such as stocks, bonds,
options, and related derivative products have returns
that are highly sensitive to future events. But in a
debt contract, the payment is generally noncontingent
in that the amount does not vary with future circumstances, such as the borrower’ wealth. Of course
s
a debt contract is contingent to the extent that the
l The
author is grateful for helpful comments on an earlier
draft from Tim Cook, Mike Dotsey, Marvin Goodfriend, Tom
Humphrey, Stacey Schreft, and Steve Williamson. The author
is solely responsible for the contents of the paper and the views
expressed do not necessarily reflect those of the Federal Reserve
Bank of Richmond or the Federal Reserve System.

r Flood (199 1) provides
of contingent claims.

an accessible

introduction

to models

L c k er
u

l

lender does not receive full repayment if the borrower
defaults. But although default is an important feature
of the arrangement, it occurs relatively rarely.
Finding plausible models in which people agree
to debt contracts, although they are allowed to
agree to any possible contingent repayment schedule,
has proven surprisingly difficult. In fact, in many
models ‘
people are much better off with a contingent
contract than they are with a debt contract. In
Section I, I present a simple, two-agent model that
shows why standard economic theory predicts that
contracts generally should be contingent. The model
also serves as a useful starting point for further
analysis.
In Section II, I present a model in which the borrower and lender agree to a loan repayment that is
noncontingent
because the borrower can conceal
future resources. Section III points out that this model
is deficient because nothing resembling default ever
occurs, and then argues that collateral, broadly
defined, is an important omitted feature of the model.
Next, in Section IV, I present a model in which an
implicitly collateralized debt contract, with occasional
default, is the chosen arrangement. Three brief sections conclude the paper: Section V surveys literature
that has addressed the same question; Section VI
briefly discusses some policy implications: and
Section VII summarizes the explanation offered here
for the ubiquity of debt contracts and notes two
remaining unsolved puzzles.

I. ASIMPLEMODEL
OFCONTINGENT
CLAIMS
To begin, consider an economy with only two
people: a borrower and a lender. The economy lasts
for just two time periods; call them periods 1 and 2.
Imagine that the two people are farmers, and that
the two periods represent the spring and fall of a
given year. In the spring the lender harvests a crop:
wheat, say. The lender’ land produces no crop in
s
the fall. The borrower’ land produces no crop in the
s
spring, but will produce a crop in the fall. Both agents
would like to consume wheat in both the spring and

FEDERAL RESERVE BANK OF RICHMOND

3

the fall. To do so, the borrower must obtain a loan
of wheat in the spring, to be repaid from the proceeds of the fall harvest. For simplicity, I ignore the
use of wheat in planting, and assume that the crops
have already been planted. I also ignore the possibility
of storing wheat from the spring to the fall; allowing
storage would not affect the results. No other goods
are available to these two agents.
To make the contingent nature of the contract of
interest, some random event has to occur between
spring and fall. I assume that in the spring the amount
of the borrower’ fall wheat harvest is uncertain. In
s
the fall the harvest is realized, and both agents learn
the exact value of the harvest. The payment contract is contingent if it depends on the amount of the
borrower’ crop. Other sources of uncertainty could
s
have been considered-shocks
to the preferences of
the two agents for example-but
in many ways,
uncertainty
concerning the borrower’ ex post
s
resources is the archetypal setting for financial contracting. If the borrower is a wage earner, for example, future income or employment might be uncertain. If the borrower is an individual entrepreneur,
future returns from the venture might be uncertain.
If the borrower is an incorporated firm, future liquid
resources of the firm might be uncertain.
To proceed, the borrower’ harvest in the fall is
s
8, and can take on one of N values: &,&,. . .,&, where
these are ordered so that O<r3i<&<
. . . ~t9r.r.~ In
the spring, both people believe that the probability
that 8 takes on the value 8, is ?m, where ?m > 0 for
n= l,Z,..., N, and C?= rnn = 1. The lender has a
harvest of e? in the spring. The lender makes a loan
advance of q in the spring, and receives a payment
of y,, in the fall if the harvest is 8,. In the spring the
lender’ consumption is et -9, while the borrower’
s
s
spring consumption is q. When the borrower’ harvest
s
is 8,, the lender’ fall consumption is y,, and the
s
borrower’ fall consumption 8, - y,,. A contract is
s
a set of payments {q,yI,y2,...,yN),
and these completely determine the consumptions
of the two
agents.
I assume that the borrower evaluates the contract
flmJ;Y..Y yN) according to the expected utility

UBh)

+

k$UB&-Ynh

(1)

where fl is a discount factor satisfying 0 < p < 1.
This is the ex ante expected utility of the borrower
in the spring. Similarly, the lender evaluates the contract according to the expected utility function
- 9) + Pn~l~~(Yn)~n.

u&I

The within-period utility functions Un and UL are
assumed to be strictly increasing, continuous, concave and smoothly differentiable.
Contracts cannot require payments that exceed the
available resources. Stated formally, contracts must
satisfy
the following
resource feasibility
constraints:
q20,.

(3)

e4 2 9,

(4)

Yn 2 0,

n=1,‘ ,..., N,
2

(5)

en 2 Y,,

n= 1,2 ,..., N.

(6)

Optimal Contracts
To obtain predictions in this simple environment
about the arrangements that the two agents will
choose, I restrict attention to optimal contracts.
A contract is optimal if it is feasible and no other
feasible contract exists that makes one agent better
off, in terms of ex ante expected utility, without
making the other agent worse off. Because of the
simple nature of the environment, an easy way of
finding optimal contracts is by maximizing the
weighted average of the two agents’ utility functions,
subject to the resource feasibility constraints. The
weights, sometimes called “Pareto weights,” are
arbitrary positive numbers, and varying their relative
size traces out a range of contracts that gives more
utility to one agent and less to the other. If a contract is optimal in this environment, then it is the
solution to the constrained maximization problem for
some Pareto weights, and vice versa.
The programming problem that finds optimal contracts, then, is the following.
Problem 1:
Maximize,
XB

UB(d

by choice of q,yi,ya,. . .,yN,
+

k#$dkYdTn

[

2 For there to be a meaningful distinction between a debt
contract with occasional default and a more general contingent
contract, I need at least three states. The notational burden of
N states is not significantly greater.
4

ECONOMIC RNIEW.

(2)

[

+ XL uL(e4-q)

N

1
1

+ S~~Iu~(yJ.rr~

subject to the resource feasibility constraints (3)-(6).
JULY/AUGUST

1991

The Pareto weights An and XL are arbitrary positive
constants.

Figure 1

THE

To show the properties of optimal contracts, I
examine the set of first-order conditions that are
necessary and sufficient for a contract to be a solution to Problem 1. If both the borrower and the
lender are enjoying positive consumption in the fall
for a given state 8,, so that 0< y,,< 8,, then the firstorder condition for y,, is
AL’
d

(yn)

=

DETERMINATION
OF FALL PAYMENTS
FOR A GIVEN HARVEST, 8”
Lender’
s

Borrower’
s Marginal
Utility, X&(0,-y,)

Marginal

,

(7)

hBU$ (en - yn) .

Condition (7) requires that the marginal utility of the
lender’ fall consumption, scaled by XL, must equal
s
the marginal utility of the borrower’ fall consumps
tion, scaled by XB. This condition determines y,, in
a manner illustrated in Figure 1. The width of the
box in Figure 1 is t9,, the realized harvest outcome
to be divided between the two agents. The payment
yn is measured horizontally from left to right, and
the lender’ marginal utility, measured vertically, falls
s
as y,, rises. Similarly, the consumption of the borrower is measured horizontally from right to left, and
the borrower’ marginal utility rises as yn rises. The
s
optimality condition (7) dictates that the payment
is determined by the intersection of the two weighted
marginal utilities. Identical conditions apply for every
other possible harvest outcome; the horizontal dimensions of the box vary with en, but otherwise the
analysis is the same.

I
en

Figure

2

THE DETERMINATION
OF FALL PAYMENTS
FOR HARVESTS 19.AND e,, WHERE e,>e,
t
4

x,u;(y”) =

x,u;(Y,)
x$&v&-Y,)

I
0

I

I
I

The Nonoptimality of Debt Contracts
I can now demonstrate that in this simple environment, the payment varies positively with the &west,
and a debt contractwill be optimai ody under special
chumstances. Consider Figure 2, in which the determination of the payments is illustrated, just as in
Figure 1, but for two possible harvest outcomes, 8,
and 8,, where m > n. The box for the larger harvest,
8,, is drawn with the same left edge, so that the origin
from which the payments are measured does not
move. Consequently,
the lender’ marginal utility
s
schedule is the same for both harvest outcomes. The
origin from which the borrower’ consumption is
s
measured shifts to the right, because 8, >&, so the
borrower’ marginal utility shifts to the right. If both
s
marginal utility schedules slope down, the point of
intersection moves down and to the right going from
harvest en to 8,. Therefore, the payment ym for the
larger harvest is larger than yn, the payment for the
smaller harvest.

l Yn

0

I
I

Yn Ym

4

-,YntYm
n

Under a debt contract there is a set of harvest
outcomes over which the payment made by the
borrower in the fall is a constant. It is easy to see
what is required for such an arrangement to satisfy
the optimality conditions. The lender’ optimal cons
sumption must remain the same, and this requires
that the marginal utility curve for the borrower be
horizontal, as in Figure 3. This in turn requires that
the borrower be risk neutral, meaning that the borrower’ utility is linear, not strictly concave. In this
s
case a shift to the right in the borrower’ marginal
s
utility leaves the point of intersection, and thus the
payment to the lender, unchanged. For a debt conn‘ to be optimalin tInienvhvnment, the beer
act
must

FEDERAL RESERVE BANK OF RICHMOND

5

Figure

THE

3

DETERMINATION
OF FALL PAYMENTS
FOR HARVESTS 8” AND 8, WHEN
THE BORROWER
IS RISK NEUTRAL

of the classical model, at least when there are no
imperfections in the availability of information. Thus,
the ubiquity of debt contracts is puzzling, at least from
the viewpoint of classical general equilibrium models.

II. DEBTCONTRACTS
INAMODELWITHLIMITEDINFORMATION
x,u;(e,

- Y,)

be rid neutral, and the lender must be rid averse.3
This situation is highly implausible.4
This simple model highlights the basic principle
that if people face contingencies that are observable
when they occur, then only under very unusual
circumstances would they choose noncontingent
arrangements. In general we should expect to see
contracts that are contingent on any future event that
affects the marginal utilities of the contracting
parties, such as shocks to the wealth of either party.
For example, under perfect information, as here, we
should observe agents insured against idiosyncratic
shocks to their own wealth by sharing risk with other
agents in the economy. Notably, a wide range of
models share this property. The example economy
I have described is merely a special case of the
classical general equilibrium model of Arrow (195 1)
and Debreu (19.59), extended to allow for uncertainty
as in Chapter 7 in Debreu, or Arrow (1964). The
principle survives in the most general specifications
3 The case in which both the borrower and the lender are
risk neutral can be ignored. If the two weighted marginal utility
schedules do not intersect, then the entire harvest is given to
one agent in every state. If the two weighted marginal utility
schedules coincide, contractual arrangements are indeterminate.
4 This seems implausible for at least three reasons. First, risk
neutrality seems inconsistent with a wide array of observed
arrangements for shedding or dispersing risk. Second, a large
class of the population (all debtors) is not likely to have such
special preferences. In fact, casual introspection suggests that
borrowers are not systematically less risk averse than lenders,
and, if anything, they are subject to more idiosyncratic risk than
lenders, as in the model presented here. Third, in many
economic models the assumption of risk neutrality is made to
capture an agent’ ability to insure against idiosyncratic risk in
s
perfect capital markets. One would expect, however, that lenders
rather than borrowers would have such privileged access.

6

Apparently, then, to explain debt contracts one
must depart from the assumptions of the classical
model. In the example above, both the lender and
the borrower are fully aware of the realized value of
the borrower’ harvest; in other words, there is
s
perfect information. Suppose instead that the
lender is uncertain of the borrower’ harvest at the
s
time the payment must be made in the fall. The
lender might be forced to rely on the borrower’
s
report about the harvest, especially if there is no
independent information available to the lender. In
this case the payment might have to be noncontingent, because otherwise the borrower would have
reason to make a misleading and self-serving report.
To explore this notion, I now modify the model
described above by assuming that the borrower is
capable of hiding any amount of the harvest. The
hidden crop can be consumed secretly, and hiding
is itself costless. The remaining crop, the part not
hidden, is displayed to the lender. This is less
stringent than assuming that the lender is incapable
of observing the harvest at all (pure private information), but still implies that the amount displayed provides only a lower bound on the actual amount of
the harvest.5
This appears to be a fairly realistic imperfection
in information. Often a borrower can divert resources
for private benefit that would otherwise be available
to repay an obligation. A consumer, for example, can
spend freely on current consumption and then default
on debts.6 Similarly, a firm’ managers can divert
s
5 This assumption is a version of “costly state falsification” (see
Lacker and Weinberg, 1989). Costly state falsification is the
assumption that one agent can misrepresent the true state at
some cost. Perfect information, as in the example in the previous
section. is a soecial case in which all falsification is orohibitivelv ,
costly. Pure private information is the assumption that the agent
can costlessly make any state appear to have been realized. The
assumption made here is that the borrower-can costlessly make
it appear that any lower harvest has occurred, but it is prohibitively costly to make it appear that a larger harvest has occurred.
1

6 An individual can spend on consumption just prior to filing for
bankruptcy, depleting liquid assets to the detriment of creditors,
both in a Chapter 7 liquidation and in a Chapter 13 plan. In
addition, the consumer can use funds to purchase “exempt assets”
that are then beyond the reach of creditors.

ECONOMIC REVIEW. JULY/AUGUST

1991

resources in a variety of ways, through direct and
indirect managerial compensation, wasteful investment, exploitation of discretion over accounting
choices, or favored treatment of particular creditor
classes.7 Often a lender has no direct knowledge
of a borrower’ total resources and thus must rely on
s
the borrower’ own financial statements. At the same
s
time, it often seems as if lenders have or can obtain
some information about a borrower. If a borrower
claims to have a certain quantity of resources, the
lender can ask the borrower for proof of his bank
balance or other readily verifiable assets. The borrower is incapable of proving that he does not control additional assets; he can display less than his
true resources but not more. This informational
imperfection is consistent with the observation that
parties to financial arrangements are often observed
exchanging information at relatively little apparent
cost.8
Incentive Constraints
Although the implication of this informational
assumption is straightforward, I display the results
more formally, since in a more complicated setting
examined later the intuition will be less clear and the
formalities more important. The borrower now has
a choice to make in the fall: if the harvest is &, the
borrower can display an amount em, where 8, can
take on the values &,&, . . . ,&. If the borrower displays
8, when the harvest is 8,, nothing is being hidden,
while if the borrower displays less than 8,, an amount
8, -8, is being hidden and consumed without the
knowledge of the lender.
As before, a contract, (q,yl,yz ,..., yN}, specifies the
spring payment to the borrower, q, and the fall payment from the borrower, y,,, contingent on the
harvest. Also as before, a contract must satisfy the
resource feasibility constraints (3)-(6). Now I impose
the further condition, called incentive feasibility,
that the borrower never has an incentive to hide any
of the harvest. If the borrower does not hide any

harvest when the harvest is en,. his utility is
u&L-y,,).
If the borrower displays Brn when the
harvest is &,, hiding the amount 8, -em, his utility
is u&& - y,). For the borrower to have no positive
incentive to hide harvest, it must be true that
UB(&-yn)
2 UB(f&yrn).
Therefore,
the set of
incentive feasibility constraints are
UB(on - yn)

2

UB(&

- yti)

for n=Z,..., N, and for m=l,...,

n-1.

(8)

The incentive feasibility constraints stated here can
be derived from a deeper formulation that allows contracts that might give the borrower incentive to hide
some of the harvest. It can be shown, however, that
the results of any arbitrary contract can be replicated
by a contract that satisfies the incentive feasibility
constraints.9
The incentive feasibility constraints
can be
simplified. To use (8) in finding an optimal contract,
the utility of not hiding any harvest must be compared to the utility of displaying any amount less than
8,. It turns out that if the constraint for harvest 8,
is satisfied for m =n - 1, then the constraints are
satisfied for all m< n. As a result (8) can be reduced
to
UB(&-Yn)

2

UB&-Yn-1)

for n=Z,...,N.

(9)

In other words, the utility of telling the truth only
needs to be compared to the temptation of displaying the next smallest possible harvest &,-1.1o
An immediate implication of (9) is that a contract is
incentive feasible if and only if yn is constant or
decreasing as 8, increases. For any given harvest
outcome, the borrower can make the payment corresponding to that harvest or to any smaller harvest;
a given payment is feasible for the corresponding
harvest and for any larger harvest outcome. Because

7There are many constraintson these abilities, course. Boards
of
of directors, or other representatives of creditors, monitor some
aspects of managerial choice. Discretion over accounting is
limited in myriad ways by accounting standards, legal requirements for certification by outside auditors and the like. The
fraudulent conveyance provision of the bankruptcy code allows
the bankruptcy court to “unwind” distributions to creditors made
90 days or less prior to filing. Nonetheless, managers retain considerable discretion and can often take actions for personal benefit
to the detriment of creditors.

9 The proof is in Appendix A and uses “The Revelation Princinle.” The terminologv is due to Mverson (1979). For an
exposition of the Revelation Principle’
in similar seitings see
Townsend (1988). A warning is in order here, however; the
display of harvest is an “action” and not a “message.” In the
present setting the distinction is immaterial, but in more general
settings in which actions involve real costs, the distinction is
important. See Lacker and Weinberg (1989), p. 1350.

s In contrast, such readily available observation is difficult to
reconcile with pure private information, where it is assumed that
the information is completely unavailable to the lender.

that (8) is satisfied. The property that only immediately
adjacei; incentive constraints ieeh to be checked-arises in a widk
variety of settings.

1

VI

*OTo prove this note that (9) implies that for n=2,3,...,N,

y,SyA, soYnSYmfor m= 12 ,...in - 1. This in turn implies

FEDERAL RESERVE BANK OF RICHMOND

7

hiding the harvest is costless, the borrower will make
the smallest possible payment and will display the
corresponding amount of harvest. Thus the borrower
will never have to make a larger payment for a larger
harvest than for a smaller harvest.
Optimal&y of a Debt Contract
I am now in a position to show that something
resembling a debt contract is optimal in this model.
As before, a programming problem is solved, but with
the addition now of the incentive-feasibility constraints (9). Specifically, I solve
Problem 2:
Maximize, by choice of q,yl,..., yN,
+

A noteworthy feature of this model is that the range
of contracts available to the two agents is severely
restricted. Because the payment, call it R, is constant across harvests, &payment can never be greater
than tlrresmdfesstpossib/e
&west (R 5 01); otherwise
the fixed payment is not feasible for small harvests.
This is potentially a quite severe restriction, since
the smallest possible harvest could be very different
from the expected
realization,
and could
imply a maximum loan repayment that is very small.
In this situation, the borrower might be left desiring
more credit than he can obtain via any incentivefeasible contract. To see this, one can combine the
first-order conditions from Problem 2 to obtain the
following equation linking the expected intertemporal
marginal rates of substitution of the two agents:

,8n&IB(on-Yn)7h
1

+

XL

N

L

UdeF-q),

+

Pn~lU~(ynhn

;

1

subject to the resource feasibility constraints (3)(6), and the incentive feasibility constraints (9).
To see why a completely noncontingent contract
is optimal, compare the incentive feasibility constraints with the contract that was optimal in Section I. First, recall that incentive-feasible contracts
can never be increasing with respect to the harvest
8,, only constant or decreasing, because if yn > y,i
and the harvest is 0,, then the borrower would lie
in order to make a smaller payment. Second, recall
that in Section I, without incentive constraints, risksharing alone determined the optimal contract and
it had a strictly increasing payment schedule. But such
a contract is not incentive feasible, and would always
give the borrower an incentive to claim that the
smallest possible harvest outcome had occurred.
Among the set of contracts that are nonincreasingand thus incentive feasible-the
constant payment
schedule is the one that is closest to the optimal contract from Section 1 in the sense that it has the largest
slope. Thus a contract with a constant payment
schedule is optimal.”
rr To complete a proof, I need to show that a contract with
yn < y,r for some n cannot be optimal. Suppose that yn <
y,-1 for some particular n. Then the incentive constraint that
relates yn and yn-r is not binding, and &, = 0, where & is the
Lagrange multiplier on the nth constraint in (9). Therefore, from
the first-order conditions we have
P[Xrui(yn-1)
=

8

-

UFml-I-yn-Ih-1

XBd(b-I

-yn-dbrrl-1
2

0

pud(en-yn)7h

n=l

=

z PULYY~G

n=l uLr(et -4)

wi(q)

+

AB$q)

(10)

The left side of (10) is the borrower’ expected
s
intertemporal marginal rate of substitution: the expected value of the ratio of marginal utility in period
2 to marginal utility in period 1. Similarly, the first
term on the right side of (10) is the lender’ expected
s
intertemporal marginal rate of substitution. The
second term contains ~1, the Lagrange multiplier on
the constraint, yi -8110.
If ~1 >O, this constraint
is binding, and the borrower’ expected marginal
s
intertemporal rate of substitution is strictly less than
the lender’ This means that the borrower would
s.
like to obtain more period 1 consumption in exchange for period 2 consumption, but cannot do so
in any feasible contract. In this sense, one might
describe such a borrower as constrained or rationed. l2

and
PbLUd(y”)
=-

UEwn+1

~BUd(&
-Y&n+1

- ydh,
5

0.

un is linear, these two conditions together imply that
y,, > y,-1, but this contradicts the initial supposition that the
opposite was true. Thus, a contingent contract cannot satisfy
the first-order conditions and thus cannot be optimal.
Unless

I2 This feature of the model is an exact restatement of an
argument made by Irving Fisher (1930, pp. 210-l 1). He noted
that a borrower’ collateral will limit the amount he can borrow,
s
and “Ii]n consequence of this limitation upon his borrowing
power, the borrower may not succeed in modifying his income
stream sufficiently to bring his rate of preference for present over
future income’
down
to agreement with the rate or rates of
interest ruling in the market” (p. 211).

ECONOMIC REVIEW, JULY/AUGUST 1991

III.

DEFAULT ANDCOLLATERAL

As a model of debt contracts, there is an obvious
deficiency in the optimal contract just described:
nothing ever occurs that resembles a default, a state
in which something less than the fixed payment, R,
is made. The optimal contract is a constant payment,
and thus is perfectly risk-free. Many debt contracts
are virtually risk-free, but it seems that in most debt
arrangements there appears to be at least a remote
possibility of default. This possibility is an important
feature of the contractual arrangement, even if the
probability is small, because a borrower will always
be tempted to simulate default. Apparently the
environment described above is incompatible with
payments that are almost always a fixed amount but
occasionally are less. l3 Can economic environments
be found that display such contracts?
To guide a search for such environments, let us
begin by asking what happens when an individual
defaults on an actual debt contract. First, and obviously, the borrower pays less at a given date than
was stipulated under the original contract.i4 This is
not all that happens, however. If the loan is explicitly collateralized the borrower may be forced to
surrender the collateral. Under an “unsecured” obligation the borrower may agree to a restructured
payment
schedule, promising to make future
payments in lieu of the current payment. Sometimes
the borrower is forced into legal bankruptcy proceedings, which often involve liquidating assets and
using the proceeds to repay claims. For managers
of incorporated businesses, bankruptcy involves at
least temporary surrender of some control rights
associated with the business, because the bankruptcy court or the trustee can assume substantial
power over management decisions. The bankrupt
that is not liquidated often must agree to a set of
restructured claims, as in Chapter 11 reorganizations
or Chapter 13 “wage-earner plans” under the U.S.
Bankruptcy Code. These outcomes are obviously
interrelated, but the salient point is that usually the
borrower surrenders something distinct from the
originally promised payment: either money at a later
date or some other asset or right.

One is thus led to consider contracts in a multiplegood environment, one in which the borrower has
more than one good to sacrifice. In such a setting
a contract specifies a payment schedule for each good
the borrower will later have available. In principle
each payment schedule can be an arbitrary function
of future circumstances. A debt contract in this
setting is a set of payment schedules with special
properties. First, in almost all circumstances fiied
noncontingent amounts of a set of goods are paid,
fixed sums of money at prespecified dates, for example. Second, in some circumstances less of these
goods is paid and positive quantities of some other
goods are surrendered, where “other goods” must be
interpreted broadly to include legal claims and the
like, as described above.
Under what circumstances would such a debt
contract be optimal? Let us abstract from multiperiod
debt contracts that stipulate a series of payments and
focus attention on an obligation to make a single
specified payment at a single future date. Consider
first the set of states in which the borrower pays the
fixed amount of the good-call
it money for now.
Perhaps the noncontingent nature of the payment
schedule over these states can be motivated in
exactly the same way as the noncontingent contract
of the previous section; if the borrower could hide
resources ex post, the payment schedule would have
to be constant to avoid giving the borrower an incentive to hide.

‘ Indeed, results like those in Section II have been widely known
3
for some time, so perhaps the central problem posed by debt
contracts is reconciling the predominantly noncontingent nature
of the contract with occasional contingent payments.

Now consider the default states in which some
other goods are paid. The fixed payment might be
larger than the smallest possible amount of money
the borrower could have available. When the borrower does not have enough money to make the fured
payment, the actual payment is obviously limited by
the amount of money the borrower has. What is to
keep the borrower from always feigning these outcomes so as to make the smallest possible payment?
With other goods available, the contract could require that if the borrower makes less than the fixed
money payment, then some other goods of equal
value to the borrower must be transferred to the
lender as well. The other goods sacrificed are enough
to dissuade the borrower from pretending to be
destitute. Thus the transfer of other “collateral” goods
ensures that the borrower will not falsely claim to
be unable to make the full payment.

I4 I neglect here the phenomenon
of “technical default,” a
common provision in many contemporary debt contracts, in
which the borrower has made all requisite payments but has
violated some auxiliary covenants. Covenants are important, but
I have nothing new to say about them and focus here entirely
on default in the sense of payment deficiency.

Such an arrangement could expand dramatically
the set of feasible contracts available to the borrower
and lender. In the environment described in Section
III, where no other goods were present, the lowest

FEDERAL RESERVE BANK OF RICHMOND

9

possible harvest, 01, placed an upper bound on the
size of the fixed payment. With other goods available,
a contract can be written with a fixed payment of
money that is larger than the smallest amount the
borrower might possess ex post. The other goods
provide a way of relaxing the sharp constraint imposed by the value of the smallest possible harvest
outcome in the environment of Section II.
But other puzzles arise in this story. Consider first
the set of states in which a noncontingent amount
of money is paid. Why, in these circumstances, pay
money rather than some other goods, such as those
paid in the default-like states? It must be because
money, at least in those states, is more valuable to
the lender than the other goods, or, equivalently, the
other goods are more valuable to the borrower,
relative to money, than they are to the lender. This
seems like a reasonable condition, one that might
be satisfied in many of the circumstances in which
debt contracts appear. When a consumer buys a
house or a car, say, it is less valuable to the lender,
relative to money, than it is to the borrower; the
lender would obtain less money by repossessing the
collateral and selling it than the borrower would spend
to retain it. Consumers quite plausibly could value
a good at more than its market price if it is indivisible and consumers only buy one. Similarly, the value
to the borrower of all that is forfeited in bankruptcy
settlements of various types is usually less than the
value of what is received by lenders. Indeed, the difference, regarded as a “deadweight loss,” seems to
motivate a wide array of arrangements-both
in and
out of formal bankruptcy proceedings-designed
to
minimize this loss.
The other goods serve as collateral. This is most
plain in loans explicitly collateralized by physical
goods such as land, structures, chattels, automobiles,
or inventories. Often a loan is collateralized by financial instruments such as accounts receivable, wareuse receipts or negotiable securities. Many debts are
implicitly collateralized, as when income or
profits in the more distant future stand behind a
promise to make a payment out of income or profits
in the near future, or when claims to a portion of the
proceeds of liquidation stand behind an unsecured
corporate obligation. Even an unsecured creditor can
obtain a judgement against a defaulting debtor, allowing the creditor to have the debtor’ assets seized
s
to satisfy the claim. While the distinctions between
these various means of collateralizing an obligation
can be quite important, they are fundamentally
similar. Indeed, in almost all instances the nonpayment of a contractual obligation provides the lender
10

with a legal claim, the content of which is jointly
determined by the terms of the original contract and
the existing body of contract and bankruptcy law.
While the resulting claim can have a wide range of
characteristics, it provides the borrower with an
incentive to make the stipulated payment whenever
possible, to “keep his heart right” in the words of
a practitioner.15 The role of collateral is not necessarily to indemnify the lender against potential loss,
although it certainly does so to a degree. Rather, collateral is a means of satisfying incentive constraints
that ensure voluntary compliance with the terms of
the loan agreement.
The main legal distinction between an explicitly
collateralized debt and an uncollateralized debt is how
the claim stands vis-a-vis third parties such as other
creditors or a bankruptcy trustee. For example, under
the current U.S. law governing secured transactions
the difference between secured and unsecured
creditors is minor when there is only one creditor.16
A creditor with a collateralized debt can obtain the
collateral to satisfy the claim, rather than see the collateral added to the pool of assets divided among all
of the creditors in bankruptcy. This suggests that the
essential role of explicit, as opposed to implicit, collateral is related to multilateral financial arrangements,
and that uncollateralized lending has much in common with explicitly collateralized lending. l7

IV. COLLATERALIZEDDEBT
In this section I describe a two-good economic
environment,’ and I find conditions under which a
collateralized debt contract is optimal for the reasons
described above. The environment, an extension of
the previous example, captures the essential elements
of the argument outlined above.‘
8
I5 This role was noted by Barro (1976). The quoted practitioner
is Chris Carlson, Richmond, VA.
l6 One exception is when the collateral is an “exempt asset” under
bankruptcy law, and is thus out of reach of any unsecured creditor
but can be recovered under a collateralized loan. Exempt assets
include the debtor’ “tools of trade,” some of the debtor’
s
s
household goods, and an interest in the debtor’ residence.
s
Another exception is when the collateral is an asset that will not
pass to the bankruptcy estate, such as the personal assets of the
manager of a corporation.
I7 Standard terminology in the theoretical finance literature,
unfortunately, is that a debt contract like the one described in
Section II is “uncollateralized” while a debt’ contract like the one
described below is “collateralized.” The literature treats collateral
as if it were exempt assets in a personal bankruptcy, or the
personal assets of a manager in a corporate bankruptcy.
I8 The model is a simplified version of my 1991 working paper.

ECONOMIC REVIEW, JULY/AUGUST 1991

The borrower is assumed to have two goods with
which to conceivably repay a loan in the fall. One
good is the fall harvest, as before, and the other good
can be thought of as chattels: durable, portable, personal property such as clothes, furniture or perhaps
tools. In a collateralized debt contract, when the
harvest is sufficient the borrower pays a fixed, noncontingent amount of the harvest (the payment
good) and none of the chattels (the collateral
good). When the fall harvest is less than the fixed
payment, the entire harvest is given to the lender
along with a positive quantity of chattels. For good
harvests the borrower does not hide the harvest
because some of the chattels would have to be surrendered as well.
To proceed formally, then, let good 1 in each
period be the wheat harvest, as in the previous
models, and let good 2 be the collateral good, the
borrower’ chattels. The borrower is endowed with
s
k units of chattels, and k is known ahead of time to
both the borrower and the lender. In the event that
the fall harvest is B,,, the borrower makes payments
of yin of good 1 and yz,, of good 2, and consumes
8, -yin of good 1 and k - yz, of good 2. As before,
the spring loan advance is q, so that the consumption of the borrower is q, and the consumption of
the lender is e? -q, the lender’ spring endowment
s
minus the loan advance. For simplicity, I assume that
the borrower derives utility from consumption of
chattels only in the fall.
The expected utilities of the two agents are now
uB(q)

+

&uB&-yin)

+ Vdk-y2n)hn

(11)

9 2 0,

(13)

4

(14)

2 9,

yin
en

1

,..., N,

(13

yin,

2

y2n

n=l,Z

09

n= 1,2 ,..., N,

(16)

0

n= 1,2 ,..., N,

(17)

n=l,Z

(18)

2

k 2

y2m

,..., N.

A contract is now a loan advance, q, and a pair of
payment

schedules,

{yll,yl2,...,ylN}

and

(~21,

yzN}, that determine the payments of good
1 and good 2, respectively, for each harvest. As
before, contracts might in general give the borrower
an incentive to hide some of the harvest in some
states, but, as before, we can restrict attention to
contracts for which the borrower never has an
incentive to hide. Contracts that have this property
satisfy the following incentive feasibility constraints:

y22,...,

uB(k

- yld

+

VB(k -5’
2d

2

uB(8n-ylm)

+

for n =Z,...,N,

VB(k-J’
2m)

m=n-1.

(19)

As in the previous model, I have written the constraint only in terms of the temptation of displaying
the next smallest possible harvest 0n-i.20
Optimal contracts can again be found as the solution to a programming problem, parallel to Problem
2. An optimal contract is a set of numbers
{q,y11,y12

,...,

ylN,y21,y22,...,y2N}

that

solve

Problem 3:
Maximize, by choice of

and
u&I

The resource feasibility constraints extend naturally
to this case:

-4)

+

On!,

Myd

+

v~(y2dh~.

(12)

I have assumed here that both agents have additively separable utility in the fall. The functions VB
and VL are the utilities of the borrower and the lender,
respectively, with respect to chattels. I assume that
both are continuous, concave and smoothly differentiable. A natural assumption to make is that VB is
strictly increasing, but VL need not be increasing.
The function VL might be decreasing if the collateral
good is worthless to the lender and disposing of it
is costly, or if yz, is viewed as a costly punishment,
such as debtor’ prison.i9
s
19Diamond (1984) displays a model of optimal debt contracts
that depends on nonpecuniary punishment of the borrower in
the event of nonpayment. His model is a special case of the
model described here.

hBUB(q)

+

+

XLudek-q)

hBfln~l[UB@n-yld

+

XLfln~l[UL(yln)

+ VB(k-Y2n)I~n

+

vL(y2n)lan

20 The simple argument used in Section II to justify restricting
attention to adjacent incentive constraints does not apply in the
two-good environment here. The approach is valid nonetheless
because I merely-want
to show that a particular candidate
contract is optimal. The set of contracts that satisfy global
incentive feasibility constraints is contained in the larger set of
contracts that satisfy the weaker local constraints in (19). The
candidate contract can be shown to satisfy global incentive
feasibility, so if it is optimal relative to contracts satisfying (19)
then it is optimal relative to the smaller set of contracts that
satisfies global incentive feasibility constraints.

FEDERAL RESERVE BANK OF RICHMOND

11

subject to the resource feasibility constraints
(13)-( 18) and the incentive feasibility constraints
(19).2’
The Collateralized Debt Contract
Under what conditions, then, does a collateralized debt contract solve Problem 3? To answer this
question I need to state precisely what constitutes
a collateralized debt contract. To start, the payment
schedule for good 1 is
yzn = yin(R) G MlN[&,,R].

cm

A fixed, noncontingent
amount R is transferred,
unless the harvest is too small and 8, < R, in which
case the entire crop is transferred. I have in mind
contracts in which R > 81, contracts that were
not incentive feasible in the earlier model with just
one repayment good. Figure 4(a) portrays a typical
payment schedule for good 1. For future reference,
define r as the largest index number for which
8,s R.22
To complete the description of a typical collateralized debt contract, I need to specify the
schedule of transfers of chattels, the collateral good.
I apply two guiding principles: first, ensure incentive feasibility of the resulting contract; and second,
minimize the consumption of the borrower’ chats
tels by the lender. T?ws, the chanelspayment schedul’
e
is rbe minimalscbeduk hut ensumst/rathe bonvwer does
nothave an incenhe tochat and hi& someof theAmwest.
The schedule is constructed recursively starting with
the payment y&r, for the largest harvest, and working down to y&, the payment for the smallest harvest,
with the payment set at each step to ensure that the
incentive feasibility constraint for that harvest outcome is met with equality. First, the payment y&
can be set freely, so to minimize the payment for
this harvest outcome set y;N = 0. Now for any arbitrary m < N, assume that the chattels payment
schedule
has already
been determined
for
n=m+l
, . . . ,N. The incentive feasibility constraint
relating the payments y& and yin, for n = m + 1, is
UB@n

-yW

+

Vdk

-yin)

+ VB(k -Y2m),

1

UB@n

-yim)

n=m+l.

(21)

21 Problem 3 is convex under the additional assumption, which
I now make, that -uS(&)/urj(&),
the coefficient of absolute
risk aversion of the borrower with respect to good 1, is nonincreasing. Under this condition the set of utilities that satisfy
feasibility constraints is convex (even though the constraints are
not convex in the choice variables).
** Therefore,
12

R is contained in the half-open interval [C&9,+ 1).

If yzm, payment of chattels from the borrower to the
lender, is so small that (21) is violated, then when
the harvest is 8, the borrower has an incentive to
lie to make the payments yim and yzm rather than
yin and yin. If yam is so large that (21) is a strict
inequality, then the chattels payment could be
reduced without violating incentive feasibility.
Choose for yim the smallest value of yzm that satisfies
(2 1). For each harvest outcome,the chattels
payment is
the snzallest
possible amount that does not give the borrower an incentive to lie.
The specific shape of a typical chattels payment
schedule is shown in Figure 4(b). For On > R, the
crop payment is the constant, R, so for m > r, (21)
reduces to vu(k -yin) >vu(k -yz,). Because yiN =
0, we can set y& = 0 for all m > r. In other words,
for harvests greater than R, the chattels payment is
zero. For m =r, (21) as an equality is
UB@+l

-R)

+

VB(k)

=

LIB&+
+ Vdk

1 -&I
- $1).

(W

This equation determines yi,. For harvests 8,<8,
(so that m<r), (21) as an equality isa3
UB(~)

+

vB(k-y&J
=

UB&-8m)

+

VB(k-y;m),

where n=m+l.

(23)

The left side of (23) is the borrower’ utility when
s
the harvest is Bn= 8,+ 1 and he pays yin = 8, and yin.
The right side of (23) is the borrower’ utility when
s
the harvest is 8, =em+ 1 and he instead pretends 8,
has occurred and pays yim =8, and yim. The chattels payment for harvest 8,, y&, is set so that the
borrower is just indifferent between these two alternatives. Note that the largest transfer of the collateral
good is yir, and occurs for the smallest possible
harvest, 81.
To summarize, a collateralized debt contract is
described by (20) and (2 1). For harvests greater than
R, the borrower transfers a fixed amount, R, of the
crop, and none of the chattels. For harvests less than
R, the borrower transfers all of the crop and some
amount of the chattels; just enough, for each harvest,
to dissuade the borrower from falsely claiming that
that harvest has occurred if the harvest is actually
larger.
23 This equation
0,-yi,,=&-t&=0,

ECONOMIC REVIEW, JULY/AUGUST

1991

uses the facts that for m<r
and en-yi,=Bn-8,=8,+,-Bm.

and n =m + 1,

Figure

A TYPICAL

4

COLLATEBALIZED

DEBT CONTRACT
Y2n

I .

I
4

R

(a) Wheat

eN

e

Payment

(b) Chattels

The borrower’ collateral, k, can sharply constrain
s
feasible contracts, because a contract cannot require
transfer of more collateral than the borrower actually has. The constraint that the largest collateral
transfer yir not exceed k is analogous to the constraint in the model of Section II that the fixed payment not exceed the smallest possible harvest; it
places an upper limit on the amount of the fured payment R. Although collateral can allow payment
schedules which would otherwise be infeasible, feasible payment schedules could still be constrained.z4
Optimality of a Collateralized Debt Contract
The next task is to examine the first-order
necessary and sufficient conditions for Problem 3,
and to see whether the collateralized debt contract
just described can satisfy those conditions. The
objective is to identify conditions on the agent’ utility
s
functions, the endowments,
and the probability
distribution governing the harvest that allow the
collateralized debt contract to satisfy the first-order
conditions.
One condition that is required for a collateralized
debt contract to be optimal is that the cofiateralgood
mustbe more vahabl’ at themargin to the borrowerthan
e
to the lender:
V$ (k -

yin)

u$& -yin)

VL!
(Yin)

’ ut(yin)

’

or, upon rearranging,
urJ(Yin)

u$(en-yin)

Vi(Yin)
- v$(k-yin)

,
-

0

(25)

.

The two ratios in (24) measure the marginal value
of the collateral good relative to the harvest good for
each agent. The inequality (24) states that the
marginal rate of substitution between chattels and
wheat is larger for the borrower than for the lender.
Indifference curves that satisfy (24) are shown in an
Edgeworth Box in Figure 5. Imagine increasing the
crop payment, yr,, and decreasing the chattels payment, yzn, by infinitesimal amounts in a way that
keeps the borrower on the same indifference curve.
If (24) holds then such a move along the borrower’
s
indifference curve (to the northwest in Figure 5) increasesthe lender’ utility. Thus condition (24) states
s
that, ceteris paribus, giving more of the crop to the
lender and more of the chattels to the borrower can
make one of them better off without making the other
worse off.
A second condition for a collateralized debt contract to be optimal is actually a strengthening of the
first condition; th direct benefi of giving mopecn$ to
the,knh- and morechaneh to th bonvwe mastbe greater
than the cost of th second-order efsect on incentive
constraints:

(24)

ur!(yin)
u$&-yin)

[
z4 One can easily derive an equation linking the two agents’
expected intertemporal marginal rates of substitution in this case,
analogous to (lo), but with the Lagrange multiplier on the constraint yzl< k playing the role of 11.

Payment

where An E

FEDERAL RESERVE BANK OF RICHMOND

-

vi(yin)

vd(k-yin)

1

X~fl~n - An 1 0, (26)

-Yi

4n+19(27)

13

Figure 5

THAT

INDIFFERENCE
CURVES
SATISFY CONDITION
(24)
Consumption

Origin for
Borrower’
s
Consumption

and where &+I is the nonnegative
Lagrange
multiplier on the incentive feasibility constraint for
harvest &,+I. The bracketed term in (26) is identical to the left side of (ZS), and measures the benefit
of giving the borrower more of the collateral good
and less of the crop when the harvest is 8,. Such a
reallocation affects the incentive constraint for harvest
8,+ 1, and the term An is the cost associated with this
effect. If the benefit term in (26) is greater than the
cost term A,,, then the debt contract is optimal.
To understand the cost term An, again imagine
increasing the crop payment yin and decreasing the
chattels payment yzn by infinitesimal amounts,
giving more of the payment good to the lender and
more of the collateral good to the borrower, in a way
that keeps the borrower on the same indifference
curve. In particular, increase yin to yin + E, for some
very small E> 0, and decrease yin to yin -6, SO as
to keep the borrower on a constant indifference
curve. This change affects the borrower’ incentive
s
to tell the truth when the harvest is &,+I, making
it more tempting to display 8, and make the corresponding payments, yin + E and yin -6. Specifically,
UB(b+l
-yin-E)
+ vg(k-yin+@
> UB&-yin)
+ VB(k-yin),
even though UB(8n-yin-E)
+
VB(k -yin +6)
= UB(8n -yin)
+VB(k -yin) by construction. The change in the right side of the incentive constraint for harvest en+1 [see condition (19)]
is approximately
[u$(&-yzn)
14

- u$(&+1 -Yin)16

G33)

a nonnegative quantity. The term An is just (28), the
amount by which the state n + 1 incentive constraint
is tightened, multiplied by &+ I, the Lagrange
multiplier, or “shadow value” for that constraint. (The
denominator of A,, rescales &+I into units of state
n utility.) The term An represents the costof a move
toward the northwest boundary of the Edgeworth Box
for state n. Therefore, condition (26) states that the
gap between the borrower’ and the lender’ marginal
s
s
rate of substitution between chattels and wheat must
exceed the cost of an indirect effect on incentive
constraints.ZS
There are two intuitive ways to think about condition (26). First, it can be thought of as a lower
bound on the gap between the borrower’ and the
s
lender’ valuation of the collateral good-the
s
bracketed term in (26)-for a given value of the cost
term An. If the gap is not large enough, the debt contract is not optimal and the best arrangement involves
more frequent transfer of the chattels to the lender.
Alternatively, condition (26) can be viewed as an
upper bound on the borrower’ risk aversion, because
s
the cost term An is approximately proportional to the
borrower’ coefficient of absolute risk aversion. The
s
25 Notice that if UB linear, so that the borrower is risk neutral
is
with respect to good 1, then the derivative u$ is a constant, An
is zero, and (26) is equivalent to (24). For very small values of
8 n+ 1 -O,, A,, is approximately proportional to - u&$&)/u~(c$‘
&
the coefficient of absolute risk aversion of the borrower with
respect to the payment good. Thus A,, is larger, ceteris paribus,
, the more risk averse is the borrower.

ECONOMIC REVIEW, JULY/AUGUST

1991

incentive constraints prevent the borrower from sharing as much risk as he would like with the lender,
so if the borrower is very risk averse the value of
relaxing an incentive constraint is large. If the borrower is too risk averse, the cost of indirectly tightening the incentive constraints outweighs the benefit
of giving the borrower the chattels, and the debt contract is not optimaLz6
As mentioned above, collateral is often described
as a means of compensating the lender for possible
losses in default, but its main role in this model is
to secure compliance with the debt agreement. The
amount of collateral transferred for a given harvest
is just enough to discourage the borrower from
pretending a low harvest has occurred when it actually has not. Thus to the borrower, the amount of
collateral transferred is equal in value to the.shortfall in the crop. The lender is actually worse off when
he receives collateral than when the full payment is
made, because the collateral is worth less to the
lender than to the borrower, relative to the crop. The
value of collateral to the lender does matter for the
arrangement because, the more the lender values the
collateral, the lower the interest rate the lender will
require.z7 However, the primary function of collateral
here is to keep

the borrower

that “[i]t must be difficult or impossible for the
insured to pretend that he has suffered a loss when
he has not done so.”
Many recent papers have proposed explanations
for debt contracts with occasional default. Douglas
Diamond (1984) described a model of debt contracts
based on private information about the borrower’
s
resources, as here, and based on the idea that a lender
can impose “nonpecuniary penalties” on a borrower
in the event of default. The amount of the penalty
varies with the borrower’ reported resources, and
s
is set optimally to ensure that the borrower does not
have an incentive to lie. Diamond’ model is virtually
s
a special case of the model presented above; the surrender of collateral serves as a penalty in my model,
and the collateral good can be interpreted quite
broadly as any action that reduces the utility of the
borrower. Thus the model presented above unifies
the treatment of collateral and penalties in loan contracts, and highlights their essential similarity.
An alternative model of debt contracts was first
proposed by Robert Townsend (1979) and is based
on the idea that the lender might be able to verify
the borrower’ report at a cost. If the borrower reports
s
a small harvest,

honest.

V. RELATEDLITERATUREON
DEBTCONTRACTS
Kenneth Arrow (1974), in his 1973 Presidential
Address to the American Economics Association, first
suggested that private information might be why noncontingent contracts are widely observed. This idea
arose in the early economics literature on markets
for insurance, particularly medical insurance, in which
the absence of insurance arrangements was traced
to the nonobservability of some key aspect of future
outcomes (see Arrow, 1963, and Spence and Zeckhauser, 1971). This observation has long been taken
for granted in the insurance industry itself. For
example, an insurance textbook (Angell, 1959) states
that one requirement for a hazard to be insurable is
z6 This reasoning is only heuristic, because independently
varying, say, the lender’ valuation of the collateral good will
s
affect the cost term as well via the multiplier &+I. Nonetheless,
parametric examples can easily be constructed that match the
intuition in the text. Also, one can easily obtain an explicit
expression for 4. in terms of the primitive elements of the
environment.
27The interest rate on a loan is just R/q - 1. I have in mind a
setting in which the lender compares the total return from the
loan contract to returns on alternative uses of funds, so the more
valuable the collateral the smaller R has to be.

the lender verifies the amount

of the

harvest and the borrower makes an agreed-upon payment. When the borrower’ harvest is sufficient to
s
make the full payment, no verification takes place.
The borrower never cheats, because verification
would occur and he would be discovered. The debt
contract is optimal in such an environment because
it minimizes the frequency of costly verification. The
logic is closely parallel to that of the model presented
in this article. In both models, default involves
deadweight loss-the
transfer of collateral to the
lender in my model and verification in the costly
verification model-and
the optimal contract seeks
to minimize the cost.
Unfortunately, debt contracts are only optimal in
the costly verification model in the presence of an
ad hoc restriction on contractual arrangements. For
each possible report by the borrower, a contract
specifies that the lender either verifies or does
not. More generally, a contract could specify that
for a given report the lender verifies with some
probability, not necessarily equal to zero or one. A
detemintitic contract is one in which verification
probabilities are all either zero or one, while a
randomizedcontractis one in which some verification
probabilities are between zero and one. In the
costly verification model, debt contracts are optimal
only when attention is restricted to deterministic

FEDERAL RESERVE BANK OF RICHMOND

1.5

contracts. Agents in the model can usually improve
upon the debt contract with a randomized contract,
and when randomized contracts are allowed the optimal contract does not, in general, resemble debt.
The reason is that when verification occurs with
positive probability, payments can be contingent.
Verifying with small probabilities over a wide range
of harvest outcomes can provide sufficient incentives
and allow improved risk-sharing, while incurring less
verification costs on average.z8
One might think that randomized economic arrangements are unrealistic, and that there must be
some as yet undiscovered reason why such arrangements are undesirable, but the possibility of randomization must be taken seriously in this context. Many
financial arrangements actually do involve randomized
audits, especially when one firm acts as an agent for
another and has the opportunity to hide resources.
The models presented above do not rely on a restriction to deterministic arrangements.z9
Michael Jensen and William Meckling (1976)
observed that because debt contracts force the borrower to bear all of the risk, he has more incentive
than he would under a risk-sharing arrangement to
take costly, private, ex ante actions that affect his
return. This has led some to suggest that perhaps
debt is selected over other feasible contingent arrangements because it provides superior incentives
to the borrower to take appropriate ex ante actions
(see Innes, 1990). Unfortunately, if one assumes that
the return is freely observable by the lender ex post,
then the debt contract is optimal only for very special
assumptions about preferences and technology, and
under strong restrictions on available contracts.30 If
instead one assumes that the return is unobservable,
then, as in Section II above, risk-free debt contracts
are optimal, independent of the ex ante action choice.
Two recent papers, by Oliver Hart and John Moore
(1989) and by Charles Kahn and Gur Huberman
2s Townsend (1979) recognized this fact, and subsequent research has shown that it is robust. See, for example, Townsend
(1988).
29 No verification is allowed in the models in this paper, as if
verification is prohibitively costly, so the issue of randomized
verification does not arise. A distinct but related issue concerns
randomized payment schedules, which for the same reasons can
in some cases improve upon deterministic arrangements. One
can easily show, however, that randomized arrangements are
never needed in the models above.
30 The optimality of the debt contract in Innes (1990) requires
risk neutrality and restrictions on probability distributions and
utilities such that the “monotone likelihood ratio property” holds
and effort choice is unique. In addition, only nondecreasing
payment schedules are allowed.
16

(1989), focus on renegotiation in debt contracts. To
motivate debt contracts as an optimal arrangement,
they assume that the borrower’ resources are obs
served by both the borrower and the lender but are
not verifiable by a third party such as a court, and
thus “enforceable” contracts cannot be made contingent. One could object by noting that courts often
ascertain litigants’ wealth, and often enforce highly
contingent contracts such as partnership agreements.
Although a wide range of literature examines the
effects of debt contracts or the choice between debt
and some other particular contract, the form of the
contracts available to agents is generally taken as
given. Thus this literature often has little to say about
why contracts are limited to particular forms.

VI. SOMEPOLICY IMPLICATIONS,
BRIEFLYNOTED
Recommended
public policies toward credit
markets are often predicated on models in which debt
contracts play a prominent role, and so a model that
explains debt contracts might have novel policy implications. What novel prescriptions for government
credit policy might be suggested by the model
described here? A complete answer is beyond the
scope of the paper and is the subject of continuing
research, but some tentative conclusions are possible.
Many policy prescriptions are sensitive to the
assumption that capital markets are “perfect,” meaning that people can borrow or lend as much as they
like on the same terms. For example, the Ricardian
Equivalence Theorem revived by Barro (1974),
which states that under certain conditions government debt policy is irrelevant, depends critically, as
Barro noted, on perfect capital markets. In the model
I presented above, the capital market imperfection
is derived endogenously from informational constraints, but a blanket endorsement of policy prescriptions that depend on capital market imperfections
seems unwarranted. Rather, one needs to assess how
the informational imperfection affects the policymaker’ ability to improve on private arrangements;
s
in some cases the policymaker may be as sharply constrained as private agents.
One category of potentially useful measures might
be termed “collateral enhancement.” I showed above
how the quantity of collateral available to the borrower could sharply constrain the loan contract.
Under current U.S. law, there are limits to the collateral a consumer can offer; one cannot offer to a

ECONOMIC REVIEW, JULY/AUGUST

1991

prospective lender one’ imprisonment for nonpays
ment of a debt, for example. Moreover, under the
“fresh start” provision of the Bankruptcy Act one
cannot waive the right to discharge unsatisfied debts
in bankruptcy. Consumers presumably could obtain
more credit if they could offer to be imprisoned or
could waive the right to discharge a debt, because
such stiff penalties would make larger repayments
credible. Interestingly, debts arising from government
guaranteed educational loans are not dischargeable
in bankruptcy during the first five years following the
date that the first payment becomes due [ 11 U.S.C.
aim in bankruptcy represented
5 523(a)(8)]. Th e c 1
by a guaranteed student loan is thus more burdensome than a dischargeable claim, and presumably
allows improved loan terms for the borrower or the
lender. The analysis of the present paper suggests
that allowing borrowers to waive the right to discharge
debts in bankruptcy might improve the functioning
of credit markets. However, there might be compelling countervailing reasons for the prohibition of
waivers of discharge that are not taken into account
by the models presented above; see Jackson (1985)
for a discussion.
Another possible rationale for government credit
policy concerns the valuation of collateral. Suppose
the borrower in the model described above faces two
possible lenders who differ only in the value they
place on the borrower’ chattels. The optimal arranges
ment is for the borrower to obtain a loan from the
lender who values the collateral good most highly,
since this will provide the borrower with a lower
interest rate. If, for some reason, a borrower’ cols
lateral has a social value that is higher than its private
value to lenders, due to an externality of some type,
then direct government lending or government loan
guarantees might be warranted. To justify such
policies one would have to argue that the public valuation of the collateral is higher than its highest private
valuation, and one can legitimately question whether
this condition holds for many current loan-guarantee
programs.31
Beyond these simple observations, little is known
as yet about the policy implications of models like
31 William Gale (1990) has described credit market models in
which borrowers have private information beforehand about the
riskiness of their future resources. He shows that in such models
government loan guarantees targeted to high-risk borrowers can
imorove efficiencv. In his 1991 oaner he aoolies this model to
exi’
sting federal credit programs and’
calculates’
that policy is likely
to be quite inefficient. Debt contracts are assumed in his model,
rather than derived endogenously, and it is unclear how the
analysis would be affected by the latter.

the one presented above. On one hand, it is difficult
to imagine policy interventions that make some
people better off without making anyone worse off
in this type of model, other than the two just mentioned. In particular, based on this model alone there
does not seem to be an efficiency rationale for loan
subsidies or more general interest rate manipulations.
Such policies could have important consequences for
the distribution of welfare, of course, but would have
to be evaluated by criteria other than Pareto optimality. On the other hand, the model leaves out some
features, such as ex ante private information, that
some economists claim rationalize credit market intervention.3z The claims usually pertain to markets
that are dominated by the use of debt contracts, and
yet the claims are based on models in which debt
contracts are imposed, rather than derived as
optimal. It is not yet known whether the conclusions
of those models would survive if they were modified
so that debt contracts arise endogenously, as in the
model I have presented here.

VII.

CONCLUDING

REMARKS

So why is there debt with occasional default?
My answer has two components. First, borrowers
can fool lenders about their circumstances,
so
having the borrower share risk with the lender gives
the borrower an irresistible temptation to cheat.
Thus payment schedules are noncontingent in such
situations. Second, if the borrower is incapable of
making the stipulated payment, the lender has
recourse either to explicit or to implicit collateral.
Such recourse is sufficient to dissuade the borrower
from withholding payment.
It is worth pointing out that important puzzles concerning debt contracts remain unsolved. The sole
source of uncertainty here is the borrower’ future
s
resources, and it seems quite reasonable to assume
that borrowers can hide resources from lenders. But
much of the uncertainty that faces borrowers and
lenders concerns widely observed events about which
neither is able to lie. Examples include publicly
known prices and published economic data. The
theory of Section I predicts that repayment contracts
ought to be contingent on many publicly observed
events. For example, officially published data on
average prices of consumer goods are widely available, and are closely correlated with the real value
32 See Stiglitz (1988).

FEDERAL RESERVE BANK OF RICHMOND

17

of the monetary payments made by debtors to
creditors. Why are so few debt contracts indexed for
inflation?
A second puzzle is perhaps related to the first. A
vast literature in monetary economics is motivated
by the observation that money is widely used in spot
exchanges for goods. And yet, almost all debt contracts are repaid in money as well. Perhaps the
widespread use of money to settle debts is an

APPENDIX

equally important puzzle. The model described above
does not have an explicit role for money, but the logic
of the model suggests a rudimentary answer. The
borrower might have some sort of advantage relative
to the lender in selling the crop, and therefore returns
money rather than the crop itself to the lender. This
answer is rudimentary because it does not explain
just why the borrower would have such an advantage. Evidently, much remains to be learned about
financial arrangements such as debt contracts.

A

A Derivation of the Incentive Feasibility Constraints
In this appendix I show that any pattern of consumptions by the two agents that can be achieved
by any arbitrary contract, possibly giving the borrower
an incentive to hide the harvest, can be achieved by
a contract that satisfies the incentive feasibility constraints and does not give the borrower an incentive
to hide any of the harvest. Therefore, a given consumption pattern can be achieved if and only if it
results from a contract that satisfies the incentive
feasibility constraints. The argument is presented in
the model of Section II, but can easily be extended
to cover the model of Section IV.

ment for the harvest 8,. Clearly, y; = ym for some
m in the set {1,2 ,..., p}. Since p< n, it is also true
that yi = ym for some m in the set {l,Z,...,n);
in
other words, the utility maximizing payment for the
harvest 8, is a payment that could have been made
for the harvest 8,. As a result, the payment y; can
provide no more utility when the harvest is 8, than
the utility maximizing payment yi. Therefore,
uB(&-y;)
2 tin&-y;).
Since both n and p are
arbitrary, this condition holds for n = 2,. . . ,N, and for
p=l , . . . ,n - 1. These are exactly the incentive feasibility constraints (19).

To begin, take as given an arbitrary contract
ye}, that satisfies the resource feasibility constraints (13)-( 18), and consider a given harvest
8,, where n > 1. The borrower can display any
harvest &,, where m can equal 1,2 ,..., n, and m
is chosen to maximize t&&-y,).
Define yt: as
the payment the borrower actually makes after
optimally choosing a utility maximizing display. It
does not matter if the utility maximizing display is
not unique, because the utility maximizing payment
is always unique. The payment y: clearly satisfies
u~(8~-y@~un(&-y~)
for m=l,Z,...,n.

I have defined a set of payments {yi,yi,...,yk),
the utility maximizing payments chosen by the borrower when the contract is {q,yr,yz,...,yN}.
Now
define a new contract {q,yi ,yi ,.. .,yA}, by substituting the actual payments for the originally stipulated
payments. This new contract satisfies the incentive
feasibility constraints, and thus does not provide any
positive incentive to hide harvest. The new contract
results in consumption patterns for both the borrower
and the lender that are identical to those resulting
from the original contract. Because the original
contract is arbitrary, I have shown that any consumption patterns that can be achieved can also be
achieved under a contract that provides no incentive to hide the harvest.

@lJlJZ,...,

Now consider an arbitrary harvest Or,<&, and
define y; analogously as the utility maximizing pay-

18

ECONOMIC REVIEW. JULY/AUGUST

1991

References
Angell, Frank J., 1959, Insurance:
New York: Ronald Press.

Principks

and Practices,

Arrow, Kenneth J., 195 1, “An Extension of the Basic Theorems
of Classical Welfare Economics,” Proceedings of the Second
Be&eky Symposium MI Mathmatial
Staritics and Pmbabihy, J. Neyman (ed.), Berkeley: University of California
Press, reprinted in Co/lected Papen of Kenneth J. Amwn,
Yoluin 2, General &ui/ibrium, Cambridge, Massachusetts:

Harvard University Press, 1983.

Economics
53, 941-69.

1963,
“Uncertainty
and the Welfare
of Medical Care,” American Economic Rewiew

1964, “The Role of Securities in the Optimal
Allocation of Risk Bearing,” Review of Economic Studks 3 1,
91-96, reprinted in collectred Papen of Kenneth J. Anw,
y,/,,,
2, General Equilibrium, Cambridge, Massachusetts:
Harvard University Press, 1983.
, 1974, “Limited Knowledge and Economic
Analysis,” American Economic Re&w Papers and Proceedings
64 (March), l-10, reprinted in Colkcted Papers of Kenneth J.
A~Iw, Volume 4, Th Economics of Infoormotion, Cambridge,
Massachusetts: Harvard University Press, 1984.
Barro, Robert J., 1974, “Are Government Bonds Net Wealth?,”
Journal of Pohicai Economy 82 (November/December),
1095-1117.
, 1976, “The Loan Market, Collateral, and Rates
of Interest,” Journal of Money, Credit, and Banking 8
(November), 439-56.

Gale, William G., 1990, “Collateral, Rationing, and Government
Intervention in Credit Markets,” in &mmetric Znfbnation,
Corporate Finance, andInvestment, R. Glenn Hubbard (ed.),
University of Chicago Press, Chicago.
, 1991, “Economic Effects of Federal Credit
Programs,” Amtian Ecwromic Review 81 (March), 133-52.
Hart, Oliver, and Moore, John, 1989, “Default and Renegotiation: A Dynamic Model of Debt,” photocopy, MIT.
Innes, Robert D., 1990, “Limited Liability and Incentive
Contracting with Ex-Ante Action Choices,” Journal of
Economic Thory 52 (September), 45-67.
Policy in
Jackson, Thomas J., 1985, “The Fresh-Start
Bankruptcy Law,” Harvard Low Review 98, 1393-1440.
Jensen, Michael, and Meckling, William, 1976, “Theory of the
Firm: Managerial Behavior, Agency Costs and Ownership
Structure,” Journal of Finatuia/ Economks 3, 30560.
Kahn, Charles, and Huberman, Gur, 1989, “Default, Foreclosure, and Strategic Renegotiation,” Law and&temporary
Pmbkms 52, 49-61.
Lacker, Jeffrey M., 1991, “Collateralized Debt as the Optimal
Contract,” Federal Reserve Bank of Richmond Working
Paper 90-3R2.
Lacker, Jeffrey M., and Weinberg, John A., 1989, “Optimal
Contracts Under Costly State Falsification,” Joumai of
PolitiGal Economy 97(6) (December),
1345-63.
Myerson, Roger B., 1979, “Incentive Compatibility
Bargaining Problem,” Ehnomem~a 47, 61-73.

and the

Debreu, Gerard, 1959, The Theory of Value, Wiley, New York.

Spence, M., and Zeckhauser, R., 1971, “Insurance, Information and Individual Action,” American Economic Review 6 1,
380-87.

Diamond, Douglas W., 1984, “Financial Intermediation and
Delegated Monitoring,” Review of Economic Studks 51,
393-414.

Stiglitz, Joseph E., 1988, “Money, Credit, and Business
Fluctuations,” The Economic Record (December), 307-22.

New

Townsend, Robert M., 1979, “Optimal Contracts and Competitive Markets with Costly State Verification,” JoumaL of
Economic Thoty 2 1, 26593.

Flood, Mark D., 1991, “An Introduction to Complete Markets,”
Federal Reserve Bank of St. Louis Review 73 (March/April),
32-57.

, 1988, “Information Constrained
Insurance:
The Revelation Principle Extended,” Jountol of Monetary
Econofnics 21, 411-50.

Fisher, Irving, 1930, Th
York.

Thory of Interest, Macmillan,

FEDERAL RESERVE BANK OF RICHMOND

19

Loan Loss Reserves
John R. Walter

“Landmark Lifts Re.wve, Takes $28 MiDionLIXS”
“‘
PNCto BoostLoss Reserves By As Much As $450 Milclion”
“‘ l’
Big oan-kx.s
prw&‘
ons, refzectinggIoomy economicprospects, continued to color the earnings
reports of regional banks . . . ”
“UJB Raises Loan Reserves and Posts$17 Milrlion
Los”
“<Bank Bostonreported Thursday that it lost $187 million in the@wth quatier, after taking a
of
$280 milion provision fir c&it Losses.Th company al’ announced plans to cut . . .
s0
IOOOjobs. . . ”
(American Banker various 199 1 issues)

DESCRIPTIONOFRESERVESFOR
LOAN

In 1990 banks throughout the United States had
total provision for loan losses of over $3 1 billion, an
amount almost twice bank profits. Since the mid198Os, provision for loan losses has been one of the
most. important factors affecting bank profitability.
Headlines and narratives like those listed above
demonstrate the interest of the financial press in
banks’ loss provisions. Yet for many banking students
the subject generates questions: What types of accounts are being discussed? Is there a difference
between loan, loss reserves, loan loss provision,
provision for credit losses, and allowance for loan
losses? Where do these reserves come from? How
do banks decide how much to add to the reserve?
Why does increasing reserves produce losses for
banks? And why do banks use reserves in the first
place?’
This paper seeks to answer these questions. In
doing so it lists and defines the terminology frequently
used in discussions of bank loan losses (see “Definitions of Terms” on p. 29) and examines the history
and current use of the reserve for loan losses. It also
discusses how and why methods for determining the
level of reserve for loan losses have changed.
1 For expositional sim licity leasing is ignored since it is
handled in essentially t l!e same manner as lending. Names of
accounts are therefore shortened throughout the article. For
example, provision for loan and lease losses as on bank Reports
of Condition and Income is called provision for loan losses.
20

ECONOMIC Rk’
IEW,

LOSSES

The primary business of banking is the collection
and investment of depositors’ funds. As a part of this
business banks bear credit risk, i.e., the possibility
that the borrower will fail to repay as promised. The
two major assets in which banks invest depositors’
funds are securities and loans. Credit losses on
securities are minimal because the bulk of these
holdings are government securities with little or no
default risk. Loans are a different story. In 1990
banks throughout the United States wrote off over
$29 billion in loans as uncollectible
(net of
recoveries), an amount almost twice total profits of
all U.S. banks for the year.
The federal banking regulators (Federal Deposit
Insurance Corporation, Office of the Comptroller of
the Currency, and Federal Reserve) require that all
banks.include in their financial statements an account
named allowance loan ioaes (also known as mserwes
for
for l’
oan Loses). Figure 1 provides an illustrative
example showing how the reserve for loan losses
(line 4) is typically reported. The account absorbs
loan losses both from loans the bank can currently
identify as bad loans and from some apparently good
loans that will later prove to be uncollectible. The
reserve for loan loss account is established and maintained by periodic charges against earnings. The
charges show up on the income statement as an
expense category named prw&ion for loan losses(see
Figure 2, line 10). The reserve for loan losses is
JULY/AUGUST

1991

When lqan losses are recognized, that is, when a
bank decides that some portion of a loan will not be
collected and therefore must be chargedofor wriz.ten
down, the amount of the loss is deducted from the
asset category loans and also from reserves for loan
losses. Suppose for example a bank had made a $100
loan but only expected to be able to collect $40 from
the borrower. In Figure 1, $60 would be deducted
from $64,000 on line 3 so as to reduce the loan portfolio by the uncollectible amount of the questionable
loan. The $60 would also be deducted from $1,000
on line 4. If the bank had already anticipated a $60
loss on the loan and had added $60 to its reserve
then the bank’ current income would not be affected
s
by the write-down. On the other hand if the loan loss
had not been anticipated before the loan was
written down, then in all likelihood the bank would
add $60 to its reserves following the write-down in
order to maintain its reserve at a level sufficient to
absorb future loan losses.

Specific Reserves
At many banks, for analytical purposes or
on internal books, the reserve is divided into
two categories, specific or allocated reserves,
and general reserves. Specific reserves are
those that a bank views as being associated
with some particular loan or group of loans.
When a bank determines that a loan presents
a greater-than-normal risk of loss it may either
add to its reserves specifically for that loan or
designate some portion of reserves to be allocated for the loan. Those reserves that are not
allocated to particular loans or groups of loans
are the general reserves. Division of the reserve
account into these two categories allows the
bank to analyze its loan loss reserve needs
more precisely. On financial reports, however,
general and specific reserves are summed and
reported simply as reserves for loan losses.

Why Banks Create Loan Loss Reserves
Displaying loans on a bank’ balance sheet as
s
the amount of funds lent without an adjustment for
expected but uncertain future losses would mislead
the bank’ board of directors, creditors, regulators,
s
and investors by overstating the bank’ assets. The
s
income-earning potential of the bank and its capital
would also be overstated, making the bank appear
stronger than it really is. One would prefer the
balance sheet to show as assets only that portion of
loans that will be collected. It is difficult, however,
for a bank’ management to determine before the fact
s
which loans will not be repaid. The compromise

increased by an amount equivalent to the amount
charged against earnings as a provision for loan losses
(Figure 3, line 4). Banks make additions to the
reserve account when (1) it has become apparent that
a loan or group of loans is more likely to be in part
or wholly uncollectible; (2) an unanticipated chargeoff has occurred for which the bank did not set aside
reserves; or (3) the amount of loans in the bank’
s
portfolio has increased.

Figure 1

Balance Sheet as of December 31, 1990
Illustrative National Bank
(000)
Assets

Liabilities

Cash

$

Securities

8,000
20,000

Total loans

$

Less: Reserves
for loan losses

-

5

Equals:

Net loans

6
7

Other real estate
Other assets

8

Total assets

64,000

9
10
11

and Equity

Deposits
Other liabilities
Total liabilities

$

74,000
19,000
$

93,000

1,000
63,000

owned

400

12

Owners’ Equity

7,000

8,600
13
$ 100,000

Total liabilities
and owners’ equity

FEDERAL RESERVE BANK OF RICHMOND

!$ 100,000
21

Figure 3

Figure 2

Calculation of Reserves for Loan Losses for

Income Statement for Year Ending
December 31, 1990

1990

Illustrative National Bank

Illustrative National Bank

(000)

(000)
Interest

1

income

1

Interest

and fees on loans

2

Interest

on securities

3

Other interest

Noninterest

income

200

Service

Other noninterest

charges

6

Total income

7

Interest

Other interest

Noninterest
9

expense

and benefits
for loan losses

11

Other noninterest

expense

Total expense

13

Income

before taxes

14

Income

$4,000
2,000

1,000
300
1,700
$ 9,000

taxes

Net income

$ 1,000
250
$

750

used by banks is to estimate the amount of losses
that are likely to result from all of the loans in the
bank’ portfolio and to call this estimate the reserve
s
or allowance for loan losses. According to the
American Institute of Certified Public Accountants
(AICPA):
“. . . the allowance for loan losses represents an amount
that, in management’ judgment, approximates the current
s
amount of loans that will not be collected” [AICPA,
(1983), p. 621.

The reserve for loan loss account appears on the
asset side of a bank’ balance sheet as a deduction
s
from total loans; it is what accountants refer to as
a contraassetaccount.The total book value of a bank’
s
loans less the reserve for loan losses should be, if
the bank is accurate in its assessment of future loan
losses, the best estimate of the net realizable value
of the loan portfolio as of the financial statement
date. Total loans less the reserve is called net loans
(Figure 1, line 5).
22

285
85
300
$ 1,000

600

expense

Provision

15

900

Informational Value of the Reserve
for Loan Losses

10

12

Reserves for loan losses, end of 1990

$

$10,000

on deposits

Salaries

during 1990

400
income

expense

8

Plus: Provision for loan losses, 1990

5

5

Interest

Plus: Recoveries during 1990 of loans
previously charged off

4

1,800

Less: Charge-offs

3

$ 7,000

income

4

Reserves for loan losses, beginning of 1990

2

Depositors,
bank stock investors, and bank
analysts are not, in general, privy to information about
the riskiness of banks’ loans beyond that revealed
by the amount of past due and nonaccrual loans which
banks are required to report. In other words, the
management of a bank has more information about
the quality of the loan portfolio than do outsiders.
Data on the amount of reserves a bank holds and
additions made to reserves are useful to outsiders,
since they provide additional information about the
quality or riskiness of the loan portfolio. The value
of this information is demonstrated by the strong
reaction of bank stock prices to unexpected news
about bank reserves.
The loan quality information or signal provided
by the reserve should be most trustworthy immediately after regulators examine a bank. Examiners provide an independent, unbiased assessment of the
quality of a bank’ loan portfolio and also have the
s
power to force the bank to restate loans and reserves
when their values deviate from the regulator’ best
s
estimates. Financial reports coming out soon after
a visit from examiners are, therefore, more likely to
include an accurate statement of expected net
realizable loan values.
LOAN CATEGORIES
At any given time a bank is likely to have some
loans in each of the following four categories:
1.

Good loans. The borrower is making
scheduled interest and principal payments and
the bank has no reason to suspect that the
borrower will not pay back the loan in full.

ECONOMIC REVIEW, JULY/AUGUST

1991

2.

Loans past due or otherwise in doubt.
Scheduled interest or principal payments have
been missed or the bank has some other
information indicating that repayment of the
loan is in doubt.

3. Written-down loans. The bank has removed some of the face value of the loan
from its books because it believes it will be
able to collect only a portion of the loan.

4. Charged-off loans. The value of the loan
has been completely removed from the bank’
s
books, because the bank believes it will be
able to collect little or nothing from the
borrower. The bank may continue to attempt
to collect funds from the borrower though it
has charged the loan off its books and may
be carrying some collateral from the loan
on its books.
Most loans stay in category 1 until repaid. Some loans
however start off in category 1 but later travel through
all three remaining categories before being closed out.
Any loan in categories 2 or 4 is a problem loan. Loans
in category 3 are often considered problem loans.
In some cases, however, when a loan has been
written down by an amount sufficient to lower its
reported value to its collectible amount, it might be
considered a good loan.
The Problem Loan
For most loans only the passage of time and
scheduled interest and principal payment dates allow
banks to distinguish good loans from problem loans.
When the borrower is more than 30 days past due
on a scheduled payment the loan is considered past
due and the bank lists it as such in its financial
statements. The bank probably will have made some
effort to contact the borrower to secure payment
before delinquency reaches this stage. As scheduled payments fall further in arrear, the likelihood
of ultimate repayment diminishes.
When repayment of a loan becomes less likely
most banks will add to the reserve in anticipation of
a possible loss. Beyond setting aside additional
reserves, past due or doubtful loans may be handled
in one of several ways depending on the bank’
s
policies. Some banks promptly charge past due or
doubtful loans off their books and then attempt to
recover from the borrower whatever funds possible.
Other banks carry such loans on their books until
the borrower recovers or until forced either by the
passage of time or by regulators to charge off the

loan. Banks will at times attempt to renegotiate the
terms of a loan if renegotiation seems likely to
encourage some repayment. In most cases if a loan
is past due more than 180 days it will be charged
off or at least written down. When a loan is charged
off, interest income accrued but not received during
the current accounting period is subtracted from current income, and interest accrued but not received
in prior accounting periods is deducted from reserves
for loan losses [Board of Governors (1984), Section
219.1, p. 41.
The decision between charging off all or only a
portion of a loan will depend on whether the bank
believes any of the loan is collectible, on the bank’
s
normal procedures for handling losses, and on
examiners’ opinions. Banks with very conservative
loan loss procedures may choose to completely
charge off any past due or doubtful loan even if it
is likely to be partially repaid. Other banks may, when
relatively certain that some portion of a loan will
ultimately be collected, deduct only a portion of the
face value of the loan from the asset category loans,
meaning the loan is written down to its collectible
amount. The amount of the write-down is also
deducted from reserves for loan losses. If it is
unlikely that any portion of a loan will be ultimately
collectible then the loan normally will be charged off
completely. Regulatory examiners may, following an
examination, require a bank to set aside additional
reserves for a loan, to write it down, or completely
charge it off, depending on their opinions of the probability of repayment.
Collection of funds on a loan that has been completely or partially charged off can be a long and
expensive process. Banks usually foreclose on or
repossess available collateral. The amount a bank will
ultimately recover from written-down or charged-off
loans depends on the financial health of the borrower,
the borrower’ willingness to pay, the value of any
s
collateral, the strength of guarantors or cosigners, and
the ability of the bank’ workout department or that
s
of the individual loan officer assigned to the account.
Any recovery of an amount previously charged off
or charged down is added to reserves upon its collection (see Figure 3, line 3).

DETERMINATIONOFTHE
SIZE OFTHE
RESERVE FORLOANLOSSES
Banks’ use of the reserve for loan losses, and
especially banks’ decisions with respect to the size
of the account, have changed since the 1940s. The
main forces shaping the change have been tax policy,

FEDERAL RESERVE BANK OF RICHMOND

23

regulators’ instructions, and the growing loan losses
of the 1980s. For the first 30 years of the routine
use of the account, tax policy determined the amount
of reserve held by banks. Then regulatory pressures
and high loan losses became dominant determinants.
The Influences of Tax Policy
From 1947 until the mid-1970s or early 198Os,
the amount of reserve for loan losses held by banks
was largely based on tax considerations. Few banks
employed the account before 1947. Most banks
relied instead on the “specific charge-off method”
since its tax treatment was straightforward [FDIC
(1947), pp. 25-26, and Blake (1952), pp. 30-351.
That method of accounting for loan losses involved
the subtraction of loan losses from current income
or net worth when the loan was charged off.
On December 8, 1947, the Commissioner of
Internal Revenue liberalized its policy for banks by
ruling that banks’ reserves for loan losses could be
calculated in a manner that differed from that of other
businesses [FDIC (1948), p. 451. Banks were allowed
to hold a reserve for loan losses equal to three times
their average yearly loan loss experience of the past
20 years. Soon after the 1947 ruling most large banks
and many small banks began holding reserves for loan
losses (see Table 1). With some modifications, this
policy continued until 1969. Banks could hold
reserves exceeding the maximum specified by the
IRS, but once the maximum was exceeded additions
to the reserve were not tax deductible. This was the
case for years before and since 1969. See Table 2
for details of tax laws and rulings.
The Tax Reform Act of 1969 broke with the most
recent 20 years of IRS policy and gradually required
banks to hold a reserve equal to their current and
past five years’ losses [U.S. Congress, House of

Table 1

Percentage of Banks with a Reserve Account
in Selected Years
1948
1950
1957
1963
1971
1975
Sources:

24

38
43
51
61
91
94

1948 and 1950 figures, FDIC (1950), p. 51; 1957 figure,
ARCB (1972), p. 11; 1963-75 figures, ARCB (1977). p. 4.

Representatives (1969), pp. 464-751. The 1969 act
was passed in part to lower banks’ tax advantage over
other businesses. The change was to be phased in
over the next 18 years (see Table 2, 1969 Tax
Reform Act). During the phase-in period a bank
could either add to reserves for loan losses until they
equaled a percentage of loans specified by the act,
or until they equaled the bank’ average ratio of loan
s
losses to loans of the past six years. The maximum
ratio of reserves for loan losses to loans specified by
the act declined every six years over the 18-year
phase-in.
In 1986 the Tax Reform Act of 1986 was passed,
eliminating, for banks with more than $500 million
in assets, the opportunity to subtract, as a pre-tax
expense, any provision for future loan losses beyond
the amount of loans actually charged off during the
year. Small banks continued to hold reserves based
on the specifications of the Tax Reform Act of 1969
[U.S. Congress, Joint Committee
on Taxation
(1987), pp. 549-531.
The rapid growth in reserves following 1947
and the maintenance of levels close to the maximum allowed by the IRS until the early 1980s are
apparent in the chart (see listing of IRS maximums
in Table 2). While bank loan losses were small and
on average fairly constant relative to total loans from
1947 through the early 197Os, banks held reserves
throughout the period that greatly exceeded losses.
Banks’ best estimates of expected loan losses
during most of the period were almost certainly
considerably lower than the amount of reserves held.
However, it was to the banks’ advantage to hold
reserves at the maximum allowed by the IRS since
doing so resulted in lower taxes.
Tax Considerations Become Less Important
Until at least the early to mid-1970s, tax rulings
and laws encouraged banks to hold reserves that
greatly exceeded losses so that significant regulatory
efforts aimed at influencing banks’ holdings of
reserves were not necessary. Beginning in 1976,
however, federal regulators began to encourage banks
to hold a reserve of at least 1 percent of total loans.
By 1976 the maximum reserve allowed by the IRS
had declined to 1.2 percent of loans.
Beginning in 198 1 bank failures began to rise and
in 1982 net loan losses relative to total loans began
a fairly steady increase that would last through the
1980s and into the 1990s (see chart). Regulators
and accountants were no longer willing to permit

ECONOMIC REVIEW, JULY/AUGUST

1991

Table

2

Tax Laws and Rulings Affecting Banks’ Reserves for Loan Losses
Year

Type of decree

Effect

on reserves

1921

Revenue

1947

Ruling

Allowed banks to cumulate reserves for loan losses from pre-tax income up to three times the
banks’ average annual losses of the past 20 years.

1954

Ruling

Banks could choose any 20-year
reserves.

1965

Ruling

All banks could accumulate
reserves from pre-tax income
Further additions must come from after-tax income.

1969

Tax Reform

Act

Allowed all businesses to make additions to bad debt reserves from pre-tax income.
set aside was to be reasonable based on loss experience of individual businesses.

Act

Mandated
provisions
1969-75

period after

the following phased reduction
could not be made from pre-tax
maximum

reserves/loans

=

1927 on which to calculate

of maximum
income:

up to 2.4
reserves

Amount

their maximum

percent

of total loans.

percentage

above which

1.8 percent

1976-81, 1.2 percent
1982-87, 0.6 percent.
Also specified eventual replacement
of percentage-of-loans
method with maximum reserves
based only on bank’ loss experience.
s
Between 1969 and 1987 banks could choose either
the appropriate percentage or the “experience method” in which the maximum reserve equals
the product of the average net charge-off to total loans ratio for the most recent six years times
current outstanding total loans. Banks could switch between percentage-of-loans
method and
experience method from year to year between 1969 and 1987. After 1987 only the experience method could be used.

1986

Tax Reform

Act

Banks with assets over $500 million must use “specific charge-off
additions
to reserves for loan losses from pre-tax
income
charge-offs.
For smaller banks, 1969 Tax Reform Act holds.

banks to base the size of their reserves either on a
standard rule or on a shrinking arbitrary percentage
set by the IRS (after 1982 banks were not taxed on
additions to reserves when the reserve was less than
.6 percent of loans). Regulators began to encourage
banks to calculate reserves based on their own
expectations of future losses in the loan portfolio.
The chart shows that in the early 1980s banks, on
average, responded to regulatory pressure, or at least

Percent

LOAN LOSSES AND RESERVES
RELATIVE TO TOTAL LOANS
All Insured U.S. Banks

4
Loan losses/Loans
3 -

2 -

Reserves/Loans

h

0
-11:
I
;
I
!
I
!
I
I
I i
I I
1930 1940 1950 1960 1970 1980 1990

method”
beyond

that permits no
current
year’
s

to growing loan losses, by maintaining reserves well
above the maximum .6 percent of total loans permitted by the IRS. The chart also demonstrates that
the gap between reserves and loan losses (both
expressed per dollar of loans) shrank from the early
1970s to 1987 but recently has returned to levels
common in the 1950s and 1960s. The earlier gap
developed in response to tax incentives, but the more
recent gap reflects expected large losses from loans
to less developed countries and from commercial real
estate loans.
While regulators have been pushing banks to base
reserves on expected loan losses, they have recently de-emphasized reserves somewhat as a component of regulatory capital. Traditionally reserves
for loan losses have been counted in regulators’
measures of capital (see “Definitions of Terms” on
p. 29 for the ratios regulators use currently in capital
adequacy measures). Before 1988 all of a bank’
s
reserve for loan losses was included in the regulators’
main measure of bank capital, primary capital, and
therefore was allowed to play an important role in
adding to bank capital adequacy. Since 1988, reserves
for loan losses have been de-emphasized somewhat
in capital adequacy measures, since they are counted
only in Tier 2 capital and only up to a specified

FEDERAL RESERVE BANK OF RICHMOND

25

proportion of assets [Board of Governors (199 l), pp.
3-474.1 and 3-474.21. According to the capital
guidelines agreed upon by all three federal regulators
in 1988, capital adequacy is measured using Tier 1
capital and total capital (the sum of Tier 1 and
Tier 2 capital). Total capital includes reserves for loan
losses, up to a specified limit, and therefore is
augmented by additions to reserves.
Determining the Size of the
Loan Loss Reserve
Banks employ various techniques to set their
reserve for loan loss levels. The amount of reserve
maintained is scrutinized by bank regulators and is
often modified following bank examinations. Banks
maintain reserves at a constant ratio to loans, to
past loan losses, or at levels comparable to those
maintained by their peers. Alternatively they set
reserves to advance income or tax management goals.
Finally they set reserve levels by performing an
analysis of potential loan losses in their portfolios.
They may even use a blend of some or all of the
preceding.
Constant
Percentage-of--Loans
Rde This technique
requires that the bank decide on some target level
for the ratio of reserves to total loans and then add
to the reserve account whenever the ratio falls below
target. The percentage-of-loans technique requires
no determination of expected future loan losses. The
method was used by the majority of banks before
the mid-1970s with the target percent determined
by the IRS and by tax laws. For large banks, since
the passage of the Tax Reform Act of 1986, and for
smalI banks, since 1988 and the beginning of the final
phase of the Tax Reform Act of 1969, there is no
tax incentive to base reserves on a percent of loans.
Some small banks, however, may continue to use
the rule, setting the ratio of reserves to loans at 1
to 2 percent.
Use of the technique limits the analysis a bank must
perform to determine the size of its reserve account
but can lead to several problems. First, regulators
and a bank’ outside accountants are likely to object
s
to the technique at some point since both the Financial Accounting Standards Board (FASB) and federal
regulators have stated plainly that the reserve is to
be based on expected losses [FASB (1989), p. 351.
Therefore a bank may be required to show that there
is a relationship between its reserves and expected
loan losses. Second,,using the technique may leave
the reserve for loan losses too small to deal with
several quarters of substantial loan losses. If instead
26

the bank were performing a more sophisticated
analysis of expected loan losses, loan losses might
be better predicted and the reserve augmented in
preparation.
Peer Equiwaient In its most basic form the peer
equivalent technique involves setting the reserve
for loan losses equal to or near the level maintained
by a bank’ peers. Financial reports for banks are
s
widely published, so determining the amount of
reserves held by peer banks of equivalent size
operating in equivalent markets is a simple matter.
The advantage of the technique is that, like the
constant percentage-of-loans technique, it allows the
bank to avoid any detailed and costly analysis of its
loans. While a few small banks may make exclusive
use of such a simple approach, most banks make use
of peer information as one of several elements in their
determination of appropriate reserve level. Banks
compare their own reserves relative to loans to that
of peers to determine if their reserve is in line with
that of their peers. Regulators also encourage banks
to compare themselves with peers but not to the
exclusion of analysis of expected losses [see, for
example, Board of Governors (1984), Section 2 19.1,
p. 3; and OCC (1984), Section 217.3, p. 1).
Loss History Most banks use prior years’ history
of loan losses to help them determine current reserves
for loan losses. Since the amount of each small bank’
s
tax benefits available from provisions for loan losses
is determined by a formula based upon past years’
loan losses, some of these banks place considerable
weight on such losses when deciding current reserves.
For other banks, prior losses on fairly homogeneous
loans such as credit card loans, auto loans, personal
loans, and home mortgages can provide a reasonable
guide to what can be expected in the future.
Since the regulatory agencies warn their examiners
not to allow banks to rely too heavily on historical
loss data, it is likely that most banks do not place
an unwarranted emphasis on past experience when
determining their appropriate reserve levels [see,
for example, OCC (1984), Section 2 17.1, p. 2; Board
of Governors (1984), Section 219.1, p. 2; and
AICPA (1983), p. 621. The problem with relying
completely on loss history is that loan losses are
affected by factors that change over time, such as
the phase of the business cycle and management
philosophy about the declaration of loan losses, so
that the experience of the last several years may not
always be a good predictor of future conditions.

ECONOMIC REVIEW, JULY/AUGUST

1991

IncomeManagement Banks can smooth variations
in reported income through their choices of when
to take provisions for loan losses. By taking small
provisions during periods of poor operating income
and large provisions when income is high, a bank
can shift reported income from prosperous to depressed times, thus smoothing its reported income
stream. Choosing the size of provisions to dampen
reported income fluctuations may, however, lead the
bank’ auditors, regulators, or the Securities and
s
Exchange Commission (SEC) to question the bank’
s
income or expenses reporting.

Figure 4

Estimate of Needed Reserves for Loan Losses

Loan Category

Large classified
Potentially

Loan AnaLlyis Regulators, in their efforts to
promote more accurate reporting of banks’ income
and net worth, have been encouraging banks to use
careful loan analysis in the determination of reserve
levels since the mid-1980s. When a bank sets its
reserves for loan losses equal to an estimate-based
on analysis of each loan or loan category-of the loss
inherent in the loan portfolio, it determines its
reserves using the loan analysis method. While
there is considerable variation among banks in the
specifics of the analysis, the basic procedures are
similar.
Banks generally divide loans into categories and
then apply differing analyses to each category to
estimate the reserves needed for each category.
These estimates are summed across categories to
arrive at a total for the loan portfolio (see Figure 4).
In general, loans are divided at a minimum into large
classified loans, other large loans, and small commercial and consumer loans.

weak

$

5,000
4,000

Doubtful

2,000
500

Loss

1,250,OOO

large loans

Problem

small commercial

Problem

small consumer

Small

commercial

Consumer

loans
loans

loans

8,000
10,000
900,000

loans

Total estimated

Estimated
Needed
- Reserve

loans

Substandard

Other

Tax Management When additions to the reserve
for loan losses were tax deductible beyond actual
charge-offs or loan. loss experience, bank income
taxes were lowered in high income years by taking
larger provisions for loan losses. When income was
down, and tax benefits were not as valuable, provisions were decreased. Banks can still produce some
tax benefits through shrewd use of the reserve account. Large, banks, for which tax deductions are
limited .to actual loan charge-offs, can to some
extent concentrate charge-offs when income is high.
Small banks, which since 1988 have been using the
experience method of determining tax-deductibility,
can set aside the maximum provisions allowed by past
loss experience when income is high, and fairly low
provisions in years when income is low. As with income management, these maneuvers are likely to
produce questions from the IRS, regulators, and
auditors.

Prinrikyl
-

1,000,000
needed

reserves

$

500
800
1,000
500
12,500
1,600

2,500
9,000
10,000
$38,400

For most banks the majority of large loans, i.e.,
those that are significant in relation to bank capital
or total loans, are found in the commercial loan portfolio. Classified loans are those that have been
placed in higher-than-normal risk classes either by
the bank’ internal loan review or by examiners. A
s
bank’ entire portfolio of large loans is frequently
s
reviewed to determine (1) which loans present
greater-than-average
risk and should therefore be
classified and (2) whether those loans already
classified should be unclassified or moved to a higher
risk category. Classified loans are scrutinized more
carefully than other loans when determining reserves
for loan losses.
An expected loss or range of losses for all classified
loans for each risk class may be estimated from past
years’ losses and recoveries for that class of loans,
from knowledge of the individual classified loans, or
from a combination of both. A reserve need is computed for each loan or class of loans as the multiplicative product of the chance of expected loss for
the loan or class times the dollar amount of the
expected loss. Some of the factors banks typically
consider when deciding the probability and amount
of loss from a classified loan are the following:
whether the loan is currently past due, and if so, how
far past due; also, the financial condition of the borrower, the availability of responsible cosigners or

FEDERAL RESERVE BANK OF RICHMOND

27

guarantors, the availability of collateral and its value,
national and regional economic trends, and, finally,
industry trends.2
The losses inherent in the portfolio of other large
loans, i.e., large loans that are not classified, must
also be estimated to determine the amount of reserves
needed for these loans. The estimate is based on
(1) historical loss data for large loans with normal
risk, classified by type of loan, (2) knowledge of
the creditworthiness of the individual borrowers, and
(3) economic and industry trends.

card loans, assuming conditions affecting losses on
such loans to be unchanged in the coming year.3 If
rising unemployment or some other factor that might
increase losses is expected in the coming year, the
amount of reserves needed for these loans would be
higher. Small commercial loans and consumer loans
that are past due or on nonaccrual status generally
require larger reserves than current loans, since a
borrower’ failure to make scheduled loan payments
s
is an indication that a future loss may be imminent.

CONCLUSION

Expected losses on small commercial loans and
consumer loans that are not past due or on nonaccrual status are estimated from loss histories of
the various types of loans and from other considerations that may influence losses in the future. For
example, a bank may have suffered losses ranging
from 2 to 4 percent per year of its credit card
portfolio over the past five years. It would be
reasonable, therefore, for the bank to maintain
reserves for credit card loans equal to 4 percent of
the average amount of the bank’ outstanding credit
s
* During 1990 the Financial Accounting Standards Board,
the primary accounting rule-making body, began considering a
proposal that could, if implemented, result in a new accounting
standard to be used by banks in their calculations of the
amount of reserve needed for individual “impaired loans” (loans
for which it is probable that the bank will not collect all principal and interest payments according to the terms of the loan
contract). Under the new standard the amount of reserve considered adequate for an impaired loan would equal the difference
between the book value of the loan and the present value of
the expected cash flow generated by the loan. The new standard would apply only to impaired loans.

28

Most banks no longer set their loan loss reserves
at some fixed percentage of total loans as was
customary until the early 1980s. Owing to (1) the
elimination of most of the tax incentive to maintain
excess loan loss reserves, (2) to regulators’ abandonment of a fixed target reserve to loans ratio, (3) to
the diminished role of reserves in regulatory capital
measures, and (4) to regulatory pressure to use loan
loss analysis in reserve determination, the reserve is
now more likely to measure potential loan losses than
in the past. Nevertheless,
the desire to smooth
reported profits, to lower taxes, and to limit the
expenses of estimating future loan losses continues
to provide an incentive for banks to hold reserves
at levels that differ from their best estimates of the
losses inherent in their loan portfolios.
3 For low value, high volume loans regulators require banks to
hold reserves only for the coming year’ expected losses, rather
s
than holding reserves for expected losses over the life of the loan,
which may exceed one year.

ECONOMIC REVIEW, JULY/AUGUST

1991

Definitions

of Terms

Allocated transfer
risk reserve

Balance sheet item, separate from loan loss reserve (LLR), that accounts for the
risk that foreign borrowers will not be able to acquire sufficient foreign exchange
to repay loans.

Charge-off

Completely removing a loan from the balance sheet by subtracting
from loans and from LLR. Also called write-off.

Default

Failure of borrower to satisfy provisions

Experience

method

its book value

of loan agreement.

Basing the amount of the addition to LLR on historical loan loss experience.

Foreclosure

Legal proceeding removing from the debtor all interest in mortgaged property when
conditions of the mortgage have been violated.

Loan loss reserves
(LW

Balance sheet account. Deducts from total loans the portion of loan principal not
expected to be paid back. Also called allowance for loan losses or reserves
for credit losses.

Loan workout

Process following default in which a bank attempts
it can.

Net loans

Total loans less LLR and allocated transfer risk reserve.

Nonaccrual

loan

to recover whatever loan funds

A loan carried on the bank’ balance sheet that no longer accrues interest.
s
payments received are deducted from principal but not booked as income.

Any

Other real estate
owned

Balance sheet account showing the book value of all real estate, other than bank
premises, owned by the bank. Consists largely of repossessed real estate.

Past due loan

A loan more than 30 days behind in interest or principal payments.

Percentage

Basing the amount of the addition to LLR on a percentage
or by tax policy.

Problem

method
loan

A loan judged likely to produce a loss. Characterized by some occurrence such as
late principal or interest payments. Includes any loan past due or on nonaccrual
status. Also called a troubled loan.

Provision for
loan losses

Income statement

Recovery

Funds received on a loan previously

Restructured

specified by regulators

loan

expense

account showing amount added to LLR.
charged off.

A loan on which the bank has granted the borrower
the borrower’ financial difficulties.
s

some concession

because of

Tier 1 capital

Stockholders’ equity + perpetual preferred stock + minority interest in consolidated
subsidiaries.

Tier 2 capital

Limited-life preferred stock + subordinated debt + reserves for loan losses up to
a specified maximum percent of risk-weighted assets (1.5 percent before 1993 and
1.25 percent after 1992).

Total capital

Tier 1 capital
Total capital.

Write-down

Reducing the book value of a loan by subtracting
loan and from LLR.

+ Tier 2 capital. Tier 2 capital cannot exceed Tier

a portion of that value from the

Source for some definitions: Glenn G. Mum, F. L. Garcia, and Charles J. Woelfel, eds. Encyc(opdiu
ofhnkingandfimncc,
Ill.: Bankers Publishing Company, 1991.

FEDERAL RESERVE BANK OF RICHMOND

1 capital in

9th ed., Rolling Meadows,

29

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