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Money, Intermediation, and Banking
David Andolfattoy

Ed Nosalz

Abstract
The business of money creation is conceptually distinct from that
of intermediation. Yet, these two activities are frequently— but not
always— combined together in the form of a banking system. We
develop a simple model to examine the question: When is banking
essential? There is a role for money due to a lack of record-keeping
and a role for intermediation due to the existence of private information: both money and intermediation are essential. When monitoring
costs associated with intermediation are su¢ ciently low, the two activities can be separated from one another. However, when monitoring
costs are su¢ ciently high, a banking system that combines these two
activities is essential.
JEL Codes: E42, G21
Keywords: money, intermediation, banking
We would like to thank a referee for extremely perceptive and helpful comments and
observations, as well as John Chant, David Laidler, Peter Rupert, Shouyong Shi, Bruce
Smith, Nurlan Turdaliev, Steve Williamson, and Randy Wright for their comments on
earlier drafts of this paper. We are grateful for the comments received on our presentations
of this work at: Hitotsubashi University (Tokyo), the Institute for Advanced Studies
(Vienna), the Institute for Monetary and Economic Studies (Bank of Japan), the Canadian
Macro Study Group, Philadelphia Fed/University of Pennsylvania Monetary Economics
Conference, and the Cleveland Fed Payments and Banking Workshop. This research was
funded in part by Social Sciences and Humanities Research Council of Canada. The views
expressed here do not necessarily re‡ those of the Federal Reserve Bank of Chicago or
ect
of the Board of Governors of the Federal Reserve System.
y
Department of Economics, Simon Fraser University, Burnaby, British Columbia,
Canada V5A 1S6, and Rimini Centre for Economic Analysis; email: dandolfa@sfu.ca
z
Federal Reserve Bank of Chicago, 230 South LaSalle Street, Chicago, IL 60604-1413;
email: ed.nosal@chi.frb.org

1

1

Introduction

We view a banking system as an institutional structure that combines two
primary activities: liquidity provision and intermediation. We de…ne liquidity provision as the supply of payments instruments and intermediation as
the pooling, monitoring, and transformation of individual securities into alternative debt instruments. These two activities are conceptually distinct;
a point highlighted by Friedman (1960), among others. In both theory and
practice, liquidity provision can occur in the absence of intermediation and
intermediation can occur in the absence of liquidity provision. Nevertheless,
we frequently observe these two activities combined within agencies that are
commonly called “banks”or institutional structures known as “banking systems.” That is, banks are unique among intermediated structures in that
their liabilities are designed to be money. To the best of our knowledge, we
are unaware of any theory that explains why banking— the way in which we
de…ne it here— might be essential.1
There is, of course, a large literature on the theory of banking. But for
most of this literature, the term bank can be replaced with intermediary.
For example, Diamond and Dybvig (1983) explain the emergence of intermediated structures. But as the liabilities of their intermediaries do not
circulate, they do not …t our de…nition of a bank. In Cavalcanti and Wallace
(1999) banks issue money that circulates in the economy, but they are not
intermediaries. Berentsen, Camera and Waller (2007) examine a monetary
economy in which a bank accepts deposits of cash and issues liabilities against
cash reserves. However, in their model too, bank liabilities do not circulate.
Similarly, in Smith (2003), banks are indistinguishable from, say, insurance
companies as their liabilities do not circulate in any meaningful sense. Cavalcanti, Erosa and Temzelides (1999, 2005) examine models in which a subset
of private agents issue liabilities backed by reserves of cash held at a clearinghouse. These agents resemble banks in that they accept cash deposits and
issue liabilities that circulate. But their banks are not intermediaries; and
hence, do not …t our de…nition of a bank. The same observation applies to
the banks studied in He, Huang and Wright (2005).
Naturally, our review of the literature above should not be construed as
1

By banking being essential we mean that more desirable allocations can be achieved if
the activities of liquidity provision and intermediation are performed jointly by one agency,
relative to having each service supplied by separate entities.

2

criticism, as most of these papers do not focus on the question of whether a
banking system is essential. To address the question that concerns us here,
we take the following approach. First, we ignore any meaningful role for …at
money. While …at money plays an important role in modern economies—
and arguably, in highly primitive ones— it seems clear that the development
of banking and private money preceded the widespread use of governmentissued …at money (Hicks, 1989). Instead, we adopt a simple …nite-horizon
model, similar to Kiyotaki and Moore (2002), to introduce the need for a
circulating medium. Moreover, to distinguish the business of banking from
insurance, we abstract from insurance motives entirely by assuming riskneutral agents. Intermediation in our model is instead motivated by the need
for a delegated monitor, along the lines of Diamond (1984) and Williamson
(1986).
Our model emphasizes two key frictions, both of which feature prominently in the literatures on money and intermediation. The …rst friction is
the absence of a public-access record-keeping technology. The second friction
is private information over the returns that are realized across individual investment projects. In the absence of either friction, the economy functions
perfectly well without anything that one might label as money or as a banking system. Absent a record-keeping device, a tangible medium of exchange is
essential. When private information is introduced and monitoring is costly,
an intermediated structure— a delegated monitor— is essential. It is not,
however, entirely obvious why the services of liquidity provision and intermediation should be performed by the same agent (or agency). Our main
result is that even when money and intermediation are both essential, banking is inessential when monitoring costs are su¢ ciently small. However, a
banking system is essential when monitoring costs are su¢ ciently large.

2

The Benchmark Environment

There are three dates, three time-dated goods and three types of agents, all
labeled i = 1; 2; 3. There are N agents of each type, where N > 1 is a …nite
integer. A type-i agent prefers good i to good i 1 (modulo 3), but receives
no bene…t from consuming good i + 1 (modulo 3).2 Preferences are linear
2

In what follows, we will suppress the “modulo 3” quali…cation.

3

and given by
ci + "ci 1 ;
where ci represents good i consumption and 0 < " < 1.
Output is divisible and nonstorable. A type-i agent produces good i 1
at date i 1. Production outcomes are random at the individual level, where
agent i’ output realization— success or failure— is revealed at date i 1.
s
There is no aggregate uncertainty. In particular, at each date F agents fail
to produce output, where 0 < F < N . From an individual perspective,
F=N represents the probability of failing to produce output. In the event of
success, an agent produces y > 0 units of output. Since there is no aggregate
uncertainty, total output at each date is given by (1
)N y, where
F=N .
Throughout, we assume that type-1 agents have a commitment technology and that all other agents types do not. In the benchmark environment,
we assume that individual outputs are observable and that there is a publicaccess record-keeping device. Later on, we modify this environment by …rst
removing the public-assess record-keeping device, and then by assuming that
individual outputs are private information. When output is assumed to be
private information— in section 5— we will introduce a monitoring technology.

3

The Ex Ante E¢ cient Allocation

Given our simple setup, the ex ante e¢ cient allocation should be obvious.
Since type-i agents value date i goods more than their own, a planner would
allocate all date i output (1
) N y to type-i agents. Because agents are
risk-neutral, each type-i agent is indi¤erent between mechanisms that, in
expectation, deliver (1
) y units of good i to him. Hence, an ex ante
e¢ cient allocation allows each agent to achieve an ex ante utility payo¤
equal to (1
)y.
The implementation scheme described below builds on the fact that: [1]
type-1 agents can commit; [2] output is observable; and [3] that there is
a public-access record-keeping device. There are potentially many ways to
implement the e¢ cient allocation. Here is one. The allocation of good i is
given by the following simple rule: the total amount of output surrendered to

4

a mechanism3 at date 1 is equally divided among all type-1 agents; the total
output surrendered to the mechanism at dates 2 and 3 is divided among the
type-2 and type-3 agents, respectively, in proportion to output surrendered
at dates 1 and 2. Agents play the following strategies: type-2 and type-3
agents surrender their output, if they have it, at dates 1 and 2, respectively;
and, type-1 agents promise to surrender their output, if they have it, at date
3.
It is easy to see that the above allocation rule and strategies constitute
an equilibrium. If all other agents play the proposed strategies, a type-2 or
type-3 agent who defects by consuming his own output receives a payo¤ of
"y, which is less than the equilibrium payo¤ of y. And, since type-1 agents
can commit, they will surrender their output at date 3.

4

Lack of Record-Keeping

The allocation rule and strategies described above are infeasible if a publicaccess record-keeping device does not exist, since they rely on some form
of public memory. For trade to occur, some sort of physical and noncounterfeitable object is needed, (Kocherlakota, 1998).
Standard monetary models feature an in…nite horizon, a complete lack
of record-keeping and no commitment. In these environments, trade is facilitated by objects that are …at in nature, such as intrinsically useless and
unbacked tokens. In contrast, our environment has a …nite horizon with some
limited commitment in the form of type-1 agents’ability to commit. Here,
monetary exchange can work o¤ the fact that a subset of agents can commit
to redeem tokens. As we shall see below, whether these tokens are created
by society and endowed to type-1 agents, or whether type-1 agents create
tokens on their own is irrelevant in terms of implementable allocations. All
that is necessary is that some monetary object exist.
Imagine, then, that each type-1 agent is endowed with a divisible, durable,
and non-counterfeitable token. Consider the following allocation rules and
strategies. The allocation rule for output is similar to that described above:
the total amount of output surrendered to the mechanism at date i is divided
3

A mechanism simply accepts and distributes output (and possibility other objects)
according to a prescribed rule.

5

among the type-i agents in proportion to the amount of tokens they surrender. The allocation rule for tokens is: at date i the total amount of tokens
surrendered to the mechanism is divided among the type-i + 1 agents in proportion to the output they surrendered. Agents play the following strategies.
The strategy for tokens is: type-i agents surrender tokens at date i if they
have them. The strategies for output are identical to the record-keeping environment: type-2 and and type-3 agents surrender their output, if they have
it, at dates 1 and 2, respectively; and, type-1 agents promise to surrender
their output, if they have it, at date 3.
The allocation rules and strategies have been constructed in a way that
makes it transparent that, in equilibrium, the supply of tokens serves as a
perfect substitute for the missing public-access record-keeping device. In
particular, if any type-2 or type-3 agent consumes his output, then he will
be unable to consume any of the date 2 or date 3 goods, respectively.
Before we proceed, some brief remarks on the …at-like nature of money
are in order. While the tokens in the equilibrium described above do not have
any explicit backing, they are not really pure …at instruments since type-1
agents commit to accept them as payment for their output. In this sense,
tokens are de facto backed by some commitment power. Therefore, instead
of endowing agents with tokens, we could alternatively assume that type-1
agents create them, with an explicit promise of to redeem them for output
in the future if they have it, and then use the above strategies and allocation
rules to implement an ex ante e¢ cient allocation.4 Under this interpretation,
4

From a date-3 perspective, tokens issued by type-1 agents will be heterogenous;
some tokens are worth y— those issued by successful type-1 agents— and while others
are worthless— those issued by unsuccessful type-1 agents. But given the allocation rules
for tokens and goods, described above, the mechanism treats all type-1 money symmetrically. (We assume that agents surrendered their tokens before the output realizations
are observed.) Implicitly, one can interpret the symmetric treatment of date-1 tokens as a
form of intermediation. For example, suppose that at the beginning of date 3, all type-3
agents holding tokens, which are claims issued by type-1 agents, collectively pool them and
issue new claims or tokens against them that give the holder proportional share of total
output; this is done prior to the revelation of the type-1 agents’date 3 output realizations.
Type-3 agents surrender output to the mechanism, type-3 agents (collectively) surrender
the tokens issued by type-1 agents, and the mechanism distributes output in proportion
to the type-3 tokens surrendered by type-3 agents. The act of the type-3 agents pooling
the tokens issued by type-1 agents and then re-issuing new “riskless” tokens is the form
of intermediation envisioned by Diamond (1984) and Williamson (1986). Note, however,
that there is nothing fundamental about having a set of the type-3 agents acting as the

6

tokens look a lot like inside money.5

5

Private Information

We now assume that each agent’ production outcome is private information
s
and that type-1 agents can commit only to what is publicly observable.6 In
this situation, the strategies and allocation rules described in the previous
section no longer constitute an equilibrium. In particular, type-1 agents will
always have an incentive to that claim their output is zero— since output is
not publicly observable— and those who actually produce y will consume it.
Without any further modi…cations to the environment, the only equilibrium
is autarky.
Following Townsend (1979) and Williamson (1986), we introduce a costly
monitoring technology. The technology works as follows. If a producing
agent fails to surrender his output, then the actual level of production— 0 or
y— can be revealed if he is monitored. The cost of monitoring a producing
agent is
0 utils. The monitoring cost can be shared or spread out over
any number of agents. If, for example, M agents each expend =M utils, then
their combined e¤ort allows them to monitor one producing agent. Individual
monitoring costs, as well as the monitoring outcome, are observable.
It turns out that monitoring is relevant only at date 3, and that only
type-1 and type-3 agents would ever have an incentive to monitor.7 Type-3
agents may have an incentive to monitor because, in any equilibrium with
trade, they are holding tokens (or inside money) that can be used to purchase
the output they value. Note that because type-3 agents have no commitment
intermediary; in principle, type-1 or type-2 agents may also perform this task.
5
The notion of inside money here is similar to that in Cavalanti and Wallace (1999). In
Cavalcanti and Wallace (1999) agents who are monitored can issue money. In our setup,
we can re-interpret type-1 agents as being monitored and assume that there exists a court
that enforces contracts on the based on observables. Furthermore, since type-2 and type-3
agents are not monitored, they are not subject to the enforcement mechanism.
6
If type-1 agents were able to commit unconditionally, then the introduction of private
information has no e¤ect on equilibrium outcomes. The assumption that (type-1) agents
can only commit to what is observable is standard in the literature, e.g., Townsend (1979)
and Williamson (1986).
7
A type-2 agent would never monitor at date 3 since he does not value date-3 output
and cannot commit to monitoring.

7

power, their decision to monitor must be sequentially rational. In contrast,
since type-1 agents can commitment, their decision to monitor (themselves)
need not respect sequential rationality.
We will de…ne an intermediary as a set of agents who collectively perform
the task of monitoring.8 Since type-2 agents do not have an incentive to
monitor, they cannot be an intermediary.

5.1

Type-3 Intermediation

In this section, we consider strategies that can be interpreted as giving rise
to an institutional structure that separates money-issue and intermediation.
More speci…cally, we assume that type-1 agents are responsible for creating the economy’ monetary instrument and type-3 agents are collectively
s
responsible for intermediation. In terms of the timing of events for type-3
intermediation, we assume that the decision to monitor or not is made after
date-3 output is surrendered (by type-1 agents) and distributed (to type-3
agents). This timing serves to emphasize the fact that type-3 agents cannot
commit to future actions.
Consider the following equilibrium strategies and allocation rules, most of
which are identical to those described in the previous section. The allocation
rule for goods at date i is to divide the total amount of goods surrendered
to the mechanism at date i among the type-i agents in proportion to the
amount of tokens they surrendered. The allocation rule for tokens divides
the total amount of tokens surrendered to the mechanism at date i among
the type-i + 1 agents in proportion to the amount of output surrendered at
date i. The strategies for goods for type-i agents to surrender output if they
have it. In addition, (i) at date 1, each type-1 agent creates a token that
is redeemable for y units of date 3 output, if he has it; and (ii) successful
8

In footnote 4, we motivated the symmetric treatment of tokens, issued by type-1
agents, at date 3 as a form of intermediation. Continuing this line of discussion, in an
environment characterized by asymmetric information, if a group of agents transforms
risky tokens issued by type-1 agents into riskless ones at date 3, they must also be willing
to perform, or at least manage, the task of monitoring in the event that total output
surrendered falls short of (1
) N y. So, the set of agents that are involved in transforming
claims are also the set of agents who must manage monitoring. Since, without loss of
generality, we assume that the mechanism treats all date-1 issued claims symmetrically,
the set of agents who do the monitoring is the intermediary.

8

type-3 producers who surrender tokens at date 3 monitor all type-1 agents
who did not surrender output at date 3, if total date-3 output surrendered
is less than (N F ) y; otherwise they do not monitor anyone.
The interesting questions to examine here are: [1] will successful type1 producers surrender their output at date 3?; and [2] will type-3 agents
monitor if total date 3 output falls below (N F ) y? Since we are interested
in implementing a truth-telling equilibrium, let us suppose that all successful
type-1 agents surrender their output at date 3, and then examine whether,
conditional on this behavior, any individual type-1 agent has an incentive to
withhold his output. Note that such a deviation will be pro…table if there is
even the smallest chance that the deviating type-1 agent escapes monitoring.
Therefore, any equilibrium requires that if total output is less than (N F ) y,
then any agent who does not surrender output is monitored with probability
one.9
Suppose then that a successful type-1 agent does not surrender his output
at date 3. The above strategies imply that type-3 agents with tokens will
monitor all of the F + 1 type-1 agents who did not surrender output. In this
case, the cost of monitoring is (F + 1)= (N F ) utils for each type-3 agent
who monitors. This monitoring activity will recover y units of the “hidden”
output.
Whether type-1 agents have an incentive to surrender output depends on
whether the delegated monitors …nds it sequentially rational to monitor in
m
the event of a defection. Let U3 denote the expected payo¤ to monitoring
n
and U3 denote the expected payo¤ to not monitoring. Then,
F +1
N F

m
U3 = y

and
n
U3 =

N

F
N

1
F

y:

m
Hence, type-3 agents will decide to monitor if U3
and only if
y
(F + 1) = ( N + 1) :
9

n
m
U3 , and U3

n
U3 if

Implicitly, we assume that sequential monitoring of type-1 agents is not possible.
Allowing for this changes a bit of the arithmetic, but not our main conclusions.

9

This inequality is obviously satis…ed if
= 0; but in general, we can
de…ne a reservation monitoring cost
such that y
( N + 1) or
=

y
N +1

:

(1)

We can conclude that monitoring by type-3 agents with money will be sequentially rational for any 2 [0; ].10 Hence, if is su¢ ciently small in
this sense, then conditional on all other successful type-1 producing agents
surrendering their output, a successful type-1 producing agent will not have
an incentive to hide his output. In other words, the ex ante e¢ cient allocation can be implemented under an institutional arrangement that separates
the businesses of the money-issue from intermediation. Hence, a banking
arrangement is not essential. If, however, > ; then the ex ante e¢ cient
allocation cannot be implemented under such an arrangement.

5.2

Type-1 Intermediation: Banking

Since type-1 agents can commit, the monitoring/intermediation function can
simply be delegated collectively to them. That is, when the type-1 agents
create their tokens (or liabilities) at date 1, they also commit to monitoring
all type-1 agents who do not surrender output at date 3, in the event that
aggregate output falls short of (N F )y. Since this threat of monitoring
is credible, no type-1 agent has an incentive to hide output at date 3; any
hidden output will ultimately be discovered and con…scated. Hence, in equilibrium, no monitoring will occur and the ex ante e¢ cient allocation can be
implementable regardless of the size of .
In the stark environment that we consider, a banking arrangement weakly
dominates an institutional arrangement that separates the businesses of moneyissue and intermediation over the entire parameter space and strictly dominates for parameter con…gurations (y; ; ; ; N ) that satisfy y < ( N + 1).
It is in these latter cases that we say that banking is essential.
It is interesting to note that
is a decreasing function of N , see (1). It
is tempting to interpret N as a measure of population size. If this is the case,
10

Suppose only a subset of type-3 agents with tokens decide to monitor after they observe
the amount the amount of output is (N F 1) y. Owing to the linearity of preferences,
the condition for monitoring for any subset of the type-3 agents with tokens is also given
by condition (1).

10

then the model has a nice implication that banking arrangements are likely to
be more prevalent in larger economies (ceteris paribus, of course). The model
also suggests that banking arrangements are likely to be more prevalent in
environments where monitoring costs are high and/or the probability of failure is high, relative to the return to investment. The parameter re‡
ects
the di¢ culty of acquiring information— say, in a bankruptcy proceeding—
and there is some reason to believe that this parameter may increase over
time as economic relationships and accounting practices grow in complexity.

6

Discussion

Our model is able to capture some, but certainly not all, aspects of the
development of money and banking in history. First, our model is consistent
with the idea that anyone with a capacity to issue money will endeavor to
do so to meet the demand for liquidity. Absent legal restrictions prohibiting
the practice of small note issue, this type of behavior is prevalent throughout
recent history. For example, Bodenhorn (1993) quotes an Italian General
Secretary of the Banco D’
Italia how, prior to 1874, “everyone was issuing
notes, even individuals and commercial …rms; the country was overrun with
little notes of 50, 25, and 20 centimes issued by everyone who liked to do so.”
The author also notes that when state legislation banned U.S. banks from
issuing notes of less than $5, railroad companies, public houses, merchants
and even churches …lled the void with their own notes. Even Adam Smith
(1937, pp. 305–
313) noted, with some disapproval one might add, how small
notes drove specie from the country.
One aspect of history that our model cannot account for is the widespread regulatory e¤orts that were expended to prohibit private small note
issue. One common argument was that holders of a few small notes had
little incentive to expend real resources on monitoring or determining authenticity. Even those holding large quantities of notes may have had little
incentive to monitor, since others might have incentive to free-ride on their
e¤orts. But as Bodenhorn (1993, pg.822) reports, in antebellum America,
at least, independent businessmen known as note brokers made markets in
banknotes; at the same time providing information and monitoring services.
This institutional setup bears some resemblance to the one that emerges in
our model where money-issue is separated from monitoring.
11

What, then, of the emergence of banking arrangements? The interpretation that we o¤er here is not with respect to the emergence of agencies often
referred to as banks per se; but rather, the emergence of what one might
call a banking system, broadly de…ned to include regulatory agencies. As
noted by Klein (1974), many early U.S. banks became members of private
certifying and monitoring agencies, which performed some of the functions
similar to modern central banks. A famous example is the Su¤olk banking
system, e.g., see Smith and Weber (1999). In an interesting paper, Gorton
and Mullineaux (1987) argue that the capacity of private note brokers to
monitor and control the behavior of bank managers was increasingly eroded
as demand deposits came to supplant bank notes during the nineteenth century. While our model is not rich enough to distinguish between bank notes
and demand deposits, this historical development can be thought of manifesting itself as an increase in our model parameter , and hence, an increase
in the likelihood of the emergence of banking.

7

Conclusion

We describe an environment where, absent record-keeping, money is essential.
Whether this money takes the form of a …at token or of an explicitly backed
private liability is indeterminate, although we do argue that a …at token in
conjunction with type 1 agents’ promises to surrender output amounts to
inside money. Either way, however, a speci…c subset of agents must initially
be in possession of the monetary instrument; whether it is endowed to them,
or whether they create it themselves, is irrelevant.
When the environment is further modi…ed by assuming that idiosyncratic
production shocks are private information and that such information can
only be revealed through costly monitoring, some form of intermediation is
essential. This is to say that it becomes essential for some group of agents
to agree collectively monitor the issuers of some pool of securities. But it
is not obvious if it matters who these agents are. If monitoring costs are
su¢ ciently small— in the sense that
— then the monitoring function
can be delegated either to those who issue the money or to those who are
ultimately in a position to redeem it. On the other hand, if monitoring costs
are su¢ ciently high— in the sense that > — then it is essential that the
monitoring function is delegated to those agents responsible for creating the
12

economy’ monetary instrument.
s
While our model is very simple, it arguably allows us to interpret some
aspects of the development of money and banking in recent history. As such,
the basic ideas embedded within the model may serve to develop a richer
class of models designed to explain more complicated aspects of the way
payments systems are organized and regulated.

13

8

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15


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