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FEDERAL RESERVE BANK of ATLANTA

Why Do Banks Promise to Pay Par on Demand?
Gerald P. Dwyer Jr. and Margarita Samartín
Working Paper 2006-26
November 2006

WORKING PAPER SERIES

FEDERAL RESERVE BANK o f ATLANTA

WORKING PAPER SERIES

Why Do Banks Promise to Pay Par on Demand?
Gerald P. Dwyer Jr. and Margarita Samartín
Working Paper 2006-26
November 2006
Abstract: We survey the theories of why banks promise to pay par on demand and examine evidence about
the conditions under which banks have promised to pay the par value of deposits and banknotes on
demand when holding only fractional reserves. The theoretical literature can be broadly divided into four
strands: liquidity provision, asymmetric information, legal restrictions, and a medium of exchange. We
assume that it is not zero cost to make a promise to redeem a liability at par value on demand. If so, then
the conditions in the theories that result in par redemption are possible explanations of why banks
promise to pay par on demand. If the explanation based on customers’ demand for liquidity is correct,
payment of deposits at par will be promised when banks hold assets that are illiquid in the short run. If
the asymmetric-information explanation based on the difficulty of valuing assets is correct, the
marketability of banks’ assets determines whether banks promise to pay par. If the legal restrictions
explanation of par redemption is correct, banks will not promise to pay par if they are not required to do
so. If the transaction explanation is correct, banks will promise to pay par value only if the deposits are
used in transactions. After the survey of the theoretical literature, we examine the history of banking in
several countries in different eras: fourth-century Athens, medieval Italy, Japan, and free banking and
money market mutual funds in the United States. We find that all of the theories can explain some of the
observed banking arrangements, and none explain all of them.
JEL classification: G21, E5
Key words: banking panics, suspension of payments, banking history

The authors thank John Boyd, Mardi Dungey, and Robert Tamura for helpful comments. The authors benefited from research
assistance by Budina Naydenova and Lee Cohen and editorial assistance by Linda Mundy. Earlier versions of this paper were
presented at a Society for Economic Dynamics meeting, the Tor Vergata Financial Conference, Fordham University, and the
University of Carlos III. Gerald Dwyer thanks the Earhart Foundation for support of early work on this project. The views
expressed here are the authors’ and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve
System. Any remaining errors are the authors’ responsibility.
Please address questions regarding content to Gerald P. Dwyer Jr., Vice President, Research Department, Federal Reserve Bank
of Atlanta, 1000 Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-7095, 404-498-8810 (fax), gerald.p.dwyer@atl.frb.org, or
Margarita Samartín, University of Carlos III, Departamento de Economía de la Empresa, Calle Madrid, 126, 28903 – Getafe,
Madrid, Spain, samartin@emp.uc3m.es.
Federal Reserve Bank of Atlanta working papers, including revised versions, are available on the Atlanta Fed’s Web site at
www.frbatlanta.org. Click “Publications” and then “Working Papers.” Use the WebScriber Service (at www.frbatlanta.org) to
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Why Do Banks Promise to Pay Par on Demand?

INTRODUCTION
Banks promise to pay the par value of certain liabilities on demand with fractional reserves
of the assets promised. It is trivially obvious that, due to gamblers’ruin, no bank holding
fractional reserves can expect to honor this promise forever. No bank customer can expect it
to be honored always either. In addition, the consequences –banking panics –are not trivial.
In the United States, banking panics happened during the free banking and National Banking
periods and at the start of the Great Depression. These are far from unique historically, and
banking crises in emerging countries are more recent related events.1
Given that these things are so, why do banks promise what they cannot deliver in the …rst
place?
It is possible that banks promise to pay par on demand because depositors want this contractual agreement. There are at least four possible reasons for this desire. Depositors may
demand a constant par value because this makes their deposit balances more predictable
under typical circumstances, thereby increasing the liquidity of deposits compared to assets
that have a longer maturity. At many times and places, banks have held largely nonmarketable assets; hence, customers cannot easily assess the assets’market values. Under these
circumstances, deposit values that vary with the value of banks’assets may not be a feasible market equilibrium and redemption on demand can keep the bank from dissipating the
depositors’wealth by exploiting superior information. Depositors may want a constant par
1

For United States history, Dwyer (1996) summarizes some banking panics before the Civil War in the
United States, Sprague (1910) summarizes banking panics in the National Banking period, and Friedman
and Schwartz (1963) analyze the banking panics at the start of the Great Depression.Over 8000 banks failed
in the U.S. from 1929 to 1933 (Friedman and Schwartz 1963.) Banking problems have not ended with the
establishment of central banks. Lindgren, Garcia and Saal (1996) indicate that 73 percent of the IMF´s
member countries su¤ered banking crises between 1980 and 1996.

1

value because it is more convenient when using deposits in transactions, a point that may
be related to the predictability of balances in the liquidity explanation. Alternatively, banks
may make this promise simply because they are required by law to do so and such promises
would not occur without that requirement.
In this paper, we survey theories about banks’promise to pay par on demand to determine
whether these theories make empirical predictions about when …nancial intermediaries will
promise to pay par on demand. We assume that it is not zero cost to make a promise to
redeem a liability at par value on demand. If so, then the conditions in the theories that
result in par redemption are possible explanations why banks promise to pay par on demand.
One interpretation of the informativeness of these theories about actual banking arrangements is that they do not and need not say anything about anything observed. These are
highly stylized theories, and we do not interpret the theories as inconsistent with banking
arrangements if, for example, the world has more than three periods. Alternatively, as one
theorist put it some years ago, “The real world is a special case, and not a very interesting
one at that.”
We think that our review of the literature shows that these theories can be interpreted
as having predictions about when banks will promise to pay par on demand and when they
will not make such promises and that the theories are informative for understanding banking
arrangements.
Each of the theories can be interpreted as making strong predictions, namely that promised
payment at par will not be observed unless the theory is relevant. Alternatively, the theories
can be interpreted as making weak predictions in the sense that the theory explains some
observed promises to pay par on demand but not necessarily all of them.
After the survey of the theoretical literature, we examine the history of banking in several
countries in di¤erent eras: fourth century Athens; medieval Italy; Japan during its period
of “seclusion”; and the United States. We have picked these cases instead of others to
mitigate the sequential dependence of observations. Ancient Rome, examined in passing, is
derivative of Ancient Athens in many ways. Western European banking development partly
re‡ects experience in Italy, to the point that Lombard Street in London has a name based
on the Lombardy bankers who set up business there. We examine banking in Japan because
2

Japan was more or less secluded from the rest of the world for over two centuries and it
is the country outside Western Europe with the largest English literature on its banking
history. The United States is considered because free banking on the U.S. frontier has some
novel aspects, as do money market mutual funds. Truly independent observations would
require examining banking on di¤erent planets before intergalactic travel –an impossibility
today. While not independent, these historical episodes are not completely dependent and
the empirical evidence is consistent with some independence.
Table 1 summarizes the evidence concerning banking in di¤erent times and places. Perhaps
most obviously, the legal restriction theory, which supposes that banks pay par because they
are required to do so, fares poorly. Other than free banks whose assets were traded on the
New York Stock Exchange, these banks have not been required to redeem their deposits
on demand. Interestingly, both the liquidity explanation and the explanation based on
asymmetric information fare equally well for historical banking, but neither appears to be
consistent with money market funds. The theory based on deposits’ use as a medium of
exchange is consistent with the more recent historical episodes.
THEORETICAL EXPLANATIONS FOR THE USE OF DEMAND
DEPOSITS
In general, a bank that takes in deposits and invests the proceeds in long term loans
exposes itself to many risks: the risk that depositors withdraw their funds, the risk that
market deposit interest rates rise, and the risk that borrowers default with collateral worth
less than the deposit funding the loan. These risks are correlated with each other and are
driven by common macroeconomic factors (Hellwig 1998).
Given the above observations, it is not immediately obvious why banks promise to pay the
par value of deposits on demand when they hold risky assets and only fractional reserves of
the asset that they promise to deliver on demand.
Theoretical research on banking provides four general explanations for making this promise:
provision of liquidity, asymmetric information, legal restrictions and deposits’ use as a
medium of exchange. In this section, we summarize the basic theoretical analyses behind
these explanations of par redemption on demand and their empirical implications.
3

Liquidity provision
One possible explanation for the use of demand deposit contracts is associated with liquidity insurance provided by …nancial intermediaries. Diamond and Dybvig (1983) introduce a
demand for liquidity by the public which supports a transformation of assets’returns provided by banks. Diamond and Dybvig demonstrate that demand deposit contracts which
transform illiquid assets into more liquid liabilities can explain both banks’ existence and
the existence of runs.
In the simplest formulation of this class of models, there is a continuum of ex ante identical
agents who are risk averse and uncertain about the timing of their desire to consume. These
individuals are endowed with one unit of the good at T = 0 and no additional endowment in
subsequent periods.2 They are subject to privately observed risk at T = 1; with probability
p of being early consumers who derive utility only from consumption in period one and
probability 1

p of being late consumers who derive utility only from consumption in period

two. Consumers can privately store the good with no appreciation or depreciation. There
also is an investment technology available to consumers in which a unit investment at T = 0
yields one unit at T = 1 or R > 1 units at T = 2. In autarky, early consumers liquidate their
investment at T = 1 and consume one unit; late consumers maintain the investment in the
technology and receive R units at T = 2. There is no aggregate uncertainty: the fraction p
of agents are early consumers and the fraction 1

p are late consumers.3

Diamond and Dybvig show how a …nancial intermediary can improve consumers’ex ante
welfare by o¤ering them a demand deposit contract. This deposit contract can support
the full-information risk-sharing equilibrium. The Pareto optimal solution is obtained by
maximizing the ex ante expected utility of agents pu(c1 ) + (1

p)u(c2 ), where u(c1 ) is an

early consumer’s utility from consumption in period one and u(c2 ) is a late consumer’s utility
from consumption in period two. This expected utility is maximized subject to the resource
constraints pc1 = L and (1

p)c2 = (1

L)R, where L is per capita the amount of the

investment liquidated at date 1. If the representative agent’s relative risk aversion is greater
2

The model presented is simpler than Diamond and Dybvig’s but has the same implications in terms of
promised payment and runs.
3
This is a detail in autarky but an important part of the model with …nancial intermediaries.

4

than one, i.e.,

cu00 (c)=u0 (c) > 1, the optimal solution satis…es 1 < c1 < c2 < R; where c1

and c2 are the optimal consumption of early and late consumers respectively. This optimal
contract insures depositors against being early consumers in the sense that c1 > 1, which is
more than they would receive in autarky, and c2 < R; which is less than they would receive
in autarky.
A deposit contract can achieve this optimal allocation. The demand deposit contract
works as follows: for each unit deposited in the intermediary at T = 0, the deposit contract
provides the option of withdrawing either r1 = c1 at T = 1 or r2 =

(1 f c1 )R
1 f

at T = 2. The

second period payment depends on f , the fraction of agents who withdraw at T = 1. If
only early consumers withdraw at T = 1, f = p, r2 = c2 and the demand deposit contract
replicates the optimal allocation.
Implementing this allocation, however, subjects the intermediary to a possible coordination
problem because a consumer’s preference for early or late consumption is private information
and the intermediary cannot guarantee that only early consumers withdraw at T = 1. In
fact, late consumers’withdrawals are strategic and depend on what other agents do. If some
late consumers withdraw at T = 1; then f > p and r2 < c2 . If enough late consumers
withdraw at T = 1, then r2 < c1 and everyone withdraws at T = 1, which can be interpreted
as a bank run.
In this model, there are two Pareto-ordered Nash equilibria: a Pareto dominant equilibrium
that achieves socially optimal risk sharing in which only early consumers withdraw at T = 1;
and a second equilibrium in which all agents withdraw at T = 1, which is the bank run
equilibrium. The model can be used to show that there are several measures to prevent
the occurrence of the bank run equilibrium.4 The equilibrium arguments implicitly assume
a sequential service constraint in which depositors are paid on a …rst-come, …rst-served
basis, an assumption that motivates the papers by Wallace (1988, 1990) and has important
implications for the discussion that follows.
There have been several important developments of this analysis. Jacklin (1987) shows
4

If there is no aggregate uncertainty about the proportion of early consumers, the Pareto optimal equilibrium could be implemented by a policy of suspending convertibility once withdrawals equal the fraction
p. This policy removes the incentive for late consumers to withdraw early; with this policy, late consumers
always obtain a higher payo¤ if they wait until the second period than if they withdraw in the …rst period.
If there is aggregate uncertainty, though, this measure is not e¤ective for some realizations of p.

5

that the optimal deposit contract also can be achieved by trading equity. Instead of making
a deposit in the intermediary, suppose that agents invest their unit of endowment in stock in
a …rm and a market for ex-dividend shares opens at T = 1. The …rm can promise a dividend
stream of L units per share invested at T = 1 and (1

L)R units at T = 2 with L = pc1 .

Early consumers want to trade their ex-dividend shares, which promise to pay (1

L)R, for

additional consumption in period 1 and are willing to do so as long as there is a positive
payo¤. Late consumers want to consume in the second period and have a storage technology
available that lets them carry over consumption at no cost from T = 1 to T = 2. As a result,
late consumers are willing to trade if the price of ex-dividend shares, Pxs , is less than or equal
L)R
to the future payment (1 L)R. Consumption for each early consumer is c1 = L+ (1 Pxs
and

consumption for each late consumer is c2 = Pxs L + (1
the equilibrium price Pxs =

p(1 L)R 5
:
(1 p)L

L)R. Market clearing implies that

It must be the case that 1

Pxs or else late consumers

would not buy the stock. In addition, it must be the case that Pxs
implies that c1 < 1. If Pxs =
In addition, c2 =

p(1 L)R
;
(1 p)L

p(1 L)R
L + (1
(1 p)L

L)
then c1 = L + (pR(1R(1
L)=(1

L)R =

p(1 L)R+(1 p)(1 L)R
1 p

=

R or else c2 > R, which
p)L
p
(1 pc1 )R
1 p

= L + (1

p)L)
(1 L)R
1 p

=

= L=p = c1 :
= c2 . These

are consumption levels identical to those promised by the deposit contract. This result rules
out a positive role for a bank or any other …nancial intermediary in the economy because
equity markets and well functioning banks are perfect substitutes, and arguably a bank is
worse than a …nancial market because a bank can have the bad equilibrium of a bank run.6
In the same paper, Jacklin noted that banks and equity contracts are not equivalent risk
sharing instruments if consumers have more general preferences about consumption timing.
If demand deposits can be traded, however, optimal risk sharing does not occur regardless
5

L)R
. As a result, in the aggregate per capita, p L +
For each early consumer, c1 = L + (1 Pxs

(1 L)R
Pxs

= L,

L)
L)
L)
or pL + pR(1
= L, or (1 p) L = pR(1
which implies that Pxs = pR(1
Pxs
Pxs
(1 p)L :
6
Recent criticisms of the Diamond and Dybvig model by Green and Lin (1999, 2000) analyze why banking
evolved with uninsured demand deposits. They examine the signi…cance of the simple deposit contract and
…nd that it is critical: con…ning agents to this type of contract is, in fact, the driving force behind the bank
run equilibrium of the model. Green and Lin show that when agents in the Diamond and Dybvig model are
allowed to use a broad class of banking contracts, the bank run equilibrium disappears even in the presence
of a sequential service constraint. Their results suggest that economists need to attempt to understand the
economic and legal environment that produces the simple deposit contract.
In a later paper, Peck and Shell (2003) show that even when banks can write more sophisticated contracts,
bank runs are possible.
Goldstein and Pauzner (2005) address some of the more fundamental problems with the multiplicity of
equilibria in Diamond and Dybvig’s model.

6

of preferences.7 In particular, Jacklin argues that …nancial intermediaries exist if trading
restrictions limit consumers to demand deposit contracts of the Diamond and Dybvig type.8
Such trading restrictions can be motivated by agents’isolation from each other.
Agents demand liquid assets because they are impatient to spend and do not have access
to asset markets in which they can sell the asset at the market price. Instead they go to the
bank to withdraw funds and the bank sequentially serves depositors. Wallace (1988, 1990)
explicitly incorporates a sequential service constraint in the Diamond and Dybvig model.
An important implication of these models is that some form of isolation of agents is needed
in order to motivate illiquid banking arrangements. Otherwise, individuals would in general
want to participate in an asset market which is superior to illiquid banking.
Further work in this area has examined the role of demand deposits when there is a securities market in which agents can meet and trade (Diamond 1997, Von Thadden 1998).
Von Thadden (1998) presents a continuous-time version of the Diamond and Dybvig model
in which depositors can continuously adjust their portfolios, i.e., they can join outside coalitions that engage in market activity. In this setting, demand deposits cannot attain the
…rst-best allocation, and the ability to trade demand deposits in …nancial markets severely
limits liquidity provision by banks. Incentive-compatible deposit contracts are second best
mechanisms for providing liquidity. At the optimum, liquidity provision is negatively correlated with the degree of irreversibility of the investment opportunity. In particular, if the
investment is completely reversible, the only incentive compatible contract is the autarky
7

Other papers in the literature have analyzed the relative degrees of risk sharing provided by banks and
equity contracts. For example, Hellwig (1994) considers a model similar to Diamond and Dybvig’s with a
stochastic technology from T = 1 to T = 2 that can be interpreted as technology-induced interest rate risk.
He shows that there would still be no role for a bank in this extended framework. Samartín (2001) shows
that in Hellwig’s model, if individuals have more general preferences, then demand deposits perform better
than equity contracts at low enough interest rates.
Jacklin and Bhattacharya (1988) and Alonso (1996) also consider the relative degree of risk sharing
provided by traded and nontraded contracts in a framework in which bank assets are risky and individuals
with smooth preferences are informed about bank asset quality. The basic result is that deposit contracts
tend to be better for …nancing low risk assets.
8
Haubrich and King (1990) reach the same conclusion, namely that
Demand deposits uniquely provide insurance only if there are restrictions on …nancial side
exchanges, which may be interpreted as exclusivity provisions or regulations on security markets. If these restrictions cannot be implemented, then our environment does not rationalize
banks; other …nancial institutions can achieve the same real allocations and welfare levels.
(Haubrich and King 1990, p. 362).

7

allocation.
Diamond (1997) examines the roles of banks and markets when there is a …nancial market
but with limited participation in the …nancial market. Such a market has an impact on bank
activities but banks remain important. The paper focuses on the interactions between the
bank provision of liquidity and the participation in the market. As more agents participate
in the market, banks are less able to provide additional liquidity. The paper delivers the
Diamond and Dybvig result when there is no participation and the Jacklin result when there
is full participation.
In summary, this strand of the literature argues that banks o¤er to pay par on demand
in order to provide liquidity insurance services to individuals who are uncertain about their
future time preferences in a framework in which investment opportunities are inconsistent
with preferred consumption paths of consumers.9 These depositors demand liquid assets
because they are impatient to spend and they do not have access to …nancial markets in
which they can sell the asset at its market price. These papers try to capture the role of
consumers who are isolated from each other and cannot go to a security market to trade.
As Wallace (1988) points out, sequential service is an outcome of this isolation assumption.
If the trading restriction assumption is dropped from these models, the role of banks is
severely limited (Jacklin 1987). A common assumption needed in most of these papers is
that demand deposits cannot be traded outside the bank.10
9

These theories can be interpreted as implying that deposits will pay interest, but it is not necessary that
they do so. Nonpecuniary services can be a substitute for explicit interest payments.
10
There have been several attempts to extend the Diamond and Dybvig framework to an overlapping
generation context, and to analyze in this dynamic framework liquidity provision by banks, without the
need of imposing trading restrictions, as in the single-generation models. Since these models allow for
intergenerational transfers, liquidity provision is made more e¢ ciently than in the …nite ones. Examples
of such work are Qi (1994), Bhattacharya and Padilla (1996), Bhattacharya, Fulghieri and Rovelli (1998),
Fulghieri and Rovelli (1998) and Qian, John and John (2004). Allen and Gale (1997) analyze a di¤erent type
of intertemporal smoothing role of …nancial intermediaries in a standard overlapping generations model.
Hölmstrom and Tirole (1998) analyze a di¤erent type of liquidity that arises in a framework in which
moral hazard limits the e¤ectiveness of transactions between …rms with excess liquidity and …rms that have
a positive demand for liquidity. Hölmstrom and Tirole show that, if there is no aggregate uncertainty, there
is a second best arrangement that allows …rms to hedge against a liquidity shock at T = 1 by buying claims
on other …rms at T = 0 and selling them at T = 1. Kashyap, Rajan and Stein (2002) also focus on banks
as creators of liquidity. They build on the observation that banks engage in two distinct activities, deposittaking and lending. In particular, these institutions issue a product that may enable them to distinguish
themselves from other lenders such as insurers or …nance companies – loan commitments or credit lines.
They develop the idea that credit lines and demand deposits can then be seen as two di¤erent manifestations
of the same function: provision of liquidity on demand. There is a complementarity between these two ways

8

Asymmetric information
A second explanation for the use of demand deposit contracts is linked to asymmetric
information about loans: banks make loans with values that are costly for others to verify,
bank managers’ behavior is di¢ cult to monitor, and some depositors acquire information
about the realization of the random return.
In this context, banking panics are not a manifestation of an inherent problem with banks;
they are a re‡ection of depositors’monitoring of banks.
We continue to assume there is a continuum of ex ante identical agents who are risk averse
and uncertain about their preferences concerning consumption. As in Diamond and Dybvig,
they are subject to a privately observed risk of being early consumers and are endowed with
one unit of the good at T = 0.11
There are two assets: a short-term asset and a long-term asset. The short term asset
generates one unit at T = 1 for each unit invested at T = 0. The long-term asset has a
random return at T = 2 which can be a high value Rh > 1 with probability q or a low value
Rl with probability 1

q and Rh > Rl > 0. For simplicity it is assumed that this long-term

asset can be liquidated at T = 1 only at su¢ cient loss that it never pays to do so. Let L
and 1

L denote the ex-ante investments in the short and long-term assets respectively.

Banks possess private information about their loan portfolio which can lead to ine¢ cient
allocations with liquidation of loans.
The bank o¤ers depositors a demand deposit contract in exchange for their endowments.
This deposit contract provides the option of withdrawing either r1 = c1 at T = 1 or r~2 =
~
(1 f c1 )R
1 f

at T = 2. The second period payment depends on f , the fraction of agents who

withdraw at T = 1, and the payo¤ from the investment in the long-term risky asset. One
way to think about this is that the bank promises an amount r2 = c2 which it can pay if
R = Rh . If R = Rl , the bank is considered insolvent and depositors get Rl =Rh of their
of providing liquidity because they are not perfectly correlated. Once this fact is recognized, it is easy to see
that there can be important synergies in o¤ering both products because the banks hold liquid assets. The
paper develops a theoretical and empirical case for this particular synergy.
11
The model presented is simpler than Jacklin and Bhattacharya’s but has the same implications in terms
of the origins of bank runs and its policy implications. Other papers, such as Chari and Jagannathan (1988)
or Allen and Gale (1998) also have versions of this basic setup.

9

promised payments.12
At T = 1, a fraction of late consumers receive correct information about the random return.13 Given this information, late consumers select their optimal strategy. They prefer the
…rst period payment of r1 to the second period payo¤ if they receive negative information
and c1 > (Rl =Rh ) c2 ; which can be rewritten Rl <

Rh c1
.
c2

If Rl <

R h c1
,
c2

then it is optimal for

all informed late consumers to withdraw their deposits in the …rst period. In this bank run
equilibrium, the bank exhausts the liquid asset among withdrawals by depositors, which includes both early consumers and informed late consumers. After withdrawals by the fraction
p of customers, payments are suspended and withdrawals are allowed in the second period
only. As a result, some early consumers may not be able to withdraw at T = 1.14
In this class of models, banking panics are not a manifestation of an inherent problem
with banks or banking contracts; they are a rational response by depositors to a bad state of
the world. This is consistent with empirical evidence, which indicates that banking panics
are explicable responses to bad states of the world (Rolnick and Weber 1984; Gorton 1988;
Economopoulos 1990; Dwyer and Hasan 2006.)
A number of papers have focused on the incentive properties of demand deposits. In these
papers, liquid deposits keep the bank’s portfolio choice in line with depositors’preferences.
The framework is similar to the one described above, but it includes the possibility that
banks take actions that bene…t the banks’owners and make depositors worse o¤. In these
papers, the threat of a bank run by informed depositors after receiving negative information
12

The optimal consumption levels, c1 and c2 ; are obtained by maximizing the expected utility subject to
the resource constraints and the incentive compatibility constraint,
max [pU (c1 ) + (1

c1 ;c2 ;L

s.t. pc1 L
(1 p)c2
c1 Ac2

(1

p)AU (c2 )]

(1)

L)Rh

(2)

where A = q + (1 q)U (Rl =Rh )
13
This assumption is motivated by the observation that, if information were costly, late consumers would
be more likely to purchase information. Also, if depositors were of di¤erent sizes, larger depositors would
more likely to acquire information. These unmodeled aspects of the problem are captured by assuming that
a fraction of late consumers is informed.
14
It should be mentioned that given the complete irreversibility assumption of the long term investment,
pure panic runs of the Diamond and Dybvig type are excluded because there is no coordination problem
among late consumers. Independent of what other agents do, informed consumers always obtain a higher
payo¤ in the good state if they wait until the second period to withdraw because the bank guarantees c2 > c1 .

10

discourages banks’owners from investing in excessively risky projects or committing fraud.
In this way, demand deposits discipline bank managers and reduce moral hazard problems.
The deposit contract serves this role due to the combination of two inherent characteristics:
the “on demand clause” and the sequential service constraint. The demandable nature of
the contract motivates some depositors to monitor the bank, while the sequential service
constraint discourages free riding by depositors on others’ monitoring (see Calomiris and
Khan 1991, Flannery 1994, Jean-Baptiste 1999, Gorton and Huang 2002, 2003).15
Other papers (Gorton and Pennachi 1990, Jacklin 1993) have emphasized that liquid
deposits protect uninformed depositors from losses they would otherwise su¤er when trading
other securities (equity) with better informed individuals. Gorton and Pennachi (1990) argue
that …nancial intermediaries create liquid deposits in response to uninformed depositors.
They de…ne a liquid security as one that has no private information associated with it and
model the proposition that trading in liquid securities such as deposit contracts protects
uninformed depositors from losses that they would otherwise su¤er if they traded illiquid
– information-sensitive – securities with informed individuals. Therefore, demand deposits
with promises to pay par value are created. In such a setup, demand deposit contracts are
not the unique solution for creating liquid securities that protect uninformed agents. Other
risk-free instruments such as government bonds can accomplish the same role, a point made
by Gorton and Pennachi.
Jacklin (1993) extends the basic framework based on Diamond and Dybvig described
above, and introduces aggregate uncertainty regarding the proportion of early consumers in
the population. The fraction p~ of early consumers can take a value p1 with probability r and
p2 with probability 1

r. As before, the bank invests in a risky asset that yields a random

~ which has a high value Rh with probability q and a low value Rl with probability
return R
q and some late consumers receive perfect information about the future payo¤ from the

1

~ can have a nonzero correlation. Jacklin
bank’s assets. The two random variables p~ and R
uses this extended analysis to compare risk sharing using demand deposits and equity.
Equity contracts and demand deposit contracts are equivalent risk sharing instruments if
15

Qi (1998) and Diamond and Rajan (2001a, 2001b, 2005a, 2005b), also study the disciplinary e¤ects of
liquid deposits in models that abstract from asymmetric information.

11

there is either risk associated with loans or aggregate risk, but not both. If there is only
aggregate uncertainty about the total number of early consumers in the population, there
exists a dividend function L(e
p) and a price of ex-dividend shares Pxs (e
p) that fully reveals
the value of pe with the …nancial market equilibrium being the same as the Pareto optimum.

The same result applies if there is a risky technology and no aggregate uncertainty. In these
two situations, equity contracts and demand deposit contracts are equivalent risk sharing
instruments. If there is both aggregate uncertainty and risky bank assets with depositors
and banks asymmetrically informed about the risky asset quality, then demand deposits and
equity contracts are not equivalent risk sharing instruments.
Jacklin’s analysis indicates that the use of demand deposit contracts by banks requires
an explanation encompassing more than just a need for liquidity transformation. Banking
evolved with demand deposit contracts because they included a form of protection to uninformed depositors, who would have otherwise been disadvantaged relative to better informed
depositors had equity contracts been used instead. The basic message is that liquidity should
be provided using equity contracts when there is little or no potential for asymmetries of
information concerning asset quality.
This strand of the literature argues that banks’promise to pay the par value of deposits is
due to asymmetric information about banks’assets. The demand deposit contract can keep
the bank from dissipating depositors’wealth by exploiting information available to the banker
but not to depositors. The demand deposit contract also protects uninformed depositors
who would be disadvantaged relative to better informed individuals if banks o¤ered equity
contracts. The deposit is payable on demand and this contract imposes costs on the bank if
it deviates from the equilibrium strategy.
Legal restrictions
A third explanation of why banks promise to pay par on demand is provided by the legal
restrictions theory, which attempts to explain the coexistence of alternative assets some of
which have signi…cantly higher returns than others and all of which have little or no nominal
risk (Wallace 1983, references therein and Bryant 1989). As Wallace (1983) points out,
an example of these paradoxical patterns of returns among assets is the coexistence of U.S.
12

currency, bank deposits and default-free interest bearing securities such as U.S. savings bonds
and Treasury bills. If currency, deposits and Treasury securities are perfect substitutes, no
agent would hold non-interest bearing currency or non-interest bearing deposits instead of
Treasury bills. This coexistence can be explained by legal restrictions on Treasury bills
which prevent them from playing the same role in transactions as do currency and deposits.
If all three assets were allowed to be used in transactions without any legal restrictions, the
prediction is that either nominal interest rates would go to zero or government currency and
bank deposits would trade at discounts from redemption value, in this way yielding interest
as time approaches maturity.16
In summary, Wallace argues that banks promise to pay par on demand because of legal
restrictions which also explains why other securities do not play the same role as demand
deposits. There is a question of who gains from such a legal restriction. The argument could
be made that the legal restriction merely formalizes a typical market contract. The counterargument, in terms of Wallace’s point, would be that the bene…ciaries are the banks who have
less competition than without legal restrictions on securities being used as a transactions
medium. The government also can gain by separating the market for securities that pay
interest and transactions media that pay no interest. If the legal restriction explanation of
par redemption is correct, banks will not promise to pay par if they are not required to do
so.
Bank liabilities as a medium of exchange
Other models have been built based on the observation that bank liabilities function as
a medium of exchange and payment (Williamson 1992, Freeman 1996a, 1996b, Green 1997,
and McAndrews and Roberds 1999). In general, these papers consider a framework in which
16

White (1987) argues that the Scottish free banking system from 1716-1844 is a counterexample to the
above theory in which non-interest bearing currency and interest-bearing securities coexisted and only noninterest bearing currency was used in transactions. He critiques Wallace’s line of argument by suggesting
that the liquidity services, or nonpecuniary yields, of currency and deposits are important in addition the
pecuniary returns and risk. He argues that if technological and computation costs are appropriately considered, interest might not be worth collecting on at least smaller denominations of currency and any rents
are dissipated by costs borne by banks in equilibrium. Hence, White argues, non-interest bearing currency
would still survive in the absence of legal restrictions. Basically, White argues that the legal restriction
theory overlooks costs involved in collecting interest on currency, recognizing only the intermediaries’costs
of converting large interest bearing assets into smaller liabilities.

13

agents are either spatially separated, so they cannot contract and trade with everyone else
at the same time due to their inability to meet at a single location, or there are other
frictions such as problems of contract enforcement or adverse selection. The papers can be
interpreted as having implications for the question of whether banks pay par value, although
the connection is not immediate.
Freeman’s (1996a) and Green’s (1997) papers are similar, with both modeling the structure
of trade and the stochastic component of agents meeting to trade. Repayment of debt at
par value is optimal in these papers and the analyses are similar in various respects, with
Green clarifying some issues in Freeman’s analysis.
In Green’s (1997) model, the structure of trade among agents requires debt outstanding
within the period. E¢ ciency requires that the market value of this debt be at face value,
because otherwise agents will be subject to uncertainty concerning whether they will be faced
with a transaction in which they receive less than face value. Depending on parameters in
the model, an equilibrium with agents acting only to buy and sell their own goods may not
be e¢ cient. A central bank and possibly a clearing house can provide a guarantee that the
debt within the period will clear at face value.
McAndrews and Roberds (1999) provide a model in which exchange banks operate and
transfer balances among depositors. In this paper, they impose par redemption rather than
derive it as an implication.
A related paper by Kahn and Roberds (2004) develops a model in which traders settle
debts with other debts. Basically, they examine transferable debt and compare it to using
credit chains to resolve payments for trades among separated agents. They take payment
at par for granted in this paper, as do McAndrews and Roberds (1999), although it may
well be possible to motivate par redemption by issues of private information and resultant
adverse selection.
In these models, private agents issue debt claims to facilitate paying for purchases. One
issue that arises is the pricing of these debt claims –if the number of agents arriving to trade
is not consistent with this debt trading at par, the liabilities trade away from par. Trading
away from par value is inconsistent with optimality in these models. These papers do not
directly explore whether private intermediaries can improve on an equilibrium without them.
14

They do point out, though, that an important characteristic of a medium of exchange may
be that it entails little or no risk, i.e., its value is independent of the state of the world.
From a narrow point of view, these papers are insu¢ ciently developed to show that …nancial intermediaries will promise to pay value even though it is clear that the intermediaries
cannot honor this promise in all states of the world. From another point of view, they point
toward su¢ cient conditions that are likely to be necessary to have this implication.
For our purposes, without any implication that the conclusion follows from the existing
literature, this literature does suggest that the use of bank liabilities as a medium of exchange
is an important characteristic. In our analyses of banking systems, we will take note of the
ones in which bank liabilities are used as a medium of exchange.
EVIDENCE
This analysis implies that there are certain crucial questions to be asked in our summary of
banking histories. Table 2 summarizes the basic analytical results in the theoretical analyses
and suggests the questions to be asked about banking arrangements. First, did one or more
institutions accept deposits and promise to pay their par value on demand and, if so, did they
hold fractional reserves of the underlying asset promised? If so, was there a legal requirement
that the banks make nothing less than payment of the amount deposited? What assets did
the banks hold? Were banks’assets illiquid: exchangeable into the promised asset only over
time or at a signi…cant cost? Did a large fraction or all of the assets held by the banks have
an idiosyncratic component under circumstances consistent with asymmetric information?
Were the liabilities of the banks used as a medium of exchange? Were banks required to pay
par value on demand?
There are two alternative interpretations of the theories, which we characterize as the
strong and weak versions of the theories. In the strong interpretation of the theories, the
theories make a prediction, namely that promises to pay par on demand will occur only
under conditions consistent with the theory. This is similar to some theories in economics and
…nance, such as the law of demand which predicts that a higher price will decrease quantity
demanded. Alternatively, the theories can be interpreted as providing explanations of why
banks promise to pay par on demand, which need not mean that one theory explains all of
15

the observations and a useful theory merely needs to be consistent with some arrangements.
It could be argued that a non-redundant theory will explain something not explicable by the
other theories.
Athens, Fourth Century B.C.
Despite the di¢ culty of determining events a millennia ago, certain aspects of banks’
operations in ancient Athens and Rome are quite clear and quite pertinent for evaluating
banking theories. The sources of much of the surviving evidence provides some indication
of the reliability and possible biases in the information available. Millett’s book-length
analysis is based on the evidence from the Attic Orators’s speeches: “published versions of
their commissioned speeches” (Millett 1991, p. 2); Cohen’s book-length analysis is based
on the evidence from court cases (Cohen 1992, p. 27).17 Much is generally agreed upon
by scholars, even though there is uncertainty and controversy. We indicate where those
disagreements a¤ect our conclusions.18
Banks were unincorporated enterprises which were moneychangers before becoming full‡edged banks. Bankers operated their businesses at tables in the marketplace. At these
tables, bankers provided currency exchange, accepted deposits of both money and other
assets and made loans. Banks generally were sole proprietorships, with some possibly being
partnerships. There is no evidence of regulations that applied to banks’ operations other
than the general set of laws applied to commercial activities.19
A banker was liable for deposits up to the value of all of the banker’s assets, and the
banker was liable for the initial value of all assets deposited with them. Deposits in banks
could be transferred to others, but there were no banknotes or checks, instruments for which
17

The discussion in Andreau (1999) and Temin (2004) indicates that, other than the type of loans made,
much of the analysis carries over to Ancient Rome.
18
The discussion in this section of the paper largely relies on Thompson (1979, 1983, 1988), Millett
(1991) and Cohen (1992). A contentious issue in the literature is whether loans were for “productive”
or “unproductive” purposes. If mapped into commercial and consumption loans, this discussion makes
some sense even though the reason for the discussion – whether Athens’ economy was “primitive” – is
irrelevant to our analysis. More generally, the issue is whether loans were impersonal transactions or loans
generally were made to people with whom the banker had some personal relationship, with Cohen supporting
impersonal transactions and Millett supporting personal transactions. Shipton (1997) provides an excellent
brief summary.
19
Banks were known as trapezitai, related to the root word trapeza which means “table”, because of this
origin as moneychangers at tables in marketplaces.

16

the underlying legal foundation had not been laid.
Overall, the evidence is consistent with fractional reserve banking. Absent enough information to create balance sheets, it is not certain whether banks generally had fractional
reserves, but there is no evidence that bankers made loans only with their own capital and
there is no reason to believe that banks holding fractional reserves were fraudulent or otherwise illegal.
Transfers could be e¤ected only by physically going to the bank. Some comments about
foreign traders suggest that the depositor did not always have to be present to make a
transfer, but the recipient of the transfer apparently did have to be present.20 Runs on most
or all of the banks – a banking panic – which might ensue from banks promising to pay
par on demand would provide further evidence of a promise to pay par. Cohen (1992, pp.
215-24) discusses one or more banking panics, although the evidence presented for panics
having occurred would not be compelling against a supposition of no banking panics.
Bankers made quite risky loans. In ancient Athens, these risky loans included real estate
loans, consumption loans, commercial loans and perhaps maritime loans.21 These maritime
loans were loans to provide funds for items included as cargo on ships in trade. Generally,
these loans were over-collateralized. If the cargo failed to generate su¢ cient revenue to
pay o¤ the loan, other collateral was at least sometimes available. These maritime loans
are an excellent example of a loan with asymmetric information and substantial risk. The
safety of passage was in doubt and the lender’s risk of loss was magni…ed by a common
provision of maritime loans: the borrower owed no interest or principal if the cargo was lost
20

There are some suggestions that banks provided payments at distant locations, although Millett (1991)
and Cohen (1992, Chapter 5) disagree in the predictable way.
21
In ancient Rome in the second century B.C., the loans made by banks were uncollateralized loans at
auctions –both auctions to pay debts and estate auctions. (Andreau 1999, pp. 39-40.) Deposits were legally
distinguished between those which were to be returned intact –e.g., the actual coins deposited –which were
sealed deposits and called “regular deposits” and non-sealed deposits (Andreau 1999, pp. 40-41). Some
deposits paid interest; some not. While it is hard to imagine that a banker paid interest on sealed deposits,
for which it is more plausible that a banker charged for the safekeeping, there seems to be no clear consensus
on what other deposits paid interest (Andreau 1999, p. 42.) Banks made short-term loans (Andreau 1999,
p. 44.) There is no evidence that bankers made maritime loans out of bank assets, although the evidence
does indicate that bankers were involved in receiving payments and storing contracts and as“intermediaries”
(Andreau 1999, p. 56.) By the second century BC, banks had at least some accounts at other banks and
transfers were made from one bank to another but there is no evidence of institutions designed to facilitate
such transfers (Andreau 1999, p. 58.)

17

enroute.22 The evidence indicates that banks …nanced these loans by deposits as well as the
banker’s own funds, in addition to soliciting funds speci…cally to …nance maritime loans and
participating in loan syndicates.23
Evidence from antiquity is informative because it is far in time from contemporary practice,
but ancient practice does not seem so far removed from contemporary practice. Banks had
deposits that appear to have been redeemable on demand and redemption at less than par
was regarded as default. From the viewpoint of the legal restrictions theory, this period is
troubling because there is no evidence that banks were required to pay par on demand and
there is evidence that they did so. The maritime loans especially, but also other loans, were
consistent with both the liquidity and asymmetric information explanations of why banks
promise to pay par. There is no reason to view these deposits as a medium of exchange, since
the deposits were transferable between individuals only at the bank, and there is no evidence
to suggest that the deposits were used widely in exchange in place of readily available coin,
even in high-valued transactions.
Italy
After the fall of the Roman Empire about 500 A.D., banks did not exist in any recognizable
form in Western Europe until the eleventh century in Southern Europe. The evidence is
consistent with a supposition that the development of banks in Italy was determined more
by opportunities at the time than by legal doctrines developed in the earlier Roman Empire
(Lopez 1979, pp. 1-3.)
How did banking develop in Italy? Banks ‡ourished in Italy during the Commercial Revolution from 1200 to 1500 and then went into decline with the cities of Italy. Banking in Italy
in the …rst stage consisted of banks operated by private individuals. These bank developed
from money changers, similar to development in Ancient Athens. Banks in the second stage
22
Nonpayment in the case of loss of the collateral at sea is a common provision of loans on cargoes. This
provision can be interpreted as a de…ning characteristic of maritime loans (Millett 1983, p. 36), although we
have not de…ned maritime loans this way.
23
See (Millett 1991, pp. 206-17; Cohen 1992, pp. 36-40, pp. 121-83; Shipton 1997; Andreau 1999, pp. 5456.) The evidence does not rule out the possibility that term deposits …nanced maritime loans. There simply
is no evidence to distinguish whether or not banks used deposits payable on demand to …nance maritime
loans.

18

were organized and operated as agencies of city governments. From the standpoint of understanding what banks promised and why, the private banks obviously are of more interest
in terms of the theories based on pro…t maximizing …rms.
The …rst known banks in medieval times with records available are in Genoa in the twelfth
century (Lopez 1979, p. 10). Banking in Italy in the 1300s was dominated by Florentine
banks. Goldthwaite (1985, 1998) found account books for Florentine local banking – as
opposed to international banking –covering the 1400s and he summarizes banking in Florence
a century later, including a summary of one local …rm’s operations. Mueller (1979, 1997) has
studied Venetian banking in detail. He (Mueller 1997, p. 8) indicates that not until almost
1300 is it possible to be sure that moneychangers in Venice had become bankers.24 English
(1988) provides some background information in a thorough study of banking in Siena from
the early 1200s to 1350.25
Banks in Italy had deposits that were redeemable on demand and deposits that were not
so redeemable. As early as 1100 A.D., banks in Genoa accepted deposits payable on demand
even though they were not required to do so and also accepted term deposits that could be
redeemed only with notice, e.g. …fteen days. Florentine banks’practices are consistent with
the existence of banks that paid par value on demand. In Venice, banks accepted demand
and term deposits as well as deposits of valuables for which restoration of the exact articles
deposited was expected.26
Because of so-called “imaginary money,”an important issue in medieval Italy is the money
in which banks promised to pay par. Accounts sometimes were denominated in terms of a
money of account that was not an existing coin or set of coins.27 After considering a series
of examples, Spu¤ord (1988, pp. 411-14) concludes that “it may be taken as axiomatic
that on closer inspection an historical explanation may be found for the existence of each
money of account, and that such an historical explanation will indicate to which real coin the
system continued to be attached.” In short, a money of account di¤erent than the medium
24

There is a clear reference to moneychangers in an 1164 contract, the names of moneychangers preserved
from 1225 and the …rst regulation of them occurs in the 1260s (Mueller 1997, p. 8.)
25
Lopez (1979, p. 10) and Kindleberger (1993, pp. 42-43) are additional useful references.
26
See (Lopez 1979, pp. 12-23; de Roover 1974, pp. 201-202; Goldthwaite 1985, pp. 19-27; Mueller 1979,
p. 51; Mueller 1997, pp. 11-15.)
27
Cipolla (1967, Ch. IV) suggests the term “ghost monies”because the monies’names are those of monies
that had not existed for some time which no one alive may have ever seen.

19

of exchange provides no evidence of nonpar redemption. It was not always the case that
banks paid current accounts at par value. Premia and discounts occurred in Venice for short
periods, and their occasional existence is not unique to Venice.28
Despite or perhaps because of these deviations from par, later centuries sometimes had
explicit legal requirements that banks pay the par value of deposits on demand. Such requirements are explicit in a law in 1321. In 1421, the Venetian Senate “insisted on the
total convertibility of bank money at par and on demand” (Mueller 1979, p. 93), a clause
still in force in 1477. This promise to pay par was backed up in Venice by a surety bond
for bankers’ deposits to provide funds to depositors in the event that a failed bank had
insu¢ cient funds.29
The evidence for fractional reserves generally is indirect because double-entry bookkeeping
was unknown for the early part of this period. A reconstructed ratio of cash to liabilities for a
…rm indicates that at least one Florentine bank de…nitely held fractional reserves. Fractional
reserves also are a reasonable inference based on the later Florentine laws requiring payment
on demandable deposits, for example in three days. If banks held one hundred percent
reserves, such a requirement would be unnecessary, as would have been the surety bond or
proposals for one hundred percent reserves.30
Bank deposits regularly were used to transfer funds between depositors. The evidence
di¤ers across cities, possibly because of real di¤erences across times and places and possibly
because of selective discussion in the histories. In Genoa, bankers transferred funds from one
depositor to another by oral order and regularly transferred them from one bank to another.
Funds in banks were used to make local and international payments. Written orders of
payment appear in Florence in the late 1300s. Goldthwaite discusses a canonical depositor
in Florence who deposits funds and then draws the balance down over several months.
These withdrawals often were made by written orders to the banker to make a payment
to the order’s bearer. These payments could, and did, include orders to pay construction
workmen from these deposits, attesting to the widespread nature of these deposits and
their use in payments. Transfers of deposits by oral order occurred in Venice from the end
28

Mueller (1979, pp. 84-94; 1997, pp. 166-74) presents evidence on premia and discounts.
See (Mueller 1979, p. 93; Mueller 1997, p. 9, pp. 16-17, pp. 52-62; Lane and Mueller 1985, pp. 10-16.)
30
See Goldthwaite (1985, pp. 37-39, Appendix B) and Mueller (1979, p. 52, pp. 73-74.)
29

20

of the thirteenth century. Such transfers were used for purchasing merchandise, buying
foreign exchange, lending among holders of accounts, paying real estate rents, and dealing
in bullion.31
Banks made a large variety of risky loans. Banks in Genoa made loans to relatively wello¤ people as well as to those engaged in trade and “craftsmen and other small fry” (Lopez
1979, p. 17). In the eleventh century, bankers were allowed to invest in a trade but were
required to obtain guarantors for their liabilities up to a speci…ed limit. Bank loans in Genoa
included maritime loans. Banks in Florence made loans based on jewelry and promissory
notes and they also purchased promised interest payments from funds established by the
government. Loans in Venice associated with silver and gold were extensions of short term
loans and involved failures in 1374. Venetian banks also made loans by overdrafts and became
involved in government …nances by buying government debt.32
The bank failures over these centuries attest to the risk that banks bore. Much of the
information on banks’ loans and investments comes from bankruptcies and liquidations.
There were bank failures in Genoa, Florence, Venice and Siena. Florence had banking panics
in 1340s and 1499-1500 and Venice had one in 1374-75. The legal aspects of failure were
a topic of political discussion in Venice and inspired a bankruptcy law in 1330. In Venice,
the problems generally were due to borrowers’di¢ culties associated with famines and war.
Such events were not the only possible causes – Sienese banks made loans to ecclesiastics
and nobility and failed during wars and con‡icts in the 1290s. The problems caused for the
banks were su¢ ciently large that debtors in Siena could seize the sons of those unable to
pay. This can be contrasted with the somewhat less drastic treatment of insolvent debtors
in Venice who were banished or imprisoned.33
Banks in medieval Italy promised to pay par, and although there were indeed laws requiring
banks to pay par on demand, these laws followed rather than preceded that promise. The
loans made by these banks were illiquid and the banks had better information on the risky
31

See (de Roover 1974, p. 202-203, p. 216; Lopez 1979, p. 16; Spallanzani 1978; Goldthwaite 1985, pp.
19-27; Mueller 1979, pp. 48-50, pp. 57-66; Mueller 1997, p. 7, p. 15-20.)
32
See (Lopez 1979, p. 11, p. 17; Goldthwaite 1985, pp. 28-31; Mueller 1979, p. 63, 67, pp. 77-84, p. 96;
Mueller 1997, p. 20.)
33
See (Lopez 1979, p. 20; Mueller 1997, p. 57, 81, pp. 122-197, 145-57, 163-64, p. 197, pp. 211-51, Ch. 6,
Appendix B; English 1988, pp. 40-41, p. 49, p. 69, p. 89, Part II.)

21

loans made in trade and to ecclesiastics and nobility than did the depositors. Deposits were
transferred across depositors and banks quite generally and, in Florence, deposits were used
as a medium of exchange in the same way that checks in the contemporary United States
are used today.
Japan
Japan has a very di¤erent development, isolated to some extent from Western Europe, in
the Tokugawa period from 1603 to 1867-69. A government decree in 1639 closed Japan to
most foreign trade.34 Japanese were forbidden to travel to other lands, communication by
private parties was cut o¤ and foreigners were restricted to a small enclave. This period of
“seclusion” ended with the arrival of Commodore Perry in 1853 to force the beginning of
trade with the United States.35
Many practices easily recognizable as banking developed in Japan in this period. In fact,
Japan had a developed …nancial system in Osaka –the major commercial center –and Edo
–the major administrative center later renamed Tokyo –by the late 1600s. Lenders in the
country evolved into …nancial intermediaries that accepted deposits and made loans by the
1800s.36 While banking developed substantially after the end of the Tokugawa period, these
later institutions were in large part intentional copies of those in the United States and
Germany.37
Japan had a uni…ed national coinage after the 1630s. The accounts of banks in Osaka were
kept in silver and the accounts of banks in Edo were kept in gold, but a well functioning
market for exchanging gold and silver developed. The major coins in actual use were gold
34

The Tokugawa period itself is interesting because it had some of the characteristics of a command
economy well before the command economies of the twentieth century and developed characteristics of a
market economy over time (Crawcour 1989; Iwahashi 2004.)
35
See Hane (1986, pp. 23-24, pp. 65-69), Jansen (2000, Ch. 3) and Tashiro (2004.)
36
Prior to the Tokugawa period, lenders were not banks and instead generally lent their own funds, in
most respect being similar to pawnshops (Gay 2001.)
37
Crawcour (1961) provides an overview of the development of banking in Tokugawa Japan. Patrick (1965,
1967) discusses the development of the banking system in the Meiji era (1868-1912) and Patrick (1967) relates
it to earlier developments. Soyeda (1896) and Tamaki (1995) are two general histories of Japanese banking
that are primarily histories of banking after the Meiji restoration in 1868. Early chapters summarize banking
in the Tokugawa period (Soyeda 1896, Ch. 1; Tamaki 1995, Ch. 1.) Toby (2004) presents a very informative
and readable account of the business activities of a country banker in the eighteenth and nineteenth centuries.

22

and copper.38
By the latter half of the 1600s, …rms in Osaka evolved from money changers into …rms
accepting deposits and issuing receipts that passed as money. These …rms are known as
ryogae.39 Wholesale merchants and …nanciers of local daimyo (local lords) were involved
in loans related to their original businesses. The money changers, though, were directly
involved in the original issues of notes, possibly as early as 1640 to the 1660s. These money
changers, who were not corporations in the sense of English or American law, were numerous.
In the 1850s, more than 1300 operated in Osaka and more than 750 operated in Edo.40
Bankers issued both bills that paid interest and passed from hand to hand, being endorsed
at each step – the depositor’s order – as well as notes that paid no interest and were not
endorsed at each step – the ryogae’s note.41 The ryogae’s note was a receipt for deposits
promising to pay that amount either on demand or with notice. A depositor could obtain
these notes in desired denominations that passed from hand to hand. If the bank had
insu¢ cient funds upon attempted redemption, a holder’s only recourse was to the bank:
the ryogae’s note was a liability of the bank. Deposits also were the basis of “depositor’s
orders” which were similar to checks except that they were negotiable. Each holder signed
the depositor’s order when using it to pay for something, until the note was returned to the
bank. If the deposit account failed to have su¢ cient funds when returned to the bank, the
holder’s recourse was to the previous holders (presumably sequentially.) If the bank failed
to honor the note because of its own di¢ culties rather than the depositor’s lack of funds, the
only recourse was to the bank. These notes could be for more than the value of the deposit,
but they might not be honored on demand.42
Banks held fractional reserves. While there is no clear evidence on the aggregate reserve
ratio, some evidence suggests reserves on the order of one quarter of deposits. Late in the
38
For this description of the Japanese monetary system, we have relied on Crawcour (1961) and Crawcour
and Yamamura (1970.) As Crawcour notes (1961, p. 346, fn. 18), the use of a money of account that is
seldom used in transactions and physical monies denominated di¤erently is not substantially di¤erent from
earlier practice in Europe.
39
The ryo was a counting unit of gold coin.
40
See (Crawcour 1961; Tamaki 1995, Ch.1).
41
Crawcour (1961) calls these instruments “deposit notes” and “withdrawal notes” instead of “ryogae’s
notes”and “depositor’s notes”as in Tamaki (1995), but the descriptions of the characteristics are the same.
42
See (Crawcour 1961, pp. 352-53; Soyeda 1896, pp. 412-13; Tamaki 1995, pp. 6-7.)

23

Tokugawa period, reserves of only one-sixth or one-seventh are mentioned.43
A group of ten money changers in Osaka known as the “Ten Money Changers” exercised
supervisory control over other bankers in Osaka, exercising some of the functions of a central
bank. Reserves were held in other successively larger banks and used as clearing balances.44
The banks’ assets were loans to private individuals, loans related to government remittances and direct loans to the local and national governments. Some banks developed from
wholesalers and provided book credit, later providing credit in the form of negotiable bills.45
These loans might be secured or unsecured. There also was an active interbank market for
funds.

46

We have found no evidence that there was a legal requirement that banks redeem notes at
par, and it is unlikely that there is any such evidence. The political system in the Tokugawa
period included a shogun – military governor – of Japan in combination with subordinate
territorial lords who ruled the country. The legal system was relatively undeveloped and
civil law consisted of proclamations combined with customary law. With rare exceptions,
civil disputes in the Tokugawa period were resolved by the disputants, possibly with outside
but not governmental assistance.47
Overall, the development of banking in Japan is informative because banking developed in
many ways similar to banking in Western Europe, despite cultural and legal di¤erences from
Western Europe. Banks promised to pay par on demand even though they held fractional
reserves and were not required to do so. Banks made loans, such as to governments, that
were not readily marketable, and loans to private individuals which would not be transparent
to depositors. Banks’notes were even more clearly a medium of exchange than were Western
European banks’liabilities.
43

Tamaki (1995, p. 6) suggests this …gure for Osaka banks and Toby (2004) suggests this …gure for a
country banker with surviving records. Crawcour (1961, p. 356) suggests reserves for Osaka banks on
the order of one-third deposits early in the Tokugawa period but possibly a ratio as low as one-sixth or
one-seventh at the end of the period.
44
See Crawcour (1961, pp. 353-54), Soyeda (1896, p. 412) and Tamaki (1995, pp. 7-8.)
45
See Crawcour (1961, pp. 347-56, p. 358; 1962, pp. 63-66), and Crawcour (1989, p. 586.)
46
See (Crawcour 1961; Patrick 1967, p. 245-47; Soyeda 1896, p. 413; Tamaki 1995, pp.5-7; Toby 2004.)
47
Glenn (2000, Ch. 9) discusses legal systems in Asia, primarily with an emphasis on China. Henderson
(1968) and Oda (1999, Ch. 2) discuss the general framekwork of Tokugawa law.

24

United States
It might seem that banking in the United States is unlikely to be of much interest for this
study because U.S. banking largely is a carryover of British institutions. Such a conclusion
is incorrect. Institutions do not appear to have been carried over from Great Britain without
thought to the di¤erent circumstances, although it is fair to say that the common law carried
over from Great Britain made those institutions the default ones. In fact, some states in the
antebellum period prohibited banks altogether, which was not true in Great Britain, while
others had novel banking systems.
Free Banking.—
In the period immediately preceding the Civil War, individual states in the United States
determined their own banking laws. Some states had a banking system patterned after the
one introduced in New York, called “free banking.”These free banking systems had certain
distinguishing characteristics. Anyone who satis…ed speci…c legal criteria was free to open a
bank, which is the basis of the name “free banking.” These banks were permitted to issue
notes that were used as a medium of exchange and were required by law to redeem their
notes at their par value when presented at the bank. As backing for the notes, banks were
required to hold government bonds –called “government stocks”in this period –which were
traded on the New York Stock Exchange. For many free banks, these bonds were the largest
part of their assets.48
This requirement to redeem notes at par value is consistent with the legal requirement
explanation for par redemptions.49 Since banks were required to redeem their notes at par
value, an economic explanation for that redemption such as asymmetric information is not
really necessary and it is not possible to be certain whether banks would have promised to
pay par if they had not been required to do so. Still, it is interesting to examine whether
those explanations are applicable.
These bonds held as backing for the notes were marketable securities traded on the New
48

See (Dwyer 1996; Dwyer and Hafer 2004; Dwyer and Hasan 2006.)
Notes were not required to trade at par away from the bank, though, and they generally did not.
Banknote prices in New York City generally deviated by a few percentage points from the par value, although
they also sometimes deviated substantially from the par value (Gorton 1996; Dwyer and Hasan 2006.)
49

25

York Stock Exchange and are not really a plausible basis for an asymmetric-information
explanation of banking. There is no reason to think that banks had better information about
states’…nances than did noteholders. Although traded on the New York Stock Exchange,
the bonds’ prices were not readily available on the minute-by-minute basis on which they
are available today. The prices generally were available, though, in the New York press
on a weekly basis. Furthermore, while a bank might know more about its balance sheet
than depositors, banks were required to publish their balance sheets periodically in local
newspapers which mitigated any lack of information by depositors.50
The bonds held by banks were traded on an organized exchange and were liquid in the
sense that trading was reasonably continuous for the larger issues of bonds held by the banks.
As a result, it is not obvious that the liquidity explanation would have been su¢ cient to
induce par redemption.
These bonds were not risk free over time. While banking panics were not common events,
there were panics and suspensions of payments in some states at the start of the Civil War.
Money Market Funds.—
Removed in time and circumstances from free banks by 150 years, money market funds
in the United States are an example of …rms that contradict most prevailing theories about
why issuers of monetary liabilities promise to redeem deposits on demand at par. Money
market funds are redeemable by check on demand. Money market funds are not required
by law to redeem their liabilities at anything other than market value, but money market
funds have gone to substantial e¤ort to avoid the par value of their liabilities falling below
the initial value of a dollar.
The Securities and Exchange Commission’s (SEC’s) website describes money market funds
well (SEC 2004a).
Money market funds typically invest in government securities, certi…cates of
deposits, commercial paper of companies, and other highly liquid and low-risk
securities. They attempt to keep their net asset value (NAV) at a constant $1.00
per share— only the dividend yield goes up and down. But a money market’s
50

See (Dwyer, Hafer and Weber 1999; Hasan and Dwyer 1994; Dwyer and Hasan 2006.)

26

per share NAV may fall below $1.00 if the investments perform poorly. While
investor losses in money market funds have been rare, they are possible.
Money market funds in the 1970s were required to mark their assets to market, although
there was variation in how the market value of the underlying assets were determined and
some methods were tailored to keep NAV constant in the face of ‡uctuating security prices.
Subject to restrictions on their portfolios, bank trust departments used amortized cost accounting to determine the value of assets in their pooled short-term investment funds and
they preferred money market funds that used amortized cost accounting (Cook and Du¢ eld
1979, pp. 20-21.)
Stock and bond mutual funds in the United States mark their assets to market, but money
market funds do not have to mark to market and do not do so. Instead money market funds
use “penny rounding” and “amortized cost accounting.” Under penny rounding, net asset
value (NAV) is determined to the nearest one percent, rather than the nearest tenth of a
percent or tenth of a penny. This technique of determining NAV avoids recognizing small
losses of a few tenths of a percent. Amortized cost accounting is most easily explained in
terms of securities with one payment at maturity that are held to maturity. Under amortized
cost accounting, the di¤erence between the price paid and the amount received at maturity
is accrued as income linearly over time. As a result, NAV cannot fall below a dollar under
amortized cost accounting if all assets are held to maturity. Money market funds using these
valuation techniques are required to monitor deviations of NAV from market value and their
portfolios’risk and maturity are restricted.51
Both methods of valuing securities imply that the value of investors’investment is diluted
when interest rates rise or fall. The underlying logic is similar to the recent controversy
concerning international funds and applies to any fund that creates predictable deviations
between NAV and market prices (Greene and Hodges 2002.) When short-term interest rates
rise, the value of the assets falls and NAV does not re‡ect this fall. As a result, an investor
in a money market fund can sell the mutual fund at NAV and buy market securities, thereby
receiving the higher market interest rate which would not be received if those funds had
been left in the money market fund. Because the investment was redeemed at NAV and
51

See Cook and Du¢ eld (1979, pp. 19-21) and SEC (2004b).

27

the underlying securities were sold by the fund at the lower market prices, the remaining
investors su¤er a loss that is recognized as a lower return over time. Some investors will
take advantage of this opportunity because it is worth the transactions costs to them. When
interest rates are rising, money market funds have more redemptions and consequently more
securities trades and higher transactions costs.
When interest rates fall, the reverse happens. Money market funds recognize capital
gains on securities over time and pay higher interest rates than the return to maturity
of the underlying securities. As a result, money market funds have in‡ows of funds and
consequently more securities trades and higher transactions costs. The in‡ows of funds
reduce the return received by current investors compared to what they would be if either
there were no funds in‡ows or capital gains were recognized immediately.
These e¤ects were well known when these valuation techniques were adopted in the late
1970s and Lyon (1984) documented that the dilution was not merely a possibility. Lyon
showed that money market funds had lower returns than the underlying portfolio when
rates increased, and out‡ows predictably followed. Lyon’s interpretation of the issue is
very di¤erent than ours though. He interprets the dilution as an undesirable e¤ect of these
valuation methods which the SEC should prohibit. We interpret the dilution as a predictable
cost of these valuations which customers and funds’managers are willing to pay. After all,
money market funds are not required to use either valuation method, and money market funds
that mark to market on a daily basis have less stringent restrictions on their portfolios.
These e¤ects of amortized cost accounting and penny rounding continue. Figure 1 shows
the di¤erential between the average return on taxable money market funds and the 90-day
Treasury bill rate by week since 1984. With occasional exceptions, the …gure shows that the
yield to maturity of a 90-day Treasury bill exceeds the return on money market funds. Ninety
days is the maximum average term to maturity permitted to funds that use amortized cost
accounting. As the analysis above predicts, the …gure shows that the Treasury bill return
rises relative to the money market return when interest rates rise and the Treasury bill return
falls relative to money market returns when interest rates fall.
How successful have money market funds been at keeping the redemption value constant?
As of 2005, only one money market fund is known to have fallen below the dollar redemption
28

value, a money market fund called Community Bankers U.S. Government Money-Market
Fund that failed in 1996 and paid 94 cents on the dollar.52 Other money market funds have
closed in circumstances that would have created an NAV less than a dollar, but the parent
…rm has put in funds to make up the di¤erence. In one case, Salomon Brothers purchased
securities from a subsidiary institutional money market fund at in‡ated prices to prevent a
progressive collapse due to withdrawals (Stigum 1983, pp. 676-79).53
This constant dollar NAV has required intermittent payments to money market funds
by a¢ liated parties. Institutional Liquid Assets in Spring 1980 returned $2 million in fees
to keep NAV from falling below $1. In 2002 when interest rates on assets held by money
market funds fell below expense rates, money market funds reduced the expenses charged to
investors in the funds to avoid having the value of the funds “bust the buck.”54
Deposits in money market funds are transferable by check. There are lower limits on the
size of transactions, which makes such checks generally not useful for daily transactions such
as purchases at a grocery store, but the limits are su¢ ciently small that they can be used to
make mortgage payments for example.
Money market funds clearly are not required to maintain an NAV of a dollar, which
means that the legal restriction theory is irrelevant. At …rst glance, it might seem that
money market funds must redeem at par because they compete with commercial banks, and
banks in the U.S. are required to redeem demand deposits at par on demand. This leaves
unanswered the question: If redemption at a constant NAV is not preferred by households,
why would money market funds follow the lead of banks unless it is privately optimal to do
so?
Money market funds hold marketable assets with prices that are readily available at virtually zero cost, which means that the asymmetric information theory is irrelevant. Does
52
Some variable annuity accounts with money market sub-accounts fell below the par value of $1 due to
annuity fees (Damato 2002b). This point is not in the original print article but is available at the end of the
online version of the article by Damato in a section “Corrections and Ampli…cations”updated on November
8, 2002.
53
Such behavior is consistent with the fund family maintaining its reputation and does not necessarily
imply that there are bene…ts to the money market fund itself from having a stable NAV. This line of
argument would require that there are bene…ts to a fund family to a stable NAV but none to the money
market fund itself. This does not seem particularly plausible to us, but we do not pursue this point.
54
See Lyon (1984, p. 1015) and Damato (2002a.)

29

this mean that the liquidity provision explanation explains why money market funds keep
NAV at a dollar? Because the market for Treasury bills is large relative to any redemptions
at money market funds to date, the assets held by money market funds can be sold at a moment’s notice and are as liquid as the deposit. Whether money market funds are a medium
of exchange is a matter of interpretation because there are minimum sizes of checks that
can be written. Money market funds are checkable deposits, and therefore with this caveat
about transaction size, are consistent with this explanation.
CONCLUSION
There is a very large theoretical literature on banks and their promise to pay par on demand. One line of the literature follows Diamond and Dybvig, in whose model banks promise
to pay par on demand because households have a demand for that contract’s liquidity. In
that analytical framework, the greater liquidity of the demand deposit liability is due to a
maturity mismatch between the bank’s assets and liabilities, but the general point is the
ability to exchange the deposit for the liquid assets at low cost. A second line of the literature takes a slightly di¤erent tack and bases the promised payment at par on information
about loan quality known to the bank but not to depositors. Uninformed depositors have
less information about loans than do bankers, and it generally is not an incentive-compatible
equilibrium for nonmarketable loans on banks’ books to be the basis of deposits that are
marked to a market value determined by the bank. Hence, the uncertain market value of
banks’assets becomes a known value of banks’liabilities by promising to pay the par value of
deposits. Because a bank can take actions such as making riskier loans to increase its pro…ts
without compensating depositors for the risk, promised payment on demand can reduce the
bank’s payo¤ from such strategies. An alternative line of argument takes the simple course,
which is not necessarily the wrong one because it is simple. Banks in the U.S. today are
required to pay the par value of “demand deposits”on demand, and the existence of such a
promise may re‡ect nothing other than that legal requirement. A fourth line of the literature
suggests that liabilities of …nancial intermediaries which are used as a medium of exchange
will be characterized by promised redemption at par value on demand.
Strong predictions from the theories have the form: Promised payment at par will be
30

observed only if certain conditions are met. For example, the legal restriction theory can
be interpreted as making the strong prediction that banks will promise to pay par on demand
only if they are required to do so. Similar statements can be made for the other theories.
The theories also can be interpreted as explanations of some but not all arrangements.
The legal restriction theory can be interpreted as making the weak prediction that banks
sometimes will promise to pay par on demand if they are required to do so and for no other
reason. In other words, an observation supporting the importance of the legal restrictions
theory would be an observation at some time and place that banks promise to pay par on
demand and none of the other theories can explain why they would make that promise.
All of the theories explain some of observed banking arrangements. This can be seen in
Table 1, which indicates that all of the theories are consistent with some of the observed
banking arrangements. At the same time, none of the theories explains all of the observed
banking arrangements. Perhaps this is as it should be given the variety of arrangements that
have existed in various times and places. That said, it is interesting that the most recently
developed theory – the one based on money as a medium of exchange – is the one that is
most consistent with recent developments.
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38

Table 1
Summary of Evidence
Time and Area

Characteristic
Pay Par on
Demand

Fractional
Reserves

Assets Not
Liquid on
Demand

Asymmetric
Information

Legal
Restriction

Negotiable

Medium of
Exchange
Away From
Bank

Ancient Greece

Yes

Yes

Yes

Yes

No

No

No

Medieval Italy

Yes

Yes

Yes

Yes

No

No

No

Tokugawa Japan

Yes

Yes

Yes

Yes

No

Yes

Yes

U.S. Free
Banking

Yes

Yes

No

No

Yes

Yes

Yes

U.S. Money
Market Funds

Yes

Yes

No

No

No

No

Yes

This table summarizes the characteristics of banking in the times and places examined. The theories are attempting to explain why the
banks paid par on demand while holding fractional reserves; hence they are necessary for the episodes to be informative about the theories.
Negotiability - which means that the order to pay can be transferred to another - is a characteristic of notes that can be exchanged or of
bills of exchange, but not of checks as used in the United States today. “Asymmetric information” is a theoretical term based on what
agents know, but is used as a summary column title to denote assets that do not have prices readily available on a reasonably continuous
basis. “Legal restriction” summarizes whether the institutions were required by statutory law to redeem some deposits on demand at par.

Table 2
Summary of Implications of Theories
Theory

Primary Antecedent Condition for Par Redemption

All

Banks promise to pay par on demand with only fractional
reserves of the promised asset

Liquidity Provision

Bank assets are exchangeable into the liability over time, at
significant cost, or both over time at significant cost

Asymmetric Information

Banks are better informed about assets than depositors with no
truth revealing equilibrium

Legal Restriction

An enforced law requires bank to pay par on demand

Bank Liabilities as a Medium of Exchange
Bank liabilities are used as a medium of exchange
This table summarizes the implications of the theories. The condition “with no truth revealing equilibrium” is an important part of the
theory but it basically is untestable unless it is false because there is such an equilibrium, so we do not consider this condition in our
analyses of actual banking.

Figure 1
Money market fund yield and 3-month Treasury bill yield

10

Money market fund yield
3-month Treasury bill yield
Money market fund less Treasury bill

6

2

-2

11/26/1981

5/19/1987

11/8/1992

5/1/1998

10/22/2003