ON THE WELFARE PROPERTIES OF FRACTIONAL RESERVE BANKING

• Date: 01 August 2016
• Published date: 01 August 2016
• DOI: http://doi.org/10.1111/iere.12181
• Author: Daniel Sanches

INTERNATIONAL ECONOMIC REVIEW

Vol. 57, No. 3, August 2016

ON THE WELFARE PROPERTIES OF FRACTIONAL RESERVE BANKING∗

BYDANIEL SANCHES1

Federal Reserve Bank of Philadelphia, U.S.A.

Monetary economists have long recognized a tension between the benefits of fractional reserve banking, such as the

ability to undertake more profitable (long-term) investment opportunities, and the difficulties associated with it, such

as the risk of insolvency for each bank and the associated losses to bank liability holders. I show that a specific banking

arrangement (a joint-liability scheme) provides an effective mechanism for ensuring the ex post transfer of reserves

from liquid banks to illiquid banks, so it is possible to select a socially efficient reserve ratio in the banking system that

preserves the safety of bank liabilities as a store of value and maximizes the rate of return paid to bank liability holders.

1. INTRODUCTION

One of the main characteristics of the modern banking system is the small amount of reserves

in lawful money that banks hold relative to the amount of short-term liabilities (such as de-

mand deposits) they issue. Economists refer to this practice as fractional reserve banking. The

proponents of fractional reserve banking have argued that a fractional system allows banks to

economize on non-interest-bearing reserves, permitting them to increase the return on their

assets and, in the case of a competitive market for bank liabilities, pay a higher return to their

liability holders. Implicit in this argument is the conjecture that a lower level of reserves neces-

sarily translates into a higher return paid on a particular class of bank liabilities: those facilitating

payments and settlement. This is usually viewed as a socially desirable outcome because one of

the main functions of banks is to provide transaction services.

Fractional reserve banking is indeed a superior form of banking provided that each bank

is able to borrow reserves from other banks if it suffers an unusual number of withdrawals.

The fact that each bank holds only a fraction of its demandable liabilities in the form of highly

liquid assets makes it prone to failure. A typical concern is whether fractional reserve banking

renders the banking system insolvent in the event that interbank markets, for some reason, fail

to perform the function of transferring reserves from more liquid banks to illiquid banks.2Thus,

there is a clear tension between the benefits of fractional reserve banking, such as the ability to

undertake more profitable (long-term) investment opportunities, and the difficulties associated

with its implementation, such as the risk of insolvency for each bank.

The goal of this article is to investigate whether it is possible to implement a fractional reserve

system that allows member banks to provide maturity transformation and liquidity services in

such a way that bank liabilities are widely accepted as a means of payment and trade at par

value. My main result is to show that a historically relevant form of private bank coalition (a

joint-liability arrangement) allows the members of the banking system to engage in fractional

∗Manuscript received March 2014; revised March 2015.

1The views expressed in this article are those of the author and do not necessarily reflect those of the Federal

Reserve Bank of Philadelphia or the Federal Reserve System. I thank Douglas Gale, Todd Keister, Guido Menzio,

Will Roberds, David Skeie, and two anonymous referees for their helpful comments. I also thank seminar participants

at Wharton, Rutgers University, and the Bank of Canada.

Please address correspondence to: Daniel Sanches, Federal Reserve Bank of Philadelphia, Research Department,

Ten Independence Mall, Philadelphia, PA 19106-1574. E-mail: Daniel.Sanches@phil.frb.org.

2For instance, Friedman (1959) argues in favor of a banking system with the property that each member bank holds

in reserve the full value of its demandable liabilities. His main concern was precisely the stability of the banking system.

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(2016) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

936 SANCHES

reserve banking in such a way that bank liabilities are widely used as a medium of exchange

and yield a higher rate of return. As opposed to markets, this organizational structure involves

the monitoring and supervision of the activities of member banks.

The kind of bank coalition studied in this article resembles the clearinghouse associations

that developed in the United States in the 19th century, as described in Friedman and Schwartz

(1963), Gorton (1984, 1985), Gorton and Mullineaux (1987), Selgin and White (1987), and

Moen and Tallman (1992, 2000). These authors have provided evidence that the clearinghouse

associations that were formed in some cities in the United States (e.g., New York, Boston, and

Chicago) in the second half of the 19th century evolved into a coalition of banks that required

each member bank to report its transactions, imposed reserve requirements on each member

bank, and supervised the note-clearing process on a daily basis. This means that clearinghouse

associations provided supervision and regulation services to member banks, allowing them

to implement risk-sharing arrangements that would otherwise be impossible under a more

decentralized organizational structure.

In my formal analysis, I construct a random-matching model in which privately issued liabil-

ities circulate as a medium of exchange. Agents meet in pairs and use bank liabilities to trade.

The redemption of bank liabilities happens periodically in a centralized location where sellers

who have sold goods to buyers take their bank liabilities to claim their face value. The key

incentive problem within the banking system arises due to hidden action: It is necessary to pro-

vide banks with incentives to induce them to voluntarily report the creation of bank liabilities

and hold the appropriate level of reserves. To deal with this incentive problem, there exists a

clearinghouse association (i.e., a record-keeping and safe-keeping device) that requires mem-

ber banks to report their transactions, imposes reserve requirements on each one of them, and

supervises the clearing of bank liabilities at each date. Thus, the kind of monitoring provided

by the clearinghouse allows each member bank to issue liabilities that effectively circulate as a

medium of exchange.

I initially characterize equilibrium allocations in the absence of any interbank risk-sharing

arrangement. In this case, a safe and sound banking system (i.e., one in which bank liability

holders do not suffer losses due to bank failures) necessarily involves an institutional arrange-

ment in which each banker is required to hold in reserve the full value of his demandable

liabilities, as advocated by Friedman (1959). This strict collateral condition implies that each

bank is fully solvent at any moment so that this form of banking certainly ensures the stability of

the payment mechanism. However, I show that such a system costs something for the members

of society. First, the banking system as a whole holds excess reserves at the end of each date,

which is clearly inefficient because these resources could have been either consumed or invested

in higher-return technologies. Second, the rate of return paid on bank liabilities is inefficiently

low, which imposes a cost on those who hold these liabilities for transaction purposes.

Subsequently, I characterize the properties of a banking system in which each banker volun-

tarily chooses to become a member of a coalition that will issue liabilities that are effectively

joint obligations of its members. Each banker continues to issue liabilities that identify him as a

debtor, but the coalition publicly announces that, in the event an individual banker is unable to

keep his promises, other members will honor any obligation of that member, according to their

joint capacity. This joint-liability scheme is an effective arrangement that permits the appropri-

ate ex post transfer of reserves from liquid banks to illiquid banks, allowing them to reduce the

share of funds invested in non-interest-bearing reserves and, consequently, increase the share of

funds invested in interest-bearing assets. As a result, it is possible to eliminate excess reserves in

the banking system and induce each banker to pay a socially efficient return on bank liabilities

without introducing the risk of individual bank failures.

The rest of the article is structured as follows: Section 2 discusses the related literature.

Section 3 presents the basic framework. Section 4 carefully describes the exchange mechanism.

In Section 5, I characterize equilibrium allocations under a strict reserve requirement that

imposes that banks must hold in reserve the full value of their demandable liabilities. In Section