This paper develops a new theory of money and banking based on an old story about money and banking. The story is that bankers originally accepted deposits for safe keeping; then their liabilities began to circulate as means of payment (bank notes or checks). We develop models where money is a medium of exchange, but subject to theft, where theft may be exogenous or endogenous. We analyze how the equilibrium circulation of cash and demand deposits varies with the cost of banking and the outside money supply. We study cases with 100 % reserves and with fractional reserves. We thank Ken Burdett, Ed Nosal, Peter Rupert, Joseph Haubrich, Warren Weber, Francois Velde, Steve Quinn and Larry Neal for suggestions or comments. We thank the NSF and the Federal Reserve Bank of Cleveland for ¯nancial support. The usual disclaimer applies. 1 The theory of banking relates primarily to the operation of commercial banking. More especially it is chie°y concerned with the activities of banks as holders of deposit accounts against which cheques are drawn for the payment of goods and services. In Anglo-Saxon countries, and in other countries where economic life is highly developed, these cheques constitute the major part of circulating medium. EB (1954, vol.3, p.49). 1

We study an economy in which exchange occurs pairwise, there is no commitment, and anonymous agents choose between random monetary trade or deterministic credit trade. To accomplish the latter, agents can exploit a costly technology that allows limited record-keeping and enforcement. An equilibrium with money and credit is shown to exist if the cost of using the technology is sufficiently small. Anonymity, record-keeping and enforcement limitations also permit some incidence of default, in equilibrium.

This paper provides a search theoretical model that captures two phenomena that have characterized several episodes of monetary history: currency shortages and the circulation of privately issued notes. As usual in these models, the media of exchange are determined as part of the equilibrium. We characterize all the different equilibria and specify the conditions under which there is a currency shortage and/or privately issued notes are used as means of payment. There is multiplicity of equilibria for the entire parameter space, but there always exist an equilibrium in which notes circulate, either alone or together with coins. Hence, credit is a self-fulfilling phenomenon that depends on the beliefs of agents about the acceptability and future repayment of notes. The degree of circulation of coins depends on two crucial parameters, the intrinsic utility of holding coins and the extent with which it is possible to find exchange opportunities in the market.

Abstract We study optimal monetary policy in an environment in which money plays a basic role in facilitating exchange, aggregate shocks affect households asymmetrically and exchange may be conducted using either bank deposits (inside money) or fiat currency (outside money). A central bank controls the stock of outside money in the long-run and responds to shocks in the short-run using an interest rate policy that manages private banks' creation of inside money and influences households' consumption. The zero bound on nominal interest rates prevents the central bank from achieving efficiency in all states. Long-run inflation can improve welfare by mitigating the effect of this bound.

This publication primarily presents economic research aimed at improving policymaking by the Federal Reserve System and other governmental authorities. Any views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.

We build a general equilibrium model to analyze how the ability of banks to create money can affect asset prices and financial stability. In the model, de-mand for liquidity takes the form of demand for money to make payments. We show that banks can provide elastic aggregate liquidity by creating and lend-ing out deposits, which will reduce the need for people to sell assets and help maintain asset price stability. We also compare two types of liquidity provision mechanisms. The first is liquidity-risk-sharing through a Diamond-and-Dybvig style coalition that pools together people’s resources, and the second is liquid-ity provision by banks though money creation. We show that without elastic aggregate liquidity provided by banks, coalitions can not actually perform their risk-sharing function, their attempt to sell assets to raise liquidity will only make asset prices decrease further, without actually raising more liquidity for shareholders hit by liquidity shocks. However, with banks providing elastic aggregate liquidity, people can indeed achieve better risk-sharing though coali-tions. Finally, we show that the central bank can help banks provide liquidity to the market by lending to banks at low interest rates during the inter-bank settlement process, so as to relax the liquidity constraint of banks.