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This paper considers the implications for monetary policy of a decreasing demand for outside money. It finds that even perpetual declines in the demand for base money pose no threat to the traditional methods employed for conducting monetary policy. The effects of such reductions in the demand for central bank liabilities, however, do depend on how monetary policy is conducted. Four monetary policy regimes are analyzed. With a policy of nominal-interest-rate targeting, a secular decline in the volume of cash transactions unambiguously leads to accelerating inflation. A policy of maintaining a fixed composition of government liabilities leads to accelerating (decelerating) inflation if agents have sufficiently high (low) levels of risk aversion. Inflation targeting produces falling nominal and real interest rates, while a policy of fixing the rate of money growth can easily lead to indeterminacy and endogenous oscillation in interest rates. It is argued that a policy of fixing the composition of government liabilities has several advantages if it is known that agents are not too risk averse and that the asymptotic demand for base money is small. If this information is not known, then interest-rate or inflation targeting have an advantage because their consequences are not sensitive to such environmental features.

It has long been thought that monetary policy affects the macroeconomy by inducing variations in the supply and demand of outside money.1 Recently, however, the traditional sources of the demand for outside money have been in pronounced decline. For example, continuous technological improvement in electronics and communication systems has made possible the development of several new, noncash means of payment. As the use of these new payment instruments has grown, there has been a noticeable shift away from the use of cash in transactions. According to The Nilson Report (1997), cash accounted for 20% of the dollar volume of U.S. payments made by consumers in 1990 and 18% in 1996, and is projected to account for only 16% in 2000 and 12% in 2005.2 At the same time, many countries have eliminated reserve requirements on most or all intermediaries, and those that have not done so (such as the United States) have permitted financial innovations that render reserve requirements virtually inconsequential.3 As a result, it seems entirely possible that the demand for base money may virtually or entirely vanish in the not-too-distant future.4 These developments necessitate the reopening of some age-old questions in monetary economics: What does a declining demand for base money – and, perhaps, a demand that is declining to zero – imply for monetary policy?5 Does it imply that certain methods of conducting monetary policy may become infeasible? Does it mean that some methods may lead to unbounded inflation or indeterminacy? And, must a central bank know whether the use of outside money will disappear altogether or just become minimal in order to determine the best course of action? Monetary economists have posed these questions for some time, and have put forth a variety of answers to them. For example, Wicksell (1898) argued that in a `pure credit’ economy the nominal rate of interest would be indeterminate, and that its realized level would have strong implications for the inflation rate. He also advocated a policy of appropriate inflation or price-level targeting to avoid these indeterminacies. One can view Patinkin (1965, p. 303) as seconding this view, and Woodford (1998) as having formalized it. Woodford also argues that a policy of targeting the rate of money growth leaves the price level indeterminate in a cashless economy. In contrast, Friedman and Schwartz (1969, p. 5) asserted that `in the hypothetical world in which there are no costs of setting up a bank and running a bank, and in which deposits transferable by check provide precisely the same services as the dominant money, there would be no limit [to the price level]…short of…infinity….’ Black (1970, p. 10) proposed that in a world with no need for cash `the price level will be indeterminate, and traditional monetary theories will be inapplicable.’ He also argued (p. 14) that even if currency always continued to be used for some small transactions, `the quantity of money can have no effect…on prices.’ Which, if any, of these views is correct remains to be determined. This paper proposes a simple framework for thinking about these issues. It begins by presenting a pure-exchange, overlapping-generations model with only two primary assets – government-issued fiat currency and government bonds. To generate a demand for cash transactions, the model incorporates spatial separation and limited communication along the lines of Townsend (1987). To generate a role for banks, the model includes shocks to liquidity needs along the lines of Diamond and Dybvig (1983). In the presence of positive nominal interest rates, these features imply a derived demand for base money that depends on the need for currency in payments and the demand by banks for cash reserves.6 The volume of cash transactions is then assumed to evolve over time in a way that affects the total demand for base money.7 The primary focus here is on the consequences of a decline in the role of cash in transactions. Because agents have an incentive to economize on cash use only if nominal rates of interest are positive, the conduct of monetary policy with positive nominal rates of interest is considered first. The presence of positive nominal interest rates, however, leads to a distortion of resource allocations, so policies implying nominal interest rates of zero also are examined. Four methods for conducting monetary policy are considered under each case. One possibility studied is that the central bank sets the mix of government bonds and money outstanding. The central bank could instead set the money growth rate. Alternatively, it could set either a nominal-interest-rate or an inflation-rate target. Since the question of how secular declines in the use of currency affect the conduct of policy is intrinsically one that focuses on long horizons, the analysis here takes the target value for the variable being controlled as set once and for all. Section 5 argues that this will – again, over long horizons – provide a reasonable approximation to the outcomes of policies conducted under nondestabilizing feedback rules. When policy is conducted so that nominal rates of interest are positive, four major findings are obtained. First, all of these standard methods for conducting policy are feasible, even in an asymptotically cashless economy, in the following sense. At each date, well-defined conditions determine all real and nominal quantities, and the central bank can achieve its target with conventional open market operations. The implication is that conventional methods for conducting monetary policy can continue to work as expected in the face of a declining demand for base money. Second, three of the policies considered – inflation targeting, nominal-interest-rate targeting, and fixing the bond-to-money ratio – imply no indeterminacies, even if the demand for base money asymptotically goes to zero. A policy of fixing the money growth rate implies no indeterminacies only if agents are not too risk averse. Otherwise, it does lead to indeterminacies and may also lead to endogenous fluctuations that might not disappear asymptotically. Indeed, monetary fluctuations due to self-fulfilling prophecies can persist indefinitely, even if the demand for base money is declining to zero. Third, the rate of inflation will necessarily remain bounded under three of the policies – inflation targeting, interest-rate targeting, and a constant rate of money creation – even if the demand for base money vanishes in the limit. Under the fourth policy – a fixed bond-to-money ratio – the price level necessarily stabilizes in finite time if cash asymptotically goes out of use and if agents are not too risk averse. When these conditions do not hold, this policy is the only one that leads to unbounded inflation in an asymptotically cashless economy. Finally, as the last observation indicates, to predict the consequences of maintaining a fixed bond-to-money ratio, it is necessary to know a good deal about the preferences of bank depositors and the asymptotic magnitude of cash use. The same is true under a policy of fixing the money growth rate, but not with inflation or interest-rate targeting. Since depositor preferences and the long-run demand for cash are difficult to determine with precision, this finding highlights an advantage of inflation or interest-rate targeting. When nominal rates of interest are zero, in contrast, there is no reason for anyone to economize on cash use. Hence, cash may continue to be used indefinitely for a large volume of transactions, even if there is no need for currency arising from the economy's fundamentals. Indeed, under certain circumstances the money supply cannot be contracted in a sustained way. Therefore, since zero nominal interest rates necessarily imply a stable price level here, both the real and nominal value of cash transactions cannot be reduced over time. Thus, there are conditions under which zero nominal interest rates are inconsistent with a secular decline in the demand for base money. In addition, certain methods of conducting monetary policy cannot guarantee the attainment of zero nominal interest rates no matter what the choice of target for the control variable. A remaining issue concerns the welfare consequences of different methods for conducting monetary policy. Under zero nominal interest rates, all methods of conducting policy lead to the same welfare levels. However, with positive nominal interest rates, a comparison of welfare consequences across policies is more vexing. The question of which policy choices deliver the highest welfare levels typically will not have an unambiguous answer without a specification of how the utility of different generations should be weighted. The analysis does, however, yield one conclusion regarding welfare. Of the policies that are commonly observed in practice (that is, ruling out policies that generate sustained deflation or a zero nominal rate of interest), there is only one that can eliminate the distortions associated with the frictions that generate monetary exchange. It is the policy of fixing the bond-to-money ratio, and it eventually eliminates such distortions only if agents are not too risk averse. Interestingly, these distortions will be eliminated in finite time even if cash never goes out of use, so long as monetary policy is not too `tight’ and long-run cash use is not too large. The remainder of the paper proceeds as follows. Section 1 describes the environment, and Section 2 analyzes bank behavior and presents the model's equilibrium conditions for environments with positive nominal interest rates. 3 and 4 analyze the various monetary policies considered for positive and zero nominal interest rate environments, respectively, while Section 5 compares the properties of the different policy regimes. Finally, Section 6 concludes by discussing the role that some of the assumptions play in generating the results obtained.

The preceding analysis abstracts from several features that are relevant to modern-day payment systems. For example, the focus on a pure-exchange economy makes it impossible for developments in the technology of payments to affect the level of production. Endogenizing production levels would allow the evolution of cash transactions to affect real activity, which in turn might modify some conclusions about how this evolution affects the behavior of the price level or the behavior of real and nominal interest rates. And by allowing for capital accumulation, the model would intrinsically have much richer dynamics. A second feature from which the model abstracts is the mechanism by which the demand for cash evolves. One can regard the specification of an exogenous law of motion for πt as a `reduced-form’ approach that implicitly takes no stand on the economic forces governing the use of cash in transactions. Clearly, it would be more satisfying to model these forces explicitly. Likewise, it would be better to model the choice between cash and other instruments to make payments. Modeling that choice (for example, as done in Schreft, 1992; Ireland, 1994) would endogenize the evolution of cash use and might not alter any of the results derived above. Third, the model abstracts from the existence of a market in which reserves can be borrowed and lent. The presence of such a market has in principle the potential to substantially affect the demand by banks for reserves. And reserve demand is at the heart of the analysis here. Introducing a market for reserves into the model is straightforward. The most natural approach is to assume that each bank faces a stochastic demand for cash withdrawals (that is, a random value of πt), but that there is no aggregate randomness. This introduces an additional feature into a bank's decision regarding its reserve holdings: banks face uncertainty regarding withdrawal demand. If banks must choose their reserve–deposit ratio before observing their withdrawal demand, then ex post some banks will have more, and some will have fewer, reserves than needed to pay depositors. This fact leads naturally to the introduction of a market in which banks with a reserve surplus (deficit) can lend (borrow) reserves. While the introduction of a stochastic withdrawal demand and a market for reserves that resembles today's federal funds market adds some notational complexity, it does not alter the fundamental behavior of the model. Indeed, all the results reported above have close analogs when these additional features are added. Thus, abstracting from a market for reserves does not affect any qualitative conclusions about how an evolving demand for cash transactions affects the economy under alternative methods of conducting monetary policy. Finally, in this economy all financial transactions are conducted through banks. If the model were modified to allow for a richer set of financial institutions, agents could very well have access to financial instruments that help them overcome the spatial separation and limited communication critical to their demand for cash for transactions. The introduction into the economy of such new financial instruments likely would lead to a faster reduction in the use of cash over time, although the implications of this observation for the conduct of monetary policy are by no means clear.