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HANDBOOK OF MONETARY ECONOMICS VOLUME 3A
ELSEVIER
Copyright © 2011 Elsevier B.V.
All right reserved. ISBN: 978-0-444-53471-2
Chapter One
The Mechanism-Design Approach to Monetary Theory Neil Wallace The Pennsylvania State University, Department of Economics
Contents
1. Introduction 4
2. Some Frictions 5
2.1 Imperfect monitoring 6
2.2 Costly connections among people 7
2.3 Imperfect recognizability 8
3. An Illustrative Model with Perfect Recognizability 8
3.1 The model 8
3.2 A class of allocations 9
3.3 Incentive-feasible allocations 10
3.4 Results 11
4. Imperfect Recognizability and Uniform Currency 14
5. Optima Under a Uniform Outside Currency 16
6. Extensions of the Illustrative Model 18
6.1 Capital 18
6.2 Endogenous monitored status 19
6.3 Other information structures and other financial instruments 20
6.4 Production and consumption at the centralized stage 21
7. Concluding Remarks 22
References 23
Abstract
The mechanism-design approach to monetary theory is the search for fruitful settings in which money is necessary for the achievement of some desirable allocations. Fruitfulness means that the settings provide insights about puzzling observations and policy questions. Settings with three frictions are considered: imperfect monitoring, costly connections among people, and imperfect recognizability of assets. An illustrative model with those frictions is used to explain as an optimum the following features of actual economies: currency is a uniform object, currency is (usually) dominated in rate of return, some transactions are accomplished using currency and others are accomplished in other ways. JEL classification: E4, E5
Keywords
Money
Frictions
Inside-money
Mechanism-design
Monetary and Fiscal policy
Outside-money
1. INTRODUCTION
The mechanism-design approach to monetary theory is the search for fruitful settings or environments in which something that resembles monetary trade actually accomplishes something —or, in Hahn's (1973) terminology, settings in which money is essential. Fruitfulness means that the settings provide new insights about puzzling observations and policy questions.
The search for settings in which money is essential is hardly new. Suggestions about absence-of-double-coincidence difficulties go back at least to the first millennium (see Monroe, 1966). However, despite being repeated over and over again ever since, those statements are incomplete. After all, if they were regarded as satisfactory, then the search would long ago have been regarded as over. If it were over, then the problem of integrating price theory and monetary theory would not have been one of the big unsolved problems in economics throughout the twentieth century.
Monetary trade accomplishes something if monetary trade is necessary for the achievement of some desirable allocations. To establish such necessity, it must be shown there is no other way to achieve those allocations. That, in turn, requires that all other ways be considered. Mechanism design is the tool that can be used to consider all other ways.
Is essentiality in the above sense a reasonable goal? I think so. Monetary trade has been a pervasive phenomenon. While it is conceivable that its appearance is accidental in the sense that it is one of many equivalent ways of achieving desirable allocations, I find that far-fetched—in part, because the settings described below in which monetary trade is essential are intrinsically attractive.
So what kinds of settings lend themselves to a mechanism-design analysis of monetary trade and are fruitful? Needless to say, models with cash-in-advance constraints — or, more generally, models with asset-specific transaction costs — and models with real balances as arguments of utility or production functions are not among the candidates for such settings. The former are ruled out because their structure does not permit us to ask about other ways of achieving allocations and the latter are ruled out because they are at best implicit versions of the former. My general suggestion is that we study environments with three types of frictions: imperfect monitoring, costly connections among people, and imperfect recognizability of assets.
One of the biggest payoffs from doing mechanism-design analysis against the background of such frictions is that it allows us to bypass the distinction between monetary and fiscal policy, and, more generally, to bypass the need to make assumptions about what policies are feasible. The frictions dictate what policies are feasible. Ignoring the frictions and their implications for feasible policies leads to extreme results. For example in Correia, Nicolini, and Teles (2008), an optimal allocation can be achieved in a variety of ways — including by command. Hence, in particular, money is not essential. Is it surprising, then, that there are policies that achieve an optimal allocation? Frictions are also ignored in getting the equivalence (Modigliani-Miller) results in Wallace (1981) and Sargent and Smith (1987). In those models, people can commit to future actions and there is no private information. It is doubtful that such results, and related results like the equivalence between open-market operations and money creation achieved by way of lump-sum transfers, would hold in the presence of frictions that make money essential.
The best that can be said about approaches that ignore the frictions that give monetary trade a role and the implied connections to feasible policies is that they rest on the view that the unmodeled features that give monetary trade a role have no implications for feasible policies. Such a view seems inconsistent with the kinds of frictions previously listed that have been shown to give monetary trade a role. It also seems inconsistent with pervasive observations. Consider currency. Despite claims to the contrary, it is the best analog of money in most existing models because currency is the outside asset that does not bear explicit interest. We know that currency is widely used in what we label the underground economy. Underground activities are those that are difficult to monitor and, therefore, difficult to tax. Hence, there seems to be a close connection between frictions that give currency a role and feasible taxes. I begin this chapter by briefly discussing the three frictions: imperfect monitoring, costly connections among people, and imperfect recognizability of assets. Then, I turn to a specific illustrative model and use it to consider how close we can get to explaining as an optimum the following features of actual economies: currency is a uniform object, currency is (usually) dominated in rate of return, some transactions are accomplished using currency and others are accomplished in other ways.
2. SOME FRICTIONS
If money is to be essential, then we need to stay away from the Arrow-Debreu model and its second welfare theorem. That is easy enough: competitive trade is not amechanism and the Arrow-Debreu model assumes that people can commit to future actions. I assume that trade is accomplished through a mechanism and that people cannot commit to future actions. We also need to stay away from folk-theorem results. This is accomplished by assuming sufficient discounting, a sufficiently large number of agents, and imperfect monitoring.
2.1 Imperfect monitoring
The ancient absence-of-double-coincidence suggestion is incomplete in at least one important sense. Does it apply if the two people being described are part of a small isolated community such as a small kibbutz, a small Amish community, or a family? It seems as if the two people are meant to be strangers. One of the first discussions of the sense in which they are meant to be strangers is by Ostroy (1973). He suggests that money is a substitute for knowledge of previous actions. The modern term for describing what is known about previous actions is monitoring: perfect monitoring means common knowledge of all previous actions; imperfect monitoring means anything else. Townsend (1989) use imperfect monitoring to motivate the use of money in an explicit intertemporal model, and Kocherlakota (1998) combines it with no commitment. Given no commitment, which I maintain throughout, the crucial proposition implicit in this work is that imperfect monitoring is necessary for money to be essential.
A proof of such necessity would proceed by contradiction. Suppose there is perfect monitoring and that there is an implementable allocation that makes use of fiat money, an intrinsically useless object. Perfect monitoring means that previous actions are common knowledge. So suppose that some initial condition, which includes the distribution of money holdings, and previous actions determine the evolution of actions and holdings of money. In other words, there is a composite mapping from previous actions to current actions, composite in the sense that an intermediate stage involves money holdings and transfers of money among people. Now, consider the implied direct mapping from previous actions to current actions without the use of money. The claim is that implementability of the actions implied by the composite mapping implies implementability of the same actions using the direct mapping. Hence, money is not essential.
The above sketch of a proof uses fiat money rather than commodity money. Fiat money is convenient because the alternative mechanism that uses the direct mapping can simply ignore the fiat money — can treat it as worthless. This could not be done with commodity money. And, with commodity money, it is not easy to distinguish between monetary trade and non-monetary trade. Indeed, the advantage of using fiat money in the argument is similar to the advantage of using it in the quantity theory of money and its neutrality proposition; something that was done by Hume (1752) and others even when actual money was a commodity.
The necessity claim is supposed to apply to any model and, in particular, to models with private information about types. And, there is no assumption about discounting. No commitment and discounting can help determine the conditions for implementability, which can always be stated in terms of actions that do not involve fiat money.
Why might money help if there is imperfect monitoring? If the people that a person will meet in the future do not directly observe what is done today, then it may help for the person to collect some evidence that can subsequently be shown. That is, acquiring money today can weaken the person's future truth-telling constraints about today's actions. If we think of fiat money as a physical and durable object like currency, then, counterfeiting aside, it can serve that role. Others can say "show me" if the person tries to overstate holdings of it.
The necessity claim implies that one route to a cashless economy is better and better monitoring. But better monitoring is not the only route to a cashless economy. More generally, while the claim asserts that imperfect monitoring is necessary for monetary trade to be essential, it says nothing about sufficient conditions. It does suggest that no monitoring at all — each person's previous actions are private information to the person— offers the best shot at making money essential. However, if we want a setting in which some form of credit exists, then no monitoring is too extreme.
(Continues...)
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