Economic Dynamics Newsletter

Payment Systems and Private Money, by Stephen Williamson

Introduction

Studying payments systems involves both the familiar (at least to students of monetary economics and banking) and the unfamiliar. Familiar issues include the role of the banking system in providing means of payment, the substitution between money and credit, and the role of monetary exchange in economic activity. For these issues, it is often possible to address the relevant questions with off-the-shelf monetary and banking theory. However, some unfamiliar issues, for example involving the analysis of arrangements for clearing and settlement, are difficult to address without investing some time in constructing new models, and this is part of what makes the study of payments systems and private money interesting.Payments systems activity involves transactions using fiat objects (e.g., government-supplied currency), circulating physical objects (e.g. private bank notes), checks, debit cards, credit cards, and interbank electronic payments (through Fedwire and the CHIPS system in the U.S.). Payments systems and private money are worthy of study for several reasons. First, there has been rapid recent growth in alternatives to cash for transactions. Second, in the U.S. the restrictions prohibiting the issue of private money have been lifted. Third, given the recent advances in information technology, payments arrangements which were formerly not feasible now are. Fourth, with the advent of many efficient alternatives to outside money in making transactions, and a higher volume of payments carried out under the auspices of the central bank (for example, through Fedwire in the U.S.), there are important issues to address concerning how monetary policy should be conducted and how the payments system should be regulated. Some key questions we might like to address are the following:

• What are the efficiency properties of a private money system?
• Are there useful lessons from historical experience with private money systems (U.S. pre-Civil War, Canada pre-1935)?
• How should payments systems be designed with respect to clearing and settlement arrangements? What are the potential risk-sharing and incentive issues?
• Does monetary policy work differently in a private money system? Do we need a central bank?

In modeling payments system arrangements, two key frictions are needed. First, there must be spatial separation, so that it not be too easy for agents to get together to coordinate exchange. Second, some form of monetary exchange must be required to overcome spatial and information frictions; it must be difficult for agents to engage in barter exchange. In this short review of my recent work with Ted Temzelides, I will describe three models of private money and payments systems, and ask what these models have to say about the relevant issues. These ideas come from two working papers, which are Temzelides and Williamson (2000a, 2000b).

A Model of Private Money and Settlement

This is a random matching model, which is most closely related to Williamson (1999), which in turn used some of the structure from existing monetary random matching models with endogenous prices, principally Shi (1995) and Trejos and Wright (1995). Other related literature is Cavalcanti, Erosa, and Temzelides (1999), Cavalcanti and Wallace (1999), Champ, Smith, and Williamson (1996), and Smith and Weber (1999).In the model, there is random matching where “local” agents are met with higher frequency than “non-locals,” and there are simple banking arrangements which permit the issue of circulating private monies (bank notes) and clearing arrangements across locations. In the paper, Temzelides and Williamson (2000b), we consider two cases. First, we suppose that there is full information, in which case the matching friction will determine discounts on non-local bank notes. Second, we consider an environment with private information concerning the assets backing a particular bank note, in which case matching frictions and informational frictions will determine the discounts on bank notes.

When there is no clearing of bank notes and full information, non-local notes either do not circulate locally, or they circulate at a discount. The discount arises because the value of holding a local note is higher than the value of holding a non-local note. The difference in values is due to the fact that non-local notes cannot be redeemed locally. Given that non-local notes are discounted, the redemption value of a local note may be sufficiently high that a local agent is not willing to exchange the note with a non-local agent at the going price.

When there is full information and a clearing arrangement for bank notes among banks, then essentially all bank notes are universally redeemable. This implies that non-local bank notes always circulate locally, and they will not trade at a discount. Welfare is higher, and there is more production and exchange. Thus, it is clear that note-clearing arrangements are a good thing when there is full information.

Now, private information about the quality of non-local bank notes changes the story considerably. Here, there are potentially good bank notes and bad ones, and there may be equilibria where only good notes circulate, where only bad ones do, or where both good and bad bank notes circulate. If the private information friction is not too severe, then we will obtain the same results as with full information, in that clearing arrangements are socially beneficial. However, with a sufficient private information friction, welfare-dominated equilibria may exist, i.e. there can be a coordination failure. Also, the clearing arrangement may increase the quantity of low-quality money in circulation relative to high-quality money, and clearing may not eliminate discounts.

These results have important implications for our interpretation of historical monetary regimes where private money was issued. For example, in the pre-Civil War United States, clearing arrangements for bank notes were unusual. Essentially the only successful clearing arrangement was the Suffolk system in New England. On the other hand, in Canada before 1935, all chartered banks issued notes in a system which appeared to have worked efficiently, with a nationwide clearing arrangement and all notes trading at par. The difference between the U.S. system and the Canadian one can be explained by the fact that private information frictions were much more severe in the U.S. than in Canada. The U.S. had many unit banks, while Canada had only a few banks with nationwide branching.

Payments and Settlement in a Deterministic Environment

This model comes from Temzelides and Williamson (2000a). The objective here is to construct a model where there is a role for monetary exchange and where a centralized payments arrangement can substitute for exchange using fiat money. This model has some advantages over monetary search models in that it relies on competitive equilibrium as an equilibrium concept, and is simple enough that results can be obtained when money is divisible. This is a spatial model sharing some elements with the turnpike model studied by Townsend (1980). Related papers in the payments system literature are Freeman (1996a, 1996b, 1998), Kahn and Roberds (1998), Fujiki, Green and Yamazaki (1997), and Lacker (1997).In the model, there is a countable infinity of locations, with a producer/shopper household at each location. Each period, the producer stays at home and produces while the shopper goes to the next location to obtain goods. There is essentially a double-coincidence-of-wants problem. A given household does not produce every third period, and households are arranged in space such that each household will follow a three-cycle, where they consume in one period but do not produce, produce and consume in the next period, produce and do not consume in the following period, etc. In each period, two thirds of the population will be consuming and two thirds will produce. There are two key elements in the model: Barter is not possible, and privately-issued IOUs will not circulate.

The approach in this paper is to consider successively sophisticated payments arrangements, and to determine the general equilibrium implications of these arrangements. The first arrangement is one where there is no using fiat currency. Effectively, there are endogenous cash-in-advance constraints, whereby households acquire cash when they produce and spend it two periods hence. In an equilibrium with a fixed fiat money stock there will be price dispersion, and a competitive equilibrium will be suboptimal, for the usual reasons. That is, households economize too much on money balances and consumption will be too low.

Now, a second arrangement is one with a centralized clearinghouse. Here, households carry out exchange using IOUs, and these IOUs are settled on net through the clearinghouse at the end of each period. Settlement takes place using outside money. It is important to note that it is important that there be net settlement; with gross settlement the equilibrium allocation is identical to what it was with the previous arrangement. Here, there may be multiple equilibria, which can be ranked in terms of welfare, but each of these equilibria dominates the first arrangement in welfare terms. Thus, a centralized payments system improves welfare, and the velocity of money also increases. The equilibrium allocation is not Pareto optimal, however.

A Pareto optimal allocation can be achieved under a third arrangement, which we can interpret as banking with interbank lending. Here, there is not only within-period credit through the clearinghouse, but borrowing and lending across periods. In this case, in spite of the fact that goods cannot be transported across locations, an efficient allocation is achieved without outside money. Imposing settlement in this environment, where there is no risk, implies that the allocation will be inefficient.

A Random Matching Model with Private Information

This model, from Temzelides and Williamson (2000a), uses a dynamic contracting approach, following Green (1987), Atkeson and Lucas (1992), Phelan (1995), Wang (1995), Williamson (1998), and Aiyagari and Williamson (1999), to study efficient risk-sharing and incentives under a payments system arrangement. This model shares some of the structure of the previous model in that there is random matching and periods when some agents cannot produce, or do not wish to consume, but here these states occur randomly. Each random match takes place between a household who receives a preference shock and a productivity shock, and another household whose preferences and technology are constant for all time. The optimal allocation is solved for, and we interpret the solution in terms of how an optimal payments arrangement should work. The conclusions we arrive at are the following:

• “Credit” is key to making incentives work in the payments system. Participants who receive a bad shock (can’t produce) can generally still consume in the present, but their future liabilities to the system are higher than they would be otherwise.
• It is important for incentive reasons that credit and risk-sharing be internalized in the payments system.
• There are endogenous credit constraints.
• Idiosyncratic shocks are propagated through the chain of transactions.

Conclusions

These three models have something to say about the functioning of private money systems and the role of payments systems in the economy. Perhaps where they fall short is that they do not address the issue of systemic risk in the payments system. Some policymakers are concerned that too much credit is extended in U.S. payments systems (Fedwire, for example), and that this leaves the system open to the possibility that the failure of a large participant to settle a transaction could lead to a chain of failures, with the Fed (in the case of Fedwire) left to bail everyone out. To evaluate whether systemic risk is in fact a legitimate concern, we need more sophisticated models of risk sharing and moral hazard in the context of centralized payments systems.

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