Bitcoin Ethereum – Can Currency Competition Work?

Jesus Fernandez-Villaverde
University of Pennsylvania – Department of Economics; National Bureau of Economic Research (NBER)

Daniel R. Sanches
Federal Reserve Banks – Federal Reserve Bank of Philadelphia

April 3, 2016

PIER Working Paper No. 16-008

Abstract:

Can competition among privately issued at currencies such as Bitcoin or Ethereum work? Only sometimes. To show this, we build a model of competition among privately issued at currencies. We modify the current workhorse of monetary economics, the Lagos-Wright environment, by including entrepreneurs who can issue their own fiat currencies in order to maximize their utility. Otherwise, the model is standard. We show that there exists an equilibrium in which price stability is consistent with competing private monies, but also that there exists a continuum of equilibrium trajectories with the property that the value of private currencies monotonically converges to zero. These latter equilibria disappear, however, when we introduce productive capital. We also investigate the properties of hybrid monetary arrangements with private and government monies, of automata issuing money, and the role of network effects.

Bitcoin Ethereum – Can Currency Competition Work?

Can competition among privately issued fiat currencies work? The sudden appearance of Bitcoin, Ethereum, and other cryptocurrencies has triggered a wave of public interest in privately issued monies.1 A similar interest in the topic has not been seen, perhaps, since the vivid polemics associated with the demise of free banking in the English-speaking world in the middle of the 19th century (White, 1995). Somewhat surprisingly, this interest has not translated, so far, into much research within monetary economics. Most papers analyzing the cryptocurrency phenomenon have either been descriptive (Bohme, Christin, Edelman, and Moore, 2015) or have dealt with governance and regulatory concerns from a legal perspective (Chuen, 2015).2 In comparison, there has been much research related to the computer science aspects of the phenomenon (Narayanan, Bonneau, Felten, Miller, and Goldfeder, 2016).

This situation is unfortunate. Without a theoretical understanding of how currency competition works, we cannot answer a long list of positive and normative questions. Among the positive questions: Will a system of private money deliver price stability? Will one currency drive all others from the market? Or will several of these currencies coexist along the equilibrium path? Will the market provide the socially optimum amount of money? Can private monies and a government-issued money compete? Do private monies require a commodity backing? Can a unit of account be separated from a medium of exchange? Among the normative questions: Should governments prevent the circulation of private monies? Should governments treat private monies as currencies or as any other regular property? Should the private monies be taxed? Even more radically, now that cryptocurrencies are technically feasible, should we revisit Friedman and Schwartz’s (1986) celebrated arguments justifying the role of governments as money issuers? There are even questions relevant for entrepreneurs: What is the best strategy to jump start the circulation of a currency? How do you maximize
the seigniorage that comes from it?

To address some of these questions, we build a model of competition among privately issued fiat currencies. We modify the workhorse of monetary economics, the Lagos and Wright (2005) (LW) environment, by including entrepreneurs who can issue their own fiat currencies in order to maximize their utility. Otherwise, the model is standard. Following LW has two important advantages. First, since the model is particularly amenable to analysis, we can derive many insights about currency competition. Second, the use of the LW framework makes our many new results easy to compare with previous findings in the literature.

Bitcoin, Currency Competition

We highlight six of our results. First, we show the existence of a stationary equilibrium with the property that the value of all privately issued currencies is constant over time. In other words, there exists an equilibrium in which price stability is consistent with competing private monies. This equilibrium captures Hayek’s (1999) vision of a system of private monies competing among themselves to provide a stable means of exchange.

Second, there exists a continuum of equilibrium trajectories with the property that the value of private currencies monotonically converges to zero. This result is intriguing because it shows that the self-fulfilling inflationary episodes highlighted by Obstfeld and Rogoff (1983) and Lagos and Wright (2003) in economies with government-issued money and a money-growth rule are not an inherent feature of public monies. Private monies are also subject to self-fulfilling inflationary episodes, even when they are issued by profit-maximizing, long-lived entrepreneurs who care about the future value of their monies.

Third, we show that although the equilibrium with stable currencies Pareto dominates all other equilibria in which the value of private currencies declines over time, a purely private monetary system does not provide the socially optimum quantity of money. Private money does not solve the trading frictions at the core of LW and, more generally, of essential models of money (Wallace, 2001). In a well-defined sense, the market fails at providing the right amount of money in ways that it does not fail at providing the right amount of other goods and services.

Fourth, we characterize asymmetric equilibria in which one private currency drives the other currencies out of the market. In these equilibria, a single entrepreneur becomes the sole issuer of currency in the economy (a possibility conjectured by Hayek, 1999). Which currency dominates is indeterminate. However, the threat of entry constrains the behavior of this surviving entrepreneur. Market participants understand the discipline imposed by free entry, even though everybody sees a single private agent supplying all currency in the economy. As in the symmetric class, these equilibria may imply a stable or a declining value of money.

Fifth, when we introduce a government competing with private money, we recover the set of equilibrium allocations characterized by LW as a particular case in our analysis. Also, we show that a hybrid monetary arrangement with constant prices requires the government to follow a constant money supply policy. Because the problem of achieving a unique efficient equilibrium remains unresolved under a money-growth rule, we investigate the extent to which the presence of government money can simultaneously promote stability and efficiency under an alternative policy rule. In particular, we study the properties of a policy rule that pegs the real value of government money. Under this alternative regime, the properties of the dynamic system substantially change as we vary the policy parameter determining the target for the real value of government money. We show that it is possible to implement an efficient allocation as the unique global equilibrium, but this requires driving private money out of the economy.

Sixth, we study the situation where the entrepreneurs use productive capital. We can think about this case as an entrepreneur, for example, issuing money to be used for purchases of goods on her internet platform. The presence of productive capital fundamentally changes the properties of the dynamic system describing the evolution of the real value of private currencies. Autarky is no longer a steady state and, as a result, there can be no equilibrium with the property that the value of private currencies converges to zero. Furthermore, it is possible to obtain an allocation that is arbitrarily close to the efficient one as the unique equilibrium provided

1, 2  - View Full Page