Indivisible Money Research Articles

Secondary currency acceptance: Experimental evidence with a dual currency search model

Motivated by the use of non-legal tender currencies in regions experiencing economic turmoil and by the growing use of cryptocurrencies such as Bitcoin, I examine in a controlled, experimental laboratory setting, the acceptance of a secondary currency when a primary currency already circulates in an economy. The underlying model is an indivisible goods / indivisible money, dual currency search model similar to that in Kiyotaki and Wright (1993) and Curtis and Waller (2000). In such models, there are two pure Nash equilibria - total acceptance or total rejection of the secondary currency - and one unstable, mixed equilibrium. This mixed equilibrium is considered an artifact of the indivisibility of money and goods in the model and is often ignored. I find that when a significant friction - in this case the inability to barter - is introduced, the equilibrium tends towards complete acceptance of the secondary currency. Conversely, when barter is readily available to subjects, the equilibrium tends towards total rejection. As predicted by theory, the tendency towards one equilibrium or the other appears to be influenced by the mixed equilibrium and the related basins of attraction.

Decentralizing constrained-efficient allocations in the Lagos–Wright pure currency economy

This paper offers two ways to decentralize the constrained-efficient allocation of the Lagos–Wright (2005) pure currency economy. The first way has divisible money, take-it-or-leave-it offers by buyers, and a transfer scheme financed by money creation. If agents are sufficiently patient, the first best is achieved for finite money growth rates. If agents are impatient, the equilibrium allocation approaches the constrained-efficient allocation asymptotically as the money growth rate tends to infinity. The second way has indivisible money, take-it-or-leave-it offers by buyers, and no government intervention. We discuss the strict implementation of constrained-efficient allocations and the applicability of our scheme to economies with Lucas trees, endogenous participation, match-specific heterogeneity, and sequential competitive markets.

Distributional Aspects of the Divisibility of Money: An Example

I highlight the importance of distributional aspects of money divisibility by comparing a search-theoretic model with random transfers of indivisible money balances, to one with deterministic transfers of partially divisible balances. Randomization allows price flexibility, as if money were fully divisible. Partial divisibility does not, but allows money redistributions. An example of the relevance of such ‘extensive margin’ aspects of divisibility is provided.

Rationality and Stability of Equilibrium in a Search-Theoretic Model of Money

In this short note, I examine the rationality of money-search equilibrium in a basic second-generation money search model, which is a perfectly divisible goods and indivisible money model. I then show that only an inflationary economy can generate a socially and individually rational stable equilibrium. On the basis of this finding, I demonstrate that there is no loss of generality in an analysis that assumes dictatorial buyers in an inflationary economy, since the properties of a dictatorial buyers model are identical to those of a general inflationary economy model. The result of this paper is especially useful for empirical applications since we are generally incapable of finding data showing bargaining power. This result also alerts us against employing the second-generation model to analyze a deflationary economy and commodity money.

On the multiplicity of monetary equilibria: Green–Zhou meets Lagos–Wright

Green and Zhou relax the assumption, made in early search-based models of monetary exchange, of indivisible money. Their paper and various extensions make much technical progress, and derive some interesting substantive results. In particular, they show there is an indeterminacy of steady-state monetary equilibria. We reconsider this result in the framework of Lagos and Wright, which is more tractable. We show that a similar multiplicity arises, and is much easier to derive and understand. We also compare the results to those in related nonmonetary models, and discuss how they depend on details, including the number of agents and the timing.

Bidding for money

We analyze monetary exchange in a model that allows for directed search and multilateral matches. We consider environments with divisible goods and indivisible money, and compare the results with those in models that use random matching and bilateral bargaining. Two different pricing mechanisms are used: ex ante price posting, and ex post bidding (auctions). Also, we consider settings both with and without lotteries. We find that the model generates very simple and intuitive equilibrium allocations that are similar to those with random matching and bargaining, but with different comparative static and welfare properties.

Money Creation in a Random Matching Model

I study money creation in versions of the Trejos-Wright (1995) and Shi (1995) models with indivisible money and individual holdings bounded at two units. I work with the same class of policies as in Deviatov and Wallace (2001), who study money creation in that model. However, I consider an alternative notion of implementability - the ex ante pairwise core. I compute a set of numerical examples to determine whether money creation is beneficial. I find beneficial effects of money creation if individuals are sufficiently risk averse (obtain sufficiently high utility gains from trade) and impatient.

Existence of a monetary steady state in a matching model: divisible money

Existence of a monetary steady state is established in a random matching model with divisible goods, divisible money, an arbitrary bound on individual money holdings, and take-it-or-leave-it offers by consumers. The monetary steady state shown to exist has nice properties: the value function, defined on money holdings, is strictly increasing and strictly concave, and the distribution over money holdings has full support. The approach is to show that the “limit” of the nice steady states for indivisible money, existence of which was established in an earlier paper, as the unit of money goes to zero is a monetary steady state for divisible money. For indivisible money, the marginal utility of consumption at zero was assumed to be large; for divisible money it is assumed to be large and finite.

Existence of a monetary steady state in a matching model: indivisible money

Existence of a monetary steady state is established for a random matching model with divisible goods, indivisible money, an arbitrary bound on individual money holdings, and take-it-or-leave-it offers by consumers. The background environment is that in papers by Shi and by Trejos and Wright. The monetary steady state shown to exist has nice properties: the value function, defined on money holdings, is strictly increasing and strictly concave, and the measure over money holdings has full support.

Money Creation in a Random Matching Model

I study money creation in versions of the Trejos-Wright (1995) and Shi (1995) models with indivisible money and bounded individual holdings. I work with the same class of policies as in Deviatov and Wallace (2001), who study money creation in that model. However, I consider two alternative notions of implementability - the ex ante pairwise core and the ex post pairwise core. I compute a set of numerical examples to determine whether money creation is beneficial in my model. I find that if the ex post pairwise core is the notion of implementability, then examples where money creation is beneficial are easily found, while I find no such examples if the notion of implementability is the ex ante pairwise core.

Another Example in which Lump-sum Money Creation is Beneficial

Abstract A probabilistic version of lump-sum money creation is studied in a random matching model with indivisible money and individual holdings bounded at 2 units. Sufficient conditions are obtained for an ex ante optimum from among implementable steady states to involve lump-sum creation of money. The role of that creation is to change the distribution of money holdings to permit more trade to occur. Beneficial money creation is impossible in a version with a 1 unit upper bound on individual holdings, but can almost certainly happen for all higher bounds.

Output Degeneracy of Ex Post Individually Rational Optima in a Matching Model of Money

I study optimal allocations in versions of the Trejos-Wright [1995] and Shi [1995] models with indivisible money and bounded individual holdings. The objective is expected discounted utility and the feasible set consists of all distributions of money holdings and trades in meetings which are mutually consistent and ex post individually rational. This problem is described in Deviatov and Wallace [2001], who study the e¤ects of money creation in that model. Although they show that money creation can be helpful, they do not describe optima because their problem is not ...nite dimensional. Here I show, under a mild additional restriction on the set of allocations, that the optimum has no randomization over output and, therefore, that the feasible set can be limited to a ...nite dimensional space. ¤I am grateful to Neil Wallace, Dmitry Dolgopyat, Sergei Izmalkov, and to participants of Cornell Penn State Macro Workshop (April 2001) and Conference on Monetary Economics at the Federal Reserve Bank of Cleveland (August 2001) for their most valuable comments. All remaining errors are solely my responsibility. yAddress for correspondence: 608 Kern Graduate building, Department of Economics, The Pennsylvania State University, University Park, PA 16802-3306; e-mail: .

Liquidity, Quality, Production Cost, and Welfare in a Search Model of Money

This paper examines a search model of money with divisible commodities of high and low quality, while keeping the assumptions of indivisible money and unit-inventory constraint. With no direct barter and a higher fixed cost of producing high relative to low quality, an increase in the money stock encourages the production of high-quality output by trading off the larger trading opportunities against the significance of higher fixed cost. As long as the fixed-cost differential between high and low quality is sufficiently small relative to the utility gain from high-quality consumption, the quality improvement outweighs the negative effect of higher money stocks on aggregate production, and hence implies higher welfare. The most important function of money is its role as a medium of exchange. Wicksell ([1906] 1967, p. 17) defined a general medium of exchange to be an object 'which is habitually, and without hesitation, taken by anybody in exchange for any commodity.' The main challenge facing monetary theory is to construct a model which permits the object's role in exchange to be endogenous.1 Kiyotaki and Wright (1991, 1993) seems to be the first fully coherent model which specifies the environment and equilibrium concept in a way that does not force at the outset the assumption on which objects will play a special role in trade. The Kiyotaki-Wright model departs from the physical environment of the standard general equilibrium model through the assumption that trading histories are private information. The medium-of-exchange role of money is obtained as an outcome of Nash equilibrium together with some bargaining rule in pairwise random meetings. However, the standard Kiyotaki-Wright model yields an undesirable welfare implication that an increase in the money stock eventually leads to a decrease in welfare because of a decrease in the number of agents who get to consume in a given period. The same welfare property is obtained in the models with divisible commodities, such as Trejos and Wright (1995) and Shi (1995).2 This property has been regarded as the outcome of the original Kiyotaki-Wright assumptions of indivisible money and the inventory constraint - agents can only carry one object, either commodity or money, at a time. Despite simplifying the distribution of money holdings, these assumptions impose the restriction that agents are not allowed to produce while they hold money.

Money Inventories in Search Equilibrium

The paper relaxes the one unit storage capacity imposed in the basic search-theoretic model of fiat money with indivisible real commodities and indivisible money. Agents can accumulate as much money as they want. It characterizes the stationary distributions of money and shows that for reasonable parameter values (e.g. production cost, discounting, degree of specialization) a monetary equilibrium exists. There are multiple stationary distributions of a given amount of money, which differ in their levels of economic activity and welfare. The model reveals two essential features of money. First, the marginal expected utility of money decreases. Second, there exists an endogenous upper bound on the money holdings: agents willingly produce and sell for money up to this bound and refuse to do so if their money holdings exceed this bound.

A Matching Model with Bounded Holdings of Indivisible Money

Recent versions of pairwise random matching models of money with divisible and perishable goods are amended to allow individuals to hold more than one unit of an indivisible asset. The asset resembles a fiat asset, except that nominal holdings of it yield a small amount of utility. There is a general upper bound on the number of units of the asset that individuals can hold. A steady state with trade is shown to exist. The model is applied to study numerically the effect on welfare of the degree to which the asset is divisible.

A model of a currency shortage

Until the mid-19th century, shortages of currency were common. Moreover, a frequent policy response was a prohibition on the export of coins. We use a random matching model with indivisible money to explain a shortage and to judge the desirability of a prohibition on the export of coins. The model, although extreme in many regards, represents better than earlier models a demand for outside money and the problems that arise when that money is indivisible. It can also rationalize a prohibition on the export of money.