Academic journal article Journal of Money, Credit & Banking

Endogenous Multiple Currencies

Academic journal article Journal of Money, Credit & Banking

Endogenous Multiple Currencies

Article excerpt

THIS PAPER PROVIDES a simple set of assumptions that prevents the indeterminacy of equilibrium in the sense of Kareken and Wallace (1981). I consider a cash-in-advance economy that is similar to those in Stockman (1980), Helpman (1981), and Lucas (1982). However, instead of assuming that sellers in one country must accept a given currency, each seller may choose which currency or currencies to accept. In the absence of any frictions, this model is identical to that in Kareken and Wallace (1981) and the exchange rate is indeterminate. I present frictions that are sufficient to eliminate this indeterminacy. Specifically, it is assumed that there is a cost for sellers to accept two currencies. It is also assumed that there is a proportional cost of trading on the foreign exchange market. If the fixed cost of accepting two currencies is sufficiently high so that no household decides to do so, then the exchange rate is no longer indeterminate.

Because of the foreign exchange cost, all households in the same country will typically accept the same currency. Indeed, they want to minimize their foreign exchange transaction costs and thus prefer to accept the same currency as the majority of other households. When households are assumed to have preferences that introduce a home-country bias, both national currencies and single-currency equilibria exist. Single-currency equilibria Pareto dominate national-currencies equilibria because no resources are wasted in the foreign exchange process.

If the stock of a currency grows "too fast," a national-currencies equilibrium may fail to exist. Suppose households in country i accept currency i and receive cash injections of currency i from a monetary authority, i = 1, 2. If the cash injection is sufficiently large, households can reduce their transactions costs by accepting the foreign currency. The amount of money growth that will induce this switch is lower if the fraction of income spent on foreign goods is "high." This is because households need more foreign currency to make their purchases of foreign goods. An interpretation of this result is that, as trade increases between countries, monetary authorities have less flexibility in choosing the growth rate of the money supply. This result also suggests that countries that have close economic ties are more likely to choose a single currency.

Few papers consider the endogenous choice of currency. Matsui (1998) develops a model where the choice of currency is endogenous but he imposes that taxes must be paid in local currency. Cooper and Kempf (2003, 2004) assume that all sellers in the same country must accept the same currency. Bachetta and van Wincoop (forthcoming) allow sellers to choose the currency they accept but consider an environment with sticky prices.

Many authors have investigated cash-in-advance models of multiple currencies. For example, Minford (1995) studies a cash-in-advance economy based on Lucas (1980), Boyer and Kingston (1987) study a credit-good, cash-good economy based on Lucas and Stokey (1987). King, Wallace, and Weber (1992) have a model with two currencies where some types of agents can accept only one type of currency while others may choose which one they accept. Fisher (1999) builds a multiple-currency model that is based on the cash-and-credit framework developed by Schreft (1992). In all of these cases, the currency that sellers accept is imposed exogenously, and thus the existence of a national currencies equilibrium is assumed rather than derived.

There is a growing literature using search models of money to study multiple currencies. The first generation of such models assumes a limit on how many units of money can be held. It is interesting to compare the model in this paper with those first generation search model, in particular Shi (1995, Section 5). (1) Both models emphasize the cost of making a transaction. In search models where the upper bound on money holding is unity, agents can only accept one type of currency. …

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