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The author is grateful to Guillermo Calvo, Carlos Végh, and participants at a Research Department seminar for helpful comments and discussions.
The term “currency substitution” may be understood in two ways: (1) that foreign money is used along with domestic money in transacting; and (2) that changes in the relative cost of holding one currency induces a change in the ratio of domestic to foreign money holdings demanded (Calvo and Rodriguez (1977)). While the model presented in this paper does not provide a theory of why foreign currency is used, it provides a theory of how the ratio of domestic to foreign demand holdings depends on factors that affect the relative cost of holding the two currencies.
Calvo’s (1980) analysis of the effects of “financial opening” in the context of a small open economy is similar to the analysis carried out in this paper. In Calvo’s (1980) model, financial opening is assumed to generate changes in a “real liquidity” function which enters the utility function. Unlike this paper, in Calvo’s (1980) currency substitution model, money serves both a store of value and as a medium of exchange.
This assumption could be relaxed without affecting qualitatively the ensuing analysis of the effects of financial innovation. The fact that, during the consumption subperiod, individuals can only withdraw currency from bonds in this predetermined way is in the spirit of cash-in-advance models; namely, while consumption takes place only a limited set of financial transactions (in this case only cash withdrawals) can be made.
Equation (2) allows for fairly general forms of the transaction cost function f(.). Even if f(.) is linear, however, the concavity of the utility function implies that the welfare cost of transacting are convex. The specific form of the transactions technology may depend on production decisions like choosing the optimal amount of ATM’s per geographical area, the optimal type of services performed by ATM’s in different locations, etc.
When thinking of time-costs, this is a natural assumption. In the context of monetary costs, as the original work of Baumol (1952) or as in Feenstra (1986), one could consider costs that are proportional to the amount of cash withdrawn.
This assumption is made for simplicity and does not affect the results. If interest is paid on average bond holdings the budget constraint would be modified using the fact that average bond holdings (in nominal values), Ba and B*a, are related to initial holdings, B and B*a, by the following equations:
The real interest factor R is defined as Rt=1/(1+r1) (1+r2) … (1+rt).
With no uncertainty and positive interest rates, the cash-in-advance constraints are always binding.
In what follows we use the expressions “terms of trade” and “real exchange rate” interchangeably.
The interpretation of (6’) is similar to that which obtains in models that introduce money in the production function or money as reducing transaction costs (Frenkel and Dornbusch (1973); McCallum (1983); Kimbrough (1986); and Végh (1989)).
One can show that ∂(αN*)/∂α = - ∂x/∂ >0. This implies that, ceteris paribus, an increase in α increases the amount of time devoted to cash withdrawals and, hence, reduces leisure.
In a “pooling equilibrium” the values of the parameter α is the same in the two countries. Assume, for simplicity, that g=g*=0.
This implies that ø= 1.