Currency Portfolios and Nominal Exchange Rates in a Dual Currency Search Economy
We analyze a dual currency search model in which agents are allowed to hold multiple units of both currencies. Hence, agents hold portfolios of currency. We study equilibria in which the two currencies are identical and equilibria in which the two currencies differ according to the magnitude of the ’inflation tax’ risk associated with each currency. The inflation tax is modeled by having government agents randomly confiscate the two currencies at different rates. We are able to obtain analytical results in a very special case but in general we must rely on numerical methods to solve for the steady-state distributions of currency portfolios, prices and value functions. We find that when one of the currencies has the right amount of ’risk’, equilibria exist in which the safe currency trades for multiple units of the risky currency (pure currency exchange). As a result, the steady state has a distribution of nominal exchange rates. The mean and variance of the nominal exchange rate distribution is based on the fundamentals of the model such as the risk of confiscation, risk preferences, matching probabilities and relative money supplies. The mean and variance of this distribution typically change in predictable ways when the fundamentals change. While the ability to trade currencies improves average welfare, in general, the benefits of currency exchange are small.
Suggested citation: Craig, Ben, and Christopher Waller, 1999. “Currency Portfolios and Nominal Exchange Rates in a Dual Currency Search Economy,” Federal Reserve Bank of Cleveland, Working Paper, no. 99-16.