Dollarization and currency exchange

We use a dual currency money search model to study dollarization. Agents hold portfolios consisting of two currencies, one of which is risky. We use numerical methods to solve for the steady-state distributions of currency portfolios, transaction patterns, and value functions. As risk increases, agents increasingly use the safe currency as a medium of exchange—dollarization occurs. Furthermore, the safe currency trades for multiple units of the risky currency. This type of currency exchange, and the corresponding nominal exchange rate, are often observed in black market or unofficial currency exchange markets in developing countries. Due to decentralized trading, a distribution of exchange rates arises, whose mean and variance change in predictable ways when currency risk increases.