Currency Markets - Equilibrium and Expectations

Abstract: The thesis consists of three essays on currency markets, equilibrium and expectations. The first essay examines currency markets in the setting of a temporary equilibrium model with two currencies and two central banks, where consumers have one-point expectations. Assuming that both central banks use floating exchange rate policies it is shown that if consumers have common expectations the current exchange rate will equal the expected future exchange rate. Under the assumptions made, there exist an equilibrium for the economy in the case where both central banks apply floating exchange rate policies as well as in the case where the banks co-operate and use fixed exchange rate policies. The possibilities for a single central bank to sustain a fixed exchange rate are discussed. Under some expectations, the economy may have more than one equilibrium exchange rate and these are related to different equilibrium allocations. In the second essay, a temporary equilibrium model with two currencies and where consumers have expectations on goods and currency prices with finite support is studied. Consequences for the individual consumer problem and equilibrium allocations are analyzed. State prices are defined for the case where asset markets are complete and these are used to derive conditions for consumers to meet increased risk with a variation in the portfolio of currencies, thus precluding precautionary saving. Equilibrium currency prices and adjustments in currency and good prices to a variation in the initial currency portfolio are examined. Perceived Pareto dominance is defined. It is argued that to get an allocation perceived to Pareto dominate the given equilibrium allocation consumers need more expensive portfolios. The third essay considers the determination of currency prices in an overlapping generations economy, with or without uncertainty. The economy with currencies is compared to an economy with money. For the case where there is no uncertainty and consumers have perfect foresight it is shown that currency prices may be chosen arbitrarily at one date but that the currency prices at other dates are then uniquely determined and constant over time. The analysis is extended to an economy with uncertainty where consumers are assumed to have rational expectations. It is shown that a given equilibrium allocation is consistent with constant as well as highly volatile currency prices. In general the currency prices and the exchange rate are only required to satisfy a martingale property. But if currency prices are assumed to depend only on a finite past history then they are forced to be constant over states and time. An equilibrium allocation may be realized also with incorrect expectations, about the currency prices, as long as expectations are consistent with the equilibrium portfolio values.