Croft, George
(2001)
Dynamic models of exchange rates.
MPhil thesis, London School of Economics and Political Science.
Abstract
The thesis starts by describing those aspects of economic theory which are relevant to the construction of dynamic models of exchange rates. The deterministic flexible price monetary model, and the deterministic price inertia (Dornbusch) model are then derived for two countries of similar size. The implied restrictions on the economic parameters of the models due to no-arbitrage considerations when three countries are connected are also investigated. A variation of the price inertia model in which the relevant economic variables and the price adjustment procedure, are in current value terms rather than traditional volumes, is then investigated. The resulting systems of ordinary differential equations are solved for the nominal and real exchange rate, and the implied limiting values for these exchange rates are considered. The thesis subsequently describes the extension of the flexible price monetary model and the price inertia model, to formulations containing a stochastic variable. The differential equations describing the models are derived using stochastic calculus, and quantitative and qualitative solutions are obtained for the two models, respectively. The thesis then shows how the stochastic models Can be used to describe the movement of the exchange rate in a target zone. Finally, an extension of the stochastic flexible price monetary model is considered for a small network of more than two countries. The situation in which some countries in the network have a target zone imposed on their exchange rate while others have freely floating rates is considered. In particular, the solution describing the movement of the exchange rate between two countries, one of which is participating in a target zone arrangement with a third country, is derived. These models are then extended to cover the situation of a small network of countries in which one of them has a central position compared with the others.
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