Exchange Rate Dynamics in a Multilateral Target Zone

This paper presents a model of exchange rate behaviour in a multilateral target zone. The model produces new economic insights beyond the well-known bilateral model of Krugman (1991), which is obtained as a special case. The paper also introduces a new class of stochastic processes in economics, namely multidimensional reflected diffusion processes.
Two main features characterize the economics of exchange rates in a multilateral target zone. (i) The restrictions on interventions imposed by cross-currency constraints: when one country changes its money supply, say because its exchange rate with a second country has hit its band, all exchange rates involving the currency of that particular country will be affected, regardless of their position within their respective bands. (ii) Cooperation in sharing the intervention burden: in general, the exchange rate between any two countries will depend on the fundamentals of third countries in a multilateral target zone. This is because if the monetary authorities intervene together, a shock in the fundamentals of any country will induce a revision of the expectation of future interventions of other countries.
The model reverts the counterfactual predictions of the bilateral model that the exchange rate steady-state density should be U-shaped and that its volatility should be a decreasing function of the distance of the exchange rate to the limits of its band. Thus, accounting for the multilateral feature of real-world target zones allows us to reconcile target zone models with the most salient empirical features of exchange rate behaviour.