Exchange Rate Bands and Realignments in a Stationary Stochastic Setting

The extent which exchange rate management can coexist with an independent monetary policy is examined in the context of a model with exchange rate bands. Using a Dornbusch model in which stochastic shocks are added to the Phillips curve, we analyze the implications of assuming that the monetary authorities follow certain simple rules for realigning the band when fundamentals have drifted too far from equilibrium. Assuming that information about whether the bands is to be defended or there is to be a realignment is revealed at the point when the exchange rate hits the edge of the band, we show how the path of the exchange rate can be completely characterized in terms of the solution to a second order nonlinear differential equation - together with jumps in the rate at the edge of the band, which satisfy a zero profit arbitrage condit.