The Dynamics of the Exchange Rate Under a Crawling Peg Regime : A Game Theory Approach

In this paper, we model the transition to a nominal peg by setting up a two-country international dynamic game in which the domestic country announces at time 0 that at time T it will peg the exchange rate at a specific value. The domestic and foreign economies are symmetric. Each country chooses its money supply time path to minimize the discounted integral of the contributions of inflation and the deviations of real output from the natural rate. The solution is calculated for both the Nash equilibrium under open loop information and the central planner solution. We find closed-form solutions for the exchange rate, the domestic and foreign price levels, and domestic and foreign outputs. Upon examination of the solutions, we find that exchange rate pegging has real effects and does not cause the exchange rate or other variables to move monotonically to their equilibrium values. Rather, exchange rate pegging produces oscillation of the exchange rate, real outputs, and the price levels of the countries. This situation cannot be corrected by conventional international policy coordination. The views expressed here are those of the author and do not necessarily represent the views of the Federal Reserve Bank of Philadelphia or the Federal Reserve System