The Dynamics of Currency Crises---Results from Intertemporal Optimization and Viscosity Solutions

We apply an infinite horizon intertemporal optimization model to a simple speculative attack framework. Thereby, the central bank faces a one control two-state variables optimization problem with endogenuous exit. By setting the interest rate the central bank can stimulate the economy or fend off speculators. We show that two focal points emerge. Depending on the time preference and the state, cycles can improve utility. A regime change is associated with costs and can be forced by the state of the economy or induced by choice. In the latter case the costs for defending outweigh the costs of an immediate opt-out. During the existence of the regime the highest growth is reached through convergence to a no stress steady state, but is only optimal for a central bank with low time preference. Therefore, we propose to take measures assuring a lower time preference like independence, long-term mandates, and long-term policy goals.