Endogenous Inflows of Speculative Capital and the Optimal Currency Appreciation Path

This paper examines the optimal appreciation path of an under-valued currency in the presence of speculative capital inflows that are endogenously affected by the appreciation path. A central bank decides the optimal appreciation path based on three factors: (i) Misalignment costs associated with the gap between the actual exchange rate and the fundamental exchange rate, (ii) short-term adjustment costs due to fast appreciation, and (iii) capital losses due to speculative capital inflows. We examine two cases in which speculators do and do not face liquidity shocks. We show that, in the case without liquidity shocks, the central bank should appreciate quickly to discourage speculative capital, and should appreciate more quickly in initial periods than in later periods. In the case with liquidity shocks, the central bank should pre-commit to a slow appreciation path to discourage speculative capital. The central bank should appreciate slowest when the probability of liquidity shocks takes middle values. If the central bank cannot commit and can only take a discretionary policy, appreciation should be faster.