Managing Capital Outflows with Limited Reserves

We analyze the optimal intervention policy for an emerging market central bank that wishes to stabilize the exchange rate during a capital outflow episode, but possesses limited reserves. We show that adding a non-negativity constraint on reserves onto a simple linear-quadratic framework generates a time consistency problem. A central bank with full commitment achieves a gradual depreciation to the pure-float level by promising sustained future intervention, such that reserves are exhausted after particularly adverse shocks. A central bank without commitment intervenes little, wishing to preserve some reserves forever, so it suffers a larger immediate depreciation and achieves lower welfare. For more persistent shocks, the time consistency problem is greater, and simple intervention rules can achieve welfare gains relative to discretion.