A Theory of Foreign Exchange Interventions

We develop a theory of foreign exchange interventions in the presence of limited capital mobility. We study a real small open economy subject to global liquidity and endowment shocks. Home and foreign bond markets are segmented and intermediaries have a limited capacity to arbitrage between both bond markets. As a result, the central bank can manipulate the spread across markets by managing its portfolio. We show that the planning problem can be entirely framed in terms of the spreads. Crucially, spreads are inherently costly, over and above the standard costs from distorting households' consumption profiles. The extra term is exactly given by the carry trade profits of foreign intermediaries, is convex in the spread - as more foreign intermediaries become active carry traders - and increasing in the openness of the capital account - as foreign intermediaries find it easier to take larger positions. Optimal interventions lean against the wind for global liquidity shocks and implement a zero spread against endowment shocks. Importantly, interventions should be small, frequent and rely on forward guidance of future interventions. The effectiveness of interventions increases if they are pre-announced and the policy is more credible. Finally, we model a world equilibrium with two types of small open economies: advanced economies, with a strong desire to save; and emerging markets, who intervene to avoid currency appreciation. In the Nash equilibrium, emerging markets engage in “reserve wars,” leading to substantial reserve over-accumulation and too depressed world interest rates. Simple coordination rules, like committing to replicating zero spreads, are shown to be strict Pareto improvements for reasonable calibrations