We study how a monetary authority pursues an exchange rate objective in an environment that features a zero lower bound (ZLB) constraint on nominal interest rates and limits to arbitrage in international capital markets. If the nominal interest rate that is consistent with interest rate parity is positive, the central bank can achieve its exchange rate objective by choosing that interest rate, a well-known result in international finance. However, if the rate consistent with parity is negative, pursuing an exchange rate objective necessarily results in zero nominal interest rates, deviations from parity, capital inflows, and welfare costs associated with the accumulation of foreign reserves by the central bank. In this latter case, all changes in external conditions that increase inflows of capital toward the country are detrimental, while policies such as negative nominal interest rates or capital controls can reduce the costs associated with an exchange rate policy. We provide a simple way of measuring these costs, and present empirical support for the key implications of our framework: when interest rates are close to zero, violations in covered interest parity are more likely, and those violations are associated with reserve accumulation by central banks.
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