In a `target zone' system, the exchange rate floats more or less freely within a specified band but is prevented from moving outside the band by foreign exchange interventions. EMS currencies fluctuate within bands of 2.25% (except Spain, which has a band), while the Nordic countries have unilateral target zones. In addition, most `fixed' exchange rate regimes have in practice been target zones: even the Gold Standard had gold points, with a band in between. But the details of exchange rate determination under rational expectations within an explicit target zone have only very recently been rigorously modelled and understood, initially by Paul Krugman. He showed that a target zone implies an inherent stabilization of exchange rates, and that interventions would be less frequent than one might first expect, because the increased probability of future interventions to reduce money supply strengthen the currency in the present.
Of particular interest in extending this analysis is the determination of the interest rate with a target zone. With free mobility of capital and world interest rates given, domestic interest rates are determined by the sum of the world interest rate and an endogenously determined differential, which is the sum of the expected depreciation of the home currency and a foreign exchange risk premium. In Discussion Paper No. 372, Research Fellow Lars Svensson examines the determination of this interest rate differential, in a Brownian motion model used in previous studies of target zones. Even though the mathematical expression for the interest rate differential is rather complicated, he is able to derive its main characteristics. For reasonable parameters, the long-run variability of the differential increases with the exchange rate band for narrow bands, reaches a maximum, and then slowly decreases for wide exchange rate bands. The instantaneous variability, in contrast, is always negatively related to the width of the exchange rate band. The addition of the risk of a realignment or devaluation implies an upward shift in the interest rate differential.
Svensson focuses on instantaneous variability. In this respect narrow bands, where this variability appears to be highest, are quite different from a completely fixed exchange rate, where it is zero. With a 1.5% band, he finds that for reasonable parameters the interest rate differential's instantaneous standard deviation is about 3% a year. The expected period before the exchange rate hits the edge, starting from the middle, may still be as large as a year, so this instantaneous variability is certainly relevant.
He also examines the determination of the foreign exchange risk premium. For narrow bands, even though the instantaneous variability of the interest rate can be high, the risk premium is so tiny that it can be disregarded. Uncovered interest arbitrage is therefore a reasonable approximation for a narrow target zone. Svensson concludes that narrow bands give little scope for monetary independence, taken to mean power to affect the risk premium and hence the substitutability of home and foreign assets. In future work he will examine variations in the interest rate differential for longer maturities

Target Zones and Interest Rate Variability
Lars E O Svensson

Discussion Paper No. 372, December 1989 (IM)