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10.6. IMPERFECT TARGET-ZONE CREDIBILITY 323there will come a time in any target-zone arrangement when it is nolonger worthwhile for the authorities to continue to defend the zone.This means that the target-zone bands cannot always be completelycredible. In fact, during the twelve years or so that the Exchange RateMechanism of the European Monetary System operated reasonably well(1979—1992), there were eleven realignments of the bands. It would bestrange to think that a zone would be completely credible given thatthere is already a history of realignments.We now modify the target-zone analysis to allow for imperfect credibilityalong the lines of Bertola and Caballero [8]. Let the bands for thefundamentals be [f, ¯f] andletβ = ¯f − f be the width of the band. Ifthe fundamentals reach the lower band, there is a probability p that theauthorities re-align and a probability 1 − p that the authorities defendthe zone.If re-alignment occurs, what used to be the lower band of the oldzone f, becomes the upper band of the new zone [f −β,f]. The realignmentis a discrete intervention that sets f = f − β/2 at the midpointof the new band. If a defense is mounted, the fundamentals are returnedto the midpoint, f = f + β/2. An analogous set of possibilitiesdescribe the intervention choices if the fundamentals reach the upperband. Figure 10.3 illustrates the intervention possibilities.⇐(217)RealignDefendf - > f - > f f + >f >Figure 10.3: Bertola-Caballero realignment and defense possibilities.We begin with the symmetric exchange rate solution (10.44) withη = 0 and an initial symmetric target zone about 0 where f = − ¯f,