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10.4. DISCRETE INTERVENTION 319Table 10.1: SMM Estimates of Krugman Target-Zone Model (units inpercent) with deutschemark as base currency.η σ α ¯f χ21Currency (s.e.) (s.e.) (s.e.) (s.e.) (p-value)Belgian 0.697 0.865 1.737 2.641 11.672franc (69.01) (83.98) (327.1) (334.3) (0.001)French 0.007 0.117 6.045 2.44 12.395franc (0.318) (1.759) (1590) (67.88) (0.000)Dutch 2.484 2.240 4.152 5.393 11.35guilder (1.317) (0.374) (146.19) (5.235) (0.001)10.4 Discrete InterventionFlood and Garber [56] study a target-zone model where the authoritiesintervene by placing the fundamentals back in the middle of the bandafter one of the bands are hit. If the band width is β = ¯f − f andeither ¯f or f is hit, the central bank intervenes in the foreign exchangemarket by resetting f = ¯f − β/2. Because the intervention producesadiscretejumpinf, the central bank loses foreign exchange reserveswhen ¯f is hit and gains reserves when f is hit.Letting à ≡ Aeλ 1 ¯f and ˜B ≡ Be λ 2f , rewrite the solution (10.33)explicitly as a function of the bands f and ¯fG(f| ¯f,f)=f + αη + Ãeλ 1(f− ¯f) + ˜Be λ 2(f−f) . (10.43)Impose the symmetry conditions, η =0andf = ¯f. It follows thatλ 1 = −λ 2 = λ = q 2/(ασ 2 ) > 0, and ˜B = −à >0. (10.43) can be ⇐(215)written asG(f|f, ¯f) =f + ˜B h e −λ(f−f) − e −λ( ¯f−f) i . (10.44)Under the symmetry assumptions you need only one extra side-conditionto determine ˜B. We get it by looking at the exchange rate at the instantt 0 that f(t) hits the upper band ¯fs(t 0 )=G[ ¯f|f, ¯f] = ¯f + ˜B[e −λβ − 1]. (10.45)