The ultimate determinants of central bank independence



27


F = 2[(1 ÷e)(1 )2÷ χ]3 u
du      <⅛1 -β )4(1+<≈)3


(B.3)


(B.3) is positive.


(6) Demonstration that dF > 0
dX

The first derivative of F with respect to χ is given by


3[(1+ε)(1 ) + χ]2U2
σ2∕1 -β )4(1+ε)3


(B.4)


It can easily be checked that (B.4) is positive.


F

(7) Demonstration that < 0.
2


The first derivative of F with respect to σμ2 is given by


F _ -[(1 +ε)(1 )2 + χ]3U2


∂σ2μ        [σ2μ(1 -β )2]2(1 + ε)3


(B.5)


(B.5) is negative.


F

(8) Demonstration that           > 0.

The first derivative of F with respect to (1-β)-1 is given by


∂F     = 2U2[2χ-(1+ε)(1 -β )2][(1 +ɛ)ɑ-β )2÷ χ]2

d(1 -β )"1                   σ2(1 -β )3(1+ε)3


(B.6)


(B.6) is positive if χ (1+g)(1 β) .




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