The ultimate determinants of central bank independence

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∂F ₌ 2[(1 ÷e)(1 -β )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 -β ) + 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.
^dσ2

The first derivative of F with respect to σ_μ² is given by

∂F _ -[(1 +ε)(1 -β)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}) .