The ultimate determinants of central bank independence

13

PROPOSITION 3.4: The higher society’s preferences for unemployment stabilization
relative to inflation stabilization (the higher χ), the higher the optimal degree of central
bank independence.

∂F

Proof: Appendix B shows that > 0, implying that when χ goes up, the curve F(ε)
^dX

in Figure 3.1 shifts upward. Thus, the equilibrium value of ε increases.

The underlying intuition is that, if society becomes more concerned with unemployment,
the time-consistent inflation rate goes up (See equation (2.14)). Therefore, society’s
credibility problem becomes more pressing. With an unchanged relative weight placed on
inflation stabilization, the balance between credibility and flexibility needs to be adjusted
in favour of increased commitment of fighting inflation.

PROPOSITION 3.5: The higher the variance of productivity shocks (the higher σ_μ²), the
lower the optimal degree of central bank independence.

Proof: Appendix B shows that ^dF < 0, implying that when σ_μ² goes up, the curve
^dσ.',

F(ε) in Figure 3.1 shifts downward. Therefore, the equilibrium value of ε decreases.

This result may be explained as follows. If the variance of productivity shocks increases,
ceteris paribus, the economy becomes more unstable. Thus, the need for active stabilizati-
on policy increases (the Γ^I component of the social loss function goes up).

With an unaltered relative weight placed on inflation stabilization the balance between
credibility and flexibility needs to be shifted towards more monetary accommodation.

PROPOSITION 3.6: If society is relatively unconcerned with inflation χ> (^1+ε)(¹ ~^β) ,
the greater the benefits of unanticipated inflation (the higher (1-β)^¹), the. higher th2      ,

optimal degree of central bank independence.

Proof: Appendix B shows that, if χ > ^{(1 + ε})(¹ ~^β)       ^dF    > о, implying that

²        ’ ∂(1 -β )-¹

when (1-β)^¹ goes up, the curve F(ε) shifts upward. Consequently, the equilibrium value of
ε increases.

The intuition behind this proposition is that, if the benefits of unanticipated inflation rise
(See equation (2.7)), it becomes more tempting to inflate the economy. Therefore,
society’s credibility problem gains in importance. With the same emphasis on inflation

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