I
ut = U
(1 -β) (1÷e) μ
(1 β)2 (1+ε) + χ t
(2.15)
III. OPTIMAL COMMITMENT IN MONETARY POLICY: CREDIBILITY
VERSUS FLEXIBILITY
III.1. Social Welfare under Central Bank Independence
We are now able to evalUate central bank independence from the perspective of society.
To facilitate exposition in later sections, following Rogoff (1985, pp. 1175— 1176), we
shall first develop a notation for evalUating the expected valUe of society’s loss fUnction
Under any arbitrary monetary policy regime "A", Et—1LtA:
Eb1LtA = ∙2[χ U2] + ∏a + ΓA6) (3.1)
where ∏a ≡ 1/2 (pA)2 , pA is the mean price level in period t, and
Γa ≡ 1 Em (χ [-1μ- + (p,A - EmpA)∕(1 -β)]2 t (pA - Et lpA)",∙
Again, the first component of Et 1LtA, ½[χ U2] is non-stochastic and invariant across
monetary regimes. It represents the deadweight loss dUe to the laboUr market distortion
(U > 0). This loss cannot be reduced through monetary policy in a time-consistent rational
expectations eqUilibriUm. The second term, ΠA, depends on the mean inflation rate. This
term is also non-stochastic bUt does depend on the choice of monetary policy regime.
The final term, ΓA, represents the stabilization component of the loss fUnction. It
measUres how sUccesfUlly the central bank offsets distUrbances to stabilize Unemployment
and inflation aroUnd their mean valUes.
By sUbstitUting the resUlts relevant for the central bank [(2.14) and (2.15)] into society’s
loss fUnction (2.9) and taking expectations we obtain the I and regime coUnterpart of
expression (3.1). Abstracting from the (common) deadweight loss, one gets
ΠI + Γi =
χ2 u2 + χ[(1 + g)2 (1 -β)2 + χ]
2[(1+ε)(1 -β)]2 2[(1+ε) (1 -β)2 + χ]2
σ2
(3.2)
6)
We derive eqUation (3.1) in Appendix A.
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