The ultimate determinants of central bank independence

L = 1 Pt² ÷ X u,²                                                                      (2.9)

^t 2          2 t

Rogoff shows that, in choosing among potential candidates, it is never optimal to choose
an individual who is known to care "too little" about unemployment.

Suppose, for example that in period t — 1 society selects an agent to head the central
bank in period t. The reputation of this individual is such that it is known that, if he is
appointed to head the central bank, he will minimize the following loss function

I = (¹⁺ ɛ) p_t² + ^χ u_t²     0 < ɛ < ∞                                              (²∙10)

^t 2            2

When i is strictly greater than zero, then this agent places a greater relative weight on
nflation stabilization then society does. Hence, following Eijffinger and Schaling (1993b,
p. 5) we view the coefficient ɛ as a measure of the political independence of the central
bank. The higher ɛ the more independent the central bank. Note that, if ɛ = 0, equation
(2.10) reduces to the social loss function (2.9).

Thus, stochastic equilibrium is derived under the assumption that the monetary authori-
ties attempt to minimize loss function I, given by equation (2.10) above.

Substituting the Phillips curve (2.7) in the loss function (2.10) yields

I = ^{1 +ε} p_t² + ^χ [U - —¹— p + —¹— Ep- —— μ_t]²                 (²∙¹¹)

^t 2            2          1 -β ^t 1 -β    ^t"^{1 t}     1 -β ^t

From the first-order conditions for a minimum of (2.11), i.e. ∂I_t∕∂p_t = 0, we obtain the
central bank’s reaction function to the union’s inflationary expectations

p_tI =------^{X (1}—^β)------U +----------^X---------- E_{t 1} p_tI------------^X---------- μ_t (2.1²)

⁽¹ -^β )²(^{1 + ε}) ⁺ χ ⁽¹ -^β )²(¹ + ^ε) ⁺ χ ^       ⁽¹ -^β )²(¹+^ε) ⁺ χ

where superscript I stands for independent central bank regime.

Taking expectations conditional on information att—1of(2.12) gives

E_t i p_tI ⁼ -------^X------- U

^t-^1pt     (1 -β )(1+β)

Equation (2.13) is the reaction function of the union. The resulting price level and
unemployment rate are

-----^X----- U - ---------^X---------μ
(1 -β)(1₊ε)       (1 - β)² (1₊ε) ₊ χ ^t

stability. See Fischer (1994, pp. 33-34).

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