Central Bank Independence in Transition Economies

Central Bank Independence… 

S&A No. 120 

9

“surprise” supply function or derived from the overlapping contracts model. In 

addition, in more realistic setting the random supply shocks may affect unemployment 

but, to keep the basic model as simple as possible, it will not be examined here. The 

effects of shocks and the optimal policymakers' responses are analysed in section four 

in the context of Rogoff's (1985) model. 

Expectations are rational, i.e., 

π

et

 = E

π

t

 and private agents have the same 

information as policymakers about the state of the economy and about policymakers' 

objectives. The policymakers can perfectly control inflation and, in each period, 

minimise the social loss function: 

 

Z

t

 = a(u

t 

- ku*)

2 

+ (

π

t

)

2

 

 

a > 0,  0 

≤ k ≤ 

1 

   (2) 

 

The first term reflects costs of deviations from a target unemployment rate. If 

k = 1, the target rate is equal to the natural rate. If k < 1 the natural rate is higher than 

efficient because of unemployment compensation, income taxation or other 

distortions. The second term in equation (2) is a cost of deviations from optimal 

inflation rate, for simplicity normalised to be zero. The optimal inflation may be 

higher than zero, e.g., if the optimal taxation on money is positive. 

In both the Phillips curve and the loss function unemployment rate and the 

natural rate of unemployment may be substituted by output and the natural level of 

output respectively. It will not change any result of the model. 

By substituting the Phillips curve (1) into social loss function (2) we have: 

 

Z

t

 = a(

λ(π

e

t 

- 

π

t

) + (1 - k)u*)

2

 + (

π

t

)

2

  

 

 

 

 

(3) 

 

The first order condition for a minimum of (3), taking 

π

e

t 

as given, produces the 

policy-makers' reaction function: 

 

π

λ

λ

λ π

λ

t

D

*

t

e

a (

k)u

a

a

a

=

−

+

+

+

1

1

1

2

2

2

 

 

 

 

 

 

 

(4) 

 

Private agents know policymakers' reaction function, so they can calculate the 

expected rate of inflation from it. Rationality requires that the expectation should 

reproduce itself through the equation (4), thus: 

 

π

t

e

 = 

π

t

D

 = 

π

t

 = a

λ(1 

- 

k)u* 

      (5) 

 

The unemployment is at the natural rate since expected and actual inflation is 

equal.  

The discretionary equilibrium is sub-optimal because excessive (positive) 

inflation does not “buy” any reduction in unemployment. The society would be better 

off if policymakers select zero inflation once-and-for-all but this rule does not have to 

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