Dynamic Macroeconomics

particular rule.
4
This chapter analyses the various issues concerning the appropriate
design of monetary policy. To analyze monetary policy, let us use the
periodic wage contracts model of chapter 17. This is an analytically
tractable new Keynesian model in which nominal wages are set periodically
by insiders in the labor market and are nonindexed. We shall use this
particular model to discuss the question of rules versus discretion and the
appropriate use of monetary policy instruments. We will also use it to
analyze alternative rules and the design of optimal monetary policy.
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20.2 Rules, Discretion, and Credibility in a New Keynesian
Model
Let us start with a simple version of the new Keynesian model based on
periodic nominal wage contracts that we analyzed in chapter 17. The model
can be summarized as follows:
where 
ŷ
t
= 
y
t
− is excess output (i.e., the deviation of (the log of) real
output from its natural rate), 
i
t
is the nominal interest rate, 
π
t
is the rate of

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inflation, 1
/θ
is the intertemporal elasticity of substitution in consumption, 0
< α <
1 is the exponent of labor in a Cobb-Douglas production with labor as
the only factor of production, 
r
N
is the natural real interest rate, and 
ε
A
is a
white noise shock to productivity.
Equation 
(20.1)
is the new neoclassical synthesis IS curve, determining
aggregate demand, and 
(20.2)
 is an expectations-augmented Phillips curve.
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To focus on the issue of rules versus discretion and simplify matters,
assume that the central bank can use its monetary policy instruments to affect
aggregate demand and therefore deviations of output from its natural rate.
Recall that in this model, the natural rate of output is lower than full
employment output because of the behavior of labor market insiders. The
deviation of full employment output from its natural rate is equal to
where is the natural rate of unemployment, assumed to be sub-optimally
high. If the natural rate of unemployment is positive, then deviations of full
employment output from the natural rate of output are also positive.
From 
(20.2)
 and 
(20.3)
, we can see that deviations of current output from
full employment output are determined by
To further simplify the analysis, let us initially assume that there are no
exogenous stochastic shocks. Thus the natural real rate of interest is constant
at 
ρ
, the pure rate of time preference, and the natural rate of unemployment is
constant at .
In the absence of productivity shocks, the model can thus be written as
Thus, 
(20.5)
and 
(20.6)
describe deviations of inflation from previously
expected inflation, and deviations of output from full employment output, in

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terms of deviations of output from its natural rate and the natural rate of
unemployment, assumed positive and constant.