Dynamic Macroeconomics

20.2.1 The Social Welfare Loss from Inflation and Unemployment
To evaluate the welfare losses from deviations of output from full
employment and from inflation, we need a criterion for social welfare.
Assume that the present value of the expected social welfare loss from
inflation and unemployment is given by
We thus assume that the one-period losses from inflation and unemployment
are quadratic. We also assume that 
β
= 1/(1 + 
ρ
) is the discount factor, which
depends on the pure rate of time preference 
ρ
; that 
ζ
is the weight of the
inflation objective relative to the output objective in the social loss function;
and that 
π
*
is the optimal inflation rate. This social welfare function can be
justified in terms of the suboptimality of deviations of output from full
employment output, and the suboptimality of deviations of inflation from the
optimal inflation target of the central bank.
Note that we have assumed that the central bank aims to stabilize output
around full employment output and not the natural rate of output, which,
because of the distortions in the labor market, is suboptimally low.
20.2.2 Monetary Policy under Discretion: The Problem of Credibility
Assume that the central bank chooses interest rates in each period to
minimize the loss function 
(20.7)
, subject to system of 
(20.5)
 and 
(20.6)
 and
taking the expectations of wage setters as given. Let us call this behavior the
discretionary policy
. From the first-order conditions for the minimization of
(20.7)
 subject to 
(20.6)
, it follows that
In rational expectations equilibrium, and because there are no exogenous
stochastic shocks, actual and expected inflation will coincide. Thus, from
(20.8)
, equilibrium inflation will be equal to

---

Equilibrium inflation under discretion 
π
D
will be higher than the optimal
inflation rate 
π
*
, which is the central bank’s target.
In rational expectations, equilibrium output will also fall short of full
employment output, because from 
(20.6)
, even when deviations of output
from its natural rate are zero, deviations of output from full employment
output will be negatively related to the natural rate of unemployment:
Thus, equilibrium inflation will be constant and higher than the optimal
central bank inflation target 
π
*
. This is because of the incentives of the
central bank to reduce unemployment below its natural rate. Inflation will be
higher than the optimal inflation target 
π
*
, because wage setters anticipate the
incentives of the central bank to increase aggregate demand in order to
reduce unemployment below its natural rate. Hence, they raise their
inflationary expectations to a level where the central bank no longer has an
incentive to create surprise increases in aggregate demand and inflation. Any
inflation rate lower than 
π
D
creates incentives for the central bank to push
inflation up in the short run, in order to reduce unemployment. Thus, an
inflation rate below 
π
D
lacks credibility.
Note that the equilibrium inflation rate depends on the parameter 
ζ
of the
social welfare function. The higher is 
ζ
(i.e., the more the social welfare
function penalizes inflation relative to output), the lower will be the
inflationary bias of discretionary monetary policy. A lower 
ζ
(i.e., a social
welfare function that penalizes unemployment more than inflation) will result
in a higher inflationary bias.
The inflationary bias of discretionary policy is depicted in 
figure 20.1
.
The equilibrium inflation rate under discretion is determined at the point
where the highest possible indifference curve of the central bank is tangent to
the short-run Phillips curve, at the natural rate of unemployment = 
u
N
.
Lower inflation rates lack credibility. Assume that the central bank
announces that it will stick to an inflation rate equal to 
π
*
. If wage setters
believe it, the short-run Phillips curve will be the optimal inflation Phillips

---

curve. If the central bank sticks to its announcement, the equilibrium will be
at 
R
, with inflation at 
π
*
and unemployment at = 
u
N
. However, under the
discretionary policy, the central bank will maximize social welfare in the
short run by raising inflation to 
π
1
so as to reduce unemployment to 
u
1
, below
the natural rate = 
u
N
. Thus, the initial announcement lacks credibility. The
only inflation rate that does not lack credibility is the rate 
π
D
, at which the
central bank has no further incentives to increase inflation in order to reduce
unemployment.