Dynamic Macroeconomics

20.2.5 Reputation as a Solution to the Problem of Inflationary Bias
Restrictive constitutions for central banks are not the only solution to the
problem of the inflationary bias of discretionary monetary policy. An
alternative is for the central bank to commit in advance to the optimal
inflation policy 
π
*
and to not succumb to the short-run incentives of following
the discretionary policy. This way, the central bank will acquire an 
anti-
inflationary reputation
, although wage setters know that it has a short-run
incentive to follow the discretionary policy. The solution based on the
acquisition of an anti-inflationary reputation was first analyzed by Barro and
Gordon [1983b]; Backus and Driffill [1985a, b], Tabellini [1985], and Barro
[1986].
To analyze this reputational mechanism, we need to explicitly analyze
monetary policy as a repeated infinite-horizon game between the central bank
and wage setters in the labor market. In this game, the central bank chooses
inflation, and wage setters choose their inflation expectations. Such repeated
games have multiple equilibria. There are at least two possible equilibria in
this case.
10
The first is the 
time-consistent equilibrium
, in which the central bank
always follows the discretionary policy. The properties of this equilibrium
are that unemployment is equal to its natural rate and inflation is higher than
the optimal inflation rate, as in 
(20.9)
.
The second is a 
time-inconsistent reputational equilibrium
, in which the
central bank chooses to continuously follow the optimal inflation strategy
(20.13)
, not succumbing to the short-run incentive to create surprise inflation
in order to reduce unemployment below its natural rate. This equilibrium
results in the optimal inflation policy, but it is time inconsistent, in the sense

---

that the central bank always has a short-run incentive to depart from the
equilibrium policy.
The question that naturally arises is: What is the mechanism that stops the
central bank from departing from the reputational policy and reverting to the
time-consistent policy, in the absence of a restrictive constitution? The short
answer is the risk of the loss of its anti-inflationary reputation.
By sticking to the reputational policy, the gain for the central bank is the
difference between the discounted future losses of the time-consistent policy
and the reputational policy. From 
(20.11)
and 
(20.14)
, this difference is
equal to
Expression 
(20.19)
 is a measure of the welfare benefits from sticking to the
time-inconsistent reputational policy rule. Thus, it measures the cost to the
central bank of losing its antiinflationary reputation.
Suppose that to reduce unemployment, the central bank succumbs to the
short-run incentive to follow the time-consistent discretionary policy and
thus creates surprise inflation. With inflationary expectations predetermined
at 
π
*
, the central bank would reduce unemployment below its natural rate and
would gain a one-period welfare benefit equal to
Thus, if by departing from the optimal policy once, the central bank risked
losing its antiinflationary reputation forever, the net gain would be the
difference between the one-period gain 
(20.20)
and the discounted loss
(20.19)
. This difference is equal to
which is always negative for a nonnegative pure rate of time preference, so
the central bank would never depart from the reputational equilibrium in this

---

model. The condition for 
(20.21)
 to be positive is (1 − 
α
)
2
<
−
βζα
2
, which
cannot be satisfied. The threat of the loss of its anti-inflationary reputation
forever is sufficient to sustain the reputational equilibrium in this case.
The reputational equilibrium can also be sustained by less extreme threats
to the anti-inflationary reputation of the central bank. Thus, if the behavior of
wage setters was such that the central bank lost its anti-inflationary
reputation only for one period and not forever, then net the gain for the
central bank would be equal to
This would be positive if and only if
The smaller the discount factor 
β
and the higher the relative weight of
inflation 
ζ
in the social welfare function, the more likely it is that even the
threat of a temporary loss of anti-inflationary reputation can sustain the
reputational equilibrium. Thus, reputational mechanisms can also be a
solution to the problem of the inflationary bias of monetary policy.