represents a straightforward generalization of a policy that would be opti-
mal even if the zero bound were expected never to bind.
Feasible Responses to Fluctuations in the Natural Rate of Interest
In order to characterize how stabilization policy is constrained by the
zero bound, we make use of a log-linear approximation to the structural
equations presented in the previous section, of a kind that is often
employed in the literature on optimal monetary stabilization policy.
33
Specifically, we log-linearize the structural equations of our model
(except for the zero bound in expression 4) around the paths of inflation,
output, and interest rates associated with a zero-inflation steady state, in
the absence of disturbances (
t
= 0). We choose to expand around these
particular paths because the zero-inflation steady state represents optimal
policy in the absence of disturbances.
34
In the event of small enough dis-
turbances, optimal policy will still involve paths in which inflation, out-
put, and interest rates are at all times close to those of the zero-inflation
steady state. Hence an approximation to our equilibrium conditions that is
accurate in the case of inflation, output, and interest rates near those val-
ues will allow an accurate approximation to the optimal responses to dis-
turbances in the case that the disturbances are small enough.
In the zero-inflation steady state, it is easily seen that the real rate of
interest is equal to r
–
≡ β
–1
– 1 > 0; this is also the steady-state nominal
interest rate. Hence, in the case of small enough disturbances, optimal
policy will involve a nominal interest rate that is always positive, and the
zero bound will not be a binding constraint. (Optimal policy in this case is
characterized in the references cited in the previous paragraph.) However,
we are interested in the case in which disturbances are at least occasion-
ally large enough for the zero bound to bind, that is, to prevent attainment
of the outcome that would be optimal in the absence of such a bound. It is
Gauti B. Eggertsson and Michael Woodford 167
33. See, for example, Clarida, Galí, and Gertler (1999); Woodford (forthcoming).
34. See Woodford (forthcoming, chapter 7) for more detailed discussion of this point.
The fact that zero inflation, rather than mild deflation, is optimal depends on our abstracting
from transactions frictions, as discussed further in footnote 40 below. As Woodford shows,
a long-run inflation target of zero is optimal in this model, even when the steady-state out-
put level associated with zero inflation is suboptimal, owing to market power. The reason is
that a commitment to inflation in some period t results both in increased output in period t
and in reduced output in period t – 1 (owing to the effect of expected inflation on the aggre-
gate supply relation, equation 25 below); because of discounting, the second effect on wel-
fare fully offsets the benefit of the first effect.
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