Diapositiva 1

1
Optimal policy implementation (Clarida R., J.
Gali and M. Gertler, 1999, The Science of
Monetary Policy A New Keynesian Perspective,
Journal of Economic Literature, XXXVII, pp.
1661-1707)
2
The standard New Keynesian model
IS
PC
3
The Policy Objective
Target rate of inflation is zero. Target for the
output gap is zero
As the Central Bank does not desire to push
output above its natural level, there is no
INFLATION BIAS.
However, since the target variables depend not
only on the current policy but also on the
expectations about future policy, credibility of
future policy intentions becomes a critical
issue.
4
Discretion
Without an explicit commitment Central Bank will
choose its target variables ( and )
and its instrument ( ) by reoptimizing each
period its objective function subject to the PC
and IS and taking private sectors expectations
as given.
Private sector forms its expectations taking into
account how the central bank adjusts policy,
given that the central bank is free to reoptimize
every period.
The Central bank has no incentive to change its
plans in an unexpected way the policy that
emerges in equilibrium under discretion is TIME
CONSISTENT.
5
The problem can be divided into two
sub-problems The central bank chooses
and to maximize the policy function,
given the PC. it determines the value of
implied by the IS curve, that will support
and .
The central bank takes private sector
expectations as given in solving the
optimization problem. The discretion problem can
be rewritten as
Taking as given
6
Lean against the wind whenever inflation is
above target, contract demand below
natural level ( by raising the interest
rate) and vice-versa when it is below
the target.
Optimality condition
Combining the optimality condition with the PC
and imposing that private expectations are
rational, we obtain the reduced form for
and
To the extent cost push inflation is present,
there exists a short run trade-off between
inflation and output variability as a rises the
optimal policy engineers a lower standard
deviation of output, but at the expense of
higher inflation volatility. In the presence of
demand shock there is no trade-off. The
unconditional expected value of inflation is
zero there is NO AVERAGE INFLATION BIAS
7
Taylor principle the coefficient on
expected inflation exceeds unity nominal
interest rate should rise sufficiently to
increase real rate
or equivalently, taking into account that
The interest rate reacts both to demand shock
and to cost push shock. However, as we have seen,
the interest rate perfectly offsets demand
shock which does not force a short run trade-off
between output and inflation.
8
Taylor Principle
A feedback rule satisfies the Taylor Principle if
it implies that in the event of a sustained
increase in the (expected) inflation rate by k
percent, the nominal interest rate will be raised
by more than k percent, in order to increase the
real interest rate. By this way, the policy rule
avoids self-fulfilling expectations and it does
not render the system unstable or introduce
multiple equilibria.
9
Consider
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Commitment
We have seen that under discretion there is no
inflationary bias, as Central Bank does not
desire to push output above its natural
level. However, as long as price setting depends
on expectations of the future, gains from
credibility emerge even when the central bank is
not trying to push output above its natural
level. A credible commitment raises welfare a
central bank that can credibly commit to a rule
influences private sectors expectations in a way
that improves the short run trade-off between
inflation and output.
11
The problem can be divided into two
sub-problems The central bank chooses a state
contingent sequence for and
to minimize
the policy function, given that the PC in every
period It determines the interest rate rule
that implement the optimal policy
12

1) 2) 3)
igt0 i0
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Substituting the optimality conditions in the PC
The lagged dependence in the policy rule arises
as a product of the central banks ability under
commitment to directly manipulate private sector
expectations.
The optimal policy under commitment is to
continue to reduce as long as
inflation remains above target.
14
Output gap response to a cost push shock
Inflation response to a cost push shock
15

Under discretion there is a STABILIZATION BIAS
output gap and inflation return to their steady
state value after the shock occurs. Under
commitment the central bank can offset the
inflationary impact of a cost push shock by
lowering the current output gap but also by
committing to lower future output gaps which, if
credible, will bring about a downward adjustment
in the sequence of expectations. As a result, in
response to a cost push shock, it can achieve any
desired level of current inflation with a
smaller decline in the current output gap. That
is the sense in which the output gap/inflation
tradeoff is improved. The commitment brings
about an improved in overall welfare relative to
the case of discretion.
16
Combining the optimality conditions and the IS we
obtain the optimal feedback policy for the
interest rate
The Central Bank adjusts demand only partially in
response to increase in expected inflation. Such
a rule involves indeterminacy.
17
Timeless Perspective Commitment
The central bank implements condition B) for all
periods, including the current period
This approach, which Woodford terms the timeless
perspective, involves ignoring the conditions
that prevail at the regimes inception by
imagining that the decision to apply A and B had
been made in the distant past. The central bank
implements the same policy in all periods,
instead of applying the standard discretionary
solution in the initial one and promising to
abstain from doing so in all future periods, as
with the ordinary commitment solution.