MONETARY POLICY II

1
MONETARY POLICY - II
The main goal of this lecture is to analyse
inflation targetting in practice. The main part
of the lecture goes through Beans demonstration
of how a simple economic model can be used to
derive a Taylor rule for interest rate
setting. Basic set-up 1. We think of r, not i, as
the instrument. This is justified in a model
where it is assumed that the current inflation
rate is known. 2. We assume that the (logarithm
of) the natural rate of output is 0, as are the
long-run equilibrium value of r and the inflation
target. These are just normalizations which
have no significance for the analysis. 3. Our
economy is hit by serially-independent supply and
demand shocks. 4. Central Bank sets r each year.
2
Beans structural equations for output and
inflation (his 7 and 8) are
(7)
(8)
Real output, y, adjusts to the real interest rate
with a one-year lag and also exhibits
persistence. We have an accelerationist Phillips
curve. The last terms in the two equations, h and
e, are demand and supply shocks. p denotes
inflation m,l,a,w are positive parameters. The
complicated second term in the inflation equation
is there because Bean derives it from other
equations - you can ignore that. In a picture, we
have
The CB can affect inflation in two years time by
its choice of r in the current year, but has no
leverage over inflation next year.
p
p1
p2
y
y1
r
3
We can lead equation 8 by two years, to get
From which,
Rearranging,
Beans (9)

• Let us look closely at this equation. It tells us
  that inflation in two years time depends on
• expected inflation next year, which is currently
  fixed and known to us
• expected output next year, which we can
  manipulate using r
• zero-mean shocks
• So the policy problem, in effect, reduces to a
  decision over how much we are going to lean
  against inflation next year by creating a
  recession next year.

4
In other words, we have to choose a parameter r
and set
If ? is set to zero, then we are purely
targetting output. In other words we are ensuring
that
Beans (9) then implies that
Inflation is a random walk in this case. At the
other extreme, if ? is set to ?/a, we are purely
targetting inflation. In this case the first and
second terms on the right hand side of Beans (9)
cancel, so we get
5
So the extreme pure cases of output and
inflation targetting mean, technically, that we
are making the variance of the target variable as
small as we can in other words stripping
everything away except the unpredictable shock
terms. However when we talk about inflation
targetting, we do not mean to imply the pure
case let us see how things look in the
intermediate case where ? lies between 0 and ?/a.
First a diagram
Ep1
pure output targetting
Ey1
pure inflation targetting
intermediate case
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The diagram shows the policy reaction function.
The more that the policymaker cares about
inflation variability as opposed to output
variability, the flatter the function is and the
larger is the chosen ?. Mathematically, we have
The second and third equations above come from
Beans 7 and 8, in each led by one year and with
expectations taken. Plugging these structural
equations into the policy reaction function gives
And we can rearrange this, putting r on the left
hand side, to get an operational policy rule
7
This is Beans equation 12, and is an example of
a Taylor Rule. A Taylor rule, in general,
prescribes an interest rate that diverges from
the (assumed known) long-run equilibrium interest
rate by an amount that depends on the output and
inflation gaps. Viz
Here a and b are reaction parameters to be chosen
and starred variables are long-run equilibria
(the target in the case of inflation). It can be
seen that the equation from Bean can be turned
into a Taylor rule just by adding p to both
sides. Note in Beans equation that (a) the CB
reacts to the output gap even if it only cares
about inflation, (b) greater aversion to
inflation variance leads to bigger reaction
parameters for both inflation and output (gaps).
8
Bean applies his model to the UK economy, by
estimating parameters for his structural model,
using UK data. He is then able to plot out a
policy frontier, showing the tradeoff between the
standard devations of output and inflation
choice of ? amounts to choosing a point on the
tradeoff.
Low ? slow p adjustment
SD of p
High ? fast p adjustment
SD of y
An important finding is that the policy frontier
is roughly L-shaped this means that there is not
much of a tradeoff. Being near the corner is
equivalent to correcting inflation shocks in 1.5
2 years.
9

• Notes on recent UK experience
• Note that it is supply rather than demand shocks
  that give rise to the choice between output and
  inflation variability Beans model predicted
  that the variance of shocks was such that Open
  Letters would be quite frequent. But it hasnt
  happened. Why?
• King (Mais lecture 2005) describes 1993-2004 as
  the Great Stability the standard deviations of
  both output and inflation have been low (the
  policy tradeoff has moved in towards the origin).
  Hence no open letters.
• King claims that expectation formation has
  changed in this period and that inflation
  expectations have become anchored on the
  inflation target. The implication is that supply
  shocks may have had smaller and shorter-lived
  effects on inflation.
• Kings Maradona theory of interest rates. If
  shocks cause expectations of policy changes, then
  the actual policy changes do not need to be very
  great. For example, an adverse supply shock, such
  as a rise in oil prices, by causing an
  expectation of interest rate rises, will
  appreciate the immediately, with a
  contractionary effect on the economy. Importance
  of heuristics.