5 Monetary Policy by maclaren1

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									     5               Monetary Policy


The aim of this chapter is to set out in more detail the way that monetary policy has been
analysed in recent years. The main idea is that central bank behaviour can be thought
about in terms of a ‘reaction function’ that the central bank uses to respond to shocks to
the economy and steer it toward an explicit or implicit inflation target.

• The first task of the reaction function is to provide a ‘nominal anchor’ for the medium
  run, which is defined in terms of an inflation or price-level target. This pins down the
  medium-run inflation rate and to the extent that forward-looking expectations play a
  role, establishes a commitment to a low inflation environment.
• The second task of the reaction function is to provide guidance as to how the central
  bank’s policy instrument, the interest rate, should be adjusted in response to different
  shocks so that the medium-run objective of stable inflation is met while minimizing
  output fluctuations.

  We show explicitly how this broad structure for monetary policy can be formalized
as an optimal monetary policy rule. By optimal monetary policy rule is meant that the
monetary rule can be derived as the solution to the problem of the government or central
bank optimizing with respect to the constraints it faces from the private sector of the
economy.
  Over the course of the past two decades, central banks in the OECD economies and
in many transition and developing countries have shifted toward inflation-targeting
regimes of this broad type—or have done so indirectly by fixing their exchange rate
to a country where the central bank uses such a framework. Before setting out the details
of an inflation-targeting regime, it is necessary to clarify why low inflation-targets have
been adopted. We begin by asking two questions:

(1) What is wrong with inflation?
(2) What is the ‘ideal’ rate of inflation—is it zero, positive or negative? Negative
    inflation is a situation in which average prices are falling; this is known as deflation.
    We are led to ask as well, what is wrong with deflation? We shall see that the
    consensus view is that costs are minimized when inflation is kept low and stable.

  In Chapters 2 and 3 the operation of monetary policy was discussed for an active,
inflation-targeting central bank that uses the interest rate as its policy instrument and
for a passive central bank that fixes the growth rate of the money supply. In section 2,
we compare these two paradigms and investigate why modern central banks typically




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target the inflation rate using an interest rate rule rather than targeting the growth of the
money supply. Section 3 sets out in detail the derivation of the central bank’s monetary
policy rule that was introduced in Chapter 3: as the MR curve in the Phillips diagram and
the MR equation in the 3-equation model. Specifically, we shall see the role played by the
following six key variables in central bank policy making:

(1) the central bank’s inflation target
(2) the central bank’s preferences
(3) the slope of the Phillips curve
(4) the interest sensitivity of aggregate demand (i.e. the slope of the IS curve)
(5) the equilibrium level of output
(6) the stabilizing interest rate.

   Section 4 focuses on how an interest rate rule such as the famous Taylor Rule can be
derived from the 3-equation model. Section 5 steps back from the mechanics of interest
rate based inflation targeting and investigates the problems with using such rules in
dealing with macroeconomic problems. In particular, the dangers posed by deflation are
explored.
   For the bulk of the chapter, we describe monetary policy making assuming it is in the
hands of the central bank. However, in section 6 we look at why it might matter whether
monetary policy decisions are actually made by the government and then implemented
by the central bank or whether the central bank is independent of the government.
Section 6 introduces the idea that if the government (or central bank) tries to achieve
a target level of output above equilibrium—perhaps for politically motivated reasons—
then the result will be that in equilibrium the inflation rate is higher than the target
rate. This is called the inflation bias. We then show how inflation bias is related to the
problem of central bank credibility and the time inconsistency of policy. To do this we
need to introduce forward-looking inflation expectations. The delegation of monetary
policy to an independent central bank is sometimes proposed as a method of reducing
or eliminating the inflation bias. In this section, we explain that the debate about ‘rules
versus discretion’ in the time-inconsistency literature uses a much narrower definition of
‘rules’ than the one adopted in our analysis of monetary policy. This can be a source of
confusion in discussing how central banks behave.
   In this chapter, we consider only a closed economy. The relationship between the
exchange rate regime and monetary policy in the open economy is explained in Chapter 9
and we extend the analysis of monetary policy rules to the open economy in Chapter 11.




1 Inflation, disinflation, and deflation

In Chapter 3, we set out the IS-PC-MR model with the following features:

  • In medium-run equilibrium, inflation is equal to the central bank’s inflation-target if
the central bank seeks to stabilize unemployment around the ERU . In the IS/LM version




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of the model, in the medium-run equilibrium, inflation is equal to the growth rate of the
money supply set by the central bank.
  • Because of delays in price and wage setting, inflation is persistent, which means that
lagged inflation affects current inflation and there will be a trade-off between inflation
and unemployment in the short run. The Phillips curves are therefore indexed by lagged
inflation (π I = π−1 ) and shift whenever π−1 changes:

                                    π = π I + α(y − ye )
                                       = π−1 + α(y − ye ).

With Phillips curves of this form, the implication is that disinflation is costly: unemploy-
ment has to rise above the ERU for inflation to fall.
  • With linear Phillips curves, the sacrifice ratio is constant and independent of the
central bank’s preferences. Although the time path of unemployment is affected by
the choice between a policy for rapid disinflation (so-called ‘cold turkey’) and a more
gradualist policy, the cumulative amount of unemployment required to achieve a given
reduction in inflation does not depend on the degree of inflation aversion of the cen-
tral bank. However, with non-linear Phillips curves, this is no longer the case: when, as
seems empirically likely, the Phillips curves become flatter as unemployment rises, a ‘cold
turkey’ policy of disinflation favoured by a more inflation-averse central bank entails a
higher sacrifice ratio than does a ‘gradualist’ policy favoured by a less inflation-averse
central bank.

  In setting out the structure of the basic short- and medium-run model, we concentrated
on the key results. It is now appropriate to investigate more deeply the presumption that
the goal of a low, stable inflation rate is an appropriate one for policy makers to have.
There seem to be obvious benefits of having a higher level of output—i.e. above the
equilibrium level set by the intersection of the WS and PS curves and therefore closer
to the competitive, full information market-clearing level. But what are the costs to the
economy of the rising inflation that would ensue? As we have already seen, if inflation
gets ‘too high’, bringing it down is likely to be costly. Finally, what problems arise when
inflation is negative, i.e. when prices are falling?



1.1 Rising inflation
In an economy in which social groups—such as unions—wield economic power, a situ-
ation of rising inflation reflects inconsistent claims on output per head in the economy.
If firms are able to adjust prices immediately after wages have been set, rising inflation
reflects a situation in which workers’ real wage aspirations are systematically frustrated:
the real wage is typically on the PS curve, not on the WS curve. If there are lags in price set-
ting as well as in wage setting, then the aspirations of neither workers nor firms are fully
satisfied (the real wage lies between the PS and WS curves). This reflects distributional
conflict as different social groups (wage setters/employees and price setters/employers)
seek to protect their interests. Social tension rises as frustration mounts. As we shall




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see, inflationary episodes of this kind have typically been followed by painful periods of
disinflation.
   As we have seen in Chapter 3, for disinflation to be costless in the sense of not entail-
ing a period of high unemployment, expectations of inflation must be formed using
the Rational Expectations Hypothesis, the commitment of the government and central
bank to a policy of low inflation at equilibrium unemployment has to be believed by
the private sector and there must be no lags in the adjustment of wages and prices. For
countries experiencing episodes of moderate inflation up to double digit rates per annum,
these conditions do not appear to have been met. Lawrence Ball examines twenty-eight
episodes of disinflation in nine OECD countries and finds that with only one excep-
tion, disinflation was contractionary, with sacrifice ratios ranging from 2.9 in Germany
(i.e. for a one percentage point reduction in inflation, the increase in unemployment was
2.9 percentage points for a year) to 0.8 in the United Kingdom and France.1


1.2 Very high inflation and hyperinflation
Once inflation rates rise above 100% per annum, additional considerations come into
play.2 Between 1960 and 1996, there were more than 40 episodes in 25 different devel-
oping countries of such high inflation, which on average lasted for about 40 months.
In addition, virtually all of the transition economies of Eastern Europe and the former
Soviet Union experienced a bout of very high inflation as a consequence of price liber-
alization at the beginning of the transition in the early 1990s. Hyperinflation has tradi-
tionally been defined as referring to a situation in which inflation rates rise above 50%
per month—this was more common in the first half of the twentieth century than either
in earlier epochs or since. Situations of very high and hyperinflation are normally the
result of governments being unable to finance their expenditure through normal means
(borrowing or taxation) and they therefore resort to monetary financing. This is known
as seignorage. The intimate connection between very high inflation and government
deficits is explored in detail in Chapter 6 on fiscal policy after the concepts of the govern-
ment deficit and debt have been elaborated. We examine there the scope for and limits
to seignorage.
   There is some evidence that the deterioration in the economic environment associated
with very high inflation perhaps paradoxically can have the effect of creating the con-
ditions for a relatively painless subsequent stabilization. Very high inflation is typically
associated with very poor economic performance: investment, consumption, and output
are all depressed. The length of wage contracts becomes very short and there is increasing
recourse to the use of foreign currency for transactions. This means that the nominal
rigidities that are one reason for costly disinflation virtually disappear. Achieving the
credibility that is also required for the reform package to succeed is more elusive. It is fair
to say that the way to achieve a successful, painless disinflation is not well understood.
It requires that the causes of the unsustainable fiscal stance be addressed and that the
central bank be prevented from financing the deficit through the creation of money but
as is often the case in macroeconomics, this is easier said than done.
 1
     Ball (1994).
 2
     For a more detailed discussion of very high inflation, see Fischer, Sahay, and Végh (2002).




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1.3 Volatile inflation
When inflation is high it also seems to be more volatile. Volatile inflation is costly because
it creates uncertainty and undermines the informational content of prices. Unexpected
changes in inflation imply changes in real variables in the economy: if money wages and
pensions are indexed by past inflation and there is an unanticipated jump in inflation,
real wages and pensions will drop. Equally, the real return on savings will fall because the
nominal interest rate only incorporates expected inflation.
   In an economy with technical progress, innovation takes place unevenly across sectors.
In sectors with rapid innovation, prices will be falling relative to other sectors where
technology is more stagnant. Volatile inflation masks the economically relevant changes
in relative prices and therefore distorts resource allocation. In short, volatile inflation has
real effects on the economy that are hard to avoid.

1.4 Constant inflation—what level is optimal?
Assuming that constant inflation is needed if expectations are to be fulfilled, we turn to
the question of ‘at what level’? In the model developed so far, this question has not been
answered. We begin by noting that there are hypothetical circumstances under which the
(constant) rate of inflation (i.e. high or low) should not matter much. Imagine that we
move from a situation in which prices are rising at 3% per year to a rate of 10% per year.
We assume that this change is announced well in advance and that the tax system is
indexed to inflation so that all the tax thresholds are raised by 10% p.a. The same is
assumed to be true of pensions and other benefits. The consequence of this change will
be that all wages, benefits, and prices will now rise at 10% p.a. and the nominal interest
rate will be 7% points higher. All real magnitudes in the economy remain unchanged.
The economy moves from a constant inflation equilibrium with π = 3% p.a. to a constant
inflation equilibrium with π = 10% p.a. The real interest rate and the levels of output
and employment remain unchanged.
  From our earlier analysis, we know that at the new equilibrium, the real money supply
will be lower than initially. Why? At high inflation, people wish to hold lower money
balances—they wish to economize on their holdings of money—so for equilibrium in
the money market, the real money supply must be lower than in the initial low inflation
equilibrium. Since

                                       MS
                                          = L(i, y )
                                       P
                                          = L(r + π E , y ),

at equilibrium output with low inflation, πL , we have:

                                  MS
                                                = L((re + πL ), ye )
                                  P      high

and at equilibrium output with high inflation, πH , we have:

                                  MS
                                               = L((re + πH ), ye ).
                                  P      low




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   This highlights the fact that even in our simple example the shift from inflation of
3% to 10% p.a. is not quite as straightforward as it seems at first. After the move to 10%
inflation, money wages, prices, the nominal money supply, and nominal output will
rise by 10% each year. But at the time of the shift, there has to be an additional upward
jump in the price level to bring down the real money supply (M S /P) to its new lower
equilibrium level ((M S /P )low ) consistent with the demand for lower real money balances
when inflation is higher.
   What are the real costs of people economizing on money balances when inflation is
high? These costs are sometimes referred to as ‘shoe-leather’ costs because of the wear
and tear associated with more frequent trips to the bank or the cash machine. Other costs
(so-called menu costs) arise because of the time and effort involved in changing price lists
frequently in an inflationary environment. These costs are estimated to be quite low. We
note here an apparent paradox: if the rate of inflation does not matter much, why should
governments incur the costs of getting inflation down from a high and stable level to a
low and stable one? One response is that it seems empirically to be the case that inflation
is more volatile when it is higher and as noted above, volatile inflation brings additional
costs. Another is that the initiation of disinflation policies frequently begins not simply
with high but with high and rising inflation. In this case, since costs will be incurred in
stabilizing inflation, it may be sensible for the government to go for low inflation as part
of a package that seeks to establish its stability-oriented credentials.
   Once we relax our assumption that indexation to inflation is widespread in the eco-
nomy and that adjustment to higher inflation is instantaneous because all parties are
fully informed and can change their prices and wages at low cost, it is clear that the
costs of switching to a high inflation economy are likely to be more substantial. The con-
tinuous reduction in individuals’ living standards between wage adjustments gives rise
to anxiety. Distributional effects are also likely to occur: unanticipated inflation shifts
wealth from creditors to debtors. It is also likely to make the elderly poorer since they
rely on imperfectly indexed pensions and on the interest income from savings. Recog-
nition of such costs is consistent with survey evidence that shows the general public
is more averse to inflation than would be expected if the costs were really as low as
they seem in the example of full information, complete indexation, and instantaneous
adjustment.
   Can we infer from this analysis that the optimal rate of inflation is zero or even negative?
In thinking about the optimal inflation rate, we are led first of all to consider the following:
the return on holding high-powered money (notes and coins) is zero so with any positive
inflation rate, the real return turns negative. The negative real return leads people to waste
effort economizing on their money holdings (shoe leather again) and this is inefficient
given that it is virtually costless to produce high-powered money. If we follow the logic
of this argument then with a positive real rate of interest, for the nominal interest rate to
be zero, inflation would have to be negative (i.e. prices falling, which is called deflation).
This was Milton Friedman’s view of the optimal rate of inflation: the rate of deflation
should equal the real rate of interest, leaving the nominal interest rate equal to zero.3 Is
deflation optimal?

 3
     Friedman (1969).




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1.5 Deflation
If inflation is negative (e.g. −2% p.a.), or equivalently there is a rate of deflation of 2%
p.a., prices and wages will be 2% lower in a year’s time than they are now. In a world of
perfect information, there would only be benefits from this as we have already seen—shoe
leather would be saved and the relative price changes associated with technical progress
would be clearly revealed.
   In spite of these arguments, there are two main reasons why deflation is not viewed
as a good target by central banks. One relates to how economies work in ‘normal times’
and the other to the dangers of the economy getting stuck in a deflation trap caused
by weakness in aggregate demand. The first reason relates to the apparent difficulty in
cutting nominal wages.4 If workers are particularly resistant to money wage cuts, then
a positive rate of inflation creates the flexibility needed to achieve changes in relative
wages. For example, if, due to a fall in demand for one kind of labour, a real wage cut is
required it can be achieved with an inflation rate of, say, 2% p.a. with the money wage left
unchanged in the sector where the real wage cut is necessary. This argument is referred
to as inflation’s role in ‘oiling the wheels of the labour market’.
   The second reason stems from the need for the central bank to maintain a defence
against a deflation trap. A deflation trap can emerge when weak aggregate demand leads
inflation to fall and eventually become negative. For this to happen, two things are
necessary: (i) the automatic self-stabilizers that operate to boost aggregate demand when
inflation is falling fail to operate sufficiently strongly and (ii) policy makers fail to stop
prices falling. Attempts to use monetary policy to stimulate the economy result in the
nominal interest rate falling. A nominal interest rate close to zero (as low as it can go)
combined with deflation implies a positive real interest rate. This may be too high to
stimulate private sector demand. Continued weak demand will fuel deflation and push
the real interest rate up, which is exactly the wrong policy impulse. This will tend to
weaken demand further and sustain the upward pressure on the real interest rate. Once
deflation takes hold, it can feed on itself and unlike a process of rising inflation, it does
not require the active cooperation of the central bank for the process to continue. The
deflation trap is explored in more detail in section 4 and the recent Japanese experience
with deflation is analysed in Chapter 17.


1.6 Summing up
The conclusion to this discussion is that policy makers should establish a nominal anchor
for the economy that keeps inflation low and stable.5 This raises a further question. Why
do we observe economies with high, rising, and volatile inflation? We have already noted
  4
    A famous study is Bewley (1999). A recent empirical study using high quality data confirms the existence of
nominal wage rigidity: Lebow, Saks, and Wilson (2003).
  5
    It is sometimes argued that a price-level target would be preferable to an inflation target since this would
require the policy maker to make good policy misses in the past. This has some attraction in the context of
deflation: e.g. following a couple of years of deflation, an inflation-targeting central bank may tighten policy
too soon once prices begin to rise whereas a price-level targeter would be more relaxed as the price level moved
back toward the target.




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that governments may be tempted to take advantage of the short-run trade-off between
inflation and unemployment. Since rising inflation reflects distributional conflict in the
economy, one interpretation is that the political system is incapable of resolving these
conflicts, which therefore come to be reflected in rising inflation. A variation on this
theme is that the origin of situations of high and/or rising inflation lies with the financing
of government spending. As we shall see in the next chapter when we discuss fiscal policy,
there are situations in which the usual methods of financing government spending via
taxation or borrowing are limited. Raising taxes may be politically unpopular and further
borrowing may be prohibitively expensive because of the level of public debt that has
already been built up. Under such circumstances, if the government is intent on raising
its spending in response to pressure from politically important groups in the economy,
it may have to get hold of the necessary resources by increasing the money supply. The
use of money to finance government spending is called seignorage. We examine the scope
for and limits to seignorage in the fiscal policy chapter, Chapter 6.
   We highlight the asymmetry in the role of the central bank in situations of high and
rising inflation as compared with situations of deflation. In the former, the active involve-
ment of the central bank is required to keep the inflationary process going; in the latter,
deflation can become self-sustaining. Many observers have argued that unlike inflation-
ary problems, which often reflect unresolved social and political conflict and require
painful and therefore politically unpopular solutions, deflation can be solved by the
government generating demand through increased government spending or tax cuts
financed by new money creation, which are popular. This suggests that it is bad policy
(and bad luck) rather than politically expedient policy that leads to deflation traps.




2 Monetary policy paradigms

The purpose of this section is to provide an overview of the shift in monetary policy
paradigm that has been discussed in a partial way and from different perspectives in
earlier chapters.6 Both paradigms take as given the inertia in inflation that produces the
Phillips curves and both incorporate the IS curve. The first paradigm, which we shall call
the money supply model or LM paradigm, is characterized by the following propositions:

(1) the ultimate determinant of the price level and rate of inflation is the money supply;
(2) the instrument of monetary policy is the money supply;
(3) the mechanism through which the economy adjusts to a new equilibrium with
    constant inflation following a shock is that embodied in the IS/LM model plus the
    inertia-augmented (or expectations-augmented) Phillips curve.

  Let us examine how an IS shock is handled in this paradigm. We assume the economy
begins at equilibrium unemployment with constant inflation equal to the growth rate of
the money supply set by the central bank. For a positive IS shock, the impact of the rise
in aggregate demand on output in the short run is dampened because the rise in income
 6
     See also Allsopp and Vines (2000).




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pushes up the demand for money. As portfolios are rebalanced, the interest rate rises. This
is a movement along the LM to the north-east. The change in output and employment
then feeds through to a rise in inflation, which given the fixed money supply growth rate
triggers a leftward shift in the LM curve. This induces a further dampening of the initial
stimulus. In this paradigm, monetary policy is passive (in the form of a fixed growth rate
of the money supply) and the economy adjusts to the new equilibrium by following a
protracted spiral-shaped path as lags in inflation interact with a shifting LM curve. The so-
called ‘Keynes effect’ is doing the work of raising the interest rate: rising inflation relative
to a fixed money supply growth reduces real money balances and leads to a portfolio
adjustment with bonds being sold. Excess supply of bonds pushes bond prices down and
the interest rate up. The higher real interest rate dampens interest-sensitive spending.
   The second paradigm, which we shall call the interest rate reaction function or MR
paradigm, is characterized as follows:

(1) the ultimate determinant of the price level and inflation is policy;
(2) the instrument of policy is the short-term nominal interest rate;
(3) the mechanism through which the economy adjusts to a new equilibrium with
    constant inflation following a shock is encapsulated in an interest rate rule.

   We take the same example as above. For a positive IS shock, the central bank responds
to the rise in inflation due to the increase in output: as a consequence it raises the interest
rate. Output falls below the equilibrium and brings inflation down: the central bank
adjusts the interest rate to guide the economy down the MR curve to achieve the inflation
target at equilibrium output.
   As far as monetary policy is concerned, the paradigm shift centres on two issues: the
choice of monetary policy instrument and the choice of an active or a passive policy.
From a stabilization perspective, it was clear a long time ago that to operate monetary
policy in a passive fashion—be it with a fixed money supply or a fixed interest rate—
was not necessarily optimal. William Poole provides a classic early treatment (1970) of
the issue by looking first at how the relative importance of LM versus IS shocks affects
the optimal choice of a money supply versus an interest rate instrument.7 By drawing
simple IS/LM diagrams, it is apparent that if the economy is characterized by LM shocks
(e.g. in the demand for money), a fixed interest rate is better for output stability than a
fixed money supply; the converse holds for IS shocks. The second contribution of Poole’s
paper is to show that an active monetary policy is normally superior to a passive one
when the economy is characterized by shocks and by lags in adjustment. Poole’s analysis
is confined to the short run with prices fixed. The tenor of his arguments is even more
persuasive when we move to the medium run and allow prices to adjust.
   From the perspective of the second paradigm, it is not sensible for policy makers to
leave the adjustment mechanism to work automatically via the Keynes effect as in the
LM paradigm. As we have seen in Chapter 3 when setting out the analysis under a fixed
monetary growth rate, the adjustment path to the new equilibrium following a distur-
bance to the economy is protracted and complicated to explain. This is because of the
interaction between inflation inertia and the portfolio adjustment process (the Keynes
 7
     Poole (1970).




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effect) through which changes in the real money supply affect the interest rate (e.g. LM
shifts left as rising inflation relative to a fixed money supply growth cuts the real money
supply). As we have seen, a further complication arises because of the impact of changes
in the inflation rate on the demand for money (LM shifts right as the demand for money
falls with rising inflation).
   The complexities of explaining the dynamic path of adjustment is not simply a problem
for those teaching macroeconomics or trying to learn about it but also reflects a problem
facing policy makers. The spiral-shaped adjustment path could be short-circuited within
the LM paradigm: having achieved a fall in inflation to the level desired (equal to the
growth rate of the money supply) with unemployment above the ERU , the monetary
authority could inject a one-off boost to the money supply to take the economy straight
to the new equilibrium. However, this is an uneasy mixture of a passive monetary policy
with occasional activism and could well be misinterpreted by the public as the inconsis-
tent implementation of policy.
   By contrast, in the second paradigm in the IS-PC-MR model, the monetary policy reac-
tion function based on the use of the interest rate as instrument is an activist policy
framework that is consistent with steering the economy toward equilibrium unemploy-
ment and providing a nominal anchor. Frequent adjustments have to be made to the
interest rate in order to achieve the central bank’s objective. This highlights the fact that
it is quite consistent to think of the central bank as following a ‘rule-based’ approach
to monetary policy, yet having to be very active. Fig. 17.14 in Chapter 17 illustrates the
frequent interest rate adjustments made by central banks in the USA, the eurozone, and
the UK since 1999.
   It is crucial to see that it is the implementation of the policy rule itself that establishes
the nominal anchor and thus ultimately determines the price level or the rate of infla-
tion in this paradigm (depending on whether the target is the price level or the rate of
inflation). The adjustment path is easy to explain and straightforward as we have seen
in Chapter 3, since the central bank responds directly to shocks by changing the inter-
est rate. The question of how to bring about the required change in the interest rate is
then a technical problem for the central bank; whereas in the first paradigm, agents are
faced with an economic problem of trying to figure out the impact of changes in inflation
on portfolio choices and hence on the interest rate. These arguments form the central
case for using the second paradigm. It is a better description of how monetary policy is
conducted and it comes closer to how it should be conducted, given the objectives of
the central bank. Milton Friedman, the most famous proponent of the use of the money
supply as policy target by the central bank, has conceded that ‘The use of the quantity
of money as a target has not been a success.’ He added: ‘I’m not sure I would as of today
push it as hard as I once did’ (Financial Times, 7 June 2003).



3 The monetary policy rule in the 3-equation model

In Chapter 3, we developed a graphical method to predict how an inflation-targeting
central bank that aims to minimize the fluctuations of output and inflation from its
targets would respond to a variety of shocks. In this section, we pin down the role played




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by the following six key variables in central bank policy making:

(1) the central bank’s inflation target, π T
(2) the central bank’s preferences, β
(3) the slope of the Phillips curve, α
(4) the interest sensitivity of aggregate demand (i.e. the slope of the IS curve), a
(5) the equilibrium level of output, ye
(6) the stabilizing interest rate, rS .

  In order to make the discussion of monetary policy rules concrete, we shall use specific
examples of the central bank’s utility function, policy instrument, and constraints. How-
ever, the basic method for deriving a monetary policy rule will be the same if different
variants are chosen. It involves the following steps:

(1) Define the central bank’s utility function in terms of both output and inflation. This
    produces the policy maker’s indifference curves in output-inflation space.
(2) Define the constraints faced by the policy maker: these are the Phillips curves, which
    are also shown in output-inflation space.
(3) Derive the optimal monetary rule in output-inflation space: this is the monetary rule,
    MR line. For a given Phillips curve that it faces, this shows the central bank’s chosen
    combination of output and inflation. Roughly, the higher is inflation as determined
    by the Phillips curve the economy is on, the lower will the central bank set aggregate
    demand and hence output in order to reduce inflation. Hidden in this relationship is
    the policy instrument, r, that the central bank will use to secure the appropriate level
    of aggregate demand and hence output. We saw this graphically in Chapter 3: the
    central bank chooses the best point along the Phillips curve that it faces and in order
    to deliver the right level of aggregate demand, it must set the interest rate at the level
    shown by the IS curve.
(4) We can also derive the interest rate rule, which tells the central bank how to adjust the
    interest rate in response to current economic conditions.




3.1 The central bank’s utility function
In Chapter 3, we introduced in an informal way the central bank’s indifference curves
representing the trade-off in its preferences between inflation and unemployment. We
now explain how these can be derived more formally. We assume that the central bank
has two concerns: the rate of inflation, π , and the level of output, y. Looking first at
inflation and following the discussion in section 2, we assume that it has a target rate
of inflation π T and that it wants to minimize fluctuations around π T . A simple way of
writing this is to assume that it wants to minimize the loss function:


                                          (π − π T )2 .




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142 THE MACROECONOMIC MODEL


Rather than having the central bank maximize a utility function, we have it minimize
a loss function. A loss function is just like a utility function except that the higher the
loss, the worse it is for the central bank (we use it rather than a utility function purely
for convenience—by putting a minus sign in front of the expression above, the central
bank will want to maximize it). This particular loss function has two implications. First,
the central bank is as concerned to avoid inflation below its target as it is inflation above
π T . If π T = 2% the loss from π = 4% is the same as the loss from π = 0%. In both cases
(π − π T )2 = 4. Second, it attaches increased importance to bringing inflation back to its
target the further it is away from π T ; the loss from π = 6% is 16, compared to the loss of
4 from π = 4%. The central bank’s marginal disutility is increasing as the gap between
inflation and the target grows.
   We turn now to the central bank’s second concern—about output and employment.
We assume the central bank’s target level of output is the equilibrium level ye and it seeks
to minimize the gap between y and ye . At this point it is useful to draw attention to the
fact that we have assumed that the equilibrium output level ye is known, that the central
bank’s target output level is ye , and that it is able to stick to this target. As we shall see
in section 6, even if ye is known, the central bank may target a higher level of output.
Output (or employment) targets are likely to arise from the interplay of interest groups
in the economy mediated by political institutions, and central banks may be unable or
unwilling to go against these pressures at particular times (e.g. just before an election).
   The central bank’s loss as a result of output being different from its target of ye is

                                           (y − ye )2 .

Note that this loss function again suggests a symmetrical attitude to positive and negative
deviations—in this case, from the equilibrium level of output. The most straightforward
way of thinking about this is that the central bank understands the model and realizes
that inflation is only constant at y = ye . If y < ye then this represents unnecessary
unemployment that should be eliminated. If y > ye , this is unsustainable and will require
costly increases in unemployment to bring the associated inflation back down. Whenever
the economy is disturbed, the central bank sees its task as steering the economy back to
this constant-inflation output level.
   If the two loss functions are added together, we have the central bank’s objective func-
tion:

                 L = (y − ye )2 + β(π − π T )2 ,                 (central bank loss function)

where β is the relative weight attached to the loss from inflation. This is a critical para-
meter: a β > 1 will characterize a central bank that places less weight on deviations in
employment from its target than on deviations in inflation, and vice versa. An inflation-
averse central bank is characterized by a higher β ; if the central bank cares only about
inflation deviations and not at all about output deviations, β = ∞.
  Let us first look at the geometry of the loss function in the Phillips curve diagram, on the
assumption that β = 1. With β = 1, the weights on output and inflation deviations are
the same, i.e. the central bank is equally concerned about inflation and output deviations
from its targets.




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                                                                                 MONETARY POLICY 143


(a)                                  (b)                                   (c)
 p                                    p                                     p




pT                                    pT                                   pT



                 ye              y                     ye              y                   ye               y
           Balanced: b = 1                   Inflation averse: b > 1         Unemployment averse: b < 1


Figure 5.1 Central bank loss functions: utility declines with distance from the ‘bull’s eye’


   The loss function is simple to draw: with β = 1, each indifference curve is a circle with
(ye , π T ) at its centre (see Fig. 5.1(a)). The loss declines as the circle gets smaller. When
π = π T and y = ye , the circle shrinks to a single point (called the ‘bliss point’) and the
loss is at a minimum, which is zero. The diagram is easy to remember if you think of it as
a target (as for archery) with the central bank’s objective to get as close to the bull’s eye
as possible. With β = 1, the central bank is indifferent between inflation 1% above (or
below) π T and output 1% below (or above) ye . They are on the same loss circle.
   Only when β = 1, do we have indifference circles. If β > 1, the central bank is indifferent
between (say) inflation 1% above (or below) π T and output 2% above (or below) ye . They
are on the same loss curve. This makes the indifference curves ellipsoid as in Fig. 5.1(b).
A central bank with less aversion to inflation (β < 1) will have ellipsoid indifference
curves with a vertical rather than a horizontal orientation (Fig. 5.1(c)). In that case, the
indifference curves are steep reflecting that the central bank is only willing to trade off a
given fall in inflation for a smaller fall in output than in the other two cases. If the central
bank cares only about inflation then β = ∞ and the loss ellipses become one dimensional
along the line at π = π T .8


3.2 The Phillips curve constraint
Next, we shall assume that the central bank can control the level of output via its ability
to use monetary policy (by setting the interest rate) to control aggregate demand, y D .
However, it cannot control inflation directly—only indirectly via y. As we have already
discussed, output affects inflation via the Phillips curve:

                                           π = π−1 + α.(y − ye ).                                        (5.1)

  8
    The central bank’s preferences can be presented in this simple way if we assume that the central bank’s
discount rate is infinite. This means that it only considers one period at a time when making its decision. In
Chapter 3, we discussed informally the role that the central bank’s discount rate can play when we compared
a rapid disinflation policy that produces a large initial rise in unemployment (‘cold turkey’) with a gradualist
policy.




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144 THE MACROECONOMIC MODEL


                                                               PC (p I = 4)
                               p
                                                    VPC
                                                                 PC (p I = 3)

                                                A                   PC (p I = 2)
                               4

                                         D
                               3


                           pT = 2
                                    C               B




                                          y1     ye                                y


Figure 5.2 Loss circles and Phillips curves


This is shown in Fig. 5.2, where the upwards sloping lines are Phillips curves. For the
moment for simplicity it is assumed that α = 1, so that each Phillips curve has a slope
of 45◦ . Each Phillips curve is labelled by lagged inflation. Assume that π−1 = π T = 2%
(remember that this PC must go through point B at which y = ye and π = 2). The central
bank is in the happy position of being able to choose the bull’s eye point B or (π T , ye ) at
which its loss is zero.
   What happens if there has been a shock to inflation and it is not equal to the inflation
target? Suppose, for example, that inflation is 4%. Given inflation inertia, this means that
the central bank is faced with the constraint of the Phillips curve shown by PC(π I = 4)
and can only choose between points along it. The bull’s eye is no longer obtainable.
The central bank faces a trade-off: if the central bank wants a level of output of y = ye
next period, then it has to accept an inflation rate above its target, i.e. π = 4 = π T
(i.e. point A). On the other hand, if it wishes to hit the inflation target next period, it must
accept a much lower level of output next period (point C). Point A corresponds to a fully
accommodating monetary policy in which the objective is purely to hit the output target
(β = 0), and point C corresponds to a completely non-accommodating policy, in which
the objective is purely to hit the inflation target (β = ∞).
   In fact, as will be evident from Fig. 5.2, if the central bank is faced by π I = 4, then given
its preferences, it can do better (achieve a loss circle closer to B) than either point A or
point C. It minimizes its loss function by choosing point D, where the PC(π I = 4) line is
tangential to the indifference curve of the loss function closest to the bull’s eye. Thus if
π I = 4 it will choose an output level y1 which will in turn imply an inflation rate of 3%.


3.3 Deriving the monetary rule, MR
For simplicity, we use the form of the loss function in which β = 1 so that we have loss
circles as in Fig. 5.2 above. This implies:

                                        L = (y − ye )2 + (π − π T )2 .




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                                                                              MONETARY POLICY 145

                           p                          PC (p I = 4)
                                                                 PC (p I = 3)
                                                                      PC (p I = 2)

                           4

                                       D
                           3
                                           C
                                               B
                       p T= 2




                                                      MR

                                       y1 y2 ye                                y


Figure 5.3 Deriving the MR line


And using the simplest version of the Phillips curve in which α = 1 so that each PC has a
45◦ slope as in Fig. 5.2:

                                           π = π−1 + y − ye .

The geometry can be seen as follows: in Fig. 5.3, the points of tangency between successive
Phillips curves and the loss circles show the level of output that the central bank needs
to choose so as to minimize its loss at any given level of π−1 . Thus when π−1 = 3, its loss
is minimized at C; or when π−1 = 4 at D. Joining these points (D, C, B) produces the MR
line that we used in Chapter 3. We can see from Fig. 5.3 that a one unit rise in π−1 implies
a half unit fall in y, for example an increase in π−1 from 3% to 4% implies a fall in y from
y2 to y1 .
   We can derive the monetary rule explicitly as follows. By choosing y to minimize L we
can derive the optimal value of y for each value of π−1 . Substituting the Phillips curve
into L and minimizing with respect to y, we have:

                         ∂L
                            = 2(y − ye ) + 2(π−1 + (y − ye ) − π T ) = 0
                         ∂y
                                = (y − ye ) + (π−1 + (y − ye ) − π T ) = 0.

Since π = π−1 + y − ye ,

                                    ∂L
                                       = (y − ye ) + (π − π T ) = 0
                                    ∂y
                                        =⇒ (y − ye ) = −(π − π T ).                  (MR equation)

The monetary rule in the Phillips diagram shows the equilibrium for the central bank: it
shows the equilibrium relationship between the inflation rate chosen indirectly and the
level of output chosen directly by the central bank to maximize its utility (minimize its
loss) given its preferences and the constraints it faces.




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146 THE MACROECONOMIC MODEL

                                   p
                                                               PC (p I = 4)
                                                                          PC (p I = 3)
                                                                               PC (p I = 2)

                                   4


                                   3
                                        D
                                                C     B
                              p T= 2
                                                                                  MR
                                                                                  b>1

                                            a
                                                          ye                                  y


Figure 5.4 Inflation-averse government: flat MR line
Note: The angle marked α in the diagram is in fact the angle whose tangent is α. We adopt this convention throughout.



  This shows the monetary rule as an inverse relation between π and y with a negative 45◦
slope (Fig. 5.3). Specifically, it shows that the central bank must reduce aggregate demand
and output, y, below ye so as to reduce π below π T by the same percentage. Thus this could
be thought of as monetary policy halfway between: (i) completely non-accommodating
when the central bank cuts output sufficiently to bring inflation straight back to π T at the
cost of a sharp rise in unemployment; and (ii) a completely accommodating one, which
leaves inflation (and output) unchanged. If the monetary rule was flat at π T we would
have a completely non-accommodating monetary policy; if it was vertical at ye , we would
have a completely accommodating monetary policy.
  The monetary rule ends up exactly halfway between an accommodating and a non-
accommodating policy because of two simplifying assumptions. By relaxing these, we
learn what it is that determines the slope of the monetary rule. We shall see that the
more inflation averse is the central bank (the flatter are the loss ellipses) and the more
responsive are wages to employment (the steeper are the Phillips curves), the flatter is the
MR line.
  The degree of inflation aversion of the central bank is captured by β in the central
bank loss function: L = (y − ye )2 + β(π − π T )2 . If β > 1, the central bank attaches
more importance to the inflation target than to the output target. This results in a flatter
monetary rule as shown in Fig. 5.4. Given these preferences, any inflation shock that
shifts the Phillips curve upward implies that the optimal position for the central bank will
involve a more significant output reduction and hence a sharper cut in inflation along
that Phillips curve than in the neutral case. Using the same reasoning, β < 1 implies that
the monetary rule is steeper than the minus 45◦ line.
  The second factor that determines the slope of the monetary rule is the responsiveness
of inflation to output (i.e. the slope of the Phillips curve): π − π−1 = α(y − ye ). This factor
was not discussed in Chapter 3. Thus far, we have assumed α = 1. Intuitively if α > 1
so the Phillips curves are steeper, any given cut in output has a greater effect in reducing
inflation than when α = 1. As we can see from Fig. 5.5, this makes the MR line flatter than




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                                                                                   MONETARY POLICY 147

                                p




                                4


                                3
                                     D            B
                           p T= 2         C

                                                                     MR1
                                                                     a>1
                                      a=1                    MR0
                                              a>1            a=1
                                                ye                                  y


Figure 5.5 High responsiveness of inflation to output: flat MR line



in the case in which α = 1: MR0 is the old and MR1 the new monetary rule line obtained
by joining up the points D, C, and B.
  By altering the slope of the Phillips curve, we also learn more about the monetary rule.
Steeper Phillips curves make the MR line flatter: let us now compare the response of a
central bank to a given rise in inflation in the case where the Phillips curves are steep with
the case where they have a slope of one. Our intuition tells us that steeper Phillips curves
make things easier for the central bank since a smaller rise in unemployment (fall in
output) is required to achieve any desired fall in inflation. Let us show this in a diagram.
In the left hand panel of Fig. 5.6 we compare two economies, one with flatter Phillips
curves (dashed) and one with steeper ones. As we have already shown, the MR line is
flatter for the economy with steeper Phillips curves: this is MR1 . Suppose there is a rise in
inflation in each economy that shifts the Phillips curves up: each economy is at point B.
We can see that a smaller cut in aggregate demand is optimal in the economy with the
steeper Phillips curves (point D). This reflects our intuitive argument above.9
  In the right hand panel, we compare two economies with identical supply sides but
in which one has an inflation-averse central bank (the oval-shaped indifference ellipse)
and show the central bank’s reaction to inflation at point B. The more inflation-averse
central bank always responds to this shock by cutting aggregate demand (and output)
more (point D).
  Having seen the role of the slope of the Phillips curve and of the central bank’s prefer-
ences in the diagrams, we now derive the more general form of the central bank’s mon-
etary rule as follows. We also make explicit the timing structure in all of the equations.
By choosing the interest rate in period zero, the central bank affects output and inflation
in period 1. We assume it is only concerned with what happens in period 1. This is the
reason that its loss function is defined in terms of y1 and π1 . If we let β and α take any

  9
      For those who are curious, with β ≥ 1, the output cut in response to a given inflation shock is always less
                                                                                            1
when α > 1 as compared with α = 1. For β < 1, the output cut is less as long as α > (1/β) 2 .




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148 THE MACROECONOMIC MODEL


              p                                           p



              4                 B                         4              B

                                                                   C
                      C
              3                                           3    D

                          D
          p T= 2

                                                  MR1                                      MR1
                                            MR0
                                                                                   MR0

                                 ye           y                           ye           y
                   a. Steeper Phillips curves                 b. Greater inflation-aversion


Figure 5.6 Comparing the response of the central bank in two cases: steeper Phillips curves and a more
inflation-averse central bank


positive values, the central bank chooses y to minimize


                                      L = (y1 − ye )2 + β(π1 − π T )2                            (5.2)


subject to


                                          π1 = π0 + α(y1 − ye ).                                 (5.3)


By substituting (5.3) into (5.2) and differentiating with respect to y1 (since this is the
variable the central bank can control via its choice of the interest rate), we have:

                          ∂L
                               = (y1 − ye ) + αβ(π0 + α(y1 − ye ) − π T ) = 0.                   (5.4)
                          ∂ y1

Substituting equation (5.3) back into equation (5.4) gives:


                          (y1 − ye ) = −αβ(π1 − π T ).                          (monetary rule, MR)


Now it can be seen directly that the larger is α (i.e. the more responsive are wages to
employment) or the larger is β (i.e. the more inflation averse is the central bank), the
flatter will be the slope of the monetary rule. In the first case this is because any reduction
in aggregate demand achieves a bigger cut in inflation, i.e. whatever its preferences, the
central bank gets a ‘bigger bang (i.e. fall in inflation) for its buck (i.e. fall in aggregate
demand)’. In the second case, this is because, whatever the labour market it faces, a more
inflation-averse central bank will wish to reduce inflation by more than a less ‘hard-
nosed’ one.




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3.4 Using the IS-PC-MR graphical model
By making explicit the determinants of the slope of the MR line, the role of each of the
six key inputs to the deliberations of the central bank is now clear.


(1) the central bank’s inflation target, π T : this affects the position of the MR line;
(2) the central bank’s preferences, β : this determines the shape of the loss ellipses and
    affects the slope of the MR line;
(3) the slope of the Phillips curve, α: this also affects the slope of the MR line;
(4) the interest sensitivity of aggregate demand, a: this determines the slope of the IS
    curve;
(5) the equilibrium level of output, ye : this determines the position of the vertical
    Phillips curve and affects the position of the MR line;
(6) the stabilizing interest rate, rS : the central bank adjusts the interest rate relative to rS
    so it must always analyse whether this has shifted, e.g. as a result of a shift in the IS or
    due to a change in the equilibrium level of output, ye .


   On the basis of the more detailed discussion provided in this chapter, the IS-PC-MR
graphical model can be used to analyse a wide variety of problems. In Chapters 3 and 4,
the graphical analysis of inflation shocks, temporary and permanent aggregate demand
shocks, and supply-side shocks is provided. In each case, the role of the six inputs to
the central bank’s decision can be analysed and experiments undertaken to evaluate the
impact of variations in them.
   We take one of those examples in order to clarify in the diagram each input to the central
bank’s decision and to highlight the role played by the lag in the effect of monetary policy
on aggregate demand and output. The example shows that the central bank is engaged
in a forecasting exercise: it must forecast next period’s Phillips curve and next period’s IS
curve. We assume that the economy starts off with output at equilibrium and inflation
at the target rate of 2% as shown in Fig. 5.7. We take a permanent positive aggregate
demand shock such as improved buoyancy of consumer expectations: the IS moves to
IS . The consequence of output above ye is that inflation will rise above target—in this
case to 4%. This defines next period’s Phillips curve (PC(π I = 4)) along which the central
bank must choose its preferred point: point C. The central bank forecasts that the IS curve
is IS , i.e. it judges that this is a permanent shock and by going vertically up to point C in
the IS diagram, it can work out that the appropriate interest rate to set is r . As the Phillips
curve shifts down with falling inflation, the central bank reduces the interest rate and the
economy moves down the MR line to point Z and down the IS curve to Z .
   This example highlights the role of the stabilizing real interest rate, rS : following the
shift in the IS curve, there is a new stabilizing interest rate and, in order to reduce inflation,
the interest rate must be raised above the new rS , i.e. to r . To summarize, the rise in
output builds a rise in inflation above target into the economy. Because of inflation
inertia, this can only be eliminated by pushing output below and (unemployment above)
the equilibrium. The graphical presentation emphasizes that the central bank raises the
interest rate in response to the aggregate demand shock because it can work out the




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150 THE MACROECONOMIC MODEL


                     r
                                      C
                     r
                     rS                      Z
                             a

                                             A                         B
                     rS


                                                                                      IS



                                                                                 IS




                     p                    VPC
                                                        PC (p I = 4)
                                                                        PC (p I =2)
                         4
                                                                       B


                                   C


                 pT= 2                           A, Z


                                                                MR

                                  a                 1/ab
                                            ye                         y    y


Figure 5.7 Permanent IS shock



consequences for inflation. The diagram highlights how the parameters a, α, and β affect
the central bank’s calculation of the required change in the interest rate.
   The central bank is forward looking and takes all available information into account:
its ability to control the economy is limited by the presence of inflation inertia i.e. lagged
inflation in the Phillips curve and by the time lag for a change in the interest rate to take
effect i.e. the lagged interest rate in the IS curve. In the IS equation it is the interest rate
at time zero that affects output at time one: y1 − ye = −a(r0 − rS ). This is because it takes
time for a change in the interest rate to feed through to consumption and investment
decisions. In Fig. 5.7 in order to choose its optimal point C on the Phillips curve (π I = 4),
the central bank must set the interest rate now at r . As is clear from the diagram, we have
been working with this assumption throughout. However, it is interesting to see what
happens if the central bank could affect output immediately, i.e. if y0 − ye = −a(r0 − rS ).
In this case, as soon as the IS shock is diagnosed, the central bank would raise the interest
rate to rS . The economy then goes directly from A to Z in the IS diagram and it remains at
A in the Phillips diagram, i.e. points A and Z coincide. Since the aggregate demand shock




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                                                                    MONETARY POLICY 151


is fully and immediately offset by the change in the interest rate, there is no chance for
inflation to rise. This underlines the crucial role of lags and hence of forecasting for the
central bank: the more timely and accurate are forecasts of shifts in aggregate demand
(and of other kinds of shock), the greater is the chance that the central bank can offset
them and limit their impact on inflation. Once inflation has been affected, the presence
of inflation inertia means that the central bank must change the interest rate and get the
economy onto the MR line in order to steer it back to the inflation target.
   In addition to providing a framework for a systematic analysis of shocks to an individual
economy and how aspects of the aggregate demand and supply-side structures affect
central bank policy, the IS-PC-MR graphical model provides a useful way to investigate
how a common currency area works, i.e. when different economies share a central bank.
As an example, we can compare two economies with the same supply side (i.e. ye and α
are the same) and a common central bank (i.e. π T and β are the same), but which differ
in the interest sensitivity of expenditure (a is different) and which are both initially in
equilibrium with constant inflation (with r = rS ). If both economies are subjected to
the same shock to autonomous demand, we can analyse the consequences using the
graphical 3-equation model (see Fig. 17.15).
   As a second example, we could look at the implications for two economies in a currency
union that are identical in all respects except for the responsiveness of inflation to changes
in the level of output, e.g. one economy has a steep WS curve and therefore steep Phillips
curves (high α) whereas the other has flat Phillips curves. If a common inflation shock
affects both economies, how would the optimal response of a national central bank differ
from that of a central bank that sets a common interest rate for both economies? Examples
of this kind are discussed further in Chapter 17.




4 A Taylor Rule in the IS-PC-MR model

4.1 Interest rate rules
In the previous section, we looked at how the IS curve is used by the central bank to
find out what interest rate to set once it has worked out its optimal output-inflation
combination in the Phillips diagram, i.e. once it has located the best available position
on the MR line. We now show how to derive an interest rate rule, which directly expresses
the change in the interest rate in terms of the current state of the economy. We then show
how it relates to the famous Taylor Rule.
  We bring together the three equations:

                                      π1 = π0 + α(y1 − ye )                 (Phillips curve)
                                  y1 − ye = −a(r0 − rS )                                 (IS)
                                              1
                                π1 − π T = −    (y1 − ye ).                            (MR)
                                             αβ

From these equations, we want to derive a formula for the interest rate, r0 in terms of
period zero observations of inflation and output in the economy. If we substitute for π1




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152 THE MACROECONOMIC MODEL


using the Phillips curve in the MR, we get

                                                       1
                            π0 + α(y1 − ye ) − π T = −   (y1 − ye )
                                                      αβ
                                                              1
                                          π0 − π T = − α +         (y1 − ye )
                                                             αβ

and if we now substitute for (y1 − ye ) using the IS, we get the interest-rate rule:

                                           1
                           r0 − rS =                 π0 − π T .                 (Interest rate rule)
                                                1
                                       a α+    αβ

We can see that            r0 − rS = 0.5 π0 − π T


if a = α = β = 1.
   Two things are immediately apparent: first, only the inflation and not the output devi-
ation is present in the rule and second, all the parameters of the 3-equation model matter
for the central bank’s response to a rise in inflation. If each parameter is equal to one, the
coefficient on the inflation deviation is one-half. If inflation is 1% point above the target,
then the interest rate rule says that the real interest rate needs to be 0.5 percentage points
higher. Since inflation is higher by 1% point, the nominal interest rate must be raised
by 1 + 0.5, i.e. by 1.5 percentage points in order to secure a rise in the real interest rate
of 0.5 percentage points. For a given deviation of inflation from target, and in each case,
comparing the situation with that in which a = α = β = 1, we can see that

• a more inflation-averse central bank (β > 1) will raise the interest rate by more;
• when the IS is flatter (a > 1), the central bank will raise the interest rate by less;
• when the Phillips curve is steeper (α > 1), the central bank will raise the interest rate
  by less.

  Let us compare the interest rate rule that we have derived from the 3-equation model
with the famous Taylor Rule,10


                         r0 − rS = 0.5.(π0 − π T ) + 0.5.(y0 − ye ),                 (Taylor Rule)


where π T is the central bank’s inflation target, ye is the equilibrium level of output, and rS
is the ‘stabilizing’ interest rate, i.e. the real interest rate on the IS curve when output is at
equilibrium. The Taylor Rule states that if output is 1% above equilibrium and inflation
is at the target, the central bank should raise the interest rate by 0.5 percentage points
relative to stabilizing interest rate. As above we interpret the difference between y and
ye as the percentage gap; this is the equivalent of defining y as the log of output. And if
inflation is 1% point above the target and output is at equilibrium, then the Taylor rule
says that the real interest rate needs to be 0.5 percentage points higher.

 10
      Taylor (1993).




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                                                                             MONETARY POLICY 153




4.2 Interest rate rules and lags
The interest rate rule derived from the 3-equation model is similar to Taylor’s rule, which
he developed as an empirical description of how central banks behaved. However, it only
requires the central bank to respond to inflation. At first sight, this seems paradoxical,
given that the central bank cares about both inflation and output as demonstrated by its
loss function (equation 5.2).
   It turns out that to get an interest rate rule that is like the Taylor rule in which both the
inflation and output deviations are present, we need to modify the 3-equation model to
bring the lag structure closer to that of a real economy. In this section, we explain how
this is done. However, for most purposes, the analysis of shocks and policy responses can
be conducted with the simpler single lag model, which we keep as our core 3-equation
IS-PC-MR model in the remainder of the book.
   As before we assume that there is no observational time lag for the monetary author-
ities, i.e. the central bank can set the interest rate (r0 ) as soon as it observes current data
(π0 and y0 ). We continue to assume that the interest rate only has an effect on output next
period, i.e. r0 affects y1 . The new assumption about timing that is required is that it takes
a year for output to affect inflation, i.e. the output level y1 affects inflation a period later,
π2 . This means that it is y0 and not y1 that is in the Phillips curve for π1 .11 The ‘double lag’
timing assumptions match the view of the Bank of England (1999):

The empirical evidence is that on average it takes up to about one year in this and other industrial
economies for the response to a monetary policy change to have its peak effect on demand and
production, and that it takes up to a further year for these activity changes to have their fullest
impact on the inflation rate.

   The double lag structure is shown in Fig. 5.8 and emphasizes that a decision taken
today by the central bank to react to a shock will only affect the inflation rate two periods
later, i.e. π2 . When the economy is disturbed in the current period (period zero), the
central bank looks ahead to the implications for inflation and sets the interest rate so
as to determine y1 , which in turn determines the desired value of π2 . As the diagram
illustrates, action by the central bank in the current period has no effect on output or
inflation in the current period or on inflation in a year’s time. Since the central bank can
only choose y1 and π2 by its interest rate decision, its loss function is

                                   L = (y1 − ye )2 + β(π2 − π T )2 .

  Given the double lag, the three equations are:

                                           π1 = π0 + α(y0 − ye )                      (Phillips curve)
                                      y1 − ye = −a(r0 − rS )                                        (IS)
                                                     1
                                     π2 − π T = −      (y1 − ye ).                                 (MR)
                                                    αβ

  11
     Three-equation models along these lines were developed by Svennson (1997) and Ball (1999b), and dis-
cussed in Romer (2001). See also Carlin and Soskice (2005).




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154 THE MACROECONOMIC MODEL

p0            y0            r0



p1            y1


                                                   Figure 5.8 Lag structure in the IS-PC-MR model
p2                                                 required to deliver a standard Taylor Rule




By repeating the same steps as above, we can derive the interest rate rule, which takes the
form of a Taylor rule:


                                    1
                    r0 − rS =                 π0 − π T + α(y0 − ye ) .
                                         1
                                a α+    αβ

            And r0 − rS = 0.5(π0 − π T ) + 0.5(y0 − ye )
                                               (Taylor rule in 3-equation (double lag) model)


if a = α = β = 1.
   We can also show how a Taylor Rule is derived geometrically from the IS-PC-MR model.
This helps bring out the role that differences in economic structure (demand and supply
sides) and in central bank preferences can have on the coefficients of Taylor Rules. In
Fig. 5.9, the initial observation of output and inflation in period zero is shown by the
large cross, ×. To work out what interest rate to set, the central bank notes that in the
following period, inflation will rise to π1 and output will still be at y0 since a change in
the interest rate can only affect y1 . The central bank therefore knows that the constraint
it faces is the PC(π1 ) and it chooses its best position on it to deliver π2 . The best position
on PC(π1 ) is shown by where the MR line crosses it. This means that output must be y1
and therefore that the central bank sets r0 in response to the initial information shown
by point ×. This emphasizes that the central bank must forecast a further period ahead
in the double lag model in order to locate the appropriate Phillips curve, and hence to
determine its optimal interest rate choice for today: it chooses r0 → y1 → π2 . Once the
economy is on the MR line, the central bank continues to adjust the interest rate to guide
the economy along the MR back to equilibrium.
   The remaining task is to give a geometric presentation of the double lag model and the
associated Taylor Rule: rt − rS = 0.5 · (πt − π T ) + 0.5 · (yt − ye ). Fig. 5.10 shows the example
in Fig. 5.9 again. As shown in the left hand panel of Fig. 5.10, the two components of the
Taylor Rule are shown by the vertical distances equal to α(y0 − ye ) and π0 − π T , where α is
the slope of the Phillips curve. If these are added together, we have the forecast of π1 − π T .
Just one more step is needed to express this forecast in terms of (r0 − rS ) and therefore to
deliver a Taylor Rule. As shown in the right hand panel of Fig. 5.10, the vertical distance
π1 − π T can also be expressed as (α + γ) · a(r0 − rS ), where α and γ = αβ reflect the slopes
                                                                                  1

of the Phillips curve and the monetary rule curve, respectively and a reflects the slope of




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                                                                                      MONETARY POLICY 155


             r


             r0


             r1

             rS



                                                                                 IS




                                                                    PC (p1)                      y
             p
                                                                              PC (p0)
             p1



             p0


             p2


             p3

             pT

                                            PC (p2 )                        MR


                                       y1              y2    ye        y0                            y


Figure 5.9 Taylor Rule example


the IS curve.12 Thus, we have

                              (α + γ) · a(r0 − rS ) = (π0 − π T ) + α(y0 − ye )

and by rearranging to write this in terms of the interest rate, we have a Taylor Rule:

                                                1
                             r 0 − rS =                     π0 − π T + α(y0 − ye )
                                             (α + γ)a
                                       = 0.5 · (π0 − π T ) + 0.5 · (y0 − ye )

if α = γ = a = 1.

  12
       Note that in the diagram, a, α, and γ refer to the angles shown and in the algebra to the gradients i.e. to
the tangents of the relevant angles.




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156 THE MACROECONOMIC MODEL

 r                                                              r

 r0                                                             r0
                  a                                                            a


 rS                                                             rS


                                                 IS                                                         IS
                      a (r0–rS)                                                    a (r0–rS)

                                       PC (p1)              y                                       PC (p1)
 p                                                              p
                                                 PC (p0)                                                  PC (p0)
 p1                                                             p1
                                       a
                                                 a(y0–ye)
          MR                                                         MR                                    aa (r0–rS)
 p0                                                             p0

 p2                                                             p2
                                                                                   a
                                                 (p0–pT)
                                                                                    g
                                                                                                           ga (r0–rS)

 pT                                                             pT
                      a (r0–rS)                                                    a (r0–rS)

                y1                ye       y0               y             y1                   ye                y



Figure 5.10 Deriving the Taylor Rule


   One striking aspect of this discussion is that it helps to dispel a common confusion
about Taylor Rules. It is often said that the relative weights on output and inflation in
a Taylor Rule indicate the central bank’s preferences for reducing inflation as compared
to output deviations. However, we have already seen that in the single lag model, the
interest rate rule only has the inflation deviation in it in spite of the fact that the loss
function places weight on both inflation and output deviations: the degree of inflation
aversion affects the size of the aggregate demand (and hence the interest rate) response
of the central bank.
   Once we modify the model to reflect the fact that a change in output takes a year to
affect inflation (the double lag model), then both the inflation and output deviations
appear in the interest rate rule and it resembles Taylor’s Rule. The reason is that the
current period output deviation serves as a means of forecasting future inflation to which
the central bank will want to react now. The central bank’s aversion to inflation affects
its reaction to inflation and to the forecast of inflation contained in the output deviation
term: it does not affect the relative weight on the inflation and output terms in the Taylor
Rule. The relative weights on inflation and output in our Taylor Rule depend only on α,
the slope of the Phillips curve, since the relative weights are used only to forecast next
period’s inflation.13
   It is the slope of the Phillips curves (α) that affect the relative weight on inflation
and output in the Taylor Rule. For α > 1, the Phillips curves are steeper and the MR
curve is flatter. There are two implications, which go in opposite directions. First, a more

     13
     Bean (1998) derives the optimal Taylor rule in a model similar to the IS-PC-MR model. However in his
model, the central bank’s preferences do affect the Taylor Rule weights. This arises from his inclusion of lagged
output in the IS equation: if the coefficient on lagged output is zero then the difference between the weight on
inflation and on output in the Taylor rule only depends on the slope of the Phillips curve and not on preferences.




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                                                                             MONETARY POLICY 157


restrictive interest rate reaction is optimal to deal with any given increase in output
because this will have a bigger effect on inflation than with α = 1 (the MR curve is flatter).
But on the other hand, a given rise in the interest rate will have a bigger negative effect on
inflation. These two effects imply that with α > 1, the balance between the coefficients
changes: the coefficient on (π0 − π T ) goes down—so the central bank reacts less to an
inflation shock whereas the coefficient on (y0 − ye ) goes up—the central bank reacts more
to an output shock as compared with the equal weights in the Taylor rule.
  We can see that Taylor’s weights of 0.5 and 0.5 on the inflation and output deviations
arise when the IS curve, the Phillips curves, and the MR curve all have a slope of one
(or more precisely in the case of the IS and the MR of minus one). This implies that the
appropriate coefficients on the Taylor rule form of the central bank’s monetary rule will
be different from (0.5, 0.5) if economies differ in

• the inflation aversion of the central bank,
• the supply-side structure as reflected in the slope of the Phillips curve, or
• in the interest-sensitivity of aggregate demand.




5 Problems with using an interest rate rule
The central bank may sometimes be thwarted in its attempt to use an interest rate rule
to stabilize the economy. One reason would be if investment or other components of
aggregate demand fail to respond or to respond enough to the change in the interest rate.
As we shall see in Chapter 7, empirical evidence for the impact of changes in the cost
of capital (of which the interest rate is a key component) relative to the expected rate of
return (measured for example by a change in Tobin’s q) is rather weak. Another reason
why the interest rate may fail to affect output in the desired manner arises from the fact
that the interest rate that is relevant to investment decisions is the long term real interest
rate. The central bank can affect the short-term nominal interest rate. As we know, the real
and the nominal interest rates differ by the expected rate of inflation. It remains to explain
how the short- and long-term interest rates are related. The relationship is referred to as
the term structure of interest rates. The long-term interest rate refers to the interest rate now
(i.e. at time t) on an n-year bond. We can express the long-term interest rate as follows:

                     in = 1/n · [i1 + i1+1|t + i1+2|t + · · · + i1+n−1|t ] + φnt .
                      t           t    t        t                t                          (5.5)

In words, this means the long-term interest rate (say, the interest rate on twenty-year
bonds) is equal to the average of the expected interest rate on one-year bonds for the next
twenty years plus the term φnt , which is called the ‘uncertainty premium’.
  In tranquil times, we would expect the long-term interest rate to exceed the short-term
rate by the uncertainty premium and we would expect short- and long-term interest rates
to move in the same direction. Monetary policy will then have the desired effect. As a
counter-example, consider the situation in which the central bank cuts the short-term
interest rate to stimulate the economy because it fears a recession is imminent. If the




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158 THE MACROECONOMIC MODEL


financial markets believe that the underlying cause of the recessionary threat is likely
to produce higher inflation in the long run, then markets will believe a higher long-run
real interest rate will be necessary. Higher long-term interest rates are likely to dampen
interest-sensitive spending at a time when the authorities are trying to stimulate the
economy.
   A third example of the limits to the use of monetary policy as a stabilization tool comes
from the fact that the nominal interest rate cannot be negative. The reason for this—
as we have seen—is that there is always the choice to hold cash with a zero nominal
return. Zero places a floor on the cuts in the nominal interest rate that are available.
Hence a problem can arise if the real interest rate required to stimulate activity in the
economy were negative. In a very low inflation economy, there is therefore limited scope
to use monetary policy to stimulate aggregate demand if the required real interest rate
is negative, e.g. with an inflation target of 2%, the zero floor to the nominal interest
rate means that real interest cannot be reduced below −2%. This is rather ironical—
the successful implementation of a stability-oriented monetary policy along the lines
outlined in this chapter may have the effect of producing an economy with low inflation
in which the scope of monetary policy to stimulate the economy if it is hit by a negative
shock is limited. We investigate the problem of a deflation trap below.
   To summarize, the reasons that monetary policy can fail to have its desired effect on
output include the following:

• investment is insensitive to the real interest rate;
• the long-run real interest rate does not move in line with changes in the short-term
  nominal interest rate;
• the central bank wishes to stimulate demand but the nominal interest rate is close to
  zero.


5.1 The deflation trap
The simplest way to see how a deflation trap may operate is to combine the fact that
the nominal interest rate cannot be negative with the fact that the real rate of interest is
approximately: r = i − π E . Since i ≥ 0, the minimum real rate of interest is min r = −π .
When inflation is positive, i.e. π > 0, this does not matter very much in general since
the minimum r is negative. But when π < 0 the minimum real rate is positive. The
problem that can arise is that the real rate needed to stabilize demand at ye is less than the
minimum feasible real rate, i.e. rs < min r (π) = −π . This condition is shown in Fig. 5.11
where the stabilizing real interest rate is below the minimum feasible rate of 1%. Given the
depressed state of aggregate demand depicted by the position of the IS curve, if inflation
has fallen to −1%, then it will be impossible to achieve the equilibrium level of output.
The approach to monetary policy described in this chapter of using the nominal interest
rate in order to set the real interest rate associated with aggregate demand at equilibrium
output then ceases to work.
  To see why, we assume the central bank sets the lowest real rate possible, namely r = −π ,
so that y = y0 and the economy is at at point A. Since y0 < ye , the consequence is that
inflation falls. That implies that the minimum real rate rises, further reducing output




                Keyn: “chap05” — 2005/11/22 — page 158 — #28
                                                                              MONETARY POLICY 159


 r




                               A         min r = –p
1
rS

                                              IS

                                                       Figure 5.11 The zero floor to the nominal
                               y0   ye             y
                                                       interest rate and the deflation trap


and hence increasing the speed at which inflation falls (in Fig. 5.11, the min r line shifts
upward). The economy is thus caught in a vicious circle or a deflation trap.
  It is clear from Fig. 5.11 that getting out of the deflation trap requires either

(1) a successful fiscal expansion or recovery of autonomous investment or consumption
    that shifts the IS curve to the right or
(2) the creation of more positive inflation expectations. If expected inflation becomes
    less negative, the min r line shifts down and the central bank can use the interest rate
    based monetary rule in the usual way to move the economy to the south-east along
    the IS curve.

  However, the idea of escaping from the deflation trap by creating positive inflation
expectations may not work in practice. Willem Buiter argues that this is ‘spitting in the
wind’ because as the announcement has no implications for any current or future mon-
etary policy instruments, it will not affect economic behaviour.14 Another way to put this
point is to say that the only way to create expectations of inflation in the future is to create
expectations of future higher aggregate demand: if the authorities do not take measures
to create the demand, it is no good hoping that people will expect higher inflation.
  He stresses however, that assiduously pursuing a target of low but positive inflation
may prevent the economy from getting into a deflation trap in the first place. Buiter
argues that a helicopter drop of money of the kind that Milton Friedman discussed—
but in a more practical form of, for example, issuing a cheque for every citizen financed
by the issue of new high-powered money—would certainly raise aggregate demand as it
would boost consumption spending (the IS curve would shift to the right). He points out
however that independent central banks may be reluctant to do this since it is a combined
fiscal and monetary policy measure (i.e. a fiscal transfer financed by new money creation).
This points to the important role of coordinated fiscal and monetary policy in solving
a deflation trap and to a largely unanticipated danger of creating independent central
banks.
  There is an additional channel through which a deflation trap can be sustained. Just as
unanticipated inflation shifts wealth from creditors to debtors in the economy as the real

     14
          See Buiter (2003).




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160 THE MACROECONOMIC MODEL


value of debts is eroded, unanticipated deflation has the opposite effect. If asset prices in
the economy (e.g. property prices) are falling as well as goods prices, then debtors in the
economy will not only find that the real burden of their debt is rising (the debt is fixed in
nominal terms but prices are falling) but also that the assets that they have used as security
or collateral for the debt are shrinking in value. This so-called balance sheet channel may
make investment less sensitive to changes in the real interest rate thereby steepening the
IS curve and weakening the investment response even if positive inflation expectations
could be generated. The situation is further complicated when deflation gets entrenched
because bankruptcies weaken the balance sheets of banks, threatening the stability of the
banking system. Alternatively, banks may continue to extend loans to failing firms so as
to prevent the bad loans from showing up on their balance sheets: this may postpone but
not prevent a banking crisis.




6 Credibility, time inconsistency, and rules versus
   discretion
6.1 Backward-looking Phillips curves and credibility
In the IS-PC-MR model, the Phillips curve is backward looking:

                                   π = π−1 + α.(y − ye ),

which means that current inflation is determined by lagged inflation (and the output
gap). This is consistent with the evidence that disinflation is costly, i.e. that in order to
reduce inflation, output must be reduced. Although the evidence on costly disinflation
discussed in section 1 indicates that reducing inflation from moderate levels appears to
require a sacrifice in terms of higher unemployment, it was noted in the discussion of
hyperinflation that relatively painless disinflation has been observed under some con-
ditions. The debate about how best to model the inflation process is a very lively one in
macroeconomic research at present and is discussed in detail in Chapter 15. The key point
to highlight here is that although the inertial or backward-looking Phillips curve matches
the empirical evidence concerning inflation persistence, it has a major shortcoming.
Because it rests on ad hoc assumptions–in particular about the inflation process–rather
than being derived from an optimizing micro model of wage or price setters’ behaviour,
it does not allow a role for ‘credibility’ in the way monetary policy affects outcomes.
   We can demonstrate the point using an example. In Fig. 5.12, we assume that the
central bank’s inflation target is 4% and the economy is initially at point A with high
but stable inflation of 4% (on PC(π I = 4)). The central bank now decides to reduce its
                             T
inflation target to 2%, i.e. π1 = 2%. With backward-looking Phillips curves, it is clear from
Fig. 5.12 that disinflation will be costly and following the announced change in inflation
target, unemployment first goes up (shown by point B). The economy then shifts only
gradually to the new equilibrium at Z as the central bank implements the monetary
rule. Whether or not the central bank’s decision is announced and if so whether it is




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                                                                                MONETARY POLICY 161

                    r




                                                 B9
                    r9
                                                      C9
                                                            A9, Z9
                    rS



                                                                           IS


                                                                                     y
                    p                                VPC
                                                                     PC (p I = 4)

                     5                                               PC (p I = 3)

                pT = 4
                 0                                         A
                                             B                       PC (p I = 2)
                     3
                                                 C
                pT = 2
                 1
                                                            Z

                     1
                                                                     MR
                     0
                                                       ye                            y


Figure 5.12 Central bank announces a new target: credibility and inertia


believed by the private sector makes no difference at all to the path of inflation. The
inflation that is built into the system takes time (with higher unemployment) to work
its way out. The inability of the model to take any account of the reaction of wage or
price setters to announced changes in monetary policy is unsatisfactory. We could make
a radically different assumption that incorporates rational expectations on the part of
wage and price setters, credibility, and the absence of nominal rigidities. In this case, the
announcement of a lower inflation target produces an immediate change in wage and
price setting so as to produce wage and price increases based on expected inflation of 2%
rather than on past inflation and the economy moves directly from A to Z without any
increase in unemployment. However, this too is unsatisfactory as the evidence suggests
that disinflation is indeed costly even when a lower inflation target is announced. As
discussed in Chapter 15, recent developments in modelling the Phillips curve aim to
provide a micro-optimizing based model that can produce both costly disinflation and a
role for the credibility of monetary policy.



6.2 Introducing inflation bias
In the IS-PC-MR model to this point, medium-run equilibrium is characterized by infla-
tion equal to the central bank’s inflation target and output at equilibrium (i.e. determined




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162 THE MACROECONOMIC MODEL


by the intersection of the WS and PS curves). However, since we have seen that imperfect
competition in product and labour markets implies that ye is less than the competitive
full-employment level, the government may have a higher target. We assume that the
government can impose this target on the central bank. How do things change if the cen-
tral bank’s target is full-employment output, or more generally a level of output above ye ?
  A starting point is to look at the central bank’s new objective function. It now wants to
minimize

                                  L = (y − y T )2 + β(π − π T )2 ,                       (5.6)

where y T > ye . This is subject as before to the Phillips curve,

                                      π = π−1 + α(y − ye ).                              (5.7)

In Fig. 5.13 the new indifference curves are shown. The central bank’s ideal point is now
point A (where y = y T and π = π T ) rather than where y = ye and π = π T (i.e. point C).
If we assume that α = β = 1 (for simplicity), then each indifference circle has its centre
at A. The whole set of loss circles have shifted to the right. Since nothing has changed on
the supply side of the economy, the Phillips curves remain unchanged.
   To work out the central bank’s monetary rule, consider the level of output it chooses
if π I = 2% Fig. 5.13 shows the Phillips curve corresponding to π I = 2%. The tangency
of PC(2) with the indifference circle shows where the central bank’s loss is minimized
(point D). Since the central bank’s monetary rule must also pass through A, it is the
downward-sloping line MR in Fig. 5.13.
   We can see immediately that the government’s target, point A, does not lie on the
Phillips curve for inertial inflation equal to the target rate of π T = 2%: the economy will
only be in equilibrium with constant inflation at point B. This is where the monetary
rule (MR) intersects the vertical Phillips curve at y = ye . At point B, inflation is above the
target: the target rate is 2% but inflation is 4%: this gap between the target rate of inflation
and inflation in the equilibrium is called the inflation bias.


                                  p                       PC (4)
                                             VPC
                                                             PC (3)

                                                                     PC (2)
                                  4                  B
                 inflation bias
                                  3                  D

                                               C               A
                            pT = 2



                                                                              MR

                                                ye            yT               y



Figure 5.13 The inflation bias




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                                                                                         MONETARY POLICY 163


   We shall now pin down the source of the inflation bias and the determinants of its
size. We begin by showing why the equilibrium is at point B. If inflation is initially at its
target rate of 2%, the central bank chooses its preferred point on the π I = 2% Phillips
curve and the economy is at D. But with output above equilibrium, inflation goes up to
3% and the Phillips curve shifts up (see Fig. 5.13). The process of adjustment continues
until point B: output is at the equilibrium and inflation does not change so the Phillips
curve remains fixed. Neither central bank nor wage setters have any incentive to change
their behaviour. The economy is in equilibrium. But neither inflation nor output are at
the central bank’s target levels (see Fig. 5.13).
   We can derive the same result mathematically and pin down the determinants of the
size of the inflation bias. Minimizing the central bank’s loss function—equation (5.6)—
subject to the Phillips curve—equation (5.7) implies

                   y − y T + αβ(π−1 + α(y − ye ) − π T ) = y − y T + αβ(π − π T )
                                                               = 0.

So the new monetary rule is:

                                         y − y T = −αβ(π − π T ).                                          (5.8)

This equation indeed goes through (π T , y T ). Since equilibrium requires that π−1 = π
when y = ye , we have

                          ye = y T − αβ(π−1 − π T )
                                                      (y T − ye )
                             ⇒ π = π−1 = π T +                    .                              (inflation bias)
                                                          αβ
                                                     inflation bias


                                                                      (y T −ye )
In equilibrium, inflation will exceed the target by                       αβ
                                                                                 .   This is called the inflation
      15                                                       T
bias. The significance of this result is that π > π whenever y T > ye . The steeper is the
central bank’s monetary rule (i.e. the less inflation averse it is), the greater will be the
inflation bias. A lower α also raises the inflation bias. A lower α implies that inflation is
less responsive to changes in output. Therefore, any given reduction in inflation is more
expensive in lost output; so, in cost-benefit terms for the central bank, it pays to allow a
little more inflation and a little less output loss. As we shall see in the next subsection, the
problem of inflation bias is usually discussed in conjunction with the problem of time
inconsistency in which the central bank or the government announces one policy but
has an incentive to do otherwise. For this kind of behaviour to arise, it is necessary to
introduce forward-looking inflation expectations.


6.3 Time inconsistency and inflation bias
We can link the problem of inflation bias to problems of credibility and time incon-
sistency by adopting a forward-looking Phillips curve. The simplest assumption to
 15
      For an early model of inflation bias with backward-looking inflation expectations, see Phelps (1967).




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164 THE MACROECONOMIC MODEL


make is that inflation expectations are formed rationally and that there is no inflation
inertia: i.e. π E = π + εt , where εt is a random disturbance. The intuition is that wage
setters know that whatever their expected rate of inflation, the condition for π E = π is
that y = ye . As we saw in Chapter 3, this is the so-called Lucas surprise supply equation,
which we reproduce here:

                        1
              yt − ye =     πt − πtE
                        α
                             1
                   yt = ye +     πt − πtE                  (Lucas surprise supply equation)
                             α
                                inflation surprise

                      = ye + ξt .

  We continue to assume that the central bank chooses y (and hence π ) after wage setters
have chosen π E . This defines the central bank as acting with discretion. Now, in order
for wage setters to have correct inflation expectations, they must choose π E such that it
pays the central bank to choose y = ye . That must be where the central bank’s monetary
rule cuts the y = ye vertical line, i.e. at point B in Fig. 5.13. Note that the positively
sloped lines are now interpreted as Lucas supply equations rather than as Phillips curves.
Inflation must be sufficiently high to remove the temptation of the central bank to raise
output toward its target. With π = 4% and y = ye , the temptation has been removed
because any increase in output from B would put the central bank on a loss circle more
distant from its bliss point A: wage and price setters rationally expect an inflation surprise
of 2% over and above the target inflation rate of 2%.
  The inflation bias presents a problem. As is clear from Fig. 5.13, the loss to the central
bank at B is greater than the loss to the central bank at C since output is the same but
inflation is higher at B. So the central bank would clearly be better off at C. Moreover,
wage setters would be just as happy at C as at B, since employment and the real wage are
the same in each case. What is to stop the central bank being at C? When wage and price
setters are forward looking, the problem is called that of time inconsistency. Although the
central bank claims to have an inflation target of π T , if wage setters act on the basis of
this target (2%), when it comes to act, the central bank does not choose the output level
consistent with its target. In short, at point B there is no incentive for the central bank to
cheat; whereas at point C, there is an incentive.



6.4 Solutions to the time-inconsistency problem
We have seen that the time-inconsistency problem arises under the following circum-
stances:

• the central bank or government has an over-ambitious output target (i.e. y T > ye )
• wage and price setters form their inflation expectations using rational expectations
• the central bank uses a rule-based reaction function but operates with discretion, i.e.
  chooses its desired level of aggregate demand after inflation expectations have been
  formed in the private sector.




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   There are three broad approaches to solving or mitigating the time-inconsistency
problem manifested in inflation bias, which are referred to as replacing discretion by
a rule; delegation; and reputation.



6.4.1 Replacing discretion by a rule: commitment
If the timing of the game between the central bank and private sector is changed so that
the central bank cannot choose the rate of inflation after wage and price setters have
formed their expectations, then the inflation bias disappears. This entails a structure
through which the central bank is prevented from optimizing after the private sector has
set wages and prices and is referred to as a policy of commitment rather than discretion.
A contract that costs the chairman of the central bank his or her job if inflation deviates
from the target is one possible method of enforcing this.



6.4.2 Delegation
                               (y T −y )
The inflation bias is equal to αβ e , and this may reflect a situation in which the gov-
ernment rather than the central bank controls monetary policy. The government could
reduce the inflation bias by transferring control of monetary policy to a central bank with
an output target closer to ye and with more inflation aversion (higher β ) than the govern-
ment’s. Since output in equilibrium is at y = ye , inflation would be brought closer to the
target and the government would be unambiguously better off if it delegates monetary
policy to an independent central bank.
   Fig. 5.14 illustrates the reduction in inflation bias through delegation of monetary
policy to the central bank. The flatter sloped monetary rule is that of the central bank,
MRCB , and the more steeply sloped that of the government, MRG . MRG evidently implies a
higher inflation bias with the equilibrium at point B. MRCB on the other hand implies that
equilibrium is at point A, with π = 3%. Wage and price setters rationally expect a smaller
inflation surprise when faced with an independent central bank than when faced by the
government. The reduction in the inflation bias is due to the flatter slope of the central
bank’s MR line and to the fact that central bank’s output target is closer to equilibrium
output than is the government’s.
   For delegation to produce a costless move from high to low inflation, there must be no
inflation inertia and expectations must be formed rationally. In this case, if wage setters
believe that the policy maker’s preferences have changed in the appropriate way, the
economy will shift directly down the vertical Phillips curve at ye from point B to the new
equilibrium with π = 3% at point A.
   One problem with this proposed solution is that if the government can delegate pow-
ers to the central bank, why can’t it take them back when it wants to? It would pay the
government to take back those powers at the moment that wage setters chose a low π E
corresponding to the loss function parameters of the central bank. For then the govern-
ment would be tempted to opt for a level of output greater than ye . This kind of reasoning
is sometimes used to explain why governments have often found it necessary to make
central banks constitutionally independent and why delegation is sometimes combined
with commitment devices like the one discussed in 6.4.1.




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166 THE MACROECONOMIC MODEL


                     VPC            PC (6)
                               B
             6
                                              PC (3)
             5     C
                                                     PC (2)

             4                                                     inflation bias: government

                           A
             3
                                                                   inflation bias: CB
        pT = 2



                                             MRCB        MRG

                               ye     yT
                                       CB           yT
                                                     G         y




Figure 5.14 Inflation bias: central bank and government


6.4.3 Reputation
A third solution to the problem of inflation bias lies with the government or central
bank building a reputation for being tough on inflation. Suppose that the government
has delegated monetary policy to the central bank but wage setters remain unsure of
just how independent the central bank is. They only know that there is a probability p
that the central bank is independent and a probability (1 − p) that it is a puppet of the
government. The only way that they can find out is by observing the decisions taken by
the central bank. If this is the case, how should the central bank behave? This problem
can be analysed in detail using game theory. This is done in Chapter 16. Here we simply
convey the flavour of the solution.
   The situation is one in which the central bank interacts with wage setters more than
once. Will a ‘weak’ central bank with an output target above the equilibrium find it
rational to behave as if it were tough—i.e. with an output target closer to the equilibrium?
If so, then we can say that it is possible to build a reputation for toughness as a method
of solving the inflation bias problem. Let us begin with the case in which the interaction
between the central bank and wage setters occurs twice: in period one, wage setters choose
  E
π1 with no knowledge of whether the central bank is weak or tough (but they know there
is a probability of p that it is tough); the central bank then chooses output in period one,
               E                                             E
y1 knowing π1 . In period two, the wage setters choose π2 knowing y1 ; the central bank
                               E
then chooses y2 knowing π2 .
   The result is that a weak central bank will choose to act like a tough one in the first
period, which will establish a low expected inflation rate in the second period, thereby




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                                                                               MONETARY POLICY 167


providing bigger gains from boosting output in the second period. The central bank
gains because in the first period, the outcome is inflation at its target (no inflation bias)
and output at the equilibrium (instead of the time inconsistency outcome of inflation
above the target and output at equilibrium) whilst in the second period, it can gain by
setting output above the equilibrium (i.e. by exploiting the short-run trade-off between
inflation and unemployment by a surprise increase in inflation). As discussed in detail in
Chapter 16, when the game is extended from two to many periods, the benefits to the
central bank from behaving as if it were tough increase. This is because the situation in
period one is repeated again and again until the last period. This type of model provides
an explanation for the process by which a reputation for toughness can be built in the
face of public scepticism.



6.5 Is y T > ye a good model of central bank behaviour?
We have seen that the inflation bias problem is eliminated if the objective of the govern-
ment or central bank is to stabilize the economy around the equilibrium level of output,
ye , i.e. when y T = ye rather than y T > ye . This is the case both when inflation expec-
tations are backward looking and when inflation expectations are rational. The central
bank objective of y T = ye is our benchmark model for monetary policy, introduced in
Chapter 3. We are then led to ask whether the assumption that y T > ye is a good way to
think about central bank behaviour. It offers insights when the central bank is susceptible
to pressure from a government, which in turn is tempted to run the economy at unem-
ployment below the equilibrium. However, in many OECD economies, this is not the key
problem for central banks, which in most cases are independent from government and
are run by officials motivated by concern about their professional reputations. This point
is summarized neatly by Peter Howitt:

The ‘temptation’ to raise the level of economic activity with some surprise inflation might exist
if society were indeed locked into expectations. In reality, however, the temptation just doesn’t
arise, as practitioners of central banking have long maintained. Central bankers are keenly aware
that although there are long and variable lags between monetary stimulus and any resulting
rise in the level of economic activity, there are no lags at all between such stimulus and the
currency depreciation and capital flight that will occur if the stimulus is taken by investors as
a signal of future weakness in the currency. Because of this, there is no reason for believing that
discretionary central banks have the inflationary bias that the game-theoretic [time-inconsistency]
view attributes to them. . . .
   [R]esponsible people entrusted with such important and delicate jobs as the management of
a country’s central bank are typically motivated by the desire to be seen as having done a good
job, to have acquitted themselves well. They pursue this objective by doing everything possible to
avoid major inflations, financial panics and runs on the currency, while carrying out the day to
day job of making available the base money needed for the financial system to function.16


  16
       Howitt (2001). Howitt refers to the useful paper by Mervyn King, then Deputy Governor of the Bank of
England; from 2003, Governor of the Bank of England: King (1997). Another useful source is the short book
of three lectures by Alan Blinder reflecting on how he used academic research when he was a Governor of the
Federal Reserve Board: Blinder (1998).




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168 THE MACROECONOMIC MODEL


6.6 Rules and expectations versus discretion and learning
We now return to the case in which there is no inflation bias and to our broader usage
of the distinction between monetary rules and discretion. The broader usage is needed
because the real-world examples of inflation-targeting central banks embody rule-based
behaviour as summarized in a monetary reaction function, which nevertheless entails
discretion in the time-inconsistency sense. We ask whether there are any gains from a
framework of a clearly defined public monetary policy rule with an explicit inflation
target as is the case for the Bank of England or the European Central Bank as com-
pared with a framework of so-called ‘constrained discretion’ as characterizes the Federal
Reserve of the USA. In practice, we observe a wide spectrum of arrangements for mone-
tary policy amongst central banks. The USA under Alan Greenspan is the most famous
case of a central bank operating constitutionally with discretion. Yet many articles have
been written suggesting that the Fed has covertly been following an inflation-targeting
rule.17 This suggests that in practice there is not a sharp distinction amongst inflation-
targeting regimes but rather some difference in emphasis on rules as compared with
discretion.
   It seems clear that there are gains from the operation of a widely understood and trans-
parent process of monetary policy making. This suggests that providing information
about the monetary policy reaction function is likely to be useful.18 The main gain arises
because economic agents are at least in part forward looking and will therefore anticipate
the reaction of the central bank to a shock. If the reaction function is well understood,
anticipation by the private sector may help to stabilize the economy’s response to a
shock.
   For example, if we think of a negative aggregate demand shock, then the monetary pol-
icy reaction function indicates that interest rates will be lowered. The knowledge of this
reaction will influence the expected future path of interest rates, which will help shift
the long-term interest rate downwards—the rate relevant for interest-sensitive spend-
ing. Asset prices such as share prices or house prices may react rapidly to the expected
path of interest rates and reinforce the efforts of the central bank to boost demand.
In our example, the expectation of a lengthy period of low interest rates would tend
to boost asset prices immediately (e.g. share prices and house prices). In turn as we
shall see in Chapter 7, this raises Tobin’s Q and permanent income and would there-
fore tend to raise investment and consumption, reinforcing the recovery of aggregate
demand.
   On the other hand, too great an emphasis on rules may take attention away from
the benefits that can arise from a central bank that sees itself as actively learning about
the economy and engaging in experiments—for example, to try to discover the equi-
librium level of unemployment in an economy experiencing a burst of technological
progress.



  17
       For example, see the discussion in Mankiw (2002).
  18
       Recent research suggests that adopting an inflation-targeting regime with an explicit inflation target
improves macroeconomic performance in terms of both inflation and output stability by anchoring the public’s
inflation expectations to the central bank’s objectives. For example, Orphanides and Williams (2005).




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7 Conclusions

In this chapter, we have put the spotlight on monetary policy. The starting point was an
examination of the phenomena of inflation, disinflation, and deflation, which was moti-
vated by the question of why low and stable inflation is considered a desirable objective
by policy makers. We examined the reasons behind episodes of rising inflation and the
unsustainability of attempts to hold output above the equilibrium level. A falling general
price level (deflation) is likely to bring dangers to macroeconomic stability.
   We highlighted the difference between two monetary policy paradigms—the LM
paradigm and the MR paradigm. In the LM paradigm, monetary policy is passive and
the money supply growth rate determines the rate of inflation in the medium-run equi-
librium. By contrast, in the MR paradigm, the central bank is active. It adjusts the interest
rate so as to steer the economy back to target inflation at equilibrium output. The rate of
inflation at medium-run equilibrium is therefore determined by policy. Since the nomi-
nal interest rate cannot be negative, monetary policy will become ineffective at very low
or negative rates of inflation.
   A systematic approach to monetary policy within the MR paradigm can be modelled
by specifying the objectives of the central bank (or the government) and identifying the
constraints it faces. The objective of the central bank is to minimize the extent to which
the economy diverges from a target rate of inflation and from a target level of output. We
have shown that

• when the output target is the equilibrium level of output, ye , a monetary policy reaction
  function will enable the central bank to steer the economy to its inflation and output
  targets if the economy experiences an inflation, aggregate demand, or supply shock.
• The central bank will do this by adjusting the nominal interest rate so as to affect
  the real interest rate and the level of aggregate demand and output. The appropriate
  change in the real interest rate will depend on whether the stabilizing real interest rate
  has changed and on the interest sensitivity of aggregate demand (the slope of the IS),
  how inflation averse the central bank is, and the response of inflation to changes in
  unemployment (the slope of the Phillips curve).
• We have shown how to derive an interest rate rule from the 3-equation model. This
  takes the form of a Taylor Rule in which the central bank adjusts the interest rate in
  response to observed deviations of inflation from target and of output from equilibrium
  when the economy is characterized by a lag in the effect of the interest rate on output
  and a lag in the effect of a change in output on inflation. If output affects inflation
  in the same period, then the interest rate rule only has the inflation term in it. This
  highlights the fact that the coefficients on inflation and output in the Taylor rule are
  not the weights on inflation and output in the central bank’s loss function.
• With a purely backward-looking Phillips curve, disinflation is always costly and that
  cost is not affected by the degree to which central bank announcements are believed.
• When the output target is above the equilibrium level of output, the central bank will
  not be able to achieve its inflation target in equilibrium. There will be an inflation bias.




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170 THE MACROECONOMIC MODEL


   We clarify the debate about rules versus discretion by explaining that the superior-
ity of a rule that prevents the central bank from optimizing rests on the specification
of the central bank’s loss function. If the central bank targets a level of employment above
the equilibrium, an inflation bias arises. When expectations are rational, this creates the
time-inconsistency problem. By contrast, in our baseline case, which it is argued matches
that of central banks in many countries, the objective is to stabilize the economy around
equilibrium output, which eliminates the inflation bias. A fuller understanding by the
public of the monetary reaction function can help to stabilize forward-looking expec-
tations and facilitate the movement of asset prices consistent with the central bank’s
stabilization objectives.



s QUESTIONS
Checklist questions

  (1)   ‘If the economy has high but stable inflation, the government has much to lose and
        little to gain by reducing inflation to a low rate.’ Explain and assess this statement.
  (2)   What are the advantages and disadvantages of an inflation rate of 3% as compared
        with one of 0% per annum? Would you advocate the replacement of the inflation
        target by a price level target?
  (3)   Explain what is meant by the central bank’s loss function. How are the central bank’s
        preferences reflected in the loss function? Use a numerical example and diagrams to
        explain how the central bank’s preferences affect its reaction to a negative aggregate
        demand shock.
  (4)   How can the central bank diagnose what kind of shock has disturbed the economy?
  (5)   Compare the response of an inflation-targeting central bank to a permanent negative
        aggregate supply shock with that to a permanent negative aggregate demand shock.
  (6)   Suppose there are two regions of the country, in one of which the WS curve is quite
        steep and in the other, the WS is quite flat. Why might this be so? Compare the
        implications for inflation and unemployment of a common positive temporary
        aggregate demand shock. How should the central bank respond?
  (7)   If a central bank adopts an interest-rate based monetary policy rule like a Taylor Rule
        rather than a monetary growth rate rule, what would you expect to happen to the
        money supply?
  (8)   In implementing a Taylor-type interest rate rule, does the central bank need to know
        anything more than the coefficients in the rule, its inflation target, and current
        output and inflation?
  (9)   Write down the Taylor Rule in terms of the real interest rate. Holding the output gap
        constant, does a rise in inflation by x percentage points call for a rise in the nominal
        interest rate by more than, less than, or by just x percentage points? Explain.
(10)    Under what circumstances will a central bank utilizing an interest rate based
        monetary rule to stabilize the economy fail in its objective of raising output?




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                                                                        MONETARY POLICY 171


(11)   The central bank faces a short-run trade-off between inflation and unemployment
       (a) if inflation expectations are backward looking or (b) if inflation expectations are
       rational but are formed before the central bank chooses its optimal inflation-output
       pair. Explain each of these cases. What difference does it make whether (a) or (b)
       holds?
(12)   Explain what is meant by the statement that a government that is determined to
       reduce inflation may have a problem in achieving this outcome because of a lack of
       credibility.


Problems and questions for discussion
QUESTION A. What are the incentives for a policy maker to exploit the short-run
trade-off between unemployment and inflation? What are the consequences? Is this a
good description of contemporary central bankers? Use official reports of a central bank
of your choice to provide support for your argument.
QUESTION B. Consider a Central Bank that maximizes the following utility function:

                                    Z = k(y − ye ) − (π − π T )2

where k is a positive constant. Its policy instrument is the growth rate of the money
supply, γM . Assume that the inflation target is π T = 0. Explain this utility function and
compare it with the loss function used in the chapter. (Hint: focus on how the central
bank’s utility rises with output. Is this central bank ‘overambitious’?) Now assume that
the central bank sets the money supply growth rate after economic agents have
incorporated their expectations about inflation into their decision making, and thus
faces a Phillips curve:

                                        π = π E + α(y − ye ).

(a) Assuming that agents have rational expectations, solve algebraically for the optimal
    inflation rate under discretion, i.e. find the inflation rate that the central bank will
    choose using its monetary policy instrument, γM . (Hint: maximize utility with
    respect to γM , having used the Phillips curve to substitute for y in the utility
    function; and used γM = π to substitute for π .)
(b) Suppose that, before private sector inflation expectations were formed, the central
    bank could commit to a particular rate of inflation. What would that rate be? Discuss.
(c) Now return to the case of discretion, and suppose that we extend the model to cover
    two periods. In other words, the central bank now cares about the sum of its loss
    functions in each period, i.e.

                                                        2                              2
            Total utility = k(y1 − ye ) − π1 − π T          + k(y2 − ye ) − π2 − π T


    where the subscripts indicate the period.




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172 THE MACROECONOMIC MODEL


  Suppose also that in the first period, agents expect no inflation (π E = 0), while when
the second period arrives agents expect that inflation will be equal to the rate that
                                                                        E
actually occurs in the first period (i.e. expectations are adaptive, so π2 = π1 ). What will
be the equilibrium rates of output and inflation in each period? Discuss your findings.
QUESTION C. Is there a trade-off between stabilizing inflation and stabilizing the real
side of the economy? Explain.
QUESTION D. Using Fig. 5.8 as a guide, draw the corresponding diagram to illustrate the
lag structure in the standard version of the 3-equation model. Now assume that there is
no lag between a change in the interest rate and its effect on output. Draw a diagram to
illustrate this lag structure. Use all three figures to provide a concise summary of the role
of lags in the operation of monetary policy. Go to the website of one of the central banks
listed in the next question (or another one of your choice) and find out their view about
the lags between a change in the interest rate and its effects on output and inflation. Do
they identify the same factors as responsible for the lags?
QUESTION E. Select two out of the following central banks: Bank of England, Reserve
Bank of New Zealand, Bank of Canada, and the Swedish Riksbank. Each of these central
banks has adopted explicit ‘inflation targeting’. For each of your chosen banks, find out
how it explains what this means to the public. How does it communicate and explain its
interest rate decisions to the public? Compare what each central bank did and how it
explained its actions following the events of 11 September 2001.




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