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Keyn: “chap05” — 2005/11/22 — page 131 — #1 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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Page 1: Carlin Chap05

Keyn: “chap05” — 2005/11/22 — page 131 — #1

5 Monetary Policy

The aim of this chapter is to set out in more detail the way that monetary policy has beenanalysed in recent years. The main idea is that central bank behaviour can be thoughtabout in terms of a ‘reaction function’ that the central bank uses to respond to shocks tothe 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 mediumrun, which is defined in terms of an inflation or price-level target. This pins down themedium-run inflation rate and to the extent that forward-looking expectations play arole, establishes a commitment to a low inflation environment.

• The second task of the reaction function is to provide guidance as to how the centralbank’s policy instrument, the interest rate, should be adjusted in response to differentshocks so that the medium-run objective of stable inflation is met while minimizingoutput fluctuations.

We show explicitly how this broad structure for monetary policy can be formalizedas an optimal monetary policy rule. By optimal monetary policy rule is meant that themonetary rule can be derived as the solution to the problem of the government or centralbank optimizing with respect to the constraints it faces from the private sector of theeconomy.

Over the course of the past two decades, central banks in the OECD economies andin many transition and developing countries have shifted toward inflation-targetingregimes of this broad type—or have done so indirectly by fixing their exchange rateto a country where the central bank uses such a framework. Before setting out the detailsof an inflation-targeting regime, it is necessary to clarify why low inflation-targets havebeen 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? Negativeinflation 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 theconsensus 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 andfor 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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132 THE MACROECONOMIC MODEL

target the inflation rate using an interest rate rule rather than targeting the growth of themoney supply. Section 3 sets out in detail the derivation of the central bank’s monetarypolicy rule that was introduced in Chapter 3: as the MR curve in the Phillips diagram andthe MR equation in the 3-equation model. Specifically, we shall see the role played by thefollowing 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 bederived from the 3-equation model. Section 5 steps back from the mechanics of interestrate based inflation targeting and investigates the problems with using such rules indealing with macroeconomic problems. In particular, the dangers posed by deflation areexplored.

For the bulk of the chapter, we describe monetary policy making assuming it is in thehands of the central bank. However, in section 6 we look at why it might matter whethermonetary policy decisions are actually made by the government and then implementedby 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 achievea 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 targetrate. This is called the inflation bias. We then show how inflation bias is related to theproblem of central bank credibility and the time inconsistency of policy. To do this weneed to introduce forward-looking inflation expectations. The delegation of monetarypolicy to an independent central bank is sometimes proposed as a method of reducingor eliminating the inflation bias. In this section, we explain that the debate about ‘rulesversus 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 ofconfusion in discussing how central banks behave.

In this chapter, we consider only a closed economy. The relationship between theexchange rate regime and monetary policy in the open economy is explained in Chapter 9and 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 ifthe 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 themoney supply set by the central bank.

• Because of delays in price and wage setting, inflation is persistent, which means thatlagged inflation affects current inflation and there will be a trade-off between inflationand unemployment in the short run. The Phillips curves are therefore indexed by laggedinflation (πI = π−1) and shift whenever π−1 changes:

π = πI + 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 thecentral bank’s preferences. Although the time path of unemployment is affected bythe choice between a policy for rapid disinflation (so-called ‘cold turkey’) and a moregradualist policy, the cumulative amount of unemployment required to achieve a givenreduction 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, asseems empirically likely, the Phillips curves become flatter as unemployment rises, a ‘coldturkey’ policy of disinflation favoured by a more inflation-averse central bank entails ahigher sacrifice ratio than does a ‘gradualist’ policy favoured by a less inflation-aversecentral bank.

In setting out the structure of the basic short- and medium-run model, we concentratedon the key results. It is now appropriate to investigate more deeply the presumption thatthe 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 theequilibrium level set by the intersection of the WS and PS curves and therefore closerto the competitive, full information market-clearing level. But what are the costs to theeconomy of the rising inflation that would ensue? As we have already seen, if inflationgets ‘too high’, bringing it down is likely to be costly. Finally, what problems arise wheninflation 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 inflationreflects 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 fullysatisfied (the real wage lies between the PS and WS curves). This reflects distributionalconflict 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 ofdisinflation.

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 usingthe Rational Expectations Hypothesis, the commitment of the government and centralbank to a policy of low inflation at equilibrium unemployment has to be believed bythe private sector and there must be no lags in the adjustment of wages and prices. Forcountries 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-eightepisodes 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 was2.9 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 intoplay.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 formerSoviet 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 eitherin earlier epochs or since. Situations of very high and hyperinflation are normally theresult of governments being unable to finance their expenditure through normal means(borrowing or taxation) and they therefore resort to monetary financing. This is knownas seignorage. The intimate connection between very high inflation and governmentdeficits 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 limitsto seignorage.

There is some evidence that the deterioration in the economic environment associatedwith very high inflation perhaps paradoxically can have the effect of creating the con-ditions for a relatively painless subsequent stabilization. Very high inflation is typicallyassociated with very poor economic performance: investment, consumption, and outputare all depressed. The length of wage contracts becomes very short and there is increasingrecourse to the use of foreign currency for transactions. This means that the nominalrigidities that are one reason for costly disinflation virtually disappear. Achieving thecredibility that is also required for the reform package to succeed is more elusive. It is fairto 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 thecentral bank be prevented from financing the deficit through the creation of money butas 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 becauseit creates uncertainty and undermines the informational content of prices. Unexpectedchanges in inflation imply changes in real variables in the economy: if money wages andpensions 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 thenominal 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 wheretechnology is more stagnant. Volatile inflation masks the economically relevant changesin relative prices and therefore distorts resource allocation. In short, volatile inflation hasreal 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 tothe question of ‘at what level’? In the model developed so far, this question has not beenanswered. 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 wemove 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 isindexed to inflation so that all the tax thresholds are raised by 10% p.a. The same isassumed to be true of pensions and other benefits. The consequence of this change willbe that all wages, benefits, and prices will now rise at 10% p.a. and the nominal interestrate will be 7% points higher. All real magnitudes in the economy remain unchanged.The economy moves from a constant inflation equilibrium withπ = 3% p.a. to a constantinflation equilibrium with π = 10% p.a. The real interest rate and the levels of outputand employment remain unchanged.

From our earlier analysis, we know that at the new equilibrium, the real money supplywill be lower than initially. Why? At high inflation, people wish to hold lower moneybalances—they wish to economize on their holdings of money—so for equilibrium inthe money market, the real money supply must be lower than in the initial low inflationequilibrium. Since

M S

P= L(i, y)

= L(r + πE, y),

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

M S

P

)high

= L((re + πL), ye)

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

M S

P

)low

= L((re + πH ), ye).

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This highlights the fact that even in our simple example the shift from inflation of3% 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 willrise by 10% each year. But at the time of the shift, there has to be an additional upwardjump in the price level to bring down the real money supply (M S/P) to its new lowerequilibrium level ((M S/P)low) consistent with the demand for lower real money balanceswhen inflation is higher.

What are the real costs of people economizing on money balances when inflation ishigh? These costs are sometimes referred to as ‘shoe-leather’ costs because of the wearand 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 listsfrequently in an inflationary environment. These costs are estimated to be quite low. Wenote here an apparent paradox: if the rate of inflation does not matter much, why shouldgovernments incur the costs of getting inflation down from a high and stable level to alow and stable one? One response is that it seems empirically to be the case that inflationis more volatile when it is higher and as noted above, volatile inflation brings additionalcosts. Another is that the initiation of disinflation policies frequently begins not simplywith high but with high and rising inflation. In this case, since costs will be incurred instabilizing inflation, it may be sensible for the government to go for low inflation as partof 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 arefully informed and can change their prices and wages at low cost, it is clear that thecosts 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 riseto anxiety. Distributional effects are also likely to occur: unanticipated inflation shiftswealth from creditors to debtors. It is also likely to make the elderly poorer since theyrely 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 publicis more averse to inflation than would be expected if the costs were really as low asthey seem in the example of full information, complete indexation, and instantaneousadjustment.

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 positiveinflation rate, the real return turns negative. The negative real return leads people to wasteeffort economizing on their money holdings (shoe leather again) and this is inefficientgiven that it is virtually costless to produce high-powered money. If we follow the logicof this argument then with a positive real rate of interest, for the nominal interest rate tobe 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 deflationshould equal the real rate of interest, leaving the nominal interest rate equal to zero.3 Isdeflation 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 ofperfect information, there would only be benefits from this as we have already seen—shoeleather would be saved and the relative price changes associated with technical progresswould be clearly revealed.

In spite of these arguments, there are two main reasons why deflation is not viewedas 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 causedby weakness in aggregate demand. The first reason relates to the apparent difficulty incutting nominal wages.4 If workers are particularly resistant to money wage cuts, thena positive rate of inflation creates the flexibility needed to achieve changes in relativewages. For example, if, due to a fall in demand for one kind of labour, a real wage cut isrequired it can be achieved with an inflation rate of, say, 2% p.a. with the money wage leftunchanged in the sector where the real wage cut is necessary. This argument is referredto 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 defenceagainst a deflation trap. A deflation trap can emerge when weak aggregate demand leadsinflation to fall and eventually become negative. For this to happen, two things arenecessary: (i) the automatic self-stabilizers that operate to boost aggregate demand wheninflation is falling fail to operate sufficiently strongly and (ii) policy makers fail to stopprices falling. Attempts to use monetary policy to stimulate the economy result in thenominal 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 tostimulate private sector demand. Continued weak demand will fuel deflation and pushthe real interest rate up, which is exactly the wrong policy impulse. This will tend toweaken demand further and sustain the upward pressure on the real interest rate. Oncedeflation takes hold, it can feed on itself and unlike a process of rising inflation, it doesnot require the active cooperation of the central bank for the process to continue. Thedeflation trap is explored in more detail in section 4 and the recent Japanese experiencewith deflation is analysed in Chapter 17.

1.6 Summing up

The conclusion to this discussion is that policy makers should establish a nominal anchorfor the economy that keeps inflation low and stable.5 This raises a further question. Whydo 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 ofnominal 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 wouldrequire the policy maker to make good policy misses in the past. This has some attraction in the context ofdeflation: e.g. following a couple of years of deflation, an inflation-targeting central bank may tighten policytoo soon once prices begin to rise whereas a price-level targeter would be more relaxed as the price level movedback toward the target.

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that governments may be tempted to take advantage of the short-run trade-off betweeninflation and unemployment. Since rising inflation reflects distributional conflict in theeconomy, one interpretation is that the political system is incapable of resolving theseconflicts, which therefore come to be reflected in rising inflation. A variation on thistheme is that the origin of situations of high and/or rising inflation lies with the financingof 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 viataxation or borrowing are limited. Raising taxes may be politically unpopular and furtherborrowing may be prohibitively expensive because of the level of public debt that hasalready been built up. Under such circumstances, if the government is intent on raisingits 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. Theuse of money to finance government spending is called seignorage. We examine the scopefor 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 andrising 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 requirepainful and therefore politically unpopular solutions, deflation can be solved by thegovernment generating demand through increased government spending or tax cutsfinanced 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 policyparadigm that has been discussed in a partial way and from different perspectives inearlier chapters.6 Both paradigms take as given the inertia in inflation that produces thePhillips curves and both incorporate the IS curve. The first paradigm, which we shall callthe 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 withconstant inflation following a shock is that embodied in the IS/LM model plus theinertia-augmented (or expectations-augmented) Phillips curve.

Let us examine how an IS shock is handled in this paradigm. We assume the economybegins at equilibrium unemployment with constant inflation equal to the growth rate ofthe money supply set by the central bank. For a positive IS shock, the impact of the risein 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. Thisis a movement along the LM to the north-east. The change in output and employmentthen feeds through to a rise in inflation, which given the fixed money supply growth ratetriggers a leftward shift in the LM curve. This induces a further dampening of the initialstimulus. In this paradigm, monetary policy is passive (in the form of a fixed growth rateof the money supply) and the economy adjusts to the new equilibrium by following aprotracted 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 relativeto a fixed money supply growth reduces real money balances and leads to a portfolioadjustment with bonds being sold. Excess supply of bonds pushes bond prices down andthe 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 MRparadigm, 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 withconstant 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 respondsto the rise in inflation due to the increase in output: as a consequence it raises the interestrate. Output falls below the equilibrium and brings inflation down: the central bankadjusts the interest rate to guide the economy down the MR curve to achieve the inflationtarget at equilibrium output.

As far as monetary policy is concerned, the paradigm shift centres on two issues: thechoice 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 monetarypolicy 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) ofthe issue by looking first at how the relative importance of LM versus IS shocks affectsthe optimal choice of a money supply versus an interest rate instrument.7 By drawingsimple 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 afixed money supply; the converse holds for IS shocks. The second contribution of Poole’spaper is to show that an active monetary policy is normally superior to a passive onewhen the economy is characterized by shocks and by lags in adjustment. Poole’s analysisis confined to the short run with prices fixed. The tenor of his arguments is even morepersuasive 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 toleave the adjustment mechanism to work automatically via the Keynes effect as in theLM paradigm. As we have seen in Chapter 3 when setting out the analysis under a fixedmonetary 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 theinteraction 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. LMshifts left as rising inflation relative to a fixed money supply growth cuts the real moneysupply). As we have seen, a further complication arises because of the impact of changesin the inflation rate on the demand for money (LM shifts right as the demand for moneyfalls with rising inflation).

The complexities of explaining the dynamic path of adjustment is not simply a problemfor those teaching macroeconomics or trying to learn about it but also reflects a problemfacing policy makers. The spiral-shaped adjustment path could be short-circuited withinthe LM paradigm: having achieved a fall in inflation to the level desired (equal to thegrowth rate of the money supply) with unemployment above the ERU , the monetaryauthority could inject a one-off boost to the money supply to take the economy straightto the new equilibrium. However, this is an uneasy mixture of a passive monetary policywith 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 policyframework that is consistent with steering the economy toward equilibrium unemploy-ment and providing a nominal anchor. Frequent adjustments have to be made to theinterest rate in order to achieve the central bank’s objective. This highlights the fact thatit is quite consistent to think of the central bank as following a ‘rule-based’ approachto monetary policy, yet having to be very active. Fig. 17.14 in Chapter 17 illustrates thefrequent interest rate adjustments made by central banks in the USA, the eurozone, andthe UK since 1999.

It is crucial to see that it is the implementation of the policy rule itself that establishesthe 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 ofinflation). The adjustment path is easy to explain and straightforward as we have seenin 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 isthen a technical problem for the central bank; whereas in the first paradigm, agents arefaced with an economic problem of trying to figure out the impact of changes in inflationon portfolio choices and hence on the interest rate. These arguments form the centralcase for using the second paradigm. It is a better description of how monetary policy isconducted and it comes closer to how it should be conducted, given the objectives ofthe central bank. Milton Friedman, the most famous proponent of the use of the moneysupply as policy target by the central bank, has conceded that ‘The use of the quantityof money as a target has not been a success.’ He added: ‘I’m not sure I would as of todaypush 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-targetingcentral bank that aims to minimize the fluctuations of output and inflation from itstargets 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, πT

(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 specificexamples 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 differentvariants are chosen. It involves the following steps:

(1) Define the central bank’s utility function in terms of both output and inflation. Thisproduces the policy maker’s indifference curves in output-inflation space.

(2) Define the constraints faced by the policy maker: these are the Phillips curves, whichare 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 chosencombination of output and inflation. Roughly, the higher is inflation as determinedby the Phillips curve the economy is on, the lower will the central bank set aggregatedemand and hence output in order to reduce inflation. Hidden in this relationship isthe policy instrument, r, that the central bank will use to secure the appropriate levelof aggregate demand and hence output. We saw this graphically in Chapter 3: thecentral bank chooses the best point along the Phillips curve that it faces and in orderto deliver the right level of aggregate demand, it must set the interest rate at the levelshown by the IS curve.

(4) We can also derive the interest rate rule, which tells the central bank how to adjust theinterest 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 curvesrepresenting the trade-off in its preferences between inflation and unemployment. Wenow explain how these can be derived more formally. We assume that the central bankhas two concerns: the rate of inflation, π, and the level of output, y. Looking first atinflation and following the discussion in section 2, we assume that it has a target rateof inflation πT and that it wants to minimize fluctuations around πT . A simple way ofwriting this is to assume that it wants to minimize the loss function:

(π − πT )2.

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142 THE MACROECONOMIC MODEL

Rather than having the central bank maximize a utility function, we have it minimizea loss function. A loss function is just like a utility function except that the higher theloss, the worse it is for the central bank (we use it rather than a utility function purelyfor convenience—by putting a minus sign in front of the expression above, the centralbank 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 aboveπT . If πT = 2% the loss from π = 4% is the same as the loss from π = 0%. In both cases(π − πT )2 = 4. Second, it attaches increased importance to bringing inflation back to itstarget the further it is away from πT ; the loss from π = 6% is 16, compared to the loss of4 from π = 4%. The central bank’s marginal disutility is increasing as the gap betweeninflation 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 seeksto minimize the gap between y and ye. At this point it is useful to draw attention to thefact that we have assumed that the equilibrium output level ye is known, that the centralbank’s target output level is ye, and that it is able to stick to this target. As we shall seein 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 groupsin the economy mediated by political institutions, and central banks may be unable orunwilling 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 negativedeviations—in this case, from the equilibrium level of output. The most straightforwardway of thinking about this is that the central bank understands the model and realizesthat inflation is only constant at y = ye. If y < ye then this represents unnecessaryunemployment that should be eliminated. If y > ye, this is unsustainable and will requirecostly increases in unemployment to bring the associated inflation back down. Wheneverthe economy is disturbed, the central bank sees its task as steering the economy back tothis 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 − πT )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 inemployment 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 aboutinflation 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 theassumption that β = 1. With β = 1, the weights on output and inflation deviations arethe same, i.e. the central bank is equally concerned about inflation and output deviationsfrom its targets.

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MONETARY POLICY 143

ye ye yey y y

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

pT

p

pT

p

pT

p

(a) (b) (c)

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. Whenπ = πT and y = ye, the circle shrinks to a single point (called the ‘bliss point’) and theloss is at a minimum, which is zero. The diagram is easy to remember if you think of it asa target (as for archery) with the central bank’s objective to get as close to the bull’s eyeas possible. With β = 1, the central bank is indifferent between inflation 1% above (orbelow) πT and output 1% below (or above) ye. They are on the same loss circle.

Only whenβ = 1, do we have indifference circles. Ifβ > 1, the central bank is indifferentbetween (say) inflation 1% above (or below) πT and output 2% above (or below) ye. Theyare 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 indifferencecurves with a vertical rather than a horizontal orientation (Fig. 5.1(c)). In that case, theindifference curves are steep reflecting that the central bank is only willing to trade off agiven fall in inflation for a smaller fall in output than in the other two cases. If the centralbank cares only about inflation thenβ =∞ and the loss ellipses become one dimensionalalong the line at π = πT .8

3.2 The Phillips curve constraint

Next, we shall assume that the central bank can control the level of output via its abilityto use monetary policy (by setting the interest rate) to control aggregate demand, yD.However, it cannot control inflation directly—only indirectly via y. As we have alreadydiscussed, 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’sdiscount rate is infinite. This means that it only considers one period at a time when making its decision. InChapter 3, we discussed informally the role that the central bank’s discount rate can play when we compareda rapid disinflation policy that produces a large initial rise in unemployment (‘cold turkey’) with a gradualistpolicy.

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144 THE MACROECONOMIC MODEL

4

3

pT = 2

p

A

VPC

PC (p I = 4)

PC (p I = 3)

PC (p I = 2)

D

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 themoment for simplicity it is assumed that α = 1, so that each Phillips curve has a slopeof 45◦. Each Phillips curve is labelled by lagged inflation. Assume that π−1 = πT = 2%(remember that this PC must go through point B at which y = ye and π = 2). The centralbank is in the happy position of being able to choose the bull’s eye point B or (πT , ye) atwhich its loss is zero.

What happens if there has been a shock to inflation and it is not equal to the inflationtarget? Suppose, for example, that inflation is 4%. Given inflation inertia, this means thatthe central bank is faced with the constraint of the Phillips curve shown by PC(πI = 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 �= πT

(i.e. point A). On the other hand, if it wishes to hit the inflation target next period, it mustaccept a much lower level of output next period (point C). Point A corresponds to a fullyaccommodating 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 whichthe 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 πI = 4, then givenits preferences, it can do better (achieve a loss circle closer to B) than either point A orpoint C. It minimizes its loss function by choosing point D, where the PC(πI = 4) line istangential to the indifference curve of the loss function closest to the bull’s eye. Thus ifπI = 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 losscircles as in Fig. 5.2 above. This implies:

L = (y − ye)2 + (π − πT )2.

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MONETARY POLICY 145

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

PC (p I = 4)

y1 y2 ye y

B

D

C

MR

pT= 2

3

4

p

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 a45◦ 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 successivePhillips curves and the loss circles show the level of output that the central bank needsto choose so as to minimize its loss at any given level of π−1. Thus when π−1 = 3, its lossis minimized at C; or when π−1 = 4 at D. Joining these points (D,C,B) produces the MRline that we used in Chapter 3. We can see from Fig. 5.3 that a one unit rise in π−1 impliesa half unit fall in y, for example an increase in π−1 from 3% to 4% implies a fall in y fromy2 to y1.

We can derive the monetary rule explicitly as follows. By choosing y to minimize L wecan derive the optimal value of y for each value of π−1. Substituting the Phillips curveinto L and minimizing with respect to y, we have:

∂L∂y

= 2(y − ye) + 2(π−1 + (y − ye)− πT ) = 0

= (y − ye) + (π−1 + (y − ye)− πT ) = 0.

Since π = π−1 + y − ye,

∂L∂y

= (y − ye) + (π − πT ) = 0

=⇒ (y − ye) = −(π − πT ). (MR equation)

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

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146 THE MACROECONOMIC MODEL

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

PC (p I = 4)

ye y

BD

C

MRb>1

a

pT= 2

p

3

4

Figure 5.4 Inflation-averse government: flat MR lineNote: 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 betweenπ and y with a negative 45◦

slope (Fig. 5.3). Specifically, it shows that the central bank must reduce aggregate demandand output, y, below ye so as to reduceπ belowπT by the same percentage. Thus this couldbe thought of as monetary policy halfway between: (i) completely non-accommodatingwhen the central bank cuts output sufficiently to bring inflation straight back to πT at thecost of a sharp rise in unemployment; and (ii) a completely accommodating one, whichleaves inflation (and output) unchanged. If the monetary rule was flat at πT we wouldhave a completely non-accommodating monetary policy; if it was vertical at ye, we wouldhave 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, welearn what it is that determines the slope of the monetary rule. We shall see that themore inflation averse is the central bank (the flatter are the loss ellipses) and the moreresponsive are wages to employment (the steeper are the Phillips curves), the flatter is theMR line.

The degree of inflation aversion of the central bank is captured by β in the centralbank loss function: L = (y − ye)2 + β(π − πT )2. If β > 1, the central bank attachesmore importance to the inflation target than to the output target. This results in a flattermonetary rule as shown in Fig. 5.4. Given these preferences, any inflation shock thatshifts the Phillips curve upward implies that the optimal position for the central bank willinvolve a more significant output reduction and hence a sharper cut in inflation alongthat Phillips curve than in the neutral case. Using the same reasoning, β < 1 implies thatthe monetary rule is steeper than the minus 45◦ line.

The second factor that determines the slope of the monetary rule is the responsivenessof inflation to output (i.e. the slope of the Phillips curve): π− π−1 = α(y− ye). This factorwas not discussed in Chapter 3. Thus far, we have assumed α = 1. Intuitively if α > 1so the Phillips curves are steeper, any given cut in output has a greater effect in reducinginflation than whenα = 1. As we can see from Fig. 5.5, this makes the MR line flatter than

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MONETARY POLICY 147

ye y

D

a = 1a > 1

pT= 2

p

3

4

MR0a = 1

MR1a > 1

CB

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 obtainedby 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 acentral bank to a given rise in inflation in the case where the Phillips curves are steep withthe case where they have a slope of one. Our intuition tells us that steeper Phillips curvesmake things easier for the central bank since a smaller rise in unemployment (fall inoutput) 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 Phillipscurves (dashed) and one with steeper ones. As we have already shown, the MR line isflatter for the economy with steeper Phillips curves: this is MR1. Suppose there is a rise ininflation 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 thesteeper Phillips curves (point D). This reflects our intuitive argument above.9

In the right hand panel, we compare two economies with identical supply sides butin 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-aversecentral 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 inflationin period 1. We assume it is only concerned with what happens in period 1. This is thereason 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

whenα > 1 as compared withα = 1. For β < 1, the output cut is less as long asα > (1/β)12 .

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148 THE MACROECONOMIC MODEL

ye y ye y

B

MR1

MR0 MR0

MR1

C

D

B

C

D

a. Steeper Phillips curves b. Greater inflation-aversion

pT= 2

3

4

p

3

4

p

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

positive values, the central bank chooses y to minimize

L = (y1 − ye)2 + β(π1 − πT )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 thevariable the central bank can control via its choice of the interest rate), we have:

∂L∂y1

= (y1 − ye) + αβ(π0 + α(y1 − ye)− πT ) = 0. (5.4)

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

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

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

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MONETARY POLICY 149

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 thesix key inputs to the deliberations of the central bank is now clear.

(1) the central bank’s inflation target, πT : this affects the position of the MR line;

(2) the central bank’s preferences, β: this determines the shape of the loss ellipses andaffects 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 IScurve;

(5) the equilibrium level of output, ye: this determines the position of the verticalPhillips 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 ordue 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-MRgraphical 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 demandshocks, and supply-side shocks is provided. In each case, the role of the six inputs tothe central bank’s decision can be analysed and experiments undertaken to evaluate theimpact of variations in them.

We take one of those examples in order to clarify in the diagram each input to the centralbank’s decision and to highlight the role played by the lag in the effect of monetary policyon aggregate demand and output. The example shows that the central bank is engagedin a forecasting exercise: it must forecast next period’s Phillips curve and next period’s IScurve. We assume that the economy starts off with output at equilibrium and inflationat the target rate of 2% as shown in Fig. 5.7. We take a permanent positive aggregatedemand shock such as improved buoyancy of consumer expectations: the IS moves toIS′. The consequence of output above ye is that inflation will rise above target—in thiscase to 4%. This defines next period’s Phillips curve (PC(πI = 4)) along which the centralbank must choose its preferred point: point C. The central bank forecasts that the IS curveis IS′, i.e. it judges that this is a permanent shock and by going vertically up to point C′ inthe IS diagram, it can work out that the appropriate interest rate to set is r′. As the Phillipscurve shifts down with falling inflation, the central bank reduces the interest rate and theeconomy 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 theshift 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 inoutput builds a rise in inflation above target into the economy. Because of inflationinertia, this can only be eliminated by pushing output below and (unemployment above)the equilibrium. The graphical presentation emphasizes that the central bank raises theinterest rate in response to the aggregate demand shock because it can work out the

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150 THE MACROECONOMIC MODEL

r

r�

MR

a 1/ab

IS

y

A, Z

B

C

A�

C�

Z�

y�ye

VPC

rS�

rSB�

IS�

a

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

4

pT = 2

p

Figure 5.7 Permanent IS shock

consequences for inflation. The diagram highlights how the parameters a,α, and β affectthe 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. laggedinflation in the Phillips curve and by the time lag for a change in the interest rate to takeeffect i.e. the lagged interest rate in the IS curve. In the IS equation it is the interest rateat time zero that affects output at time one: y1 − ye = −a(r0 − rS). This is because it takestime for a change in the interest rate to feed through to consumption and investmentdecisions. In Fig. 5.7 in order to choose its optimal point C on the Phillips curve (πI = 4),the central bank must set the interest rate now at r′. As is clear from the diagram, we havebeen working with this assumption throughout. However, it is interesting to see whathappens 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 interestrate to r′S. The economy then goes directly from A′ to Z′ in the IS diagram and it remains atA 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 forinflation to rise. This underlines the crucial role of lags and hence of forecasting for thecentral 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 offsetthem and limit their impact on inflation. Once inflation has been affected, the presenceof inflation inertia means that the central bank must change the interest rate and get theeconomy 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 individualeconomy and how aspects of the aggregate demand and supply-side structures affectcentral bank policy, the IS-PC-MR graphical model provides a useful way to investigatehow 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 αare the same) and a common central bank (i.e. πT and β are the same), but which differin the interest sensitivity of expenditure (a is different) and which are both initially inequilibrium with constant inflation (with r = rS). If both economies are subjected tothe same shock to autonomous demand, we can analyse the consequences using thegraphical 3-equation model (see Fig. 17.15).

As a second example, we could look at the implications for two economies in a currencyunion that are identical in all respects except for the responsiveness of inflation to changesin the level of output, e.g. one economy has a steep WS curve and therefore steep Phillipscurves (high α) whereas the other has flat Phillips curves. If a common inflation shockaffects both economies, how would the optimal response of a national central bank differfrom that of a central bank that sets a common interest rate for both economies? Examplesof 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 tofind out what interest rate to set once it has worked out its optimal output-inflationcombination in the Phillips diagram, i.e. once it has located the best available positionon the MR line. We now show how to derive an interest rate rule, which directly expressesthe change in the interest rate in terms of the current state of the economy. We then showhow 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)

π1 − πT = − 1αβ

(y1 − ye). (MR)

From these equations, we want to derive a formula for the interest rate, r0 in terms ofperiod 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

π0 + α(y1 − ye)− πT = − 1αβ

(y1 − ye)

π0 − πT = −(α+

1αβ

)(y1 − ye)

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

r0 − rS =1

a(α+ 1

αβ

) (π0 − πT). (Interest rate rule)

We can see that r0 − rS = 0.5(π0 − πT

)

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 matterfor the central bank’s response to a rise in inflation. If each parameter is equal to one, thecoefficient 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 pointshigher. Since inflation is higher by 1% point, the nominal interest rate must be raisedby 1 + 0.5, i.e. by 1.5 percentage points in order to secure a rise in the real interest rateof 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 rateby less.

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

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

where πT 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 atequilibrium. The Taylor Rule states that if output is 1% above equilibrium and inflationis at the target, the central bank should raise the interest rate by 0.5 percentage pointsrelative to stabilizing interest rate. As above we interpret the difference between y andye as the percentage gap; this is the equivalent of defining y as the log of output. And ifinflation is 1% point above the target and output is at equilibrium, then the Taylor rulesays 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, whichhe developed as an empirical description of how central banks behaved. However, it onlyrequires 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 itsloss function (equation 5.2).

It turns out that to get an interest rate rule that is like the Taylor rule in which both theinflation and output deviations are present, we need to modify the 3-equation model tobring the lag structure closer to that of a real economy. In this section, we explain howthis is done. However, for most purposes, the analysis of shocks and policy responses canbe conducted with the simpler single lag model, which we keep as our core 3-equationIS-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 nextperiod, i.e. r0 affects y1. The new assumption about timing that is required is that it takesa 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 industrialeconomies for the response to a monetary policy change to have its peak effect on demand andproduction, and that it takes up to a further year for these activity changes to have their fullestimpact on the inflation rate.

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

L = (y1 − ye)2 + β(π2 − πT )2.

Given the double lag, the three equations are:

π1 = π0 + α(y0 − ye) (Phillips curve)

y1 − ye = −a(r0 − rS) (IS)

π2 − πT = − 1αβ

(y1 − ye). (MR)

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

p1

p2

y1

r0

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

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

r0 − rS =1

a(α+ 1

αβ

) [(π0 − πT)

+ α(y0 − ye)].

And r0 − rS = 0.5(π0 − πT ) + 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 supplysides) and in central bank preferences can have on the coefficients of Taylor Rules. InFig. 5.9, the initial observation of output and inflation in period zero is shown by thelarge cross, ×. To work out what interest rate to set, the central bank notes that in thefollowing period, inflation will rise to π1 and output will still be at y0 since a change inthe interest rate can only affect y1. The central bank therefore knows that the constraintit faces is the PC(π1) and it chooses its best position on it to deliver π2. The best positionon 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 shownby point ×. This emphasizes that the central bank must forecast a further period aheadin the double lag model in order to locate the appropriate Phillips curve, and hence todetermine its optimal interest rate choice for today: it chooses r0 → y1 → π2. Once theeconomy is on the MR line, the central bank continues to adjust the interest rate to guidethe economy along the MR back to equilibrium.

The remaining task is to give a geometric presentation of the double lag model and theassociated Taylor Rule: rt − rS = 0.5 · (πt −πT )+ 0.5 · (yt −ye). Fig. 5.10 shows the examplein Fig. 5.9 again. As shown in the left hand panel of Fig. 5.10, the two components of theTaylor Rule are shown by the vertical distances equal toα(y0− ye) and π0−πT , whereα isthe slope of the Phillips curve. If these are added together, we have the forecast of π1−πT .Just one more step is needed to express this forecast in terms of (r0 − rS) and therefore todeliver a Taylor Rule. As shown in the right hand panel of Fig. 5.10, the vertical distanceπ1 − πT can also be expressed as (α+ γ) · a(r0 − rS), where α and γ = 1

αβreflect the slopes

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

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MONETARY POLICY 155

r

yy0

MR

yey2y1

rS

r1

r0

PC (p2)

PC (p0)

IS

yPC (p1)

p1

p

pT

p2

p0

p3

Figure 5.9 Taylor Rule example

the IS curve.12 Thus, we have

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

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

r0 − rS =1

(α+ γ)a

[(π0 − πT

)+ α(y0 − ye)

]

= 0.5 · (π0 − πT ) + 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. tothe tangents of the relevant angles.

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156 THE MACROECONOMIC MODEL

PC (p0)a

yy0yey1 yyey1

PC (p1) PC (p1)PC (p0)

IS IS

MR

a

MR

a

a (r0–rS) a (r0–rS)

a (r0–rS) a (r0–rS)

a(y0–ye)aa (r0–rS)

ga (r0–rS)(p0–pT)

r

rS

r0

p1

p

p0

p2

pT

r

rS

y

r0

p1

p

p0

p2

pT

ag

Figure 5.10 Deriving the Taylor Rule

One striking aspect of this discussion is that it helps to dispel a common confusionabout Taylor Rules. It is often said that the relative weights on output and inflation ina Taylor Rule indicate the central bank’s preferences for reducing inflation as comparedto output deviations. However, we have already seen that in the single lag model, theinterest rate rule only has the inflation deviation in it in spite of the fact that the lossfunction places weight on both inflation and output deviations: the degree of inflationaversion affects the size of the aggregate demand (and hence the interest rate) responseof the central bank.

Once we modify the model to reflect the fact that a change in output takes a year toaffect inflation (the double lag model), then both the inflation and output deviationsappear in the interest rate rule and it resembles Taylor’s Rule. The reason is that thecurrent period output deviation serves as a means of forecasting future inflation to whichthe central bank will want to react now. The central bank’s aversion to inflation affectsits reaction to inflation and to the forecast of inflation contained in the output deviationterm: it does not affect the relative weight on the inflation and output terms in the TaylorRule. 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 nextperiod’s inflation.13

It is the slope of the Phillips curves (α) that affect the relative weight on inflationand output in the Taylor Rule. For α > 1, the Phillips curves are steeper and the MRcurve 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 hismodel, the central bank’s preferences do affect the Taylor Rule weights. This arises from his inclusion of laggedoutput in the IS equation: if the coefficient on lagged output is zero then the difference between the weight oninflation 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 outputbecause this will have a bigger effect on inflation than withα = 1 (the MR curve is flatter).But on the other hand, a given rise in the interest rate will have a bigger negative effect oninflation. These two effects imply that with α > 1, the balance between the coefficientschanges: the coefficient on (π0 − πT ) goes down—so the central bank reacts less to aninflation shock whereas the coefficient on (y0−ye) goes up—the central bank reacts moreto 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 deviationsarise 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 theappropriate coefficients on the Taylor rule form of the central bank’s monetary rule willbe 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 ruleto stabilize the economy. One reason would be if investment or other components ofaggregate 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 costof capital (of which the interest rate is a key component) relative to the expected rate ofreturn (measured for example by a change in Tobin’s q) is rather weak. Another reasonwhy the interest rate may fail to affect output in the desired manner arises from the factthat the interest rate that is relevant to investment decisions is the long term real interestrate. The central bank can affect the short-term nominal interest rate. As we know, the realand the nominal interest rates differ by the expected rate of inflation. It remains to explainhow the short- and long-term interest rates are related. The relationship is referred to asthe 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:

int = 1/n · [i1

t + i1t+1|t + i1

t+2|t + · · ·+ i1t+n−1|t ] + φnt . (5.5)

In words, this means the long-term interest rate (say, the interest rate on twenty-yearbonds) is equal to the average of the expected interest rate on one-year bonds for the nexttwenty 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-termrate by the uncertainty premium and we would expect short- and long-term interest ratesto move in the same direction. Monetary policy will then have the desired effect. As acounter-example, consider the situation in which the central bank cuts the short-terminterest 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 likelyto produce higher inflation in the long run, then markets will believe a higher long-runreal interest rate will be necessary. Higher long-term interest rates are likely to dampeninterest-sensitive spending at a time when the authorities are trying to stimulate theeconomy.

A third example of the limits to the use of monetary policy as a stabilization tool comesfrom 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 nominalreturn. 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 theeconomy were negative. In a very low inflation economy, there is therefore limited scopeto use monetary policy to stimulate aggregate demand if the required real interest rateis negative, e.g. with an inflation target of 2%, the zero floor to the nominal interestrate means that real interest cannot be reduced below −2%. This is rather ironical—the successful implementation of a stability-oriented monetary policy along the linesoutlined in this chapter may have the effect of producing an economy with low inflationin which the scope of monetary policy to stimulate the economy if it is hit by a negativeshock 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 onoutput 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-termnominal interest rate;

• the central bank wishes to stimulate demand but the nominal interest rate is close tozero.

5.1 The deflation trap

The simplest way to see how a deflation trap may operate is to combine the fact thatthe nominal interest rate cannot be negative with the fact that the real rate of interest isapproximately: 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 sincethe minimum r is negative. But when π < 0 the minimum real rate is positive. Theproblem that can arise is that the real rate needed to stabilize demand at ye is less than theminimum feasible real rate, i.e. rs < min r(π) = −π. This condition is shown in Fig. 5.11where the stabilizing real interest rate is below the minimum feasible rate of 1%. Given thedepressed state of aggregate demand depicted by the position of the IS curve, if inflationhas 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 interestrate in order to set the real interest rate associated with aggregate demand at equilibriumoutput 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 thatinflation falls. That implies that the minimum real rate rises, further reducing output

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MONETARY POLICY 159

r

rS

A

IS

y0 ye y

min r = –p1

Figure 5.11 The zero floor to the nominalinterest rate and the deflation trap

and hence increasing the speed at which inflation falls (in Fig. 5.11, the min r line shiftsupward). 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 consumptionthat shifts the IS curve to the right or

(2) the creation of more positive inflation expectations. If expected inflation becomesless negative, the min r line shifts down and the central bank can use the interest ratebased monetary rule in the usual way to move the economy to the south-east alongthe IS curve.

However, the idea of escaping from the deflation trap by creating positive inflationexpectations may not work in practice. Willem Buiter argues that this is ‘spitting in thewind’ 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 thispoint is to say that the only way to create expectations of inflation in the future is to createexpectations of future higher aggregate demand: if the authorities do not take measuresto 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 inflationmay prevent the economy from getting into a deflation trap in the first place. Buiterargues 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 financedby the issue of new high-powered money—would certainly raise aggregate demand as itwould boost consumption spending (the IS curve would shift to the right). He points outhowever that independent central banks may be reluctant to do this since it is a combinedfiscal 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 solvinga deflation trap and to a largely unanticipated danger of creating independent centralbanks.

There is an additional channel through which a deflation trap can be sustained. Just asunanticipated 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 inthe economy (e.g. property prices) are falling as well as goods prices, then debtors in theeconomy will not only find that the real burden of their debt is rising (the debt is fixed innominal terms but prices are falling) but also that the assets that they have used as securityor collateral for the debt are shrinking in value. This so-called balance sheet channel maymake investment less sensitive to changes in the real interest rate thereby steepening theIS curve and weakening the investment response even if positive inflation expectationscould be generated. The situation is further complicated when deflation gets entrenchedbecause bankruptcies weaken the balance sheets of banks, threatening the stability of thebanking system. Alternatively, banks may continue to extend loans to failing firms so asto prevent the bad loans from showing up on their balance sheets: this may postpone butnot prevent a banking crisis.

6 Credibility, time inconsistency, and rules versusdiscretion

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 outputgap). This is consistent with the evidence that disinflation is costly, i.e. that in order toreduce inflation, output must be reduced. Although the evidence on costly disinflationdiscussed in section 1 indicates that reducing inflation from moderate levels appears torequire a sacrifice in terms of higher unemployment, it was noted in the discussion ofhyperinflation 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 inmacroeconomic research at present and is discussed in detail in Chapter 15. The key pointto highlight here is that although the inertial or backward-looking Phillips curve matchesthe empirical evidence concerning inflation persistence, it has a major shortcoming.Because it rests on ad hoc assumptions–in particular about the inflation process–ratherthan 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 thecentral bank’s inflation target is 4% and the economy is initially at point A with highbut stable inflation of 4% (on PC(πI = 4)). The central bank now decides to reduce itsinflation target to 2%, i.e.πT

1 = 2%. With backward-looking Phillips curves, it is clear fromFig. 5.12 that disinflation will be costly and following the announced change in inflationtarget, unemployment first goes up (shown by point B). The economy then shifts onlygradually to the new equilibrium at Z as the central bank implements the monetaryrule. Whether or not the central bank’s decision is announced and if so whether it is

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MONETARY POLICY 161

r

r9

rS

5

B

A

Z

VPC

B9C9

A9, Z9

IS

PC (p I = 4)

PC (p I = 3)

PC (p I = 2)

MR

ye y

y

3

1

0

pT1 = 2

pT0 = 4

p

C

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. Theinflation that is built into the system takes time (with higher unemployment) to workits way out. The inability of the model to take any account of the reaction of wage orprice setters to announced changes in monetary policy is unsatisfactory. We could makea radically different assumption that incorporates rational expectations on the part ofwage and price setters, credibility, and the absence of nominal rigidities. In this case, theannouncement of a lower inflation target produces an immediate change in wage andprice 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 anyincrease in unemployment. However, this too is unsatisfactory as the evidence suggeststhat disinflation is indeed costly even when a lower inflation target is announced. Asdiscussed in Chapter 15, recent developments in modelling the Phillips curve aim toprovide a micro-optimizing based model that can produce both costly disinflation and arole 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 imperfectcompetition in product and labour markets implies that ye is less than the competitivefull-employment level, the government may have a higher target. We assume that thegovernment 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 tominimize

L = (y − yT )2 + β(π − πT )2, (5.6)

where yT > 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 nowpoint A (where y = yT and π = πT ) rather than where y = ye and π = πT (i.e. point C).If we assume that α = β = 1 (for simplicity), then each indifference circle has its centreat A. The whole set of loss circles have shifted to the right. Since nothing has changed onthe 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 choosesif πI = 2% Fig. 5.13 shows the Phillips curve corresponding to πI = 2%. The tangencyof 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 thedownward-sloping line MR in Fig. 5.13.

We can see immediately that the government’s target, point A, does not lie on thePhillips curve for inertial inflation equal to the target rate of πT = 2%: the economy willonly be in equilibrium with constant inflation at point B. This is where the monetaryrule (MR) intersects the vertical Phillips curve at y = ye. At point B, inflation is above thetarget: the target rate is 2% but inflation is 4%: this gap between the target rate of inflationand inflation in the equilibrium is called the inflation bias.

p

4

inflation bias

VPCPC (4)

PC (3)

PC (2)B

D

C A

MR

ye yT y

3

pT = 2

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 itssize. We begin by showing why the equilibrium is at point B. If inflation is initially at itstarget rate of 2%, the central bank chooses its preferred point on the πI = 2% Phillipscurve and the economy is at D. But with output above equilibrium, inflation goes up to3% and the Phillips curve shifts up (see Fig. 5.13). The process of adjustment continuesuntil point B: output is at the equilibrium and inflation does not change so the Phillipscurve remains fixed. Neither central bank nor wage setters have any incentive to changetheir behaviour. The economy is in equilibrium. But neither inflation nor output are atthe central bank’s target levels (see Fig. 5.13).

We can derive the same result mathematically and pin down the determinants of thesize of the inflation bias. Minimizing the central bank’s loss function—equation (5.6)—subject to the Phillips curve—equation (5.7) implies

y − yT + αβ(π−1 + α(y − ye)− πT ) = y − yT + αβ(π − πT )

= 0.

So the new monetary rule is:

y − yT = −αβ(π − πT ). (5.8)

This equation indeed goes through (πT , yT ). Since equilibrium requires that π−1 = π

when y = ye, we have

ye = yT − αβ(π−1 − πT )

⇒ π = π−1 = πT +(yT − ye)

αβinflation bias

. (inflation bias)

In equilibrium, inflation will exceed the target by (yT−ye)αβ

. This is called the inflationbias.15 The significance of this result is that π > πT whenever yT > ye. The steeper is thecentral bank’s monetary rule (i.e. the less inflation averse it is), the greater will be theinflation bias. A lower α also raises the inflation bias. A lower α implies that inflation isless responsive to changes in output. Therefore, any given reduction in inflation is moreexpensive in lost output; so, in cost-benefit terms for the central bank, it pays to allow alittle more inflation and a little less output loss. As we shall see in the next subsection, theproblem of inflation bias is usually discussed in conjunction with the problem of timeinconsistency in which the central bank or the government announces one policy buthas an incentive to do otherwise. For this kind of behaviour to arise, it is necessary tointroduce 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 inflationinertia: i.e. πE = π + εt , where εt is a random disturbance. The intuition is that wagesetters know that whatever their expected rate of inflation, the condition for πE = π isthat y = ye. As we saw in Chapter 3, this is the so-called Lucas surprise supply equation,which we reproduce here:

yt − ye =1α

(πt − πE

t

)

yt = ye +1α

(πt − πE

t

)inflation surprise

(Lucas surprise supply equation)

= ye + ξt .

We continue to assume that the central bank chooses y (and hence π) after wage settershave chosen πE. This defines the central bank as acting with discretion. Now, in orderfor wage setters to have correct inflation expectations, they must choose πE such that itpays the central bank to choose y = ye. That must be where the central bank’s monetaryrule cuts the y = ye vertical line, i.e. at point B in Fig. 5.13. Note that the positivelysloped 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 raiseoutput toward its target. With π = 4% and y = ye, the temptation has been removedbecause any increase in output from B would put the central bank on a loss circle moredistant from its bliss point A: wage and price setters rationally expect an inflation surpriseof 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 centralbank at B is greater than the loss to the central bank at C since output is the same butinflation 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 arethe same in each case. What is to stop the central bank being at C? When wage and pricesetters are forward looking, the problem is called that of time inconsistency. Although thecentral bank claims to have an inflation target of πT , if wage setters act on the basis ofthis target (2%), when it comes to act, the central bank does not choose the output levelconsistent with its target. In short, at point B there is no incentive for the central bank tocheat; 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. yT > 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 beenformed in the private sector.

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MONETARY POLICY 165

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

6.4.1 Replacing discretion by a rule: commitmentIf the timing of the game between the central bank and private sector is changed so thatthe central bank cannot choose the rate of inflation after wage and price setters haveformed their expectations, then the inflation bias disappears. This entails a structurethrough which the central bank is prevented from optimizing after the private sector hasset 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 deviatesfrom the target is one possible method of enforcing this.

6.4.2 DelegationThe inflation bias is equal to (yT−ye)

αβ, and this may reflect a situation in which the gov-

ernment rather than the central bank controls monetary policy. The government couldreduce the inflation bias by transferring control of monetary policy to a central bank withan 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 thetarget and the government would be unambiguously better off if it delegates monetarypolicy to an independent central bank.

Fig. 5.14 illustrates the reduction in inflation bias through delegation of monetarypolicy 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 ahigher inflation bias with the equilibrium at point B. MRCB on the other hand implies thatequilibrium is at point A, with π = 3%. Wage and price setters rationally expect a smallerinflation surprise when faced with an independent central bank than when faced by thegovernment. The reduction in the inflation bias is due to the flatter slope of the centralbank’s MR line and to the fact that central bank’s output target is closer to equilibriumoutput than is the government’s.

For delegation to produce a costless move from high to low inflation, there must be noinflation inertia and expectations must be formed rationally. In this case, if wage settersbelieve that the policy maker’s preferences have changed in the appropriate way, theeconomy will shift directly down the vertical Phillips curve at ye from point B to the newequilibrium 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 thegovernment to take back those powers at the moment that wage setters chose a low πE

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 reasoningis sometimes used to explain why governments have often found it necessary to makecentral banks constitutionally independent and why delegation is sometimes combinedwith commitment devices like the one discussed in 6.4.1.

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166 THE MACROECONOMIC MODEL

MRCB MRG

PC (6)

PC (3)

PC (2)

A

C

6

5

4

3

pT = 2

ye yTCB yT

G y

inflation bias: CB

inflation bias: government

B

VPC

Figure 5.14 Inflation bias: central bank and government

6.4.3 ReputationA third solution to the problem of inflation bias lies with the government or centralbank building a reputation for being tough on inflation. Suppose that the governmenthas delegated monetary policy to the central bank but wage setters remain unsure ofjust how independent the central bank is. They only know that there is a probability pthat the central bank is independent and a probability (1 − p) that it is a puppet of thegovernment. The only way that they can find out is by observing the decisions taken bythe central bank. If this is the case, how should the central bank behave? This problemcan be analysed in detail using game theory. This is done in Chapter 16. Here we simplyconvey the flavour of the solution.

The situation is one in which the central bank interacts with wage setters more thanonce. Will a ‘weak’ central bank with an output target above the equilibrium find itrational 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 methodof solving the inflation bias problem. Let us begin with the case in which the interactionbetween the central bank and wage setters occurs twice: in period one, wage setters chooseπE

1 with no knowledge of whether the central bank is weak or tough (but they know thereis a probability of p that it is tough); the central bank then chooses output in period one,y1 knowing πE

1 . In period two, the wage setters choose πE2 knowing y1; the central bank

then chooses y2 knowing πE2 .

The result is that a weak central bank will choose to act like a tough one in the firstperiod, which will establish a low expected inflation rate in the second period, thereby

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providing bigger gains from boosting output in the second period. The central bankgains 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 inflationabove the target and output at equilibrium) whilst in the second period, it can gain bysetting output above the equilibrium (i.e. by exploiting the short-run trade-off betweeninflation and unemployment by a surprise increase in inflation). As discussed in detail inChapter 16, when the game is extended from two to many periods, the benefits to thecentral bank from behaving as if it were tough increase. This is because the situation inperiod one is repeated again and again until the last period. This type of model providesan explanation for the process by which a reputation for toughness can be built in theface 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 yT = ye rather than yT > ye. This is the case both when inflation expec-tations are backward looking and when inflation expectations are rational. The centralbank objective of yT = ye is our benchmark model for monetary policy, introduced inChapter 3. We are then led to ask whether the assumption that yT > ye is a good way tothink about central bank behaviour. It offers insights when the central bank is susceptibleto 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 keyproblem for central banks, which in most cases are independent from government andare run by officials motivated by concern about their professional reputations. This pointis summarized neatly by Peter Howitt:

The ‘temptation’ to raise the level of economic activity with some surprise inflation might existif society were indeed locked into expectations. In reality, however, the temptation just doesn’tarise, as practitioners of central banking have long maintained. Central bankers are keenly awarethat although there are long and variable lags between monetary stimulus and any resultingrise in the level of economic activity, there are no lags at all between such stimulus and thecurrency depreciation and capital flight that will occur if the stimulus is taken by investors asa signal of future weakness in the currency. Because of this, there is no reason for believing thatdiscretionary 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 ofa country’s central bank are typically motivated by the desire to be seen as having done a goodjob, to have acquitted themselves well. They pursue this objective by doing everything possible toavoid major inflations, financial panics and runs on the currency, while carrying out the day today 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 ofEngland; from 2003, Governor of the Bank of England: King (1997). Another useful source is the short bookof three lectures by Alan Blinder reflecting on how he used academic research when he was a Governor of theFederal Reserve Board: Blinder (1998).

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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 usageof the distinction between monetary rules and discretion. The broader usage is neededbecause the real-world examples of inflation-targeting central banks embody rule-basedbehaviour as summarized in a monetary reaction function, which nevertheless entailsdiscretion in the time-inconsistency sense. We ask whether there are any gains from aframework of a clearly defined public monetary policy rule with an explicit inflationtarget 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 FederalReserve 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 famouscase of a central bank operating constitutionally with discretion. Yet many articles havebeen written suggesting that the Fed has covertly been following an inflation-targetingrule.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 withdiscretion.

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 informationabout the monetary policy reaction function is likely to be useful.18 The main gain arisesbecause economic agents are at least in part forward looking and will therefore anticipatethe 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 ashock.

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 thisreaction will influence the expected future path of interest rates, which will help shiftthe 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 expectedpath 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 tendto boost asset prices immediately (e.g. share prices and house prices). In turn as weshall 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 aggregatedemand.

On the other hand, too great an emphasis on rules may take attention away fromthe benefits that can arise from a central bank that sees itself as actively learning aboutthe economy and engaging in experiments—for example, to try to discover the equi-librium level of unemployment in an economy experiencing a burst of technologicalprogress.

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’sinflation 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 anexamination 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 objectiveby policy makers. We examined the reasons behind episodes of rising inflation and theunsustainability of attempts to hold output above the equilibrium level. A falling generalprice level (deflation) is likely to bring dangers to macroeconomic stability.

We highlighted the difference between two monetary policy paradigms—the LMparadigm and the MR paradigm. In the LM paradigm, monetary policy is passive andthe 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 interestrate so as to steer the economy back to target inflation at equilibrium output. The rate ofinflation 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 lowor negative rates of inflation.

A systematic approach to monetary policy within the MR paradigm can be modelledby specifying the objectives of the central bank (or the government) and identifying theconstraints it faces. The objective of the central bank is to minimize the extent to whichthe economy diverges from a target rate of inflation and from a target level of output. Wehave shown that

• when the output target is the equilibrium level of output, ye, a monetary policy reactionfunction will enable the central bank to steer the economy to its inflation and outputtargets 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 affectthe real interest rate and the level of aggregate demand and output. The appropriatechange in the real interest rate will depend on whether the stabilizing real interest ratehas 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 inunemployment (the slope of the Phillips curve).

• We have shown how to derive an interest rate rule from the 3-equation model. Thistakes the form of a Taylor Rule in which the central bank adjusts the interest rate inresponse to observed deviations of inflation from target and of output from equilibriumwhen the economy is characterized by a lag in the effect of the interest rate on outputand a lag in the effect of a change in output on inflation. If output affects inflationin the same period, then the interest rate rule only has the inflation term in it. Thishighlights the fact that the coefficients on inflation and output in the Taylor rule arenot 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 thatcost 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 willnot be able to achieve its inflation target in equilibrium. There will be an inflation bias.

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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 specificationof the central bank’s loss function. If the central bank targets a level of employment abovethe equilibrium, an inflation bias arises. When expectations are rational, this creates thetime-inconsistency problem. By contrast, in our baseline case, which it is argued matchesthat of central banks in many countries, the objective is to stabilize the economy aroundequilibrium output, which eliminates the inflation bias. A fuller understanding by thepublic 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’sstabilization objectives.

■ QUESTIONS

Checklist questions

(1) ‘If the economy has high but stable inflation, the government has much to lose andlittle 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 comparedwith one of 0% per annum? Would you advocate the replacement of the inflationtarget by a price level target?

(3) Explain what is meant by the central bank’s loss function. How are the central bank’spreferences reflected in the loss function? Use a numerical example and diagrams toexplain how the central bank’s preferences affect its reaction to a negative aggregatedemand 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 negativeaggregate 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 quitesteep and in the other, the WS is quite flat. Why might this be so? Compare theimplications for inflation and unemployment of a common positive temporaryaggregate demand shock. How should the central bank respond?

(7) If a central bank adopts an interest-rate based monetary policy rule like a Taylor Rulerather than a monetary growth rate rule, what would you expect to happen to themoney supply?

(8) In implementing a Taylor-type interest rate rule, does the central bank need to knowanything more than the coefficients in the rule, its inflation target, and currentoutput and inflation?

(9) Write down the Taylor Rule in terms of the real interest rate. Holding the output gapconstant, does a rise in inflation by x percentage points call for a rise in the nominalinterest 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 basedmonetary rule to stabilize the economy fail in its objective of raising output?

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(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 arerational but are formed before the central bank chooses its optimal inflation-outputpair. 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 toreduce inflation may have a problem in achieving this outcome because of a lack ofcredibility.

Problems and questions for discussion

QUESTION A. What are the incentives for a policy maker to exploit the short-runtrade-off between unemployment and inflation? What are the consequences? Is this agood description of contemporary central bankers? Use official reports of a central bankof 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 − πT )2

where k is a positive constant. Its policy instrument is the growth rate of the moneysupply, γM . Assume that the inflation target is πT = 0. Explain this utility function andcompare it with the loss function used in the chapter. (Hint: focus on how the centralbank’s utility rises with output. Is this central bank ‘overambitious’?) Now assume thatthe central bank sets the money supply growth rate after economic agents haveincorporated their expectations about inflation into their decision making, and thusfaces a Phillips curve:

π = πE + α(y − ye).

(a) Assuming that agents have rational expectations, solve algebraically for the optimalinflation rate under discretion, i.e. find the inflation rate that the central bank willchoose using its monetary policy instrument, γM . (Hint: maximize utility withrespect to γM , having used the Phillips curve to substitute for y in the utilityfunction; and used γM = π to substitute for π.)

(b) Suppose that, before private sector inflation expectations were formed, the centralbank 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 covertwo periods. In other words, the central bank now cares about the sum of its lossfunctions in each period, i.e.

Total utility =[

k(y1 − ye)−(π1 − πT

)2]

+[

k(y2 − ye)−(π2 − πT

)2]

where the subscripts indicate the period.

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Suppose also that in the first period, agents expect no inflation (πE = 0), while whenthe second period arrives agents expect that inflation will be equal to the rate thatactually occurs in the first period (i.e. expectations are adaptive, so πE

2 = π1). What willbe 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 realside of the economy? Explain.

QUESTION D. Using Fig. 5.8 as a guide, draw the corresponding diagram to illustrate thelag structure in the standard version of the 3-equation model. Now assume that there isno lag between a change in the interest rate and its effect on output. Draw a diagram toillustrate this lag structure. Use all three figures to provide a concise summary of the roleof lags in the operation of monetary policy. Go to the website of one of the central bankslisted in the next question (or another one of your choice) and find out their view aboutthe lags between a change in the interest rate and its effects on output and inflation. Dothey identify the same factors as responsible for the lags?

QUESTION E. Select two out of the following central banks: Bank of England, ReserveBank of New Zealand, Bank of Canada, and the Swedish Riksbank. Each of these centralbanks has adopted explicit ‘inflation targeting’. For each of your chosen banks, find outhow it explains what this means to the public. How does it communicate and explain itsinterest rate decisions to the public? Compare what each central bank did and how itexplained its actions following the events of 11 September 2001.