VIEWS: 4 PAGES: 42 POSTED ON: 1/2/2012 Public Domain
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 Keyn: “chap05” — 2005/11/22 — page 131 — #1 132 THE MACROECONOMIC MODEL target the inﬂation rate using an interest rate rule rather than targeting the growth of the money supply. Section 3 sets out in detail the derivation of the central bank’s monetary policy rule that was introduced in Chapter 3: as the MR curve in the Phillips diagram and the MR equation in the 3-equation model. Speciﬁcally, we shall see the role played by the following six key variables in central bank policy making: (1) the central bank’s inﬂation target (2) the central bank’s preferences (3) the slope of the Phillips curve (4) the interest sensitivity of aggregate demand (i.e. the slope of the IS curve) (5) the equilibrium level of output (6) the stabilizing interest rate. Section 4 focuses on how an interest rate rule such as the famous Taylor Rule can be derived from the 3-equation model. Section 5 steps back from the mechanics of interest rate based inﬂation targeting and investigates the problems with using such rules in dealing with macroeconomic problems. In particular, the dangers posed by deﬂation are explored. For the bulk of the chapter, we describe monetary policy making assuming it is in the hands of the central bank. However, in section 6 we look at why it might matter whether monetary policy decisions are actually made by the government and then implemented by the central bank or whether the central bank is independent of the government. Section 6 introduces the idea that if the government (or central bank) tries to achieve a target level of output above equilibrium—perhaps for politically motivated reasons— then the result will be that in equilibrium the inﬂation rate is higher than the target rate. This is called the inﬂation bias. We then show how inﬂation bias is related to the problem of central bank credibility and the time inconsistency of policy. To do this we need to introduce forward-looking inﬂation expectations. The delegation of monetary policy to an independent central bank is sometimes proposed as a method of reducing or eliminating the inﬂation bias. In this section, we explain that the debate about ‘rules versus discretion’ in the time-inconsistency literature uses a much narrower deﬁnition of ‘rules’ than the one adopted in our analysis of monetary policy. This can be a source of confusion in discussing how central banks behave. In this chapter, we consider only a closed economy. The relationship between the exchange rate regime and monetary policy in the open economy is explained in Chapter 9 and we extend the analysis of monetary policy rules to the open economy in Chapter 11. 1 Inﬂation, disinﬂation, and deﬂation In Chapter 3, we set out the IS-PC-MR model with the following features: • In medium-run equilibrium, inﬂation is equal to the central bank’s inﬂation-target if the central bank seeks to stabilize unemployment around the ERU . In the IS/LM version Keyn: “chap05” — 2005/11/22 — page 132 — #2 MONETARY POLICY 133 of the model, in the medium-run equilibrium, inﬂation is equal to the growth rate of the money supply set by the central bank. • Because of delays in price and wage setting, inﬂation is persistent, which means that lagged inﬂation affects current inﬂation and there will be a trade-off between inﬂation and unemployment in the short run. The Phillips curves are therefore indexed by lagged inﬂation (π I = π−1 ) and shift whenever π−1 changes: π = π I + α(y − ye ) = π−1 + α(y − ye ). With Phillips curves of this form, the implication is that disinﬂation is costly: unemploy- ment has to rise above the ERU for inﬂation to fall. • With linear Phillips curves, the sacriﬁce ratio is constant and independent of the central bank’s preferences. Although the time path of unemployment is affected by the choice between a policy for rapid disinﬂation (so-called ‘cold turkey’) and a more gradualist policy, the cumulative amount of unemployment required to achieve a given reduction in inﬂation does not depend on the degree of inﬂation aversion of the cen- tral bank. However, with non-linear Phillips curves, this is no longer the case: when, as seems empirically likely, the Phillips curves become ﬂatter as unemployment rises, a ‘cold turkey’ policy of disinﬂation favoured by a more inﬂation-averse central bank entails a higher sacriﬁce ratio than does a ‘gradualist’ policy favoured by a less inﬂation-averse central bank. In setting out the structure of the basic short- and medium-run model, we concentrated on the key results. It is now appropriate to investigate more deeply the presumption that the goal of a low, stable inﬂation rate is an appropriate one for policy makers to have. There seem to be obvious beneﬁts of having a higher level of output—i.e. above the equilibrium level set by the intersection of the WS and PS curves and therefore closer to the competitive, full information market-clearing level. But what are the costs to the economy of the rising inﬂation that would ensue? As we have already seen, if inﬂation gets ‘too high’, bringing it down is likely to be costly. Finally, what problems arise when inﬂation is negative, i.e. when prices are falling? 1.1 Rising inﬂation In an economy in which social groups—such as unions—wield economic power, a situ- ation of rising inﬂation reﬂects inconsistent claims on output per head in the economy. If ﬁrms are able to adjust prices immediately after wages have been set, rising inﬂation reﬂects a situation in which workers’ real wage aspirations are systematically frustrated: the real wage is typically on the PS curve, not on the WS curve. If there are lags in price set- ting as well as in wage setting, then the aspirations of neither workers nor ﬁrms are fully satisﬁed (the real wage lies between the PS and WS curves). This reﬂects distributional conﬂict as different social groups (wage setters/employees and price setters/employers) seek to protect their interests. Social tension rises as frustration mounts. As we shall Keyn: “chap05” — 2005/11/22 — page 133 — #3 134 THE MACROECONOMIC MODEL see, inﬂationary episodes of this kind have typically been followed by painful periods of disinﬂation. As we have seen in Chapter 3, for disinﬂation to be costless in the sense of not entail- ing a period of high unemployment, expectations of inﬂation must be formed using the Rational Expectations Hypothesis, the commitment of the government and central bank to a policy of low inﬂation at equilibrium unemployment has to be believed by the private sector and there must be no lags in the adjustment of wages and prices. For countries experiencing episodes of moderate inﬂation up to double digit rates per annum, these conditions do not appear to have been met. Lawrence Ball examines twenty-eight episodes of disinﬂation in nine OECD countries and ﬁnds that with only one excep- tion, disinﬂation was contractionary, with sacriﬁce ratios ranging from 2.9 in Germany (i.e. for a one percentage point reduction in inﬂation, the increase in unemployment was 2.9 percentage points for a year) to 0.8 in the United Kingdom and France.1 1.2 Very high inﬂation and hyperinﬂation Once inﬂation rates rise above 100% per annum, additional considerations come into play.2 Between 1960 and 1996, there were more than 40 episodes in 25 different devel- oping countries of such high inﬂation, which on average lasted for about 40 months. In addition, virtually all of the transition economies of Eastern Europe and the former Soviet Union experienced a bout of very high inﬂation as a consequence of price liber- alization at the beginning of the transition in the early 1990s. Hyperinﬂation has tradi- tionally been deﬁned as referring to a situation in which inﬂation rates rise above 50% per month—this was more common in the ﬁrst half of the twentieth century than either in earlier epochs or since. Situations of very high and hyperinﬂation are normally the result of governments being unable to ﬁnance their expenditure through normal means (borrowing or taxation) and they therefore resort to monetary ﬁnancing. This is known as seignorage. The intimate connection between very high inﬂation and government deﬁcits is explored in detail in Chapter 6 on ﬁscal policy after the concepts of the govern- ment deﬁcit and debt have been elaborated. We examine there the scope for and limits to seignorage. There is some evidence that the deterioration in the economic environment associated with very high inﬂation perhaps paradoxically can have the effect of creating the con- ditions for a relatively painless subsequent stabilization. Very high inﬂation is typically associated with very poor economic performance: investment, consumption, and output are all depressed. The length of wage contracts becomes very short and there is increasing recourse to the use of foreign currency for transactions. This means that the nominal rigidities that are one reason for costly disinﬂation virtually disappear. Achieving the credibility that is also required for the reform package to succeed is more elusive. It is fair to say that the way to achieve a successful, painless disinﬂation is not well understood. It requires that the causes of the unsustainable ﬁscal stance be addressed and that the central bank be prevented from ﬁnancing the deﬁcit through the creation of money but as is often the case in macroeconomics, this is easier said than done. 1 Ball (1994). 2 For a more detailed discussion of very high inﬂation, see Fischer, Sahay, and Végh (2002). Keyn: “chap05” — 2005/11/22 — page 134 — #4 MONETARY POLICY 135 1.3 Volatile inﬂation When inﬂation is high it also seems to be more volatile. Volatile inﬂation is costly because it creates uncertainty and undermines the informational content of prices. Unexpected changes in inﬂation imply changes in real variables in the economy: if money wages and pensions are indexed by past inﬂation and there is an unanticipated jump in inﬂation, real wages and pensions will drop. Equally, the real return on savings will fall because the nominal interest rate only incorporates expected inﬂation. In an economy with technical progress, innovation takes place unevenly across sectors. In sectors with rapid innovation, prices will be falling relative to other sectors where technology is more stagnant. Volatile inﬂation masks the economically relevant changes in relative prices and therefore distorts resource allocation. In short, volatile inﬂation has real effects on the economy that are hard to avoid. 1.4 Constant inﬂation—what level is optimal? Assuming that constant inﬂation is needed if expectations are to be fulﬁlled, we turn to the question of ‘at what level’? In the model developed so far, this question has not been answered. We begin by noting that there are hypothetical circumstances under which the (constant) rate of inﬂation (i.e. high or low) should not matter much. Imagine that we move from a situation in which prices are rising at 3% per year to a rate of 10% per year. We assume that this change is announced well in advance and that the tax system is indexed to inﬂation so that all the tax thresholds are raised by 10% p.a. The same is assumed to be true of pensions and other beneﬁts. The consequence of this change will be that all wages, beneﬁts, and prices will now rise at 10% p.a. and the nominal interest rate will be 7% points higher. All real magnitudes in the economy remain unchanged. The economy moves from a constant inﬂation equilibrium with π = 3% p.a. to a constant inﬂation equilibrium with π = 10% p.a. The real interest rate and the levels of output and employment remain unchanged. From our earlier analysis, we know that at the new equilibrium, the real money supply will be lower than initially. Why? At high inﬂation, people wish to hold lower money balances—they wish to economize on their holdings of money—so for equilibrium in the money market, the real money supply must be lower than in the initial low inﬂation equilibrium. Since MS = L(i, y ) P = L(r + π E , y ), at equilibrium output with low inﬂation, πL , we have: MS = L((re + πL ), ye ) P high and at equilibrium output with high inﬂation, πH , we have: MS = L((re + πH ), ye ). P low Keyn: “chap05” — 2005/11/22 — page 135 — #5 136 THE MACROECONOMIC MODEL This highlights the fact that even in our simple example the shift from inﬂation of 3% to 10% p.a. is not quite as straightforward as it seems at ﬁrst. After the move to 10% inﬂation, money wages, prices, the nominal money supply, and nominal output will rise by 10% each year. But at the time of the shift, there has to be an additional upward jump in the price level to bring down the real money supply (M S /P) to its new lower equilibrium level ((M S /P )low ) consistent with the demand for lower real money balances when inﬂation is higher. What are the real costs of people economizing on money balances when inﬂation is high? These costs are sometimes referred to as ‘shoe-leather’ costs because of the wear and tear associated with more frequent trips to the bank or the cash machine. Other costs (so-called menu costs) arise because of the time and effort involved in changing price lists frequently in an inﬂationary environment. These costs are estimated to be quite low. We note here an apparent paradox: if the rate of inﬂation does not matter much, why should governments incur the costs of getting inﬂation down from a high and stable level to a low and stable one? One response is that it seems empirically to be the case that inﬂation is more volatile when it is higher and as noted above, volatile inﬂation brings additional costs. Another is that the initiation of disinﬂation policies frequently begins not simply with high but with high and rising inﬂation. In this case, since costs will be incurred in stabilizing inﬂation, it may be sensible for the government to go for low inﬂation as part of a package that seeks to establish its stability-oriented credentials. Once we relax our assumption that indexation to inﬂation is widespread in the eco- nomy and that adjustment to higher inﬂation is instantaneous because all parties are fully informed and can change their prices and wages at low cost, it is clear that the costs of switching to a high inﬂation economy are likely to be more substantial. The con- tinuous reduction in individuals’ living standards between wage adjustments gives rise to anxiety. Distributional effects are also likely to occur: unanticipated inﬂation shifts wealth from creditors to debtors. It is also likely to make the elderly poorer since they rely on imperfectly indexed pensions and on the interest income from savings. Recog- nition of such costs is consistent with survey evidence that shows the general public is more averse to inﬂation than would be expected if the costs were really as low as they seem in the example of full information, complete indexation, and instantaneous adjustment. Can we infer from this analysis that the optimal rate of inﬂation is zero or even negative? In thinking about the optimal inﬂation rate, we are led ﬁrst of all to consider the following: the return on holding high-powered money (notes and coins) is zero so with any positive inﬂation rate, the real return turns negative. The negative real return leads people to waste effort economizing on their money holdings (shoe leather again) and this is inefﬁcient given that it is virtually costless to produce high-powered money. If we follow the logic of this argument then with a positive real rate of interest, for the nominal interest rate to be zero, inﬂation would have to be negative (i.e. prices falling, which is called deﬂation). This was Milton Friedman’s view of the optimal rate of inﬂation: the rate of deﬂation should equal the real rate of interest, leaving the nominal interest rate equal to zero.3 Is deﬂation optimal? 3 Friedman (1969). Keyn: “chap05” — 2005/11/22 — page 136 — #6 MONETARY POLICY 137 1.5 Deﬂation If inﬂation is negative (e.g. −2% p.a.), or equivalently there is a rate of deﬂation of 2% p.a., prices and wages will be 2% lower in a year’s time than they are now. In a world of perfect information, there would only be beneﬁts from this as we have already seen—shoe leather would be saved and the relative price changes associated with technical progress would be clearly revealed. In spite of these arguments, there are two main reasons why deﬂation is not viewed as a good target by central banks. One relates to how economies work in ‘normal times’ and the other to the dangers of the economy getting stuck in a deﬂation trap caused by weakness in aggregate demand. The ﬁrst reason relates to the apparent difﬁculty in cutting nominal wages.4 If workers are particularly resistant to money wage cuts, then a positive rate of inﬂation creates the ﬂexibility needed to achieve changes in relative wages. For example, if, due to a fall in demand for one kind of labour, a real wage cut is required it can be achieved with an inﬂation rate of, say, 2% p.a. with the money wage left unchanged in the sector where the real wage cut is necessary. This argument is referred to as inﬂation’s role in ‘oiling the wheels of the labour market’. The second reason stems from the need for the central bank to maintain a defence against a deﬂation trap. A deﬂation trap can emerge when weak aggregate demand leads inﬂation to fall and eventually become negative. For this to happen, two things are necessary: (i) the automatic self-stabilizers that operate to boost aggregate demand when inﬂation is falling fail to operate sufﬁciently strongly and (ii) policy makers fail to stop prices falling. Attempts to use monetary policy to stimulate the economy result in the nominal interest rate falling. A nominal interest rate close to zero (as low as it can go) combined with deﬂation implies a positive real interest rate. This may be too high to stimulate private sector demand. Continued weak demand will fuel deﬂation and push the real interest rate up, which is exactly the wrong policy impulse. This will tend to weaken demand further and sustain the upward pressure on the real interest rate. Once deﬂation takes hold, it can feed on itself and unlike a process of rising inﬂation, it does not require the active cooperation of the central bank for the process to continue. The deﬂation trap is explored in more detail in section 4 and the recent Japanese experience with deﬂation is analysed in Chapter 17. 1.6 Summing up The conclusion to this discussion is that policy makers should establish a nominal anchor for the economy that keeps inﬂation low and stable.5 This raises a further question. Why do we observe economies with high, rising, and volatile inﬂation? We have already noted 4 A famous study is Bewley (1999). A recent empirical study using high quality data conﬁrms the existence of nominal wage rigidity: Lebow, Saks, and Wilson (2003). 5 It is sometimes argued that a price-level target would be preferable to an inﬂation target since this would require the policy maker to make good policy misses in the past. This has some attraction in the context of deﬂation: e.g. following a couple of years of deﬂation, an inﬂation-targeting central bank may tighten policy too soon once prices begin to rise whereas a price-level targeter would be more relaxed as the price level moved back toward the target. Keyn: “chap05” — 2005/11/22 — page 137 — #7 138 THE MACROECONOMIC MODEL that governments may be tempted to take advantage of the short-run trade-off between inﬂation and unemployment. Since rising inﬂation reﬂects distributional conﬂict in the economy, one interpretation is that the political system is incapable of resolving these conﬂicts, which therefore come to be reﬂected in rising inﬂation. A variation on this theme is that the origin of situations of high and/or rising inﬂation lies with the ﬁnancing of government spending. As we shall see in the next chapter when we discuss ﬁscal policy, there are situations in which the usual methods of ﬁnancing government spending via taxation or borrowing are limited. Raising taxes may be politically unpopular and further borrowing may be prohibitively expensive because of the level of public debt that has already been built up. Under such circumstances, if the government is intent on raising its spending in response to pressure from politically important groups in the economy, it may have to get hold of the necessary resources by increasing the money supply. The use of money to ﬁnance government spending is called seignorage. We examine the scope for and limits to seignorage in the ﬁscal policy chapter, Chapter 6. We highlight the asymmetry in the role of the central bank in situations of high and rising inﬂation as compared with situations of deﬂation. In the former, the active involve- ment of the central bank is required to keep the inﬂationary process going; in the latter, deﬂation can become self-sustaining. Many observers have argued that unlike inﬂation- ary problems, which often reﬂect unresolved social and political conﬂict and require painful and therefore politically unpopular solutions, deﬂation can be solved by the government generating demand through increased government spending or tax cuts ﬁnanced by new money creation, which are popular. This suggests that it is bad policy (and bad luck) rather than politically expedient policy that leads to deﬂation traps. 2 Monetary policy paradigms The purpose of this section is to provide an overview of the shift in monetary policy paradigm that has been discussed in a partial way and from different perspectives in earlier chapters.6 Both paradigms take as given the inertia in inﬂation that produces the Phillips curves and both incorporate the IS curve. The ﬁrst paradigm, which we shall call the money supply model or LM paradigm, is characterized by the following propositions: (1) the ultimate determinant of the price level and rate of inﬂation is the money supply; (2) the instrument of monetary policy is the money supply; (3) the mechanism through which the economy adjusts to a new equilibrium with constant inﬂation following a shock is that embodied in the IS/LM model plus the inertia-augmented (or expectations-augmented) Phillips curve. Let us examine how an IS shock is handled in this paradigm. We assume the economy begins at equilibrium unemployment with constant inﬂation equal to the growth rate of the money supply set by the central bank. For a positive IS shock, the impact of the rise in aggregate demand on output in the short run is dampened because the rise in income 6 See also Allsopp and Vines (2000). Keyn: “chap05” — 2005/11/22 — page 138 — #8 MONETARY POLICY 139 pushes up the demand for money. As portfolios are rebalanced, the interest rate rises. This is a movement along the LM to the north-east. The change in output and employment then feeds through to a rise in inﬂation, which given the ﬁxed money supply growth rate triggers a leftward shift in the LM curve. This induces a further dampening of the initial stimulus. In this paradigm, monetary policy is passive (in the form of a ﬁxed growth rate of the money supply) and the economy adjusts to the new equilibrium by following a protracted spiral-shaped path as lags in inﬂation interact with a shifting LM curve. The so- called ‘Keynes effect’ is doing the work of raising the interest rate: rising inﬂation relative to a ﬁxed money supply growth reduces real money balances and leads to a portfolio adjustment with bonds being sold. Excess supply of bonds pushes bond prices down and the interest rate up. The higher real interest rate dampens interest-sensitive spending. The second paradigm, which we shall call the interest rate reaction function or MR paradigm, is characterized as follows: (1) the ultimate determinant of the price level and inﬂation is policy; (2) the instrument of policy is the short-term nominal interest rate; (3) the mechanism through which the economy adjusts to a new equilibrium with constant inﬂation following a shock is encapsulated in an interest rate rule. We take the same example as above. For a positive IS shock, the central bank responds to the rise in inﬂation due to the increase in output: as a consequence it raises the interest rate. Output falls below the equilibrium and brings inﬂation down: the central bank adjusts the interest rate to guide the economy down the MR curve to achieve the inﬂation target at equilibrium output. As far as monetary policy is concerned, the paradigm shift centres on two issues: the choice of monetary policy instrument and the choice of an active or a passive policy. From a stabilization perspective, it was clear a long time ago that to operate monetary policy in a passive fashion—be it with a ﬁxed money supply or a ﬁxed interest rate— was not necessarily optimal. William Poole provides a classic early treatment (1970) of the issue by looking ﬁrst at how the relative importance of LM versus IS shocks affects the optimal choice of a money supply versus an interest rate instrument.7 By drawing simple IS/LM diagrams, it is apparent that if the economy is characterized by LM shocks (e.g. in the demand for money), a ﬁxed interest rate is better for output stability than a ﬁxed money supply; the converse holds for IS shocks. The second contribution of Poole’s paper is to show that an active monetary policy is normally superior to a passive one when the economy is characterized by shocks and by lags in adjustment. Poole’s analysis is conﬁned to the short run with prices ﬁxed. The tenor of his arguments is even more persuasive when we move to the medium run and allow prices to adjust. From the perspective of the second paradigm, it is not sensible for policy makers to leave the adjustment mechanism to work automatically via the Keynes effect as in the LM paradigm. As we have seen in Chapter 3 when setting out the analysis under a ﬁxed monetary growth rate, the adjustment path to the new equilibrium following a distur- bance to the economy is protracted and complicated to explain. This is because of the interaction between inﬂation inertia and the portfolio adjustment process (the Keynes 7 Poole (1970). Keyn: “chap05” — 2005/11/22 — page 139 — #9 140 THE MACROECONOMIC MODEL effect) through which changes in the real money supply affect the interest rate (e.g. LM shifts left as rising inﬂation relative to a ﬁxed money supply growth cuts the real money supply). As we have seen, a further complication arises because of the impact of changes in the inﬂation rate on the demand for money (LM shifts right as the demand for money falls with rising inﬂation). The complexities of explaining the dynamic path of adjustment is not simply a problem for those teaching macroeconomics or trying to learn about it but also reﬂects a problem facing policy makers. The spiral-shaped adjustment path could be short-circuited within the LM paradigm: having achieved a fall in inﬂation to the level desired (equal to the growth rate of the money supply) with unemployment above the ERU , the monetary authority could inject a one-off boost to the money supply to take the economy straight to the new equilibrium. However, this is an uneasy mixture of a passive monetary policy with occasional activism and could well be misinterpreted by the public as the inconsis- tent implementation of policy. By contrast, in the second paradigm in the IS-PC-MR model, the monetary policy reac- tion function based on the use of the interest rate as instrument is an activist policy framework that is consistent with steering the economy toward equilibrium unemploy- ment and providing a nominal anchor. Frequent adjustments have to be made to the interest rate in order to achieve the central bank’s objective. This highlights the fact that it is quite consistent to think of the central bank as following a ‘rule-based’ approach to monetary policy, yet having to be very active. Fig. 17.14 in Chapter 17 illustrates the frequent interest rate adjustments made by central banks in the USA, the eurozone, and the UK since 1999. It is crucial to see that it is the implementation of the policy rule itself that establishes the nominal anchor and thus ultimately determines the price level or the rate of inﬂa- tion in this paradigm (depending on whether the target is the price level or the rate of inﬂation). The adjustment path is easy to explain and straightforward as we have seen in Chapter 3, since the central bank responds directly to shocks by changing the inter- est rate. The question of how to bring about the required change in the interest rate is then a technical problem for the central bank; whereas in the ﬁrst paradigm, agents are faced with an economic problem of trying to ﬁgure out the impact of changes in inﬂation on portfolio choices and hence on the interest rate. These arguments form the central case for using the second paradigm. It is a better description of how monetary policy is conducted and it comes closer to how it should be conducted, given the objectives of the central bank. Milton Friedman, the most famous proponent of the use of the money supply as policy target by the central bank, has conceded that ‘The use of the quantity of money as a target has not been a success.’ He added: ‘I’m not sure I would as of today push it as hard as I once did’ (Financial Times, 7 June 2003). 3 The monetary policy rule in the 3-equation model In Chapter 3, we developed a graphical method to predict how an inﬂation-targeting central bank that aims to minimize the ﬂuctuations of output and inﬂation from its targets would respond to a variety of shocks. In this section, we pin down the role played Keyn: “chap05” — 2005/11/22 — page 140 — #10 MONETARY POLICY 141 by the following six key variables in central bank policy making: (1) the central bank’s inﬂation target, π T (2) the central bank’s preferences, β (3) the slope of the Phillips curve, α (4) the interest sensitivity of aggregate demand (i.e. the slope of the IS curve), a (5) the equilibrium level of output, ye (6) the stabilizing interest rate, rS . In order to make the discussion of monetary policy rules concrete, we shall use speciﬁc examples of the central bank’s utility function, policy instrument, and constraints. How- ever, the basic method for deriving a monetary policy rule will be the same if different variants are chosen. It involves the following steps: (1) Deﬁne the central bank’s utility function in terms of both output and inﬂation. This produces the policy maker’s indifference curves in output-inﬂation space. (2) Deﬁne the constraints faced by the policy maker: these are the Phillips curves, which are also shown in output-inﬂation space. (3) Derive the optimal monetary rule in output-inﬂation space: this is the monetary rule, MR line. For a given Phillips curve that it faces, this shows the central bank’s chosen combination of output and inﬂation. Roughly, the higher is inﬂation as determined by the Phillips curve the economy is on, the lower will the central bank set aggregate demand and hence output in order to reduce inﬂation. Hidden in this relationship is the policy instrument, r, that the central bank will use to secure the appropriate level of aggregate demand and hence output. We saw this graphically in Chapter 3: the central bank chooses the best point along the Phillips curve that it faces and in order to deliver the right level of aggregate demand, it must set the interest rate at the level shown by the IS curve. (4) We can also derive the interest rate rule, which tells the central bank how to adjust the interest rate in response to current economic conditions. 3.1 The central bank’s utility function In Chapter 3, we introduced in an informal way the central bank’s indifference curves representing the trade-off in its preferences between inﬂation and unemployment. We now explain how these can be derived more formally. We assume that the central bank has two concerns: the rate of inﬂation, π , and the level of output, y. Looking ﬁrst at inﬂation and following the discussion in section 2, we assume that it has a target rate of inﬂation π T and that it wants to minimize ﬂuctuations around π T . A simple way of writing this is to assume that it wants to minimize the loss function: (π − π T )2 . Keyn: “chap05” — 2005/11/22 — page 141 — #11 142 THE MACROECONOMIC MODEL Rather than having the central bank maximize a utility function, we have it minimize a loss function. A loss function is just like a utility function except that the higher the loss, the worse it is for the central bank (we use it rather than a utility function purely for convenience—by putting a minus sign in front of the expression above, the central bank will want to maximize it). This particular loss function has two implications. First, the central bank is as concerned to avoid inﬂation below its target as it is inﬂation above π T . If π T = 2% the loss from π = 4% is the same as the loss from π = 0%. In both cases (π − π T )2 = 4. Second, it attaches increased importance to bringing inﬂation back to its target the further it is away from π T ; the loss from π = 6% is 16, compared to the loss of 4 from π = 4%. The central bank’s marginal disutility is increasing as the gap between inﬂation and the target grows. We turn now to the central bank’s second concern—about output and employment. We assume the central bank’s target level of output is the equilibrium level ye and it seeks to minimize the gap between y and ye . At this point it is useful to draw attention to the fact that we have assumed that the equilibrium output level ye is known, that the central bank’s target output level is ye , and that it is able to stick to this target. As we shall see in section 6, even if ye is known, the central bank may target a higher level of output. Output (or employment) targets are likely to arise from the interplay of interest groups in the economy mediated by political institutions, and central banks may be unable or unwilling to go against these pressures at particular times (e.g. just before an election). The central bank’s loss as a result of output being different from its target of ye is (y − ye )2 . Note that this loss function again suggests a symmetrical attitude to positive and negative deviations—in this case, from the equilibrium level of output. The most straightforward way of thinking about this is that the central bank understands the model and realizes that inﬂation is only constant at y = ye . If y < ye then this represents unnecessary unemployment that should be eliminated. If y > ye , this is unsustainable and will require costly increases in unemployment to bring the associated inﬂation back down. Whenever the economy is disturbed, the central bank sees its task as steering the economy back to this constant-inﬂation output level. If the two loss functions are added together, we have the central bank’s objective func- tion: L = (y − ye )2 + β(π − π T )2 , (central bank loss function) where β is the relative weight attached to the loss from inﬂation. This is a critical para- meter: a β > 1 will characterize a central bank that places less weight on deviations in employment from its target than on deviations in inﬂation, and vice versa. An inﬂation- averse central bank is characterized by a higher β ; if the central bank cares only about inﬂation deviations and not at all about output deviations, β = ∞. Let us ﬁrst look at the geometry of the loss function in the Phillips curve diagram, on the assumption that β = 1. With β = 1, the weights on output and inﬂation deviations are the same, i.e. the central bank is equally concerned about inﬂation and output deviations from its targets. Keyn: “chap05” — 2005/11/22 — page 142 — #12 MONETARY POLICY 143 (a) (b) (c) p p p pT pT pT ye y ye y ye y Balanced: b = 1 Inflation averse: b > 1 Unemployment averse: b < 1 Figure 5.1 Central bank loss functions: utility declines with distance from the ‘bull’s eye’ The loss function is simple to draw: with β = 1, each indifference curve is a circle with (ye , π T ) at its centre (see Fig. 5.1(a)). The loss declines as the circle gets smaller. When π = π T and y = ye , the circle shrinks to a single point (called the ‘bliss point’) and the loss is at a minimum, which is zero. The diagram is easy to remember if you think of it as a target (as for archery) with the central bank’s objective to get as close to the bull’s eye as possible. With β = 1, the central bank is indifferent between inﬂation 1% above (or below) π T and output 1% below (or above) ye . They are on the same loss circle. Only when β = 1, do we have indifference circles. If β > 1, the central bank is indifferent between (say) inﬂation 1% above (or below) π T and output 2% above (or below) ye . They are on the same loss curve. This makes the indifference curves ellipsoid as in Fig. 5.1(b). A central bank with less aversion to inﬂation (β < 1) will have ellipsoid indifference curves with a vertical rather than a horizontal orientation (Fig. 5.1(c)). In that case, the indifference curves are steep reﬂecting that the central bank is only willing to trade off a given fall in inﬂation for a smaller fall in output than in the other two cases. If the central bank cares only about inﬂation then β = ∞ and the loss ellipses become one dimensional along the line at π = π T .8 3.2 The Phillips curve constraint Next, we shall assume that the central bank can control the level of output via its ability to use monetary policy (by setting the interest rate) to control aggregate demand, y D . However, it cannot control inﬂation directly—only indirectly via y. As we have already discussed, output affects inﬂation via the Phillips curve: π = π−1 + α.(y − ye ). (5.1) 8 The central bank’s preferences can be presented in this simple way if we assume that the central bank’s discount rate is inﬁnite. This means that it only considers one period at a time when making its decision. In Chapter 3, we discussed informally the role that the central bank’s discount rate can play when we compared a rapid disinﬂation policy that produces a large initial rise in unemployment (‘cold turkey’) with a gradualist policy. Keyn: “chap05” — 2005/11/22 — page 143 — #13 144 THE MACROECONOMIC MODEL PC (p I = 4) p VPC PC (p I = 3) A PC (p I = 2) 4 D 3 pT = 2 C B y1 ye y Figure 5.2 Loss circles and Phillips curves This is shown in Fig. 5.2, where the upwards sloping lines are Phillips curves. For the moment for simplicity it is assumed that α = 1, so that each Phillips curve has a slope of 45◦ . Each Phillips curve is labelled by lagged inﬂation. Assume that π−1 = π T = 2% (remember that this PC must go through point B at which y = ye and π = 2). The central bank is in the happy position of being able to choose the bull’s eye point B or (π T , ye ) at which its loss is zero. What happens if there has been a shock to inﬂation and it is not equal to the inﬂation target? Suppose, for example, that inﬂation is 4%. Given inﬂation inertia, this means that the central bank is faced with the constraint of the Phillips curve shown by PC(π I = 4) and can only choose between points along it. The bull’s eye is no longer obtainable. The central bank faces a trade-off: if the central bank wants a level of output of y = ye next period, then it has to accept an inﬂation rate above its target, i.e. π = 4 = π T (i.e. point A). On the other hand, if it wishes to hit the inﬂation target next period, it must accept a much lower level of output next period (point C). Point A corresponds to a fully accommodating monetary policy in which the objective is purely to hit the output target (β = 0), and point C corresponds to a completely non-accommodating policy, in which the objective is purely to hit the inﬂation target (β = ∞). In fact, as will be evident from Fig. 5.2, if the central bank is faced by π I = 4, then given its preferences, it can do better (achieve a loss circle closer to B) than either point A or point C. It minimizes its loss function by choosing point D, where the PC(π I = 4) line is tangential to the indifference curve of the loss function closest to the bull’s eye. Thus if π I = 4 it will choose an output level y1 which will in turn imply an inﬂation rate of 3%. 3.3 Deriving the monetary rule, MR For simplicity, we use the form of the loss function in which β = 1 so that we have loss circles as in Fig. 5.2 above. This implies: L = (y − ye )2 + (π − π T )2 . Keyn: “chap05” — 2005/11/22 — page 144 — #14 MONETARY POLICY 145 p PC (p I = 4) PC (p I = 3) PC (p I = 2) 4 D 3 C B p T= 2 MR y1 y2 ye y Figure 5.3 Deriving the MR line And using the simplest version of the Phillips curve in which α = 1 so that each PC has a 45◦ slope as in Fig. 5.2: π = π−1 + y − ye . The geometry can be seen as follows: in Fig. 5.3, the points of tangency between successive Phillips curves and the loss circles show the level of output that the central bank needs to choose so as to minimize its loss at any given level of π−1 . Thus when π−1 = 3, its loss is minimized at C; or when π−1 = 4 at D. Joining these points (D, C, B) produces the MR line that we used in Chapter 3. We can see from Fig. 5.3 that a one unit rise in π−1 implies a half unit fall in y, for example an increase in π−1 from 3% to 4% implies a fall in y from y2 to y1 . We can derive the monetary rule explicitly as follows. By choosing y to minimize L we can derive the optimal value of y for each value of π−1 . Substituting the Phillips curve into L and minimizing with respect to y, we have: ∂L = 2(y − ye ) + 2(π−1 + (y − ye ) − π T ) = 0 ∂y = (y − ye ) + (π−1 + (y − ye ) − π T ) = 0. Since π = π−1 + y − ye , ∂L = (y − ye ) + (π − π T ) = 0 ∂y =⇒ (y − ye ) = −(π − π T ). (MR equation) The monetary rule in the Phillips diagram shows the equilibrium for the central bank: it shows the equilibrium relationship between the inﬂation rate chosen indirectly and the level of output chosen directly by the central bank to maximize its utility (minimize its loss) given its preferences and the constraints it faces. Keyn: “chap05” — 2005/11/22 — page 145 — #15 146 THE MACROECONOMIC MODEL p PC (p I = 4) PC (p I = 3) PC (p I = 2) 4 3 D C B p T= 2 MR b>1 a ye y Figure 5.4 Inﬂation-averse government: ﬂat MR line Note: The angle marked α in the diagram is in fact the angle whose tangent is α. We adopt this convention throughout. This shows the monetary rule as an inverse relation between π and y with a negative 45◦ slope (Fig. 5.3). Speciﬁcally, it shows that the central bank must reduce aggregate demand and output, y, below ye so as to reduce π below π T by the same percentage. Thus this could be thought of as monetary policy halfway between: (i) completely non-accommodating when the central bank cuts output sufﬁciently to bring inﬂation straight back to π T at the cost of a sharp rise in unemployment; and (ii) a completely accommodating one, which leaves inﬂation (and output) unchanged. If the monetary rule was ﬂat at π T we would have a completely non-accommodating monetary policy; if it was vertical at ye , we would have a completely accommodating monetary policy. The monetary rule ends up exactly halfway between an accommodating and a non- accommodating policy because of two simplifying assumptions. By relaxing these, we learn what it is that determines the slope of the monetary rule. We shall see that the more inﬂation averse is the central bank (the ﬂatter are the loss ellipses) and the more responsive are wages to employment (the steeper are the Phillips curves), the ﬂatter is the MR line. The degree of inﬂation aversion of the central bank is captured by β in the central bank loss function: L = (y − ye )2 + β(π − π T )2 . If β > 1, the central bank attaches more importance to the inﬂation target than to the output target. This results in a ﬂatter monetary rule as shown in Fig. 5.4. Given these preferences, any inﬂation shock that shifts the Phillips curve upward implies that the optimal position for the central bank will involve a more signiﬁcant output reduction and hence a sharper cut in inﬂation along that Phillips curve than in the neutral case. Using the same reasoning, β < 1 implies that the monetary rule is steeper than the minus 45◦ line. The second factor that determines the slope of the monetary rule is the responsiveness of inﬂation to output (i.e. the slope of the Phillips curve): π − π−1 = α(y − ye ). This factor was not discussed in Chapter 3. Thus far, we have assumed α = 1. Intuitively if α > 1 so the Phillips curves are steeper, any given cut in output has a greater effect in reducing inﬂation than when α = 1. As we can see from Fig. 5.5, this makes the MR line ﬂatter than Keyn: “chap05” — 2005/11/22 — page 146 — #16 MONETARY POLICY 147 p 4 3 D B p T= 2 C MR1 a>1 a=1 MR0 a>1 a=1 ye y Figure 5.5 High responsiveness of inﬂation to output: ﬂat MR line in the case in which α = 1: MR0 is the old and MR1 the new monetary rule line obtained by joining up the points D, C, and B. By altering the slope of the Phillips curve, we also learn more about the monetary rule. Steeper Phillips curves make the MR line ﬂatter: let us now compare the response of a central bank to a given rise in inﬂation in the case where the Phillips curves are steep with the case where they have a slope of one. Our intuition tells us that steeper Phillips curves make things easier for the central bank since a smaller rise in unemployment (fall in output) is required to achieve any desired fall in inﬂation. Let us show this in a diagram. In the left hand panel of Fig. 5.6 we compare two economies, one with ﬂatter Phillips curves (dashed) and one with steeper ones. As we have already shown, the MR line is ﬂatter for the economy with steeper Phillips curves: this is MR1 . Suppose there is a rise in inﬂation in each economy that shifts the Phillips curves up: each economy is at point B. We can see that a smaller cut in aggregate demand is optimal in the economy with the steeper Phillips curves (point D). This reﬂects our intuitive argument above.9 In the right hand panel, we compare two economies with identical supply sides but in which one has an inﬂation-averse central bank (the oval-shaped indifference ellipse) and show the central bank’s reaction to inﬂation at point B. The more inﬂation-averse central bank always responds to this shock by cutting aggregate demand (and output) more (point D). Having seen the role of the slope of the Phillips curve and of the central bank’s prefer- ences in the diagrams, we now derive the more general form of the central bank’s mon- etary rule as follows. We also make explicit the timing structure in all of the equations. By choosing the interest rate in period zero, the central bank affects output and inﬂation in period 1. We assume it is only concerned with what happens in period 1. This is the reason that its loss function is deﬁned in terms of y1 and π1 . If we let β and α take any 9 For those who are curious, with β ≥ 1, the output cut in response to a given inﬂation shock is always less 1 when α > 1 as compared with α = 1. For β < 1, the output cut is less as long as α > (1/β) 2 . Keyn: “chap05” — 2005/11/22 — page 147 — #17 148 THE MACROECONOMIC MODEL p p 4 B 4 B C C 3 3 D D p T= 2 MR1 MR1 MR0 MR0 ye y ye y a. Steeper Phillips curves b. Greater inflation-aversion Figure 5.6 Comparing the response of the central bank in two cases: steeper Phillips curves and a more inﬂation-averse central bank positive values, the central bank chooses y to minimize L = (y1 − ye )2 + β(π1 − π T )2 (5.2) subject to π1 = π0 + α(y1 − ye ). (5.3) By substituting (5.3) into (5.2) and differentiating with respect to y1 (since this is the variable the central bank can control via its choice of the interest rate), we have: ∂L = (y1 − ye ) + αβ(π0 + α(y1 − ye ) − π T ) = 0. (5.4) ∂ y1 Substituting equation (5.3) back into equation (5.4) gives: (y1 − ye ) = −αβ(π1 − π T ). (monetary rule, MR) Now it can be seen directly that the larger is α (i.e. the more responsive are wages to employment) or the larger is β (i.e. the more inﬂation averse is the central bank), the ﬂatter will be the slope of the monetary rule. In the ﬁrst case this is because any reduction in aggregate demand achieves a bigger cut in inﬂation, i.e. whatever its preferences, the central bank gets a ‘bigger bang (i.e. fall in inﬂation) for its buck (i.e. fall in aggregate demand)’. In the second case, this is because, whatever the labour market it faces, a more inﬂation-averse central bank will wish to reduce inﬂation by more than a less ‘hard- nosed’ one. Keyn: “chap05” — 2005/11/22 — page 148 — #18 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 the six key inputs to the deliberations of the central bank is now clear. (1) the central bank’s inﬂation target, π T : this affects the position of the MR line; (2) the central bank’s preferences, β : this determines the shape of the loss ellipses and affects the slope of the MR line; (3) the slope of the Phillips curve, α: this also affects the slope of the MR line; (4) the interest sensitivity of aggregate demand, a: this determines the slope of the IS curve; (5) the equilibrium level of output, ye : this determines the position of the vertical Phillips curve and affects the position of the MR line; (6) the stabilizing interest rate, rS : the central bank adjusts the interest rate relative to rS so it must always analyse whether this has shifted, e.g. as a result of a shift in the IS or due to a change in the equilibrium level of output, ye . On the basis of the more detailed discussion provided in this chapter, the IS-PC-MR graphical model can be used to analyse a wide variety of problems. In Chapters 3 and 4, the graphical analysis of inﬂation shocks, temporary and permanent aggregate demand shocks, and supply-side shocks is provided. In each case, the role of the six inputs to the central bank’s decision can be analysed and experiments undertaken to evaluate the impact of variations in them. We take one of those examples in order to clarify in the diagram each input to the central bank’s decision and to highlight the role played by the lag in the effect of monetary policy on aggregate demand and output. The example shows that the central bank is engaged in a forecasting exercise: it must forecast next period’s Phillips curve and next period’s IS curve. We assume that the economy starts off with output at equilibrium and inﬂation at the target rate of 2% as shown in Fig. 5.7. We take a permanent positive aggregate demand shock such as improved buoyancy of consumer expectations: the IS moves to IS . The consequence of output above ye is that inﬂation will rise above target—in this case to 4%. This deﬁnes next period’s Phillips curve (PC(π I = 4)) along which the central bank must choose its preferred point: point C. The central bank forecasts that the IS curve is IS , i.e. it judges that this is a permanent shock and by going vertically up to point C in the IS diagram, it can work out that the appropriate interest rate to set is r . As the Phillips curve shifts down with falling inﬂation, the central bank reduces the interest rate and the economy moves down the MR line to point Z and down the IS curve to Z . This example highlights the role of the stabilizing real interest rate, rS : following the shift in the IS curve, there is a new stabilizing interest rate and, in order to reduce inﬂation, the interest rate must be raised above the new rS , i.e. to r . To summarize, the rise in output builds a rise in inﬂation above target into the economy. Because of inﬂation inertia, this can only be eliminated by pushing output below and (unemployment above) the equilibrium. The graphical presentation emphasizes that the central bank raises the interest rate in response to the aggregate demand shock because it can work out the Keyn: “chap05” — 2005/11/22 — page 149 — #19 150 THE MACROECONOMIC MODEL r C r rS Z a A B rS IS IS p VPC PC (p I = 4) PC (p I =2) 4 B C pT= 2 A, Z MR a 1/ab ye y y Figure 5.7 Permanent IS shock consequences for inﬂation. The diagram highlights how the parameters a, α, and β affect the central bank’s calculation of the required change in the interest rate. The central bank is forward looking and takes all available information into account: its ability to control the economy is limited by the presence of inﬂation inertia i.e. lagged inﬂation in the Phillips curve and by the time lag for a change in the interest rate to take effect i.e. the lagged interest rate in the IS curve. In the IS equation it is the interest rate at time zero that affects output at time one: y1 − ye = −a(r0 − rS ). This is because it takes time for a change in the interest rate to feed through to consumption and investment decisions. In Fig. 5.7 in order to choose its optimal point C on the Phillips curve (π I = 4), the central bank must set the interest rate now at r . As is clear from the diagram, we have been working with this assumption throughout. However, it is interesting to see what happens if the central bank could affect output immediately, i.e. if y0 − ye = −a(r0 − rS ). In this case, as soon as the IS shock is diagnosed, the central bank would raise the interest rate to rS . The economy then goes directly from A to Z in the IS diagram and it remains at A in the Phillips diagram, i.e. points A and Z coincide. Since the aggregate demand shock Keyn: “chap05” — 2005/11/22 — page 150 — #20 MONETARY POLICY 151 is fully and immediately offset by the change in the interest rate, there is no chance for inﬂation to rise. This underlines the crucial role of lags and hence of forecasting for the central bank: the more timely and accurate are forecasts of shifts in aggregate demand (and of other kinds of shock), the greater is the chance that the central bank can offset them and limit their impact on inﬂation. Once inﬂation has been affected, the presence of inﬂation inertia means that the central bank must change the interest rate and get the economy onto the MR line in order to steer it back to the inﬂation target. In addition to providing a framework for a systematic analysis of shocks to an individual economy and how aspects of the aggregate demand and supply-side structures affect central bank policy, the IS-PC-MR graphical model provides a useful way to investigate how a common currency area works, i.e. when different economies share a central bank. As an example, we can compare two economies with the same supply side (i.e. ye and α are the same) and a common central bank (i.e. π T and β are the same), but which differ in the interest sensitivity of expenditure (a is different) and which are both initially in equilibrium with constant inﬂation (with r = rS ). If both economies are subjected to the same shock to autonomous demand, we can analyse the consequences using the graphical 3-equation model (see Fig. 17.15). As a second example, we could look at the implications for two economies in a currency union that are identical in all respects except for the responsiveness of inﬂation to changes in the level of output, e.g. one economy has a steep WS curve and therefore steep Phillips curves (high α) whereas the other has ﬂat Phillips curves. If a common inﬂation shock affects both economies, how would the optimal response of a national central bank differ from that of a central bank that sets a common interest rate for both economies? Examples of this kind are discussed further in Chapter 17. 4 A Taylor Rule in the IS-PC-MR model 4.1 Interest rate rules In the previous section, we looked at how the IS curve is used by the central bank to ﬁnd out what interest rate to set once it has worked out its optimal output-inﬂation combination in the Phillips diagram, i.e. once it has located the best available position on the MR line. We now show how to derive an interest rate rule, which directly expresses the change in the interest rate in terms of the current state of the economy. We then show how it relates to the famous Taylor Rule. We bring together the three equations: π1 = π0 + α(y1 − ye ) (Phillips curve) y1 − ye = −a(r0 − rS ) (IS) 1 π1 − π T = − (y1 − ye ). (MR) αβ From these equations, we want to derive a formula for the interest rate, r0 in terms of period zero observations of inﬂation and output in the economy. If we substitute for π1 Keyn: “chap05” — 2005/11/22 — page 151 — #21 152 THE MACROECONOMIC MODEL using the Phillips curve in the MR, we get 1 π0 + α(y1 − ye ) − π T = − (y1 − ye ) αβ 1 π0 − π T = − α + (y1 − ye ) αβ and if we now substitute for (y1 − ye ) using the IS, we get the interest-rate rule: 1 r0 − rS = π0 − π T . (Interest rate rule) 1 a α+ αβ We can see that r0 − rS = 0.5 π0 − π T if a = α = β = 1. Two things are immediately apparent: ﬁrst, only the inﬂation and not the output devi- ation is present in the rule and second, all the parameters of the 3-equation model matter for the central bank’s response to a rise in inﬂation. If each parameter is equal to one, the coefﬁcient on the inﬂation deviation is one-half. If inﬂation is 1% point above the target, then the interest rate rule says that the real interest rate needs to be 0.5 percentage points higher. Since inﬂation is higher by 1% point, the nominal interest rate must be raised by 1 + 0.5, i.e. by 1.5 percentage points in order to secure a rise in the real interest rate of 0.5 percentage points. For a given deviation of inﬂation from target, and in each case, comparing the situation with that in which a = α = β = 1, we can see that • a more inﬂation-averse central bank (β > 1) will raise the interest rate by more; • when the IS is ﬂatter (a > 1), the central bank will raise the interest rate by less; • when the Phillips curve is steeper (α > 1), the central bank will raise the interest rate by less. Let us compare the interest rate rule that we have derived from the 3-equation model with the famous Taylor Rule,10 r0 − rS = 0.5.(π0 − π T ) + 0.5.(y0 − ye ), (Taylor Rule) where π T is the central bank’s inﬂation target, ye is the equilibrium level of output, and rS is the ‘stabilizing’ interest rate, i.e. the real interest rate on the IS curve when output is at equilibrium. The Taylor Rule states that if output is 1% above equilibrium and inﬂation is at the target, the central bank should raise the interest rate by 0.5 percentage points relative to stabilizing interest rate. As above we interpret the difference between y and ye as the percentage gap; this is the equivalent of deﬁning y as the log of output. And if inﬂation is 1% point above the target and output is at equilibrium, then the Taylor rule says that the real interest rate needs to be 0.5 percentage points higher. 10 Taylor (1993). Keyn: “chap05” — 2005/11/22 — page 152 — #22 MONETARY POLICY 153 4.2 Interest rate rules and lags The interest rate rule derived from the 3-equation model is similar to Taylor’s rule, which he developed as an empirical description of how central banks behaved. However, it only requires the central bank to respond to inﬂation. At ﬁrst sight, this seems paradoxical, given that the central bank cares about both inﬂation and output as demonstrated by its loss function (equation 5.2). It turns out that to get an interest rate rule that is like the Taylor rule in which both the inﬂation and output deviations are present, we need to modify the 3-equation model to bring the lag structure closer to that of a real economy. In this section, we explain how this is done. However, for most purposes, the analysis of shocks and policy responses can be conducted with the simpler single lag model, which we keep as our core 3-equation IS-PC-MR model in the remainder of the book. As before we assume that there is no observational time lag for the monetary author- ities, i.e. the central bank can set the interest rate (r0 ) as soon as it observes current data (π0 and y0 ). We continue to assume that the interest rate only has an effect on output next period, i.e. r0 affects y1 . The new assumption about timing that is required is that it takes a year for output to affect inﬂation, i.e. the output level y1 affects inﬂation a period later, π2 . This means that it is y0 and not y1 that is in the Phillips curve for π1 .11 The ‘double lag’ timing assumptions match the view of the Bank of England (1999): The empirical evidence is that on average it takes up to about one year in this and other industrial economies for the response to a monetary policy change to have its peak effect on demand and production, and that it takes up to a further year for these activity changes to have their fullest impact on the inﬂation rate. The double lag structure is shown in Fig. 5.8 and emphasizes that a decision taken today by the central bank to react to a shock will only affect the inﬂation rate two periods later, i.e. π2 . When the economy is disturbed in the current period (period zero), the central bank looks ahead to the implications for inﬂation and sets the interest rate so as to determine y1 , which in turn determines the desired value of π2 . As the diagram illustrates, action by the central bank in the current period has no effect on output or inﬂation in the current period or on inﬂation in a year’s time. Since the central bank can only choose y1 and π2 by its interest rate decision, its loss function is L = (y1 − ye )2 + β(π2 − π T )2 . Given the double lag, the three equations are: π1 = π0 + α(y0 − ye ) (Phillips curve) y1 − ye = −a(r0 − rS ) (IS) 1 π2 − π T = − (y1 − ye ). (MR) αβ 11 Three-equation models along these lines were developed by Svennson (1997) and Ball (1999b), and dis- cussed in Romer (2001). See also Carlin and Soskice (2005). Keyn: “chap05” — 2005/11/22 — page 153 — #23 154 THE MACROECONOMIC MODEL p0 y0 r0 p1 y1 Figure 5.8 Lag structure in the IS-PC-MR model p2 required to deliver a standard Taylor Rule By repeating the same steps as above, we can derive the interest rate rule, which takes the form of a Taylor rule: 1 r0 − rS = π0 − π T + α(y0 − ye ) . 1 a α+ αβ And r0 − rS = 0.5(π0 − π T ) + 0.5(y0 − ye ) (Taylor rule in 3-equation (double lag) model) if a = α = β = 1. We can also show how a Taylor Rule is derived geometrically from the IS-PC-MR model. This helps bring out the role that differences in economic structure (demand and supply sides) and in central bank preferences can have on the coefﬁcients of Taylor Rules. In Fig. 5.9, the initial observation of output and inﬂation in period zero is shown by the large cross, ×. To work out what interest rate to set, the central bank notes that in the following period, inﬂation will rise to π1 and output will still be at y0 since a change in the interest rate can only affect y1 . The central bank therefore knows that the constraint it faces is the PC(π1 ) and it chooses its best position on it to deliver π2 . The best position on PC(π1 ) is shown by where the MR line crosses it. This means that output must be y1 and therefore that the central bank sets r0 in response to the initial information shown by point ×. This emphasizes that the central bank must forecast a further period ahead in the double lag model in order to locate the appropriate Phillips curve, and hence to determine its optimal interest rate choice for today: it chooses r0 → y1 → π2 . Once the economy is on the MR line, the central bank continues to adjust the interest rate to guide the economy along the MR back to equilibrium. The remaining task is to give a geometric presentation of the double lag model and the associated Taylor Rule: rt − rS = 0.5 · (πt − π T ) + 0.5 · (yt − ye ). Fig. 5.10 shows the example in Fig. 5.9 again. As shown in the left hand panel of Fig. 5.10, the two components of the Taylor Rule are shown by the vertical distances equal to α(y0 − ye ) and π0 − π T , where α is the slope of the Phillips curve. If these are added together, we have the forecast of π1 − π T . Just one more step is needed to express this forecast in terms of (r0 − rS ) and therefore to deliver a Taylor Rule. As shown in the right hand panel of Fig. 5.10, the vertical distance π1 − π T can also be expressed as (α + γ) · a(r0 − rS ), where α and γ = αβ reﬂect the slopes 1 of the Phillips curve and the monetary rule curve, respectively and a reﬂects the slope of Keyn: “chap05” — 2005/11/22 — page 154 — #24 MONETARY POLICY 155 r r0 r1 rS IS PC (p1) y p PC (p0) p1 p0 p2 p3 pT PC (p2 ) MR y1 y2 ye y0 y Figure 5.9 Taylor Rule example the IS curve.12 Thus, we have (α + γ) · a(r0 − rS ) = (π0 − π T ) + α(y0 − ye ) and by rearranging to write this in terms of the interest rate, we have a Taylor Rule: 1 r 0 − rS = π0 − π T + α(y0 − ye ) (α + γ)a = 0.5 · (π0 − π T ) + 0.5 · (y0 − ye ) if α = γ = a = 1. 12 Note that in the diagram, a, α, and γ refer to the angles shown and in the algebra to the gradients i.e. to the tangents of the relevant angles. Keyn: “chap05” — 2005/11/22 — page 155 — #25 156 THE MACROECONOMIC MODEL r r r0 r0 a a rS rS IS IS a (r0–rS) a (r0–rS) PC (p1) y PC (p1) p p PC (p0) PC (p0) p1 p1 a a(y0–ye) MR MR aa (r0–rS) p0 p0 p2 p2 a (p0–pT) g ga (r0–rS) pT pT a (r0–rS) a (r0–rS) y1 ye y0 y y1 ye y Figure 5.10 Deriving the Taylor Rule One striking aspect of this discussion is that it helps to dispel a common confusion about Taylor Rules. It is often said that the relative weights on output and inﬂation in a Taylor Rule indicate the central bank’s preferences for reducing inﬂation as compared to output deviations. However, we have already seen that in the single lag model, the interest rate rule only has the inﬂation deviation in it in spite of the fact that the loss function places weight on both inﬂation and output deviations: the degree of inﬂation aversion affects the size of the aggregate demand (and hence the interest rate) response of the central bank. Once we modify the model to reﬂect the fact that a change in output takes a year to affect inﬂation (the double lag model), then both the inﬂation and output deviations appear in the interest rate rule and it resembles Taylor’s Rule. The reason is that the current period output deviation serves as a means of forecasting future inﬂation to which the central bank will want to react now. The central bank’s aversion to inﬂation affects its reaction to inﬂation and to the forecast of inﬂation contained in the output deviation term: it does not affect the relative weight on the inﬂation and output terms in the Taylor Rule. The relative weights on inﬂation and output in our Taylor Rule depend only on α, the slope of the Phillips curve, since the relative weights are used only to forecast next period’s inﬂation.13 It is the slope of the Phillips curves (α) that affect the relative weight on inﬂation and output in the Taylor Rule. For α > 1, the Phillips curves are steeper and the MR curve is ﬂatter. There are two implications, which go in opposite directions. First, a more 13 Bean (1998) derives the optimal Taylor rule in a model similar to the IS-PC-MR model. However in his model, the central bank’s preferences do affect the Taylor Rule weights. This arises from his inclusion of lagged output in the IS equation: if the coefﬁcient on lagged output is zero then the difference between the weight on inﬂation and on output in the Taylor rule only depends on the slope of the Phillips curve and not on preferences. Keyn: “chap05” — 2005/11/22 — page 156 — #26 MONETARY POLICY 157 restrictive interest rate reaction is optimal to deal with any given increase in output because this will have a bigger effect on inﬂation than with α = 1 (the MR curve is ﬂatter). But on the other hand, a given rise in the interest rate will have a bigger negative effect on inﬂation. These two effects imply that with α > 1, the balance between the coefﬁcients changes: the coefﬁcient on (π0 − π T ) goes down—so the central bank reacts less to an inﬂation shock whereas the coefﬁcient on (y0 − ye ) goes up—the central bank reacts more to an output shock as compared with the equal weights in the Taylor rule. We can see that Taylor’s weights of 0.5 and 0.5 on the inﬂation and output deviations arise when the IS curve, the Phillips curves, and the MR curve all have a slope of one (or more precisely in the case of the IS and the MR of minus one). This implies that the appropriate coefﬁcients on the Taylor rule form of the central bank’s monetary rule will be different from (0.5, 0.5) if economies differ in • the inﬂation aversion of the central bank, • the supply-side structure as reﬂected in the slope of the Phillips curve, or • in the interest-sensitivity of aggregate demand. 5 Problems with using an interest rate rule The central bank may sometimes be thwarted in its attempt to use an interest rate rule to stabilize the economy. One reason would be if investment or other components of aggregate demand fail to respond or to respond enough to the change in the interest rate. As we shall see in Chapter 7, empirical evidence for the impact of changes in the cost of capital (of which the interest rate is a key component) relative to the expected rate of return (measured for example by a change in Tobin’s q) is rather weak. Another reason why the interest rate may fail to affect output in the desired manner arises from the fact that the interest rate that is relevant to investment decisions is the long term real interest rate. The central bank can affect the short-term nominal interest rate. As we know, the real and the nominal interest rates differ by the expected rate of inﬂation. It remains to explain how the short- and long-term interest rates are related. The relationship is referred to as the term structure of interest rates. The long-term interest rate refers to the interest rate now (i.e. at time t) on an n-year bond. We can express the long-term interest rate as follows: in = 1/n · [i1 + i1+1|t + i1+2|t + · · · + i1+n−1|t ] + φnt . t t t t t (5.5) In words, this means the long-term interest rate (say, the interest rate on twenty-year bonds) is equal to the average of the expected interest rate on one-year bonds for the next twenty years plus the term φnt , which is called the ‘uncertainty premium’. In tranquil times, we would expect the long-term interest rate to exceed the short-term rate by the uncertainty premium and we would expect short- and long-term interest rates to move in the same direction. Monetary policy will then have the desired effect. As a counter-example, consider the situation in which the central bank cuts the short-term interest rate to stimulate the economy because it fears a recession is imminent. If the Keyn: “chap05” — 2005/11/22 — page 157 — #27 158 THE MACROECONOMIC MODEL ﬁnancial markets believe that the underlying cause of the recessionary threat is likely to produce higher inﬂation in the long run, then markets will believe a higher long-run real interest rate will be necessary. Higher long-term interest rates are likely to dampen interest-sensitive spending at a time when the authorities are trying to stimulate the economy. A third example of the limits to the use of monetary policy as a stabilization tool comes from the fact that the nominal interest rate cannot be negative. The reason for this— as we have seen—is that there is always the choice to hold cash with a zero nominal return. Zero places a ﬂoor on the cuts in the nominal interest rate that are available. Hence a problem can arise if the real interest rate required to stimulate activity in the economy were negative. In a very low inﬂation economy, there is therefore limited scope to use monetary policy to stimulate aggregate demand if the required real interest rate is negative, e.g. with an inﬂation target of 2%, the zero ﬂoor to the nominal interest rate means that real interest cannot be reduced below −2%. This is rather ironical— the successful implementation of a stability-oriented monetary policy along the lines outlined in this chapter may have the effect of producing an economy with low inﬂation in which the scope of monetary policy to stimulate the economy if it is hit by a negative shock is limited. We investigate the problem of a deﬂation trap below. To summarize, the reasons that monetary policy can fail to have its desired effect on output include the following: • investment is insensitive to the real interest rate; • the long-run real interest rate does not move in line with changes in the short-term nominal interest rate; • the central bank wishes to stimulate demand but the nominal interest rate is close to zero. 5.1 The deﬂation trap The simplest way to see how a deﬂation trap may operate is to combine the fact that the nominal interest rate cannot be negative with the fact that the real rate of interest is approximately: r = i − π E . Since i ≥ 0, the minimum real rate of interest is min r = −π . When inﬂation is positive, i.e. π > 0, this does not matter very much in general since the minimum r is negative. But when π < 0 the minimum real rate is positive. The problem that can arise is that the real rate needed to stabilize demand at ye is less than the minimum feasible real rate, i.e. rs < min r (π) = −π . This condition is shown in Fig. 5.11 where the stabilizing real interest rate is below the minimum feasible rate of 1%. Given the depressed state of aggregate demand depicted by the position of the IS curve, if inﬂation has fallen to −1%, then it will be impossible to achieve the equilibrium level of output. The approach to monetary policy described in this chapter of using the nominal interest rate in order to set the real interest rate associated with aggregate demand at equilibrium output then ceases to work. To see why, we assume the central bank sets the lowest real rate possible, namely r = −π , so that y = y0 and the economy is at at point A. Since y0 < ye , the consequence is that inﬂation falls. That implies that the minimum real rate rises, further reducing output Keyn: “chap05” — 2005/11/22 — page 158 — #28 MONETARY POLICY 159 r A min r = –p 1 rS IS Figure 5.11 The zero ﬂoor to the nominal y0 ye y interest rate and the deﬂation trap and hence increasing the speed at which inﬂation falls (in Fig. 5.11, the min r line shifts upward). The economy is thus caught in a vicious circle or a deﬂation trap. It is clear from Fig. 5.11 that getting out of the deﬂation trap requires either (1) a successful ﬁscal expansion or recovery of autonomous investment or consumption that shifts the IS curve to the right or (2) the creation of more positive inﬂation expectations. If expected inﬂation becomes less negative, the min r line shifts down and the central bank can use the interest rate based monetary rule in the usual way to move the economy to the south-east along the IS curve. However, the idea of escaping from the deﬂation trap by creating positive inﬂation expectations may not work in practice. Willem Buiter argues that this is ‘spitting in the wind’ because as the announcement has no implications for any current or future mon- etary policy instruments, it will not affect economic behaviour.14 Another way to put this point is to say that the only way to create expectations of inﬂation in the future is to create expectations of future higher aggregate demand: if the authorities do not take measures to create the demand, it is no good hoping that people will expect higher inﬂation. He stresses however, that assiduously pursuing a target of low but positive inﬂation may prevent the economy from getting into a deﬂation trap in the ﬁrst place. Buiter argues that a helicopter drop of money of the kind that Milton Friedman discussed— but in a more practical form of, for example, issuing a cheque for every citizen ﬁnanced by the issue of new high-powered money—would certainly raise aggregate demand as it would boost consumption spending (the IS curve would shift to the right). He points out however that independent central banks may be reluctant to do this since it is a combined ﬁscal and monetary policy measure (i.e. a ﬁscal transfer ﬁnanced by new money creation). This points to the important role of coordinated ﬁscal and monetary policy in solving a deﬂation trap and to a largely unanticipated danger of creating independent central banks. There is an additional channel through which a deﬂation trap can be sustained. Just as unanticipated inﬂation shifts wealth from creditors to debtors in the economy as the real 14 See Buiter (2003). Keyn: “chap05” — 2005/11/22 — page 159 — #29 160 THE MACROECONOMIC MODEL value of debts is eroded, unanticipated deﬂation has the opposite effect. If asset prices in the economy (e.g. property prices) are falling as well as goods prices, then debtors in the economy will not only ﬁnd that the real burden of their debt is rising (the debt is ﬁxed in nominal terms but prices are falling) but also that the assets that they have used as security or collateral for the debt are shrinking in value. This so-called balance sheet channel may make investment less sensitive to changes in the real interest rate thereby steepening the IS curve and weakening the investment response even if positive inﬂation expectations could be generated. The situation is further complicated when deﬂation gets entrenched because bankruptcies weaken the balance sheets of banks, threatening the stability of the banking system. Alternatively, banks may continue to extend loans to failing ﬁrms so as to prevent the bad loans from showing up on their balance sheets: this may postpone but not prevent a banking crisis. 6 Credibility, time inconsistency, and rules versus discretion 6.1 Backward-looking Phillips curves and credibility In the IS-PC-MR model, the Phillips curve is backward looking: π = π−1 + α.(y − ye ), which means that current inﬂation is determined by lagged inﬂation (and the output gap). This is consistent with the evidence that disinﬂation is costly, i.e. that in order to reduce inﬂation, output must be reduced. Although the evidence on costly disinﬂation discussed in section 1 indicates that reducing inﬂation from moderate levels appears to require a sacriﬁce in terms of higher unemployment, it was noted in the discussion of hyperinﬂation that relatively painless disinﬂation has been observed under some con- ditions. The debate about how best to model the inﬂation process is a very lively one in macroeconomic research at present and is discussed in detail in Chapter 15. The key point to highlight here is that although the inertial or backward-looking Phillips curve matches the empirical evidence concerning inﬂation persistence, it has a major shortcoming. Because it rests on ad hoc assumptions–in particular about the inﬂation process–rather than being derived from an optimizing micro model of wage or price setters’ behaviour, it does not allow a role for ‘credibility’ in the way monetary policy affects outcomes. We can demonstrate the point using an example. In Fig. 5.12, we assume that the central bank’s inﬂation target is 4% and the economy is initially at point A with high but stable inﬂation of 4% (on PC(π I = 4)). The central bank now decides to reduce its T inﬂation target to 2%, i.e. π1 = 2%. With backward-looking Phillips curves, it is clear from Fig. 5.12 that disinﬂation will be costly and following the announced change in inﬂation target, unemployment ﬁrst goes up (shown by point B). The economy then shifts only gradually to the new equilibrium at Z as the central bank implements the monetary rule. Whether or not the central bank’s decision is announced and if so whether it is Keyn: “chap05” — 2005/11/22 — page 160 — #30 MONETARY POLICY 161 r B9 r9 C9 A9, Z9 rS IS y p VPC PC (p I = 4) 5 PC (p I = 3) pT = 4 0 A B PC (p I = 2) 3 C pT = 2 1 Z 1 MR 0 ye y Figure 5.12 Central bank announces a new target: credibility and inertia believed by the private sector makes no difference at all to the path of inﬂation. The inﬂation that is built into the system takes time (with higher unemployment) to work its way out. The inability of the model to take any account of the reaction of wage or price setters to announced changes in monetary policy is unsatisfactory. We could make a radically different assumption that incorporates rational expectations on the part of wage and price setters, credibility, and the absence of nominal rigidities. In this case, the announcement of a lower inﬂation target produces an immediate change in wage and price setting so as to produce wage and price increases based on expected inﬂation of 2% rather than on past inﬂation and the economy moves directly from A to Z without any increase in unemployment. However, this too is unsatisfactory as the evidence suggests that disinﬂation is indeed costly even when a lower inﬂation target is announced. As discussed in Chapter 15, recent developments in modelling the Phillips curve aim to provide a micro-optimizing based model that can produce both costly disinﬂation and a role for the credibility of monetary policy. 6.2 Introducing inﬂation bias In the IS-PC-MR model to this point, medium-run equilibrium is characterized by inﬂa- tion equal to the central bank’s inﬂation target and output at equilibrium (i.e. determined Keyn: “chap05” — 2005/11/22 — page 161 — #31 162 THE MACROECONOMIC MODEL by the intersection of the WS and PS curves). However, since we have seen that imperfect competition in product and labour markets implies that ye is less than the competitive full-employment level, the government may have a higher target. We assume that the government can impose this target on the central bank. How do things change if the cen- tral bank’s target is full-employment output, or more generally a level of output above ye ? A starting point is to look at the central bank’s new objective function. It now wants to minimize L = (y − y T )2 + β(π − π T )2 , (5.6) where y T > ye . This is subject as before to the Phillips curve, π = π−1 + α(y − ye ). (5.7) In Fig. 5.13 the new indifference curves are shown. The central bank’s ideal point is now point A (where y = y T and π = π T ) rather than where y = ye and π = π T (i.e. point C). If we assume that α = β = 1 (for simplicity), then each indifference circle has its centre at A. The whole set of loss circles have shifted to the right. Since nothing has changed on the supply side of the economy, the Phillips curves remain unchanged. To work out the central bank’s monetary rule, consider the level of output it chooses if π I = 2% Fig. 5.13 shows the Phillips curve corresponding to π I = 2%. The tangency of PC(2) with the indifference circle shows where the central bank’s loss is minimized (point D). Since the central bank’s monetary rule must also pass through A, it is the downward-sloping line MR in Fig. 5.13. We can see immediately that the government’s target, point A, does not lie on the Phillips curve for inertial inﬂation equal to the target rate of π T = 2%: the economy will only be in equilibrium with constant inﬂation at point B. This is where the monetary rule (MR) intersects the vertical Phillips curve at y = ye . At point B, inﬂation is above the target: the target rate is 2% but inﬂation is 4%: this gap between the target rate of inﬂation and inﬂation in the equilibrium is called the inﬂation bias. p PC (4) VPC PC (3) PC (2) 4 B inflation bias 3 D C A pT = 2 MR ye yT y Figure 5.13 The inﬂation bias Keyn: “chap05” — 2005/11/22 — page 162 — #32 MONETARY POLICY 163 We shall now pin down the source of the inﬂation bias and the determinants of its size. We begin by showing why the equilibrium is at point B. If inﬂation is initially at its target rate of 2%, the central bank chooses its preferred point on the π I = 2% Phillips curve and the economy is at D. But with output above equilibrium, inﬂation goes up to 3% and the Phillips curve shifts up (see Fig. 5.13). The process of adjustment continues until point B: output is at the equilibrium and inﬂation does not change so the Phillips curve remains ﬁxed. Neither central bank nor wage setters have any incentive to change their behaviour. The economy is in equilibrium. But neither inﬂation nor output are at the central bank’s target levels (see Fig. 5.13). We can derive the same result mathematically and pin down the determinants of the size of the inﬂation bias. Minimizing the central bank’s loss function—equation (5.6)— subject to the Phillips curve—equation (5.7) implies y − y T + αβ(π−1 + α(y − ye ) − π T ) = y − y T + αβ(π − π T ) = 0. So the new monetary rule is: y − y T = −αβ(π − π T ). (5.8) This equation indeed goes through (π T , y T ). Since equilibrium requires that π−1 = π when y = ye , we have ye = y T − αβ(π−1 − π T ) (y T − ye ) ⇒ π = π−1 = π T + . (inﬂation bias) αβ inﬂation bias (y T −ye ) In equilibrium, inﬂation will exceed the target by αβ . This is called the inﬂation 15 T bias. The signiﬁcance of this result is that π > π whenever y T > ye . The steeper is the central bank’s monetary rule (i.e. the less inﬂation averse it is), the greater will be the inﬂation bias. A lower α also raises the inﬂation bias. A lower α implies that inﬂation is less responsive to changes in output. Therefore, any given reduction in inﬂation is more expensive in lost output; so, in cost-beneﬁt terms for the central bank, it pays to allow a little more inﬂation and a little less output loss. As we shall see in the next subsection, the problem of inﬂation bias is usually discussed in conjunction with the problem of time inconsistency in which the central bank or the government announces one policy but has an incentive to do otherwise. For this kind of behaviour to arise, it is necessary to introduce forward-looking inﬂation expectations. 6.3 Time inconsistency and inﬂation bias We can link the problem of inﬂation bias to problems of credibility and time incon- sistency by adopting a forward-looking Phillips curve. The simplest assumption to 15 For an early model of inﬂation bias with backward-looking inﬂation expectations, see Phelps (1967). Keyn: “chap05” — 2005/11/22 — page 163 — #33 164 THE MACROECONOMIC MODEL make is that inﬂation expectations are formed rationally and that there is no inﬂation inertia: i.e. π E = π + εt , where εt is a random disturbance. The intuition is that wage setters know that whatever their expected rate of inﬂation, the condition for π E = π is that y = ye . As we saw in Chapter 3, this is the so-called Lucas surprise supply equation, which we reproduce here: 1 yt − ye = πt − πtE α 1 yt = ye + πt − πtE (Lucas surprise supply equation) α inﬂation surprise = ye + ξt . We continue to assume that the central bank chooses y (and hence π ) after wage setters have chosen π E . This deﬁnes the central bank as acting with discretion. Now, in order for wage setters to have correct inﬂation expectations, they must choose π E such that it pays the central bank to choose y = ye . That must be where the central bank’s monetary rule cuts the y = ye vertical line, i.e. at point B in Fig. 5.13. Note that the positively sloped lines are now interpreted as Lucas supply equations rather than as Phillips curves. Inﬂation must be sufﬁciently high to remove the temptation of the central bank to raise output toward its target. With π = 4% and y = ye , the temptation has been removed because any increase in output from B would put the central bank on a loss circle more distant from its bliss point A: wage and price setters rationally expect an inﬂation surprise of 2% over and above the target inﬂation rate of 2%. The inﬂation bias presents a problem. As is clear from Fig. 5.13, the loss to the central bank at B is greater than the loss to the central bank at C since output is the same but inﬂation is higher at B. So the central bank would clearly be better off at C. Moreover, wage setters would be just as happy at C as at B, since employment and the real wage are the same in each case. What is to stop the central bank being at C? When wage and price setters are forward looking, the problem is called that of time inconsistency. Although the central bank claims to have an inﬂation target of π T , if wage setters act on the basis of this target (2%), when it comes to act, the central bank does not choose the output level consistent with its target. In short, at point B there is no incentive for the central bank to cheat; whereas at point C, there is an incentive. 6.4 Solutions to the time-inconsistency problem We have seen that the time-inconsistency problem arises under the following circum- stances: • the central bank or government has an over-ambitious output target (i.e. y T > ye ) • wage and price setters form their inﬂation expectations using rational expectations • the central bank uses a rule-based reaction function but operates with discretion, i.e. chooses its desired level of aggregate demand after inﬂation expectations have been formed in the private sector. Keyn: “chap05” — 2005/11/22 — page 164 — #34 MONETARY POLICY 165 There are three broad approaches to solving or mitigating the time-inconsistency problem manifested in inﬂation bias, which are referred to as replacing discretion by a rule; delegation; and reputation. 6.4.1 Replacing discretion by a rule: commitment If the timing of the game between the central bank and private sector is changed so that the central bank cannot choose the rate of inﬂation after wage and price setters have formed their expectations, then the inﬂation bias disappears. This entails a structure through which the central bank is prevented from optimizing after the private sector has set wages and prices and is referred to as a policy of commitment rather than discretion. A contract that costs the chairman of the central bank his or her job if inﬂation deviates from the target is one possible method of enforcing this. 6.4.2 Delegation (y T −y ) The inﬂation bias is equal to αβ e , and this may reﬂect a situation in which the gov- ernment rather than the central bank controls monetary policy. The government could reduce the inﬂation bias by transferring control of monetary policy to a central bank with an output target closer to ye and with more inﬂation aversion (higher β ) than the govern- ment’s. Since output in equilibrium is at y = ye , inﬂation would be brought closer to the target and the government would be unambiguously better off if it delegates monetary policy to an independent central bank. Fig. 5.14 illustrates the reduction in inﬂation bias through delegation of monetary policy to the central bank. The ﬂatter sloped monetary rule is that of the central bank, MRCB , and the more steeply sloped that of the government, MRG . MRG evidently implies a higher inﬂation bias with the equilibrium at point B. MRCB on the other hand implies that equilibrium is at point A, with π = 3%. Wage and price setters rationally expect a smaller inﬂation surprise when faced with an independent central bank than when faced by the government. The reduction in the inﬂation bias is due to the ﬂatter slope of the central bank’s MR line and to the fact that central bank’s output target is closer to equilibrium output than is the government’s. For delegation to produce a costless move from high to low inﬂation, there must be no inﬂation inertia and expectations must be formed rationally. In this case, if wage setters believe that the policy maker’s preferences have changed in the appropriate way, the economy will shift directly down the vertical Phillips curve at ye from point B to the new equilibrium with π = 3% at point A. One problem with this proposed solution is that if the government can delegate pow- ers to the central bank, why can’t it take them back when it wants to? It would pay the government to take back those powers at the moment that wage setters chose a low π E corresponding to the loss function parameters of the central bank. For then the govern- ment would be tempted to opt for a level of output greater than ye . This kind of reasoning is sometimes used to explain why governments have often found it necessary to make central banks constitutionally independent and why delegation is sometimes combined with commitment devices like the one discussed in 6.4.1. Keyn: “chap05” — 2005/11/22 — page 165 — #35 166 THE MACROECONOMIC MODEL VPC PC (6) B 6 PC (3) 5 C PC (2) 4 inflation bias: government A 3 inflation bias: CB pT = 2 MRCB MRG ye yT CB yT G y Figure 5.14 Inﬂation bias: central bank and government 6.4.3 Reputation A third solution to the problem of inﬂation bias lies with the government or central bank building a reputation for being tough on inﬂation. Suppose that the government has delegated monetary policy to the central bank but wage setters remain unsure of just how independent the central bank is. They only know that there is a probability p that the central bank is independent and a probability (1 − p) that it is a puppet of the government. The only way that they can ﬁnd out is by observing the decisions taken by the central bank. If this is the case, how should the central bank behave? This problem can be analysed in detail using game theory. This is done in Chapter 16. Here we simply convey the ﬂavour of the solution. The situation is one in which the central bank interacts with wage setters more than once. Will a ‘weak’ central bank with an output target above the equilibrium ﬁnd it rational to behave as if it were tough—i.e. with an output target closer to the equilibrium? If so, then we can say that it is possible to build a reputation for toughness as a method of solving the inﬂation bias problem. Let us begin with the case in which the interaction between the central bank and wage setters occurs twice: in period one, wage setters choose E π1 with no knowledge of whether the central bank is weak or tough (but they know there is a probability of p that it is tough); the central bank then chooses output in period one, E E y1 knowing π1 . In period two, the wage setters choose π2 knowing y1 ; the central bank E then chooses y2 knowing π2 . The result is that a weak central bank will choose to act like a tough one in the ﬁrst period, which will establish a low expected inﬂation rate in the second period, thereby Keyn: “chap05” — 2005/11/22 — page 166 — #36 MONETARY POLICY 167 providing bigger gains from boosting output in the second period. The central bank gains because in the ﬁrst period, the outcome is inﬂation at its target (no inﬂation bias) and output at the equilibrium (instead of the time inconsistency outcome of inﬂation above the target and output at equilibrium) whilst in the second period, it can gain by setting output above the equilibrium (i.e. by exploiting the short-run trade-off between inﬂation and unemployment by a surprise increase in inﬂation). As discussed in detail in Chapter 16, when the game is extended from two to many periods, the beneﬁts to the central bank from behaving as if it were tough increase. This is because the situation in period one is repeated again and again until the last period. This type of model provides an explanation for the process by which a reputation for toughness can be built in the face of public scepticism. 6.5 Is y T > ye a good model of central bank behaviour? We have seen that the inﬂation bias problem is eliminated if the objective of the govern- ment or central bank is to stabilize the economy around the equilibrium level of output, ye , i.e. when y T = ye rather than y T > ye . This is the case both when inﬂation expec- tations are backward looking and when inﬂation expectations are rational. The central bank objective of y T = ye is our benchmark model for monetary policy, introduced in Chapter 3. We are then led to ask whether the assumption that y T > ye is a good way to think about central bank behaviour. It offers insights when the central bank is susceptible to pressure from a government, which in turn is tempted to run the economy at unem- ployment below the equilibrium. However, in many OECD economies, this is not the key problem for central banks, which in most cases are independent from government and are run by ofﬁcials motivated by concern about their professional reputations. This point is summarized neatly by Peter Howitt: The ‘temptation’ to raise the level of economic activity with some surprise inﬂation might exist if society were indeed locked into expectations. In reality, however, the temptation just doesn’t arise, as practitioners of central banking have long maintained. Central bankers are keenly aware that although there are long and variable lags between monetary stimulus and any resulting rise in the level of economic activity, there are no lags at all between such stimulus and the currency depreciation and capital ﬂight that will occur if the stimulus is taken by investors as a signal of future weakness in the currency. Because of this, there is no reason for believing that discretionary central banks have the inﬂationary bias that the game-theoretic [time-inconsistency] view attributes to them. . . . [R]esponsible people entrusted with such important and delicate jobs as the management of a country’s central bank are typically motivated by the desire to be seen as having done a good job, to have acquitted themselves well. They pursue this objective by doing everything possible to avoid major inﬂations, ﬁnancial panics and runs on the currency, while carrying out the day to day job of making available the base money needed for the ﬁnancial system to function.16 16 Howitt (2001). Howitt refers to the useful paper by Mervyn King, then Deputy Governor of the Bank of England; from 2003, Governor of the Bank of England: King (1997). Another useful source is the short book of three lectures by Alan Blinder reﬂecting on how he used academic research when he was a Governor of the Federal Reserve Board: Blinder (1998). Keyn: “chap05” — 2005/11/22 — page 167 — #37 168 THE MACROECONOMIC MODEL 6.6 Rules and expectations versus discretion and learning We now return to the case in which there is no inﬂation bias and to our broader usage of the distinction between monetary rules and discretion. The broader usage is needed because the real-world examples of inﬂation-targeting central banks embody rule-based behaviour as summarized in a monetary reaction function, which nevertheless entails discretion in the time-inconsistency sense. We ask whether there are any gains from a framework of a clearly deﬁned public monetary policy rule with an explicit inﬂation target as is the case for the Bank of England or the European Central Bank as com- pared with a framework of so-called ‘constrained discretion’ as characterizes the Federal Reserve of the USA. In practice, we observe a wide spectrum of arrangements for mone- tary policy amongst central banks. The USA under Alan Greenspan is the most famous case of a central bank operating constitutionally with discretion. Yet many articles have been written suggesting that the Fed has covertly been following an inﬂation-targeting rule.17 This suggests that in practice there is not a sharp distinction amongst inﬂation- targeting regimes but rather some difference in emphasis on rules as compared with discretion. It seems clear that there are gains from the operation of a widely understood and trans- parent process of monetary policy making. This suggests that providing information about the monetary policy reaction function is likely to be useful.18 The main gain arises because economic agents are at least in part forward looking and will therefore anticipate the reaction of the central bank to a shock. If the reaction function is well understood, anticipation by the private sector may help to stabilize the economy’s response to a shock. For example, if we think of a negative aggregate demand shock, then the monetary pol- icy reaction function indicates that interest rates will be lowered. The knowledge of this reaction will inﬂuence the expected future path of interest rates, which will help shift the long-term interest rate downwards—the rate relevant for interest-sensitive spend- ing. Asset prices such as share prices or house prices may react rapidly to the expected path of interest rates and reinforce the efforts of the central bank to boost demand. In our example, the expectation of a lengthy period of low interest rates would tend to boost asset prices immediately (e.g. share prices and house prices). In turn as we shall see in Chapter 7, this raises Tobin’s Q and permanent income and would there- fore tend to raise investment and consumption, reinforcing the recovery of aggregate demand. On the other hand, too great an emphasis on rules may take attention away from the beneﬁts that can arise from a central bank that sees itself as actively learning about the economy and engaging in experiments—for example, to try to discover the equi- librium level of unemployment in an economy experiencing a burst of technological progress. 17 For example, see the discussion in Mankiw (2002). 18 Recent research suggests that adopting an inﬂation-targeting regime with an explicit inﬂation target improves macroeconomic performance in terms of both inﬂation and output stability by anchoring the public’s inﬂation expectations to the central bank’s objectives. For example, Orphanides and Williams (2005). Keyn: “chap05” — 2005/11/22 — page 168 — #38 MONETARY POLICY 169 7 Conclusions In this chapter, we have put the spotlight on monetary policy. The starting point was an examination of the phenomena of inﬂation, disinﬂation, and deﬂation, which was moti- vated by the question of why low and stable inﬂation is considered a desirable objective by policy makers. We examined the reasons behind episodes of rising inﬂation and the unsustainability of attempts to hold output above the equilibrium level. A falling general price level (deﬂation) is likely to bring dangers to macroeconomic stability. We highlighted the difference between two monetary policy paradigms—the LM paradigm and the MR paradigm. In the LM paradigm, monetary policy is passive and the money supply growth rate determines the rate of inﬂation in the medium-run equi- librium. By contrast, in the MR paradigm, the central bank is active. It adjusts the interest rate so as to steer the economy back to target inﬂation at equilibrium output. The rate of inﬂation at medium-run equilibrium is therefore determined by policy. Since the nomi- nal interest rate cannot be negative, monetary policy will become ineffective at very low or negative rates of inﬂation. A systematic approach to monetary policy within the MR paradigm can be modelled by specifying the objectives of the central bank (or the government) and identifying the constraints it faces. The objective of the central bank is to minimize the extent to which the economy diverges from a target rate of inﬂation and from a target level of output. We have shown that • when the output target is the equilibrium level of output, ye , a monetary policy reaction function will enable the central bank to steer the economy to its inﬂation and output targets if the economy experiences an inﬂation, aggregate demand, or supply shock. • The central bank will do this by adjusting the nominal interest rate so as to affect the real interest rate and the level of aggregate demand and output. The appropriate change in the real interest rate will depend on whether the stabilizing real interest rate has changed and on the interest sensitivity of aggregate demand (the slope of the IS), how inﬂation averse the central bank is, and the response of inﬂation to changes in unemployment (the slope of the Phillips curve). • We have shown how to derive an interest rate rule from the 3-equation model. This takes the form of a Taylor Rule in which the central bank adjusts the interest rate in response to observed deviations of inﬂation from target and of output from equilibrium when the economy is characterized by a lag in the effect of the interest rate on output and a lag in the effect of a change in output on inﬂation. If output affects inﬂation in the same period, then the interest rate rule only has the inﬂation term in it. This highlights the fact that the coefﬁcients on inﬂation and output in the Taylor rule are not the weights on inﬂation and output in the central bank’s loss function. • With a purely backward-looking Phillips curve, disinﬂation is always costly and that cost is not affected by the degree to which central bank announcements are believed. • When the output target is above the equilibrium level of output, the central bank will not be able to achieve its inﬂation target in equilibrium. There will be an inﬂation bias. Keyn: “chap05” — 2005/11/22 — page 169 — #39 170 THE MACROECONOMIC MODEL We clarify the debate about rules versus discretion by explaining that the superior- ity of a rule that prevents the central bank from optimizing rests on the speciﬁcation of the central bank’s loss function. If the central bank targets a level of employment above the equilibrium, an inﬂation bias arises. When expectations are rational, this creates the time-inconsistency problem. By contrast, in our baseline case, which it is argued matches that of central banks in many countries, the objective is to stabilize the economy around equilibrium output, which eliminates the inﬂation bias. A fuller understanding by the public of the monetary reaction function can help to stabilize forward-looking expec- tations and facilitate the movement of asset prices consistent with the central bank’s stabilization objectives. s QUESTIONS Checklist questions (1) ‘If the economy has high but stable inﬂation, the government has much to lose and little to gain by reducing inﬂation to a low rate.’ Explain and assess this statement. (2) What are the advantages and disadvantages of an inﬂation rate of 3% as compared with one of 0% per annum? Would you advocate the replacement of the inﬂation target by a price level target? (3) Explain what is meant by the central bank’s loss function. How are the central bank’s preferences reﬂected in the loss function? Use a numerical example and diagrams to explain how the central bank’s preferences affect its reaction to a negative aggregate demand shock. (4) How can the central bank diagnose what kind of shock has disturbed the economy? (5) Compare the response of an inﬂation-targeting central bank to a permanent negative aggregate supply shock with that to a permanent negative aggregate demand shock. (6) Suppose there are two regions of the country, in one of which the WS curve is quite steep and in the other, the WS is quite ﬂat. Why might this be so? Compare the implications for inﬂation and unemployment of a common positive temporary aggregate demand shock. How should the central bank respond? (7) If a central bank adopts an interest-rate based monetary policy rule like a Taylor Rule rather than a monetary growth rate rule, what would you expect to happen to the money supply? (8) In implementing a Taylor-type interest rate rule, does the central bank need to know anything more than the coefﬁcients in the rule, its inﬂation target, and current output and inﬂation? (9) Write down the Taylor Rule in terms of the real interest rate. Holding the output gap constant, does a rise in inﬂation by x percentage points call for a rise in the nominal interest rate by more than, less than, or by just x percentage points? Explain. (10) Under what circumstances will a central bank utilizing an interest rate based monetary rule to stabilize the economy fail in its objective of raising output? Keyn: “chap05” — 2005/11/22 — page 170 — #40 MONETARY POLICY 171 (11) The central bank faces a short-run trade-off between inﬂation and unemployment (a) if inﬂation expectations are backward looking or (b) if inﬂation expectations are rational but are formed before the central bank chooses its optimal inﬂation-output pair. Explain each of these cases. What difference does it make whether (a) or (b) holds? (12) Explain what is meant by the statement that a government that is determined to reduce inﬂation may have a problem in achieving this outcome because of a lack of credibility. Problems and questions for discussion QUESTION A. What are the incentives for a policy maker to exploit the short-run trade-off between unemployment and inﬂation? What are the consequences? Is this a good description of contemporary central bankers? Use ofﬁcial reports of a central bank of your choice to provide support for your argument. QUESTION B. Consider a Central Bank that maximizes the following utility function: Z = k(y − ye ) − (π − π T )2 where k is a positive constant. Its policy instrument is the growth rate of the money supply, γM . Assume that the inﬂation target is π T = 0. Explain this utility function and compare it with the loss function used in the chapter. (Hint: focus on how the central bank’s utility rises with output. Is this central bank ‘overambitious’?) Now assume that the central bank sets the money supply growth rate after economic agents have incorporated their expectations about inﬂation into their decision making, and thus faces a Phillips curve: π = π E + α(y − ye ). (a) Assuming that agents have rational expectations, solve algebraically for the optimal inﬂation rate under discretion, i.e. ﬁnd the inﬂation rate that the central bank will choose using its monetary policy instrument, γM . (Hint: maximize utility with respect to γM , having used the Phillips curve to substitute for y in the utility function; and used γM = π to substitute for π .) (b) Suppose that, before private sector inﬂation expectations were formed, the central bank could commit to a particular rate of inﬂation. What would that rate be? Discuss. (c) Now return to the case of discretion, and suppose that we extend the model to cover two periods. In other words, the central bank now cares about the sum of its loss functions in each period, i.e. 2 2 Total utility = k(y1 − ye ) − π1 − π T + k(y2 − ye ) − π2 − π T where the subscripts indicate the period. Keyn: “chap05” — 2005/11/22 — page 171 — #41 172 THE MACROECONOMIC MODEL Suppose also that in the ﬁrst period, agents expect no inﬂation (π E = 0), while when the second period arrives agents expect that inﬂation will be equal to the rate that E actually occurs in the ﬁrst period (i.e. expectations are adaptive, so π2 = π1 ). What will be the equilibrium rates of output and inﬂation in each period? Discuss your ﬁndings. QUESTION C. Is there a trade-off between stabilizing inﬂation and stabilizing the real side of the economy? Explain. QUESTION D. Using Fig. 5.8 as a guide, draw the corresponding diagram to illustrate the lag structure in the standard version of the 3-equation model. Now assume that there is no lag between a change in the interest rate and its effect on output. Draw a diagram to illustrate this lag structure. Use all three ﬁgures to provide a concise summary of the role of lags in the operation of monetary policy. Go to the website of one of the central banks listed in the next question (or another one of your choice) and ﬁnd out their view about the lags between a change in the interest rate and its effects on output and inﬂation. Do they identify the same factors as responsible for the lags? QUESTION E. Select two out of the following central banks: Bank of England, Reserve Bank of New Zealand, Bank of Canada, and the Swedish Riksbank. Each of these central banks has adopted explicit ‘inﬂation targeting’. For each of your chosen banks, ﬁnd out how it explains what this means to the public. How does it communicate and explain its interest rate decisions to the public? Compare what each central bank did and how it explained its actions following the events of 11 September 2001. Keyn: “chap05” — 2005/11/22 — page 172 — #42