Chapter 11: Time Inconsistency and Inflation Bias PDF

Summary

This chapter discusses the widely held belief that inflation is primarily a monetary phenomenon. It examines how monetary policy decisions can affect real output and employment in the short run. The concepts of 'inflation bias' and the roles of central banks are explored in this chapter.

Full Transcript

Chapter 11 Time inconsistency and inflation bias 11.1 Introduction As discussed in Chapters 5 and 6 there is widespread belief among economists that inflation is largely a monetary phenomenon. If monetary variations lead to inflation variations, and if there is a positive statistical relationship...

Chapter 11 Time inconsistency and inflation bias 11.1 Introduction As discussed in Chapters 5 and 6 there is widespread belief among economists that inflation is largely a monetary phenomenon. If monetary variations lead to inflation variations, and if there is a positive statistical relationship between inflation and real output (or employment) in the short run, governments or politically motivated monetary policy makers may be tempted to exploit these short run relationships in order to achieve different objectives. These may range from achieving temporary high real output, reducing unemployment, financing budget deficits and even attaining balance of payments objectives by generating surprise inflation. While such outcomes may be feasible in the short-term, inflationary consequences distort economic agents incentives in the medium to long run. What is more, economic agents learn the type of policy makers over time such that they can not be easily fooled. Once consumers, firms and other agents in the economy understand the incentives of policy makers to create surprise inflation, they adjust their inflation expectations accordingly such that even in the short run there can be no output gains to achieve. Thus, we will discuss the so called inflation bias and ways reduce this bias. A simple game theoretic framework will allow us to analyse the importance of central banks credibility in the combat of inflation. 11.2 Aims This chapter aims to discuss strategic interactions between policy makers and economic agents which may differ in their incentives with ultimate welfare deterioration for the society. We also study how to resolve these conflicts of interests. 11.3 Learning outcomes By the end of this chapter, and having completed the Essential reading and activities, you should be able to: describe the causes of ‘inflation bias’ in an economy distinguish between ‘wet’ and ‘hard nosed’ central banks outline institutional and behavioural ways inflation bias can be reduced or avoided describe the workings of the Taylor rule and give conditions needed for stability. 151 11. Time inconsistency and inflation bias 11.4 Reading advice There is no single textbook that covers the material in this chapter but the most appropriate are those by Carlin and Soskice (2006) and Goodhart (1989) and you should read these while working through this section. The articles by Carlin and Soskice (2005), Barro and Gordon (1983), Kydland and Prescott (1977) are also essential reading. The Goodhart article gives a more historical account of monetary policy, especially in the UK and US and the article by Orphanides (2007) provides a neat overview of Taylor rules. 11.5 Essential reading Barro, R.J. and D.B. Gordon ‘A positive theory of monetary policy in a natural rate model’, Journal of Political Economy 91(3) 1983, pp.589–610. Carlin, W. and D. Soskice ‘The 3-equation New Keynesian model – A graphical exposition’, BE Journals in Macroeconomics: Contributions, 5(1) 2005, pp.1–38. Goodhart, C.A.E. Money, Information and Uncertainty. (London: Macmillan, 1989) Chapters 14 and 15. Kydland, F.E. and E.C. Prescott ‘Rules rather than discretion: the inconsistency of optimal plans’, Journal of Political Economy 85(3)1977, pp.473–492. Orphanides, A. ‘Taylor rules’, Finance and Economics Discussion Series: Divisions of Research Statistics and Monetary Affairs, Federal Reserve Board, Washington, D.C., 200718, (2007). (http://www.federalreserve.gov/Pubs/FEDS/2007/200718/200718pap.pdf) Taylor, J.B. ‘An historical analysis of monetary policy rules’, National Bureau of Economic Research working paper, w6768, (1998).(http://papers.nber.org/papers/W6768) 11.6 Further reading Books Carlin,W. and D. Soskice Macroeconomics: Imperfections, Institutions and Policies. (Oxford: Oxford University Press, 2006) Chapter 6. Journal articles Clarida, R., J. Gali and M. Gertler ‘Monetary policy rules and macroeconomic stability: evidence and some theory’, Quarterly Journal of Economics 115(1) 2000, pp.147–80. Goodhart, C.A.E. ‘The conduct of monetary policy’, Economic Journal 99(396) 1989, pp.293–346. 152 11.7. Time inconsistency and inflation bias Rogoff, K. ‘The optimal degree of commitment to an intermediate monetary target’, Quarterly Journal of Economics 100(4) 1985, pp.1169–1189. Sargent, T.J. and N. Wallace ‘Rational expectations, the optimal monetary instrument and the optimal money supply rule’, Journal of Political Economy 83(1) 1975, pp.241–54. Walsh, C.E. ‘Is New Zealand’s Reserve Bank Act of 1989 an optimal Central Bank contract?’, Journal of Money, Credit and Banking 27(4, Part 1) 1995, pp.1179–191. 11.7 Time inconsistency and inflation bias Throughout this subject guide we have stressed that money should be neutral in the long run but, using models such as the expectations-augmented Phillips curve or the Lucas supply curve, money can have real effects in the short run. Here, we will use such a framework to show that in equilibrium, a positive rate of inflation may be present even though a zero rate may be optimal. If there are no institutional or behaviourial restrictions, the monetary authorities have an incentive to increase inflation (when inflation is zero) in an attempt to move along the Phillips curve to increase output. An ‘inflation bias’ may then result in the economy. Let us call such policy makers as being ‘wet’ and those policy makers who always aim for target inflation as being ‘hard nosed’. Consider for example, the aggregate supply curve in (11.1). This is the same as an expectations-augmented Phillips curve or a Lucas supply curve, only we use inflation, πt , instead of the price level. yt = y ∗ + α(πt − Et−1 [πt ]) + εt (11.1) y ∗ is the market clearing level of output and εt is a productivity shock term where its mean is set equal to zero. Suppose the monetary authorities can choose the inflation rate directly and try to minimise the following loss function: L = πt2 + λ(yt − ky ∗ )2 where k > 1. (11.2) λ is a preference parameter showing the authorities’ preference for output fluctuations relative to inflation fluctuations. We assume that k > 1 so that a level of output greater than the market clearing level is desired reflecting political biases towards higher output. If output is at the market clearing level, a social loss is still incurred, (y ∗ − ky ∗ )2 > 0, since the socially optimum level of output may be greater than the market clearing level. This may be due to the fact y ∗ is too low because of the monopoly powers of firms, for example, which causes output levels to be sub-optimal and hence unemployment to be too high. This is shown in Figure 11.1. Initially, we are at the market clearing level of output and have zero inflation, point A. If output equals its market clearing level in the long term, this point is the best (welfare-maximising) that can be achieved. However, the monetary authorities know that by increasing inflation unexpectedly, we can move along the Phillips curve to point B, obtaining a higher level of welfare. At point B the inflation rate is higher than expected since E[π] = 0. Expected inflation therefore increases and the Phillips curve shifts up. The equilibrium compatible with expected inflation, point E, is the point where the Phillips curve is tangential to the indifference curve. At this point the 153 11. Time inconsistency and inflation bias Figure 11.1: authorities have no incentive to increase inflation since to do so will result in lower social welfare. Note that at point E, we have a positive rate of inflation, the inflation bias, and we are on a lower level of social welfare than at point A, our starting point. To calculate the inflation bias, substitute the Phillips curve into the loss function, (11.2). L = πt2 + λ((1 − k)y ∗ + α(πt − Et−1 [πt ]) + εt )2 . (11.3) Differentiating this with respect to the choice variable, π, taking expectations of inflation as given, setting equal to zero and solving for πt will give us: (1 + α2 λ)πt = α2 λEt−1 [πt ] + αλ((k − 1)y ∗ − εt ). (11.4) Taking expectations of (11.4) conditional on information at date t − 1, noting that Et−1 [εt ] = 0, will give a solution for Et−1 [πt ]. Substituting back into (11.1) will give a solution for inflation. Et−1 [πt ] = αλ(k − 1) = y ∗ πt = αλ(k − 1)y ∗ − αλεt . 1 + α2 λ (11.5) The inflation bias is given by Et−1 [πt ] = αλ(k − 1)y ∗ and represents the vertical distance AE in Figure 11.1. Note that when parameter k = 0, there is no inflation bias as we have seen in the previous chapter. 154 11.8. Inflation aversion, steepness of the Phillips curve and interest rates 11.8 Inflation aversion, steepness of the Phillips curve and interest rates There are three elements that determine the level of inflation bias. the political bias towards higher output parameter (k > 1) the degree of central bank inflation aversion in the loss function (λ) the responsiveness of inflation to output in the Phillips curve (α). The parameter λ in the central bank’s loss function (equation (11.2) governs the inflation aversion of the central bank. If λ is equal to 1, indifference curves in Figure 11.2a. are circles and the central bank assigns equal weight to inflation and real output in the loss function. In alternative scenarios where λ is not equal to 1, indifference curves are elliptical. If λ is less than 1, the central bank is inflation averse (hard nosed). Finally, if λ is more than 1, the central bank is real output (or unemployment) averse (wet). These scenarios are depicted in Figure 11.2. Figures 11.2b and 11.2c show differences between central bank responses. Given a Phillips curve, Figure 11.2b shows that when current inflation deviates from a target inflation level, the central bank will respond more aggressively to stabilise inflation back to its target level and Figure 11.2c shows that the central bank’s response will be muted when inflation deviates from its target level since the central bank is more concerned with real output. Figure 11.2: The parameter α measures the slope of the Phillips curve or alternatively, the responsiveness of inflation to changes in output. The higher the parameter α, the more responsive is inflation to changes in output. Given the central bank preferences, a steeper Phillips curve implies less aggressive policy response when the inflation deviates from the target level. A steeper Phillips curve allows the central bank to do less in response to an inflation shock since inflation responds strongly to a fall in output 155 11. Time inconsistency and inflation bias associated with a tight monetary policy. For more discussion on the matter, see Carlin and Soskice (2005). We will now outline a number of ways in which this inflation bias can be reduced/negated. 11.9 Ways inflation bias can be reduced 11.9.1 Delegation of monetary policy to a conservative central bank: central bank independence If the role of monetary policy was delegated to such a conservative central bank, which is less concerned with output variations than the society, in other words, has a loss function of the form in (11.2) where µ < λ: LCB = πt2 + µ(yt − ky ∗ )2 (11.6) then we will still be faced with an inflation bias but the bias will be of the form αµ(k − 1)y ∗ and since µ < λ, the inflation bias will be lower. One way to formalise a conservative central bank is to establish an independent central bank with a formal price stability mandate. The popularity of independent central banks during the 1990s can be seen as an attempt to separate monetary policymaking from political interference. Establishing an independent central bank, of course, is not sufficient to guarantee price stability if price stability is not part of their mandate. In order to ensure their commitment to price stability, most central banks in advanced economies recently adopted the so called ‘inflation targeting policy’. This typically takes the form of a targeting policy with an explicit inflation target around two percent to tie down inflation expectations. While in some advanced economies, notably in the case of the US Federal Reserve, there is no formal central bank independence, historical practice suggests that there is no political pressure. Also, there were regular announcements by Fed officials about the desired level of inflation. In 2012, the than Chairman of the Federal Reserve, Ben Bernanke announced an inflation target of 2 percent departing from the non-committal stance of the Federal Reserve. Interestingly, in the aftermath of the global financial crisis in September 2008 there has been serious questioning of such inflation targeting policies in particular at times of high unemployment and weak output performance. A renewed scrutiny of the role of monetary policy other than price stability (such as unemployment and real output) in an economy has started and the debate is as yet unsettled. (See for instance writings of Paul Krugman in popular press.) One possible alternative to inflation targeting is the so called ‘nominal income targeting’ as such policy captures both inflation and real output at the same time. 11.9.2 Inflation contract for the central bank Suppose the central bank was penalised, by way of reduced salary, for allowing any inflation above the socially desired level, set in this case at zero. The loss function that would be minimised would then be: LContract = πt2 + λ(yt − ky ∗ )2 + Ψπt . 156 (11.7) 11.10. A reminder of your learning outcomes So that the central bank’s loss depends on the level of inflation through the Ψ parameter as well as squared inflation and squared output deviations. If we substitute the Phillips curve into (11.7) and minimise the loss function by choosing πt (using the same method as above), it can be shown that the inflation bias, Et−1 [πt ], is given by: Et−1 [πt ] = αλ(k − 1)y ∗ − Ψ . 2 (11.8) Therefore, if the contract was written for the central bank such that Ψ = 2αλ(k − 1)y ∗ , then the inflation bias would be zero and one would achieve the point of highest attainable welfare, point A in Figure 11.1, as a time-consistent equilibrium. 11.9.3 Reputation Policy credibility is at the core of monetary policymaking. A ‘hard nosed’ central bank cares only about inflation, whereas a ‘wet’ central bank attempts to exploit short-term relationships. However, even a ‘wet’ central bank can avoid inflation bias problem by establishing a reputation that it is serious about inflation. Such reputation can only be achieved in a multi period game between sceptical wage setters and the policy maker. Carlin and Soskice (2006) illustrate the point by using a two period game. Let us suppose that in period 1, the society chooses an expected inflation (π1E ) with the knowledge that there is a certain probability, p, that the central bank is serious about inflation. Equipped with this knowledge, the central bank chooses output at, say, y1 . In period 2 the society chooses (π2E ) knowing how the central bank behaved in period 1 (that is they observe y1 ); the central bank chooses y2 knowing (π2E ), and so on. In this scenario, even a ‘wet’ central bank will behave in period 1 as if it is ‘hard nosed’ about inflation. This is because by behaving tough on inflation in period 1, inflation will be on target and output on equilibrium. In period 2 (terminal period), however, the central can set output above the equilibrium by creating surprise inflation. When the reasoning extended to many periods, it pays off for the central bank to build a reputation of being tough on inflation. The ‘wet’ central bank would behave as if it is a ‘hard nosed’ central bank in all periods except the very last one of the game. The model provides a justification for the incentives to build a reputation of inflation toughness when the society is sceptical about the ‘nature’ of the central bank. 11.10 A reminder of your learning outcomes By the end of this chapter, and having completed the Essential reading and activities, you should be able to: describe the causes of ‘inflation bias’ in an economy distinguish between ‘wet’ and ‘hard nosed’ central banks outline institutional and behavioral ways inflation bias can be reduced or avoided describe the workings of the Taylor rule and give conditions needed for stability. 157

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