Chapter 9 Keynesian Models with Money Supply PDF

Chapter 9 Keynesian models with money supply as a policy instrument 9.1 Introduction In the last chapter we examined the effects of monetary policy and saw that frictions in the classical model (in the form of asymmetric information, the requirement to hold cash before you could buy, and limited p...

Chapter 9 Keynesian models with money supply as a policy instrument 9.1 Introduction In the last chapter we examined the effects of monetary policy and saw that frictions in the classical model (in the form of asymmetric information, the requirement to hold cash before you could buy, and limited participation in financial markets) all led to money having real effects. Here, we will examine one particular type of friction, namely the friction to prices. If prices, of goods or of labour, are sticky then changes in the money supply will cause changes to real money balances and/or to the real wage. A change in the stock of nominal money will then have consequences in the real economy. Despite some of these models being thought up and refined in the latter years of the 20th century, we put such models of nominal rigidities under the umbrella of ‘Keynesian models’, the term that is usually used when referring to them. 9.2 Aims This chapter aims to introduce models with nominal (price) frictions where the monetary policy instrument is a monetary aggregate. We find short-term real effects of monetary policy under certain conditions. 9.3 Learning outcomes By the end of this chapter, and having completed the Essential reading and activities, you should be able to: explain the importance of nominal rigidities and why such sticky prices occur in the real world examine the effects of monetary policy in the short and long run when there are nominal rigidities describe the workings of the Phillips curve and augmented Phillips curve, noting the differences between the two build and work through models of sticky prices, examining the effects of monetary policy 119 9. Keynesian models with money supply as a policy instrument explain why multi-period pricing can lead to real and persistent effects of monetary policy discuss the merits of various sticky price models, noting, in particular, the different short-run and long-run effects of monetary policy. 9.4 Reading advice The content of this chapter, especially the latter half, is based primarily on McCallum (1989), Chapters 9 and 10, and it is recommended that you read these chapters while working through this section. However, before doing so you should refresh your memory with the Keynesian macroeconomic models, found in all macro textbooks. (see for example Mankiw (2002) or Branson (1989)). The review article by Phelps in the New Palgrave Dictionary of Money and Finance is also very good and should be read after completing this chapter. The article by Blanchard is thorough but difficult and should only be read when you feel comfortable with the material here and in the other readings. For empirical evidence of nominal rigidities, see Gordon. 9.5 Essential reading Gordon, R.J. ‘A century of evidence on wage and price stickiness in the US, the UK and Japan’, in Tobin, J. (ed.) Macroeconomics, Prices and Quantities. (Oxford: Blackwell, 1983). Hargreaves Heap, S.P. The New Keynesian Macroeconomics: Time, Belief and Social Independence. (Edward Elgar Publishing, 1992) Chapters 5 and 6. McCallum, B. Monetary Economics. (New York; Macmillan; London: Collier Macmillan, 1989) Chapters 9 and 10. Phelps, E.S. ‘Phillips curve’, in Newman, P., M. Milgate and J. Eatwell (eds) The New Palgrave Dictionary of Money and Finance. (London: Macmillan, 1994). 9.6 Further reading Books Blanchard, O.J. ‘Why does money affect output? A survey’, in Friedman, B. and F. Hahn (eds) Handbook of Monetary Economics. (Amsterdam: North-Holland, 1990). Branson, W.H. Macroeconomic Theory and Policy. (New York; London: Harper and Row, 1989). Mankiw, N.G. Macroeconomics. (New York: Worth Publishers, 2002). Phelps, E.S. Microeconomic Foundations of Employment and Inflation Theory. (New York: Norton, 1970). 120 9.7. Keynesian aggregate supply function Rotemberg, J.J. and M.Woodford ‘Dynamic general equilibrium models with imperfectly competitive markets’, in Cooley, T. (ed.) Frontiers of Business Cycle Research. (Princeton, N.J.; Chichester: Princeton University Press, 1995). Journal articles Friedman, M. ‘The role of monetary policy’, American Economic Review 58(1) 1968, pp.1–17. Phillips, A.W. ‘The relation between unemployment and the rate of change of money wage rates in the United Kingdom’, Economica 25(100) 1958, pp.283–99. 9.7 Keynesian aggregate supply function An early model of nominal rigidities was that of sticky nominal wages. Labour unions were argued to negotiate wages on a yearly basis, which would not allow nominal wages to adjust instantaneously to changes in market conditions. As in Chapter 8, output is produced from capital and labour, and firms employ workers up to the point where the marginal product of labour is equal to the marginal cost, the real wage. However, unlike in classical models, labour employed, and hence output produced, only depends on labour demand (not on the intersection of demand and supply!). Firms are assumed to have the ‘right to manage’, whereby firms can choose how much labour to employ, even if this is more than the amount workers wish to supply at the going real wage. This could happen, for example, by firms asking, or forcing, labour to work overtime. Similarly, if the demand for labour by firms was below that which workers wish to supply, this will result in unemployment.1 The aggregate supply curve in the economy is then going to be upward sloping. If the nominal wage is fixed at W ∗ , an increase in the price level will cause the real wage, W ∗ /P , to fall, resulting in higher labour demand. More labour employed (if firms have the right to manage) will lead to more output supplied, implying an upward-sloping aggregate supply schedule. However, in the long run, wages will be renegotiated to the market clearing level, at which point employment, output and other real variables are determined by tastes and technology, not the price level. The long-run aggregate supply schedule is then vertical as in Chapter 7. The effect of monetary policy The effect of monetary policy can best be shown by using a similar set of diagrams to those of Figure 8.2. This is shown, for sticky nominal wages, in Figure 9.1. The middle left panel shows the labour market when the nominal wage is fixed at W ∗ and the bottom left panel shows the standard production function with diminishing marginal returns to labour. The top right diagram shows the IS–LM curves and the middle right panel shows aggregate demand and supply. Note that aggregate supply is upward sloping as explained above. 1 Note that the ‘right to manage’ is not needed where the real wage is above the market-clearing wage rate. 121 9. Keynesian models with money supply as a policy instrument Figure 9.1: 122 9.7. Keynesian aggregate supply function Expansionary monetary policy causes the aggregate demand schedule to shift out and also causes the LM curve to shift to the right. Since the AD shift causes a price rise, this will tend to reduce real money balances, causing a partial offsetting of the outward LM shift. As in the analysis in Chapter 8, a monetary expansion causes the labour demand curve to shift out. The increase in the price level reduces the real wage for any given nominal wage, leading to an increase in labour demand. However, since the nominal wage is fixed, and given the ‘right to manage’ assumption, firms employ more labour so that employment increases to l00 and output increases to y 00 . A monetary expansion therefore has real effects caused by nominal wages being sticky. In the long run, however, the nominal wage will be bid up as workers renegotiate their contracts to counter the fall in their real wage. In the long run, employment will remain at l0 , output will remain at y 0 and the monetary expansion simply causes a one-for-one movement in prices and nominal wages.2 The Phillips curve The assumption of sticky nominal wages can easily explain the short-run real effects of monetary policy. However, this implies that the real wage is strongly countercyclical; clearly inconsistent with empirical findings. Also, despite the ability of the above model to explain the existence of unemployment, it sheds very little light on to the mechanism by which wages are determined. If wages are predetermined in the current period, then changes in the economy must be reflected in wages in the next period. This is not explicitly modelled above, but was the focus of research made by Phillips (1958). Phillips overcame the problem of assuming exogenously fixed wages by assuming that the nominal wage depends on recent values of unemployment. This assumption was based on an empirical regularity between unemployment and nominal wage inflation in the UK from 1861 to 1957. This is shown in Figure 9.2. Intuitively, if unemployment was high, trade unions, and labour in general, could not negotiate larger pay increases since firms would have a large pool of unemployed with which to fill its vacancies. When unemployment is high, labour tends to be in a weak bargaining position. The specification Phillips gave for the relationship was: ln Wt = ζ(ut−1 ) + ln Wt−1 ⇒ ∆wt = ζ(ut−1 ) with ζ 0 < 0 (9.1) where wt is the log of the nominal wage, = ln Wt , and ∆ denotes the first difference operator. Firms that maximise profits will set the marginal product of labour equal to the real wage, Wt /Pt , which implies that an increase in the nominal wage will be associated with an increase in the price level. ∆wt and ∆pt will be highly correlated, with the result that (9.1) can be written as: ∆pt = ζ(ut−1 ) with ζ 0 < 0. (9.2) The relationship states that there is a permanent trade-off between inflation and unemployment. It appeared that all policy makers had to do to lower unemployment 2 The increase in the price level from P1 to the long-run equilibrium of P2 should cause the labour demand and supply schedules to shift up from I1d and I1s but this is ignored here as it would simply complicate the diagram. 123 9. Keynesian models with money supply as a policy instrument Figure 9.2: and increase output was to allow inflation to rise. However, in the 1970s the Phillips curve relationship broke down and this was explained, and indeed predicted, by Friedman (1968) and Phelps (1970) who emphasised the importance of inflation expectations, which had been ignored thus far. Augmented Phillips curve Friedman and Phelps claimed that agents cared, not about their nominal wage, but about how many goods such a wage could buy (i.e. what really mattered was their real wage). By augmenting (9.1) with inflation, ∆pt , unemployment in period t − 1 would determine changes in real wages. This is shown in (9.3). ∆wt − ∆pt = ζ(ut−1 ). (9.3) However, since there is no current information about ∆pt (inflation is only realised after nominal wages have been negotiated), this has to be anticipated. If ∆pet is the expectation formed at date t − 1 of inflation at date t, then the expectations-augmented Phillips curve can be written as: ∆wt = ζ(ut−1 ) + ∆pet with ζ 0 < 0. (9.4) The expectations augmented Phillips curve explained the breakdown of the simple version that occurred in the 1970s. There were argued to be a number of short-run Phillips curves, one for each level of expected inflation. Unexpected inflation would move you along a given short-run Phillips curve but in the long run there would be no trade-off between unemployment and inflation. As people’s expectations of inflation increased to meet actual inflation we would move to another short-run Phillips curve. In 124 9.7. Keynesian aggregate supply function equilibrium, when inflation was equal to expected inflation, unemployment would be constant at its natural rate. In the long run, any attempt to reduce unemployment to below its natural rate would simply be inflationary. The reason the Phillips curve broke down was because of the persistent and high inflation of the 1970s, caused partly by policy makers trying to exploit the Phillips curve to reduce unemployment and partly by the supply side shocks in the form of large oil price rises in 1974. The high inflation caused expectations of inflation to increase, causing the existing ‘stable’ Phillips curve to shift. In the period 1861 to 1957, although there were periods of notable price rises and falls, inflation, and therefore expected inflation, was on the whole rather stable. Okun’s law As can be seen in Figure 9.1, there is somewhat negative relationship between unemployment and departures of output from potential, y ∗ . This is known as Okun’s law, which can be applied to the Phillips curve to transform (7.4) into: ∆pt = γ(yt − y ∗ ) + ∆pet 1 ⇒ yt = y ∗ + (∆pt − ∆pet ). γ with γ 0 > 0 (9.5) This is the same as the Lucas aggregate supply curve, where d = 1/g and we have replaced unanticipated prices by unanticipated inflation. Note, however, that even though both Lucas model and Okun’s law have similar predictions (real effects of unanticipated monetary policy caused by an upward-sloping aggregate supply curve), they have different microfoundations. The Lucas supply curve is based on imperfect information on the sources of good specific price changes that affects real output and employment fluctuations are voluntary, whereas the Phillips curve assumes nominal rigidities that leads to involuntary employment fluctuations. Menu costs and sticky prices We now outline a model of sticky prices in the goods market. Prices are set at the beginning of the period and cannot change to accommodate shocks or other developments in the economy. As employment was demand determined at the start of this chapter in the case of sticky wages, output is demand determined in this situation of sticky goods prices. Firms produce as much as is demanded at the price that was set at the beginning of the period, even if this means supplying more than they would ordinarily wish to produce given those market conditions. Activity 9.1 Why would a firm want to produce at a level that is demand determined? (Hint: think of the relationship between customers and producers!) How can we justify the assumption of sticky prices? If, after setting a price, market conditions change, why do firms not change their prices to accommodate such developments and thus maximise profits? There are a number of theories to rationalise sticky prices. Two common arguments are the existence of menu costs and the attempts by firms not to disturb the loyal customer base with frequent price changes. If prices do 125 9. Keynesian models with money supply as a policy instrument change frequently, a number of repeat customers may look elsewhere in the market. Prices may then be kept constant in order to keep these valuable customers happy. Menu costs, on the other hand, refer to the costs that firms face when they change their list prices. Such costs arise due to the need to issue updated catalogues, for example. It should then not be that unreasonable to assume that prices are, to a greater or lesser extent, inflexible. Activity 9.2 What industries can you think of that have very sticky prices? Which industries have very flexible prices? A model of sticky prices This model is taken from McCallum (1989), Chapter 10, and you are strongly recommended to read this chapter while working through what follows. First consider aggregate demand. By combining the IS and LM equations, we can derive an AD expression of the form: yt = β0 + β1 (mt − pt ) + β2 Et−1 [pt+1 − pt ] + vt . (9.6) yt , mt and pt are the logs of real output, nominal money balances and the price level, respectively, at date t. vt is a random demand shock with zero mean (i.e. an element of aggregate demand that is not picked up by real money balances or expected inflation). β0 , β1 and β2 are positive parameters and Et−1 is the rational expectations operator with the t − 1 subscript denoting the date the expectation was formed. In rational expectations, people not only take all available information into account when they form their expectations, but their expectations are also consistent with the way in which the variables actually evolve. Rational expectations are sometimes also known as ‘model consistent’ expectations.3 The equation states that aggregate demand depends positively on real money balances and positively on expected inflation; for any given nominal interest rate, higher inflation implies a lower real interest rate, making investment cheaper. Aggregate supply is a little more difficult to specify because of the assumption that prices are set at the beginning of the period, with supply being demand determined. Denote the price that clears the market at date t as p∗t . Where is the price stickiness in the model coming from? We assume that the prices the firms set at date t − 1, to be operational in the market at date t, pt , are the prices they expect to clear the market at date t, i.e.: pt = Et−1 [p∗t ]. (9.7) As in time t − 1, shocks are unknown, these cannot be taken into account when setting the prices. Also, denote the output level that clears the market at date t as yt∗ . Then, if the price equals that which allows markets to clear, by definition markets must clear and so yt∗ must equal the demand when pt = p∗t . yt∗ = β0 + β1 (mt − p∗t ) + β2 Et−1 [pt+1 − p∗t ] + vt . 3 (9.8) You should refer for a refresher on rational expectations to work with expectations operators. Also, see Branson (1989), Chapter 11. 126 9.7. Keynesian aggregate supply function Rearranging (7.8) to obtain p∗t on the left-hand side gives: p∗t = β0 − yt∗ + β1 mt + β2 Et−1 [pt+1 ] + vt β1 + β2 (9.9) noting that Et−1 [p∗t ] equals pt from (9.7) and that in the situation of market clearing, pt = p∗t . We now need an expression telling us how the market clearing/full employment level of output, yt∗ , evolves over time. Here we will generalise the process used in McCallum (1989) so that yt∗ increases gradually through time but also depends positively on last period’s full employment output level, which allows persistence of full employment output. If full employment output is high today, it is likely to be high tomorrow. ∗ yt∗ = δ0 + δ1 t + δ2 yt−1 + ut . (9.10) ut is a zero mean, random supply, shock, which could include the discovery of oil reserves or other raw materials or a sudden technological breakthrough that can increase the productive capacity of the economy. Activity 9.3 Consider expressions for yt∗ of the form, i. yt∗ = δ0 + δ1 t + ut and ii. ∗ yt∗ = yt−1 + δ0 + ut . What are the differences between these two processes? (Hint: what is the persistence of the shock, ut , in both equations; how long does the shock last?) (9.7), (9.9) and (9.10) together can be regarded as constituting aggregate supply. Along with aggregate demand, (9.6), we can solve for the output level, yt , in terms of deviations from yt∗ , and also for the price level, pt . The solution method is given in McCallum, Chapter 10, and you should read the relevant section in order to see how the solution is derived. However, a brief outline is given below. Take expectations of (9.10) conditional on information available at date t − 1: ∗ Et−1 [yt∗ ] = δ0 + δ1 t + δ2 yt−1 ⇒ Et−1 [yt∗ ] = yt∗ − ut . (9.11) Do the same for (9.8), noting that Et−1 [vt ] = 0: Et−1 [yt∗ ] = β0 + β1 Et−1 [mt − p∗t ] + β2 Et−1 [pt+1 − p∗t ]. (9.12) Equating (9.11) and (9.12), noting that Et−1 [p∗t ] in (9.12) is equal to pt (from (9.7)) gives: yt∗ = β0 + β1 (Et−1 [mt ] − pt ) + β2 (Et−1 [pt+1 ] − pt ) + ut . (9.13) If we subtract (9.13) from (9.6), we will have an expression for yt − yt∗ (i.e. deviations of output from the market clearing level). yt − yt∗ = β1 (mt − Et−1 [mt ]) + vt − ut . (9.14) 127 9. Keynesian models with money supply as a policy instrument Monetary policy Imagine that the money supply set by the authorities changes according to: mt = µ0 + µ1 mt−1 + et (9.15) where et is a zero mean, random error representing monetary policy shocks. Taking expectations of (9.15) conditional on information at date t − 1 will give us an expression for the unexpected money supply at date t, mt − Et−1 [mt ], which simply equals et . Substituting this into (9.14) will give us a solution for the output deviation, yt − yt∗ . yt − yt∗ = β1 et + vt − ut . (9.16) Notice that the systematic component of monetary policy (µ0 + µ1 mt−1 ) does not have any real effects here. This is because at date t − 1, when prices for date t are set, firms take into consideration what they expect the monetary authorities will do. If they expect the money supply to increase, knowing that money should have no real effects, they will increase their prices for date t accordingly. Only the random component of monetary policy, the monetary policy shock et , will have real effects since this is realised after the prices have been set. This result, that the systematic component of monetary policy has no real effect, will be discussed in more detail in the next section ‘policy ineffectiveness proposition’. Activity 9.4 What happens if the monetary authorities react to last period’s ∗ ) to the monetary policy output deviation, in other words, if we add µ2 (yt−1 − yt−1 rule (9.15)? Explain your results. Why would the monetary authorities want to respond to lagged deviations in the first place? The fact that unanticipated monetary policy, in the form of the shock, et, has real effects, is essentially because prices are fixed for one period. Prices are set at date t − 1 for the market at date t. Any event occurring, relevant for the market at date t, after prices have been set will naturally be reflected in real variables such as output and employment. Now consider what happens when prices are set for two periods. The model of multiperiod pricing, again from McCallum, Chapter 10, will be used to analyse the effects of monetary policy in this setting. Multi-period pricing Let there be two types of firms, ‘A’ firms and ‘B’ firms. Both set prices for two periods, but at different times. At date t − 2 (based on the information available at that date) ‘A’ firms set, possibly different, prices for the market at dates t − 1 and t. ‘B’ firms also set prices for two periods but do so a period later (i.e. at date t − 1 they set prices for the market at dates t and t + 1). This is shown more clearly in Figure 9.3. At date t − 2, ‘A’ firms set their prices (for the market at t − 1 and t) at the level they expect will clear the market. ‘B’ firms set their prices at date t − 1 for t and t + 1 similarly. Therefore, at date t, the price level will be the average of the prices set by ‘A’ 128 9.7. Keynesian aggregate supply function Figure 9.3: firms and by ‘B’ firms. This is just the average of prices set by ‘A’ and ‘B’, conditional on the information available at the time they were set. pt = Et−1 [p∗t ] + Et−2 [p∗t ] . 2 (9.17) To solve the model, we simplify the aggregate demand function by setting β2 = 0, i.e. yt = β0 + β1 (mt − pt ) + vt . Also, assume that the market clearing output level, yt∗ , follows the process given by yt∗ = d0 + d1 t, i.e. yt∗ is purely deterministic, subject to no shocks. Using the methods outlined above, aggregate demand will equal the market clearing level of output when the price is equal to that which clears the market, pt = p∗t . yt∗ = β0 + β1 (mt − p∗t ) + vt . (9.18) Taking expectations of (9.18) conditional on information available at t − 1 and t − 2 will give: Et−1 [yt∗ ] = β0 + β1 Et−1 [mt − p∗t ] (9.19) Et−2 [yt∗ ] = β0 + β1 Et−2 [mt − p∗t ]. Averaging these two expressions, noting that Et−1 [yt∗ ] = Et−2 [yt∗ ] = yt∗ from the fact yt∗ = δ0 + δ1 t, gives us: 1 1 yt∗ = β0 + β1 · (Et−1 [mt ] + Et−2 [mt ]) − β1 · (Et−1 [p∗t ] + Et−2 [p∗t ]) . {z } 2 2| (9.20) pt Subtracting (7.20) from the expression for aggregate demand results in: 1 1 yt − yt∗ = β1 · (mt − Et−1 [mt ]) + β1 · (mt − Et−2 [mt ]) + vt . 2 2 (9.21) Let monetary policy be the same as before: mt = µ0 + µ1 mt−1 + et = µ0 + µ1 (µ0 + µ1 mt−2 + et−1 ) + et . (9.22) 129 9. Keynesian models with money supply as a policy instrument In order to find an expression for Et−2 [mt ], for us to solve (7.), we need to write mt in terms of variables that we know at date t − 2. Hence we replace mt−1 by backward substitution. As before, we take expectations of mt conditional on information available to us at t − 1 and t − 2 and we can find that: mt − Et−1 [mt ] = et mt − Et−2 [mt ] = µ1 et−1 + et . (9.23) ∗ . Substituting these expressions into (9.21) will give us our solution for yt − yt−1 1 yt − yt∗ = β1 et + β1 µ1 et−1 + vt . (9.24) 2 This is the main result of the assumption of multi (two)-period pricing. A shock to the supply of money, et−1 , not only has real effects at date t − 1, but also in the following period, t. The reason why it affects output at t − 1 should be clear; prices for the market at date t − 1 were set at t − 2 (‘A’ firms) and t − 3 (‘B’ firms) so a shock at date t − 1 will cause output to change at t − 1. However, once the shock has been realised, only ‘B’ firms can take this into account when they set period t prices (see Figure 7.3). ‘A’ firms cannot take et−1 into consideration since their period t prices were set at date t − 2. Since not all firms can change strategies after the realisation of new market conditions, the shock at date t − 1 will have real effects at date t. With multi-period pricing, monetary shocks can have real and, more importantly, persistent effects. The more periods for which a firm sets its prices, the longer and more persistent any monetary shocks will be. Not only that, but also the output deviation, yt − yt∗ , now depends on the parameters of the monetary policy rule, m1 . The systematic component of monetary policy now has real effects (by determining the persistence of any shocks) although the choice of the m parameters will not cause permanent deviations of output from y ∗ . Money, in the long run, is still neutral. 9.8 Predictable and unpredictable components of the money supply The monetary authorities react to events in the economy; if inflation is high in one period, the authorities may reduce the money supply in an attempt to reduce the undesired inflation. Alternatively, the current money stock may be dependent on past output, unemployment, lagged money supplies, and so on. One can call the part of the money stock that depends on these variables the predictable component of monetary policy, since the monetary authorities change the stock of money ‘systematically’ with the observed economic variables known to them when they make their policy choice. The remainder of the money supply can be considered as a monetary shock, either originating from the authorities themselves or in the financial markets, if for example there was a change in the public’s desired currency-deposit ratio that affects the money multiplier (see Chapter 4). The money supply in the last chapter (Lucas misperceptions model) followed a process of the form: + et (9.25) mt = µ0 + µ1 mt−1 |{z} {z } | predictable component monetary shock 130 9.8. Predictable and unpredictable components of the money supply We assume that the monetary shock is purely random/white noise and so our best guess of it before it is realised, Et−1 [et ], is its unconditional mean, zero. Under the assumption of rational expectations, the expectation of mt , based on information available at date t − 1, will be given by: Et−1 [mt ] = µ0 + µ1 mt−1 . (9.26) For simple models, where the monetary authorities and the public share the same information sets, the expected money supply will simply be the predictable component and the unpredictable component of the money supply will be the monetary shock, et . Policy ineffectiveness proposition (PIP) As we saw in the previous chapter, monetary shocks have real effects in the economy while changes in the predictable component of monetary policy do not change output at all. This is because people can change their prices in anticipation of the change in policy. Whereas the model in the previous chapter assumed sticky prices in order for monetary shocks to have real (short-run) effects, one can easily use the Lucas supply curve model to obtain a similar result for flexible price economies. Activity 9.5 Assume aggregate demand is given by yt = β0 + β1 (mt − pt ) + vt and aggregate supply is given by yt = y ∗ + α(pt − Et−1 [pt ]). If monetary policy follows the rule of (9.25), show that the predictable component of monetary policy has no real effects. (Hint: to answer this, equate AD and AS and bring all terms in pt only over to the left hand side. Take expectations of this conditional on date t − 1 information and hence obtain an expression for pt − Et−1 [pt ] in terms of mt , Et−1 [mt ], etc. Substitute this expression into the AS function and use (9.26) to solve for yt − y ∗ .) So even when prices are perfectly flexible, monetary shocks can have real effects, caused by the asymmetric information assumption of the Lucas model. The predictable component of monetary policy, showing how the authorities change the money supply depending on the state of the economy, has no effect at all on real variables. This is the policy ineffectiveness proposition (PIP). A policy of the form mt = µ0 + et will have the same effect on the economy as when money depends on lagged money, inflation, output, and so on. Rational expectations models and PIP When proving that PIP holds in the sticky price and Lucas models, we assumed that agents had rational expectations when forming estimates of future variables. Hence the mt − Et−1 [mt ] term which enters the output equation can be replaced by et , the monetary shock. It may appear that the only reason that PIP holds is because of the assumption of rational expectations. However, PIP does not hold in all rational expectations, RE, models. Consider the aggregate demand function in (9.27). yt = β0 + β1 (mt − pt ) + β2 Et [pt+1 − pt ] + vt . (9.27) 131 9. Keynesian models with money supply as a policy instrument This is exactly the same as (9.6) in the sticky price model, only the expectation of inflation is made at date t, not t − 1. When making similar assumptions as before, pt = Et−1 [p∗t ] and yt∗ = d0 + d1 t, we can show that yt∗ can be given by: yt∗ = β0 + β1 (mt − p∗t ) + β2 Et [pt+1 − p∗t ] + vt . (9.28) Taking expectations of (9.28), conditioning on t − 1 information, noting that Et−1 [yt∗ ] = yt∗ and that Et−1 [Et [p∗t ]] = Et−1 [p∗t ], from the law of iterative expectations (see for example, Branson (1989) Chapter 11), which equals pt , then we obtain: yt∗ = β0 + β1 (Et−1 [mt ] − pt ) + β2 (Et−1 [pt+1 ] − pt ). (9.29) Subtracting (9.29) from the aggregate demand equation, (9.27), will give us an expression for the output deviation, yt − yt∗ . yt − yt∗ = β1 (mt − Et−1 [mt ]) + β2 (Et [pt+1 ] − Et−1 [pt+1 ]) + vt . (9.30) The monetary shock term, mt − Et−1 [mt ], enters as before, but a change in the predictable component of monetary policy could indeed alter people’s expectations of tomorrow’s price level. If a change in the predictable component of monetary policy causes a change in expectations (between dates t − 1 and t) of pt+1 , then PIP no longer holds even though rational expectations are assumed. Monetary policy can then have real effects, but again only in the short run. Prices are set at date t − 1 for date t and so can only contain information available up until date t − 1. Aggregate demand, on the other hand, depends on the expectation of inflation made at date t (relevant for investment decisions through the Fisher equation). Firms, setting their prices at the level they expect to clear the market, have to make an expectation of this term but do so at date t − 1. The fact that expected inflation can rise with new information means aggregate demand can be greater than firms initially anticipated, causing output to increase. Lucas critique The Lucas critique refers to the instability of reduced-form expressions used for policy making or policy appraisal. In the sticky price model of the previous section, the structural equations were given by the aggregate demand equation, the price equation, pt = Et−1 [p∗t ], the equation showing how yt∗ evolves and the monetary policy reaction function showing how mt depends on the state of the economy. When we solve for yt − yt∗ , the equation we derive is a reduced-form equation; a mixture of aggregate demand, aggregate supply and the authorities’ reaction function. For example, consider the sticky price model and the reduced-form expression, (9.16), yt − yt∗ = β1 et + vt − ut . Instead of et , write mt = Et−1 [mt ] = mt − µ0 − µ1 mt−1 . yt − yt∗ = −β1 µ0 + β1 mt − β1 µ1 mt−1 + (vt − ut ). (9.31) If this equation were given to an econometrician, he or she would run a regression of the form: yt − yt∗ = γ0 + γ1 mt + γ2 mt−1 + η1 (9.32) and would find a positive coefficient for γ1 since we know γ1 = β1 (only if the economy was accurately represented by the structural equations given above!). Since γ1 > 0, we 132 9.9. A reminder of your learning outcomes may then think that an increase in the money supply should cause an increase in output above yt∗ . For example if γ1 was found to equal 0.5, then increasing the money supply by 2% should cause a 1% increase in output. However, as we saw in the earlier section, the predictable component of monetary policy had no real effects. Even though we may think an increase in the money supply will increase output (from the reduced form equation, (9.32)), in reality the change in people’s expectations associated with this policy change will cause the reduced form to break down. If the authorities increased the money supply by increasing µ0 , indeed this will have a positive effect on output, via γ1 , but it will also have a negative effect on output since γ0 = −β1 µ0 . The effect of an expansionary monetary policy will be purely inflationary. Quoting Romer (2001) p.251, ‘If policy makers attempt to take advantage of statistical relationships, effects operating through expectations may cause the relationships to break down. This is the famous Lucas critique.’ 9.9 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: explain the importance of nominal rigidities and why such sticky prices occur in the real world examine the effects of monetary policy in the short and long run when there are nominal rigidities describe the workings of the Phillips curve and augmented Phillips curve, noting the differences between the two build and work through models of sticky prices, examining the effects of monetary policy explain why multi-period pricing can lead to real and persistent effects of monetary policy discuss the merits of various sticky price models, noting, in particular, the different short-run and long-run effects of monetary policy. 9.10 Sample examination questions Section A Specify whether the following statement is true, false or uncertain. Explain your answer in a short paragraph. 1. ‘The assumption of rational expectations implies that agents know that prices are flexible.’ 133