EC3115 Monetary Economics

Transcription

1 EC3115 :: L.10 : Old Keynesian macroeconomics Almaty, KZ :: 20 November 2015 EC3115 Monetary Economics Lecture 10: Old Keynesian macroeconomics Anuar D. Ushbayev International School of Economics Kazakh-British Technical University Tengri Partners Merchant Banking & Private Equity a.ushbayev@tengripartners.com Almaty, Kazakhstan, 20 November 2015

2 EC3115 :: L.10 : Old Keynesian macroeconomics - 2 / 62 - Relevant reading Book treatment B. McCallum. (1989). Monetary Economics, Chapters 9 & 10. F. Mishkin. (2016). The Economics of Money, Banking and Financial Markets, 11 th edition, Pearson Education, Web Chapter 1 and its Appendix. Must-read articles B. Bernanke, A. Blinder. (1988). Credit, Money, and Aggregate Demand, American Economic Review, Vol. 78, No. 2, pp

3 EC3115 :: L.10 : Old Keynesian macroeconomics - 3 / 62 - The basic sticky-wage Keynesian model Section 1 The basic sticky-wage Keynesian model

4 EC3115 :: L.10 : Old Keynesian macroeconomics - 4 / 62 - The basic sticky-wage Keynesian model 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. Like in the classical model, output here 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 the classical model, 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 ability to choose how much labour to employ, even if this is more than workers wish to supply at the prevailing 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.

5 EC3115 :: L.10 : Old Keynesian macroeconomics - 5 / 62 - The basic sticky-wage Keynesian model 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 work force supply 1 ) 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 the classical model. 1 Only needed when the real wage is below the labour market-clearing wage rate.

6 EC3115 :: L.10 : Old Keynesian macroeconomics - 6 / 62 - The basic sticky-wage Keynesian model Graphical depiction of the mechanics of the basic Keynesian model

7 EC3115 :: L.10 : Old Keynesian macroeconomics - 7 / 62 - The basic sticky-wage Keynesian model The effect of monetary policy in a model with sticky wages In the above diagram set: The middle left panel shows the labour market when the nominal wage is fixed at W. The bottom left panel shows the standard production function with diminishing marginal returns to labour. The top right diagram shows the IS-LM curves. The middle right panel shows aggregate demand and supply. Note that aggregate supply is upward sloping as explained above. 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.

8 EC3115 :: L.10 : Old Keynesian macroeconomics - 8 / 62 - The basic sticky-wage Keynesian model As in the classical model, 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 l and output increases to y. 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, and thus employment will remain at l, output will remain at y and the monetary expansion simply causes a one-for-one movement in prices and nominal wages. 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. Again, there is some controversy here, but evidence seems to suggest that the real wage is weakly procyclical.

9 EC3115 :: L.10 : Old Keynesian macroeconomics - 9 / 62 - The basic sticky-wage Keynesian model Revisiting the Phillips curve 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. Remember that Phillips (1958) overcame the problem of assuming exogenously fixed wages by assuming 2 that the nominal wage depends on recent values of unemployment. 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. 2 Phillips extrapolated from the money wages-unemployment relationship to a price inflation-unemployment one, although in reality even the link between rate of change of money wages and unemployment is highly nonlinear.

10 EC3115 :: L.10 : Old Keynesian macroeconomics - 10 / 62 - The basic sticky-wage Keynesian model The specification Phillips gave for the relationship was: ln W }{{} t = ζ ut 1 + ln Wt 1 :=w t w t = ζ u t 1 with ζ < 0 Firms that maximise profits will set the marginal product of labour equal to the real wage, W t /P t, which implies that an increase in the nominal wage will be associated with an increase in the price level. Extrapolating from w t to p t : p = ζ u t 1 with ζ < 0 The relationship states that there is a permanent trade-off between inflation and unemployment.

11 EC3115 :: L.10 : Old Keynesian macroeconomics - 11 / 62 - The basic sticky-wage Keynesian model It appeared that all policy makers had to do to lower unemployment and increase output was to allow inflation to rise.

12 EC3115 :: L.10 : Old Keynesian macroeconomics - 12 / 62 - The basic sticky-wage Keynesian model However, in the 1970s the Phillips curve relationship broke down and this was explained, and indeed predicted, by Friedman (1968) 3 and Phelps (1970) 4 who emphasised the importance of inflation expectations, which had been ignored thus far. The introduction of the Phillips curve, as a fundamental structural relationship that characterises the wage adjustment process, into economic analysis marked a shift from the original Keynesian definition of full employment in terms of job openings to job seekers ratio to one that assumed an existence of trade-off between inflation and unemployment. The original Phillips curve is no longer used because of its over-simplification of reality, but expectations-augmented Phillips curve-like relations figure even in modern New Keynesian DSGE models. 3 M. Friedman. (1968). The role of monetary policy, American Economic Review, Vol. 58, No. 1, pp E. Phelps. (1970). Microeconomic Foundations of Employment and Inflation Theory. New York: Norton.

13 EC3115 :: L.10 : Old Keynesian macroeconomics - 13 / 62 - The basic sticky-wage Keynesian model Friedman and Phelps claimed that agents cared, not about their nominal wage, but about their real purchasing power, and thus the real wage. By augmenting the original Phillips curve with inflation, unemployment in period t 1 would determine changes in real wages: w t p t = ζ u t 1 However, since there is no current information about p t (inflation is only realised after nominal wages have been negotiated), its future realised value has to be anticipated. Denoting by p e t the expectation formed at date t 1 of inflation at date t, the expectations-augmented Phillips curve can be written as: w t = ζ u t 1 + p e t with ζ < 0

14 EC3115 :: L.10 : Old Keynesian macroeconomics - 14 / 62 - The basic sticky-wage Keynesian model 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 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.

15 EC3115 :: L.10 : Old Keynesian macroeconomics - 15 / 62 - The basic sticky-wage Keynesian model The reason the Phillips curve broke down was because of the persistent and high inflation of the 1970s. This was 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 Incidentally, this is a good example of Goodhart s law in action: when a stable relationship is discovered and starts to be used, it breaks down 5. 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. 5 Original formulation: any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes C. Goodhart. (1975). Problems of Monetary Management: The U.K. Experience, Papers in Monetary Economics, Reserve Bank of Australia.

16 EC3115 :: L.10 : Old Keynesian macroeconomics - 16 / 62 - The basic sticky-wage Keynesian model Okun s law The basic Keynesian model suggests exists is a somewhat negative relationship between unemployment and the output gap, y t y. This is known as Okun s law, which can be applied to the expectations-augmented Phillips curve to transform it into: p t = γ y t y + p e with γ > 0 t y t = y + 1 pt p e t γ Note that this is similar to the Lucas misperceptions model: y t = y + d P t E t 1 Pt where d = 1/γ, and where the unanticipated change in the price level has been replaced by the unanticipated change in inflation. Note that although both the Lucas model and Okun s law have similar predictions i.e. 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 lead to involuntary employment fluctuations.

17 EC3115 :: L.10 : Old Keynesian macroeconomics - 17 / 62 - A sticky-price Keynesian model Section 2 A sticky-price Keynesian model

18 EC3115 :: L.10 : Old Keynesian macroeconomics - 18 / 62 - A sticky-price Keynesian model The case of sticky prices We now turn to studying a McCallum (1989) economy with sticky prices, where the aggregate demand expression is derived from the standard IS and LM equations: y t = β 0 + β 1 mt p t + β2 E t 1 pt+1 p t + vt where y t log of real output at time t, m t log of nominal money balances, p t log the price level, v t 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), β 0, β 1 and β 2 are positive parameters. E t 1 [ ] is the expectations operator denoting expectations of future values of a variable formed at time t 1.

19 EC3115 :: L.10 : Old Keynesian macroeconomics - 19 / 62 - A sticky-price Keynesian model In rational expectations, agents 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 (i.e. agents know the model ). Therefore rational expectations are sometimes also known as model consistent expectations. The above 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.

20 EC3115 :: L.10 : Old Keynesian macroeconomics - 20 / 62 - A sticky-price Keynesian model Aggregate supply is a little trickier to specify because of the assumption that prices are set at the beginning of the period, with supply being demand determined. Denote the goods market-clearing price at time t by p t, and the market-clearing level of output by y t. We assume that the prices p t that the firms set at time t 1 to be operational in the market at time t are their expectations of the market-clearing prices for time t, such that: p t = E t 1 p t Since random demand shocks, v t, are not known in advance and have zero mean, they do not figure in the price-setting equation. Then, if the price equals that which allows markets to clear, by definition markets must clear and so y t must equal the demand whenever p t = p t : y t = β 0 + β 1 mt p t + β2 E t 1 pt+1 p t + vt

21 EC3115 :: L.10 : Old Keynesian macroeconomics - 21 / 62 - A sticky-price Keynesian model Rearranging the above: y t = β 0 + β 1 m t β 1 p t + β 2E t 1 pt+1 β2 E t 1 p t +v t }{{} =p t = β 0 + β 1 m t + β 2 E t 1 pt+1 + vt β 1 p t β 2p t Now, noting that with market clearing we have p t = p t : y t = β 0 + β 1 m t + β 2 E t 1 pt+1 + vt β 1 + β 2 p t And therefore solving for p t gives: p t = β 0 y t + β 1m t + β 2 E t 1 pt+1 + vt β 1 + β 2

22 EC3115 :: L.10 : Old Keynesian macroeconomics - 22 / 62 - A sticky-price Keynesian model We now need an expression for the dynamics of the market-clearing / full-employment level of output, y t. The model of McCallum (1989) uses the following dynamic equation for y t : y t = δ 0 + δ 1 t + δ 2 y t 1 + u t which includes a linear time trend and also a term that depends on the last period s full employment output level, plus a zero-mean random supply shock. The presence of δ 2 y t 1 allows persistence of full employment output. To see this compare the above with an equation that only includes a time trend y t = δ 0 + δ 1 t + u t y t+1 = δ 0 + δ 1 + δ1 t + u t+1 where the expression for the next period market-clearing output does not include the previous-period u t term, so the shock is short-lived.

23 EC3115 :: L.10 : Old Keynesian macroeconomics - 23 / 62 - A sticky-price Keynesian model In contrast, when the equation for y t we have: includes its own lagged value, y t = δ 0 + δ 1 t + δ 2 y t 1 + u t y t+1 = δ 0 + δ 1 + δ1 t + δ 2 y t + u t+1 = δ 0 + δ 1 + δ1 t + δ 2 δ0 + δ 1 t + δ 2 y t 1 + u t + ut+1 = δ 0 + δ 1 + δ 0 δ 2 + δ1 + δ 1 δ 2 t + δ 2 2 y t 1 + δ 2u t + u t+1 Thus the shock is long-lived: e.g. a positive value of u t increases y t by the same amount, which in turn increases y t+1 by δ 2u t, which in turn increases y t+2 by δ2 2 u t and so on. If full employment output is high today, it is likely to be high tomorrow.

24 EC3115 :: L.10 : Old Keynesian macroeconomics - 24 / 62 - A sticky-price Keynesian model We now have the four equations that close the model. Aggregate demand: y t = β 0 + β 1 mt p t + β2 E t 1 pt+1 p t + vt Aggregate supply: p t p t y t = E t 1 p t = β 0 y t + β 1m t + β 2 E t 1 pt+1 + vt β 1 + β 2 = δ 0 + δ 1 t + δ 2 y t 1 + u t

25 EC3115 :: L.10 : Old Keynesian macroeconomics - 25 / 62 - A sticky-price Keynesian model Taking expectations of the last expression for aggregate supply y t : E t 1 y t = Et 1 δ0 + δ 1 t + δ 2 y t 1 + u t = δ 0 + δ 1 t + δ 2 y t 1 + E t 1 ut }{{} :=0 = δ 0 + δ 1 t + δ 2 y t 1 E t 1 y t = y t u t Taking expectations of the expression for aggregate demand at full employment (i.e. at y t ): E t 1 y t = Et 1 β0 + β 1 mt p t + β2 E t 1 pt+1 p t + vt = β 0 + β 1 E t 1 mt β1 E t 1 p +β t 2 E t 1 pt+1 β2 E t 1 p + E t t 1 vt }{{}}{{}}{{} =p t =p t = β 0 + β 1 Et 1 mt pt + β2 Et 1 pt+1 pt :=0

26 EC3115 :: L.10 : Old Keynesian macroeconomics - 26 / 62 - A sticky-price Keynesian model Thus we have: E t 1 y t = β0 + β 1 Et 1 mt pt + β2 Et 1 pt+1 pt Noting also that from the expectation of aggregate supply we have: Then, combining, we get: E t 1 y t = y t u t y t = β 0 + β 1 Et 1 mt pt + β2 Et 1 pt+1 pt + ut Subtracting the above from the expression for aggregate demand we have and equation for the output gap: y t y t = β 0 + β 1 mt p t + β 2 Et 1 pt+1 pt + vt β 0 β 1 Et 1 mt p t β 2 Et 1 pt+1 pt ut = β 1 mt E t 1 mt + vt u t

27 EC3115 :: L.10 : Old Keynesian macroeconomics - 27 / 62 - A sticky-price Keynesian model Monetary policy in a McCallum (1989) economy Imagine that the central bank uses the money supply as the policy instrument,and sets its level according to the following rule: m t = Taking expectations gives: µ 0 + µ 1 m }{{ t 1 } + e }{{} t systematic component random shock component E t 1 mt = µ0 + µ 1 E t 1 mt 1 + E t 1 et }{{}}{{} known at time t 1 :=0 = µ 0 + µ 1 m t 1 Therefore the unexpected part of the money supply at time t is equal to: m t E t 1 mt = et

28 EC3115 :: L.10 : Old Keynesian macroeconomics - 28 / 62 - A sticky-price Keynesian model Substituting this into the expression for the output gap gives: y t y t = β 1 mt E t 1 mt + vt u t = β 1 e t + v t u t We observe that the systematic component of monetary policy, µ0 + µ 1 m t 1 has no effects on the output gap in this model. This is because at time t 1, when prices for time 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 time t accordingly. Only the random component of monetary policy, the monetary policy shock e t, will have real effects since this is realised after the prices have been set.

29 EC3115 :: L.10 : Old Keynesian macroeconomics - 29 / 62 - A sticky-price Keynesian model This apparent result, that the systematic component of monetary policy has no real effect is known as the policy ineffectiveness proposition. The fact that unanticipated monetary policy, in the form of the shock, e t, has real effects, is essentially because prices are fixed for one period. Prices are set at time 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.

30 EC3115 :: L.10 : Old Keynesian macroeconomics - 30 / 62 - A sticky-price Keynesian model Multi-period pricing Now we turn to considering what happens when prices are set for two periods. Let there be two types of firms, type A and type B firms, of equal proportion. Both set prices for two periods, but at different times. At time t 2 (based on the information available at that time) type A firms set, possibly different, prices for the market at times t 1 and t. Type B firms also set prices for two periods but do so 1 period later (i.e. at times t 1 they set prices for the market at times t and t + 1).

31 EC3115 :: L.10 : Old Keynesian macroeconomics - 31 / 62 - A sticky-price Keynesian model At date t 2, type A firms set their prices (for the market at t 1 and t) at the level they expect will clear the market. Type B firms set their prices at time t 1 for t and t + 1 similarly. Therefore, at time t, the price level will be the average of the prices set by type A and type B firms: p t = E t 1 p t + Et 2 p t 2 remembering that we assume that the prices p t that the firms set ahead of future markets are their expectations of the market-clearing prices for future periods.

32 EC3115 :: L.10 : Old Keynesian macroeconomics - 32 / 62 - A sticky-price Keynesian model Here we will use two simplifications such that: inflation expectations of agents do not affect aggregate demand (i.e. β 2 = 0): y t = β 0 + β 1 mt p t + vt market clearing output level is deterministic with a linear trend: y t = δ 0 + δ 1 t The market clearing level of output will therefore equal aggregate demand at the market clearing price level: y t = β 0 + β 1 mt p t + vt Taking expectations of the above conditional on information available at the time of price-setting by type A and type B firms gives: E t 2 y t = β0 + β 1 E t 2 mt p t E t 1 y t = β0 + β 1 E t 1 mt p t

33 EC3115 :: L.10 : Old Keynesian macroeconomics - 33 / 62 - A sticky-price Keynesian model Noting that E t 1 y t = Et 1 y t = y t since y t is purely deterministic here with y t = δ 0 + δ 1 t, and taking the average for two types of firms we have: y t = β β 1E t 2 mt p 1 t + 2 β 1E t 1 mt p t = β β 1 1 Et 2 mt + Et 1 mt 2 β 1 Et 2 p t + Et 1 p t }{{} =2p t Subtracting the resulting expression for aggregate market-clearing output from the expression for aggregate demand we get: y y t = β 0 +β 1 m t β 1 p t +v t β β 1 Et 2 mt + Et 1 mt + β 1 p t y y t = β 1m t 1 2 β 1 Et 2 mt + Et 1 mt + vt

34 EC3115 :: L.10 : Old Keynesian macroeconomics - 34 / 62 - A sticky-price Keynesian model Which can be rearranged as: y y t = 1 2 β 1m t β 1m t 1 2 β 1 Et 2 mt + Et 1 mt + vt = 1 2 β 1 mt E t 2 mt β 1 Using the same monetary policy rule as before: m t = µ 0 + µ 1 m t 1 + e t = µ 0 + µ 1 µ0 + µ 1 m t 2 + e t 1 + et mt E t 1 mt + vt = µ 0 + µ 0 µ 1 + µ 2 1 m t 2 + e t + µ 1 e t 1 Taking expectations of the above conditional on information available at the time of price-setting by type A and type B firms gives: E t 2 mt = µ0 + µ 0 µ 1 + µ 2 1 E t 2 mt 2 E t 1 mt = µ0 + µ 1 E t 1 mt 1

35 EC3115 :: L.10 : Old Keynesian macroeconomics - 35 / 62 - A sticky-price Keynesian model Therefore the unexpected parts of the money supply at time t is equal to: m t E t 1 mt = et m t E t 2 mt = et + µ 1 e t 1 Plugging these into the expression for the output gap we find: y y t = 1 2 β 1 1 mt E t 2 mt + 2 β 1 mt E t 1 mt + vt = 1 2 β 1 1 et + µ 1 e t β 1 et + vt = β 1 e t β 1µ 1 e t 1 + v t

36 EC3115 :: L.10 : Old Keynesian macroeconomics - 36 / 62 - A sticky-price Keynesian model Let s compare the case of one- and two-period pricing with no supply shocks: (1-period pricing) y y t = β 1 e t + v t (2-period pricing) y y t = β 1 e t β 1µ 1 e t 1 + v t It is clear that, in this model, multi-period pricing allows monetary policy shocks to have real effects not only contemporaneously, but also in the next period. The reason why it affects output at t 1 is the fact prices for the market at t 1 were set at both t 2 (by type A firms) and t 3 (by type B firms), and thus a shock at time t 1 will cause output to change at t 1. However, once the shock has been realised, only type B firms can take this into account when they set period t prices. Type A firms cannot take e t 1 into consideration since their period t prices were already set at time t 2.

37 EC3115 :: L.10 : Old Keynesian macroeconomics - 37 / 62 - A sticky-price Keynesian model Thus, since not all firms can change strategies after the realisation of new market conditions, the shock at time 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 gap, y y t, now depends on the parameters of the monetary policy rule, µ 1. Thus, unlike under one-period pricing, multi-period pricing allows the systematic component of monetary policy to have real effects (by determining the persistence of any shocks). Nevertheless, the choice of the monetary policy parameters will not cause permanent deviations of output from its full-employment level. Money, in the long run, is still neutral.

38 EC3115 :: L.10 : Old Keynesian macroeconomics - 38 / 62 - A sticky-price Keynesian model Policy Ineffectiveness Proposition Since the central bank usually acts to compensate the various economic disturbances in order to stabilize prices, a significant part of its behaviour can be regarded as systematic and thus can lend itself reasonably well to expectation by the public, if the public and the central bank share the same information set. The remainder of the money supply can be considered as a shock to monetary conditions, arising as a result of a mistake or a change in the monetary policy rule, or from a change in the microstructure of financial markets and agent preferences. As we saw in the case of the McCallum economy, it is possible for monetary shock to have real effects, while at the same time the predictable systematic component of monetary policy has no effect on real output, since agents will adjust their prices in anticipation of the change in monetary policy.

39 EC3115 :: L.10 : Old Keynesian macroeconomics - 39 / 62 - A sticky-price Keynesian model In fact we also saw before that one does not need to assume sticky prices for monetary shocks to have real effects in the short run, cf. the Lucas misperceptions model with flexible prices and real effects of money. So even when prices are perfectly flexible, monetary shocks can have real effects, caused e.g. by the asymmetric information assumption of the Lucas model. The predictable component of monetary policy, showing how the authorities change the money supply (in the simplistic framework which assumes that the central bank monetary base a the policy instrument) depending on the state of the economy, has no effect at all on real variables. This is known as the policy ineffectiveness proposition (PIP). A policy of the form m t = µ 0 + e t will have the same effect on the economy as when money depends on lagged money, inflation, output, and so on.

40 EC3115 :: L.10 : Old Keynesian macroeconomics - 40 / 62 - A sticky-price Keynesian model The role of rational expectations In both the sticky price and the Lucas models, we assumed that agents had rational expectations when forming estimates of future variables, which made the deviation of actual from the expected monetary policy stance simply noise: hence giving rise the PIP. m t E t 1 mt = et In fact, however, not all rational expectations (RE) models exhibit such behaviour. Replace the McCallum economy aggregate demand function by y t = β 0 + β 1 mt p t + β2 E t 1 pt+1 p t + vt y t = β 0 + β 1 mt p t + β2 E t pt+1 p t + vt such that expectations are formed contemporaneously instead of one period in advance.

41 EC3115 :: L.10 : Old Keynesian macroeconomics - 41 / 62 - A sticky-price Keynesian model If we continue to make the same assumptions of: price-setting in accordance with the expectations of future market-clearing prices: p t = E t 1 p t the market clearing output being deterministic with a linear trend: y t = δ 0 + δ 1 t We can deduce that the expression for the market-clearing level of output will be given by: y t = β 0 + β 1 mt p t + β2 E t pt+1 p t + vt

42 EC3115 :: L.10 : Old Keynesian macroeconomics - 42 / 62 - A sticky-price Keynesian model Taking expectations of the above, remembering: that y t is deterministic: E t 1 y t = Et 1 δ0 + δ 1 t = δ 0 + δ 1 t = y t and the tower property of the expectations operator: E t 1 Et p t = Et 1 p t we get: E t 1 y = β t 0 + β 1 Et 1 mt Et 1 p t + β2 Et 1 Et pt+1 Et 1 p t y = β t 0 + β 1 Et 1 mt pt + β2 Et 1 pt+1 pt Which produces a slightly different expression for the output gap: y t y t = β 1 mt E t 1 mt + β2 Et pt+1 Et 1 pt+1 + vt

43 EC3115 :: L.10 : Old Keynesian macroeconomics - 43 / 62 - A sticky-price Keynesian model The monetary shock term, m t E t 1 mt, is present just as before, but here also a change in the predictable component of monetary policy can have real effects by altering agents expectations of the future price level. If a change in the predictable component of monetary policy causes a change in expectations (between times t 1 and t) of p t+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 time t 1 for time t and so can only contain information available up until time t 1. Aggregate demand, on the other hand, depends on the expectation of inflation made at time 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 time 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.

44 EC3115 :: L.10 : Old Keynesian macroeconomics - 44 / 62 - A sticky-price Keynesian model The Lucas critique Due to Robert Lucas who won Nobel Prize in 1995 for his work on rational expectations. For some time, central banks have been building large macroeconometric models, which until recently were large versions of the IS-LM or AD-AS model. They would then use these models to provide simulations for the effects of various different kinds of policies, estimated with historical data. Lucas pointed out that it may be unwise to believe in the invariance of the model parameters and in the validity of such models predictions since policy changes would likely alter agents expectations in a way that changes the fundamental relationships between variables.

45 EC3115 :: L.10 : Old Keynesian macroeconomics - 45 / 62 - A sticky-price Keynesian model Example: Prediction (based on past experience): An increase in the money growth rate will reduce unemployment. The Lucas critique points out that increasing the money growth rate may raise expected inflation, in which case unemployment would not necessarily fall. The Lucas critique refers to the instability of reduced-form expressions used for policy making or policy appraisal. In the sticky price McCallum model above, the structural equations were given by the aggregate demand equation, the price equation, the equation of the dynamics for market clearing output and the monetary policy reaction function. When we solve for the output gap, the equation derived is one of reduced-form (endogenous variable expressed in terms of exogenous or known lagged endogenous variables): a mixture of aggregate demand, aggregate supply and the central bank s reaction function.

46 EC3115 :: L.10 : Old Keynesian macroeconomics - 46 / 62 - A sticky-price Keynesian model Consider the expression for the output gap in the original one-period price-setting McCallum economy: y t y t = β 1e t + v t u t Replace the noise term e t by m t E t 1 mt : y t y t = β 1 mt E t 1 mt + vt u t and open up the expectation of the money supply to give: y t y t = β 1 mt µ 0 + µ 1 m t 1 + vt u t = β 1 µ 0 + β 1 m t β 1 µ 1 m t 1 + v t u t If we do not know that the economy indeed fundamentally follows this law, we could be tempted to simply employ econometrics to estimate an equation of such form, i.e.: yt y t = α + γ1 m t + γ 2 m t 1 + ε t

47 EC3115 :: L.10 : Old Keynesian macroeconomics - 47 / 62 - A sticky-price Keynesian model Our estimation would establish the values of parameters α, γ 1 and γ 2 for a given historical dataset. Should we encounter a positive value of γ 1, we might be led to believe that a monetary expansion causes output to increase. However, once the central bank attempts to exploit this apparent relationship and tries to increase the money supply by changing the policy rule from m t = µ 0 + µ 1 m t 1 + e t to ˆm t = ˆµ 0 + µ 1 m t 1 + e t s.t. ˆµ0 = µ 0 + ξ, what would happen (if the underlying true model is indeed true, of course), is that the true model s parameters would change, resulting in: y t y t = β 1 ˆµ 0 + β 1 ˆm t β 1 µ 1 m t 1 + v t u t

48 EC3115 :: L.10 : Old Keynesian macroeconomics - 48 / 62 - A sticky-price Keynesian model We observe that the expansion of the money supply in this manner will have two effects on output: y t y t = β 1 ˆµ 0 + β 1 ˆm t β 1 µ 1 m t 1 + v t u t = β 1 µ0 + ξ + β 1 mt + ξ β 1 µ 1 m t 1 + v t u t = β 1 µ 0 + β 1 m t β 1 µ 1 m t 1 + v t u t + β 1 ξ β 1 ξ Thus the two effects are mutually annihilating, output is unchanged and the monetary expansion simply leads to an increase in prices. The change in people s expectations associated with this policy change thus causes the reduced form to break down and the predictions of a model estimated on historical data become invalid. The key problem here obviously is the assumption that parameters being estimated are structural and independent of policy choices. In fact this is a generic identification problem of RE models.

49 EC3115 :: L.10 : Old Keynesian macroeconomics - 49 / 62 - A sticky-price Keynesian model In practice, it is : often quite difficult after estimating empirical relationships to determine whether they are structural or merely reduced-forms of some more fundamental model. hard to identify shocks in the data. hard to tell how outcomes would have been different had actual policies not been used. The Lucas critique can be seen as a reformulation of Goodhart s law that notes the fact that since the parameters of reduced-form models are not structural (i.e. not policy-invariant), they will necessarily change whenever policy changes. 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. David Romer, (2001), Advanced Macroeconomics, Second edition, Mc- Graw Hill Irwin.

50 EC3115 :: L.10 : Old Keynesian macroeconomics - 50 / 62 - Bernanke-Blinder model Section 3 Bernanke-Blinder model

51 EC3115 :: L.10 : Old Keynesian macroeconomics - 51 / 62 - Bernanke-Blinder model IS-LM plus credit The model of Bernanke and Blinder (1988) is a extension of the standard static IS-LM framework that includes credit as a third asset in the model in addition to money and government bonds. We assume existence of no physical cash, and thus the monetary base consists only of reserves: M = R which the central manages by open market operations. The money supply thus also only consists of deposits: M = D Assume a bank credit (loan) demand function of the following kind: L d = L ρ, i, y where L ρ < 0 L y > 0 L i > 0

52 EC3115 :: L.10 : Old Keynesian macroeconomics - 52 / 62 - Bernanke-Blinder model Bank credit is imperfectly substitutable for bond finance. The balance sheet of the banking sector consists of reserves, loans and bonds on the asset side, and deposits on the liability side: R + L + B = D Reserves are made up of required reserves and excess reserves (non-remunerated): R }{{} E+τD +L + B = D where τ is the required reserves ratio. E + L + B = (1 τ) D The job of the bank is thus to choose an appropriate portfolio structure of the asset side of its balance sheet.

53 EC3115 :: L.10 : Old Keynesian macroeconomics - 53 / 62 - Bernanke-Blinder model The structure of the asset side portfolio is given by: E (i) = λ E (i) (1 τ) D excess reserves demand L s i, ρ = λ L i, ρ (1 τ) D credit supply B i, ρ = 1 λ E (i) λ L i, ρ (1 τ) D bond demand }{{} λ B(i,ρ) where i is the bond interest rate, ρ is the loan interest rate, λ E + λ L + λ B = 1 and: λ E (i) < 0 i λ L (i) λ B (i) < 0 > 0 i i λ B (i) ρ > 0 λ B (i) ρ < 0

54 EC3115 :: L.10 : Old Keynesian macroeconomics - 54 / 62 - Bernanke-Blinder model The reserves of the commercial bank thus are: R = τd + E = τd + λ E (i) (1 τ) D = τ + λ E (i) (1 τ) D The money multiplier therefore equals: D R = m (i) = 1 τ + λ E (i) (1 τ) The multiplier thus depends on the bank s portfolio considerations and is endogenously determined by the interest rate i. Note, that i is determined on the bond market and the central bank is an agent in the bond market. Money supply is given by the multiplier, M s = D = m (i) R, while the money demand follows the standard assumptions D d i, y (with positive dependency on y and negative dependency on i).

55 EC3115 :: L.10 : Old Keynesian macroeconomics - 55 / 62 - Bernanke-Blinder model The equilibrium in the money market is given by the LM curve: D d i, y = M = m (i) R The equilibrium in the goods market is given by the IS curve: y = Y ρ, i It is assumed that non-banks also hold a portfolio of bonds and money so that the loan demand is determined by i (positively) and ρ (negatively). The equilibrium on the credit market is determined by 6 : which implies: L d ρ, i, y = L s i, ρ = λ L i, ρ (1 τ) D L d ρ, i, y = L s i, ρ = λ L i, ρ (1 τ) D = λ L i, ρ (1 τ) m (i) R 6 Note: the bond market also clears, automatically, by Walras Law.

56 EC3115 :: L.10 : Old Keynesian macroeconomics - 56 / 62 - Bernanke-Blinder model The above can be solves to give the equilibrium interest rate on loans, ρ: ρ = φ i, y, R with ρ > 0 an increase in loan demand pushes up the interest rate. y ρ < 0 an increase in reserves, for a given money multiplier, results R in an increase in loanable funds 7. Thus the new IS curve the CC (commodity-credit) curve becomes: y = Y φ i, y, R, i The Bernanke-Blinder model thus adds one more observable variable to the IS-LM framework to allow better analysis of the dynamics of the economy and financial markets. 7 Caution! No such thing in reality.

57 EC3115 :: L.10 : Old Keynesian macroeconomics - 57 / 62 - Bernanke-Blinder model The CC curve has a negative slope similar to the IS curve. Unlike the IS curve, however, the CC curve is affected by monetary policy (change in reserves) and by credit market shock that affect either the L ( ) or λ ( ) functions.

58 EC3115 :: L.10 : Old Keynesian macroeconomics - 58 / 62 - Bernanke-Blinder model If riskiness of the marginal investment project rises, the CC curve shifts in. If the money multiplier falls, both the CC and LM curves shift in. If some financial institutions fail, both the CC and LM curves shift in.

59 EC3115 :: L.10 : Old Keynesian macroeconomics - 59 / 62 - Bernanke-Blinder model In reaction to above the central bank can either increase reserves, or directly lend to the financial institutions. This is shown above as a shift outward of the LM curve, and of the CC curve.

60 EC3115 :: L.10 : Old Keynesian macroeconomics - 60 / 62 - Bernanke-Blinder model Effects of shocks on observable variables in the CC-LM model Increase in Income Money Credit i on bonds Bank reserves Money demand Credit supply Credit demand Commodity demand Expenditure shock shifts CC like IS. Money demand shock shifts LM. Rise in bank reserves is expansionary through both LM and CC 8. Increase in credit supply shifts the CC-curve outward. 8 Creates an identification problem.

61 EC3115 :: L.10 : Old Keynesian macroeconomics - 61 / 62 - Bernanke-Blinder model Concluding remarks Beyond the level of interest rates on government bonds, we can also observe interest rate differentials (i.e. spreads). Changes in these spreads are indications of the supply and demand for credit and bonds. The loan-bond spread, ρ i, is a positive function of loan riskiness (not explicitly shown in the original model). The CC curve reduces to the IS curve if a) bonds and loans are assumed to be perfect substitutes to borrowers or lenders, or b) if commodity demand is insensitive to the loan rate. In case of a liquidity trap, where money and bonds are perfect substitutes 9, the LM curve would become horizontal and hence monetary policy could only work through the credit market directly, affecting the CC curve. 9 Not exactly the original Keynes formulation.

62 EC3115 :: L.10 : Old Keynesian macroeconomics - 62 / 62 - Bernanke-Blinder model IS-LM assumes money is special and has no close substitutes. CC-LM allows credit to be special due to information problems in financial markets and various balance sheet effects. Credit-GDP relationship is more stable than Money-GDP-relationship, cf. Werner s Quantity Theory of Credit.