Macroeconomic Theory

1. Macroeconomic Theory Chapter 3 Inflation, Unemployment and Monetary Rules

2. Central banks are now typically viewed as operating through adjusting r in order to keep the economy close to its inflation target at the eq level of output. • Inflation is constant at eq output. If IS shifts to the RHS → higher inflation. This will be incorporated in future wage and price setting which will be squeezed out of the economy by a period of above equnemp. • Central banks aim is to minimize the cost of shocks to the economy in terms of higher inflation and unemployment. It will raise r to guide the economy back toward target inflation and equnemp. This behavior is known as “reaction function”, or “monetary policy rule”. • By combining PC, IS and monetary rule we have the 3 equation model IS-PC-MR.

3. Inflation and Phillips curves • Inflation is the rate of change in prices: π = P-P-1/P-1 • Policy makers are concerned about π. • High inflation tends to be volatile and creates uncertainty • Inflation undermines the way P convey information. • It is costly to bring inflation down, as unemp will↑. • Inflation inertia • In the standard model inflation depends on • Past inflation π-1 • The gape between current unemp and the ERU. • interpretations of the π-1. • Wage setters expect inflation this period to continue as it is in the last period. This is “adaptive expectations” πE= πE-1 + a(π-1- πE-1), 0 1 Adaptive expectations • Expected π equals last period πE plus a correction term (forecast error)

4. If forecast errors are fully corrected so that a=1 • πE= πE-1 (simple adaptive expectations). • This is an implausible way to form expectations. Why we look entirely to the past. • Anther realistic interpretation of why we include past inflation is inertia that characterize the wage and price setting. Wage setters incorporate past inflation in order to make up for any erosion in living standards taken place since last wage round. Wage setters are assumed not to be able to expected future changes in their current bargain. • We denote inflation inertia using the lagged inflation πl π = π-1 + a (y-ye) • i.e., current inflation equals inflation inertia plus output gap. (this is expectations augmented PC).

5. Deriving Phillips curves • We have seen that at eqWS and PS curves cross at a uniqueunemp rate at which the labor market is in eq and there is no incentive for wage and price setters to change their behavior. We will examine the relationship between unemp and inflation. • If inflation is 4% and unemp is at the ERU. In fig 3.1 emp is E1 and w is w1. to keep w constant at w1, wage setters require a money wage rise that will make up for. Since prices have risen by 4%, W will rise by 4%. • Firms set prices according to their pricing rule. Since P=(1+μhat) . W/λ ΔP/P = ΔW/W - Δλ/λ • When average productivity of labor λ is constant ΔP/P = ΔW/W • See the following table and figure 3.1. Results of the table can be illustrated using a Phillips curve diagram.

6. Figure 3.1

7. Constant, rising and falling inflation

8. In reality there is not one for one relationship between a rise in y and a fall in unemp. This is due to: • Labor hoarding • Economically inactive labor • A change in y by 1% tends to be associated with a change in unemp by less than 0.5% (Okun’s law). • Using the data in table 3.1 we can plot the other Phillips curves as they are shown in fig 3.2. • Each Phillips curve is defined by two characteristics: • The lagged inflation rate which is equal to past inflation and fixes the height of PC on a vertical line above the level of output associated with ERU. • The slope of WS curve, which fixes its slope. PC will be steeper if WS curve is steeper and vice versa.

9. W increase by lagged inflation plus an amount to close the gape between existing real wage (on PS curve) and the w on the WS curve. The percentage gap is a function of y and ye. So for simplicity: π = πl + a (y-ye) π = π-1 + a (y-ye) π = inflation inertia + output gape. • a is a positive constant. The y deviation is approximately equal to (y – ye). If (y-ye) is positive inflation will be higher than last period, And if (y-ye) is negative, inflation will fall below last period, finally if (y=ye) inflation is constant. • Hence the PC shifts up or down whenever lagged inflation changes and that its slope depends on a, which in turn reflects the slope of the WS curve.

10. Deriving the Phillips Curves fig 3.2

11. Phillips’ original curve • If the economy is affected by random shocks to AD, the economy would be observed at the points shown in fig 3.3. this is one way to present the original PC using data for the UK between 1861-1957. fig 3.4 is a reproduction for the period 1861-1913 • Phillips original curve may exist but it cannot be exploited • Can the govt use policy to shift the economy from its customary position to a higher level (from A to B in fig 3.3). • Suppose that the govt increases MS, i falls, and y increases. Unlike the original PC we have quite different situation: the govt is seeking to keep y at y2 to lower unemployment even with inflation. The tendency of the economy to be near point B is taken in the calculations of workers. They will claim for a W rise by 2%, and expected inflation will rise from 0 to 2%, the PC curve shifts up.

12. Figure 3.3

13. Figure 3.4

14. If the govt persists with its policy of holding y at y2, PC will continue to shift up and lower unemp will be associated with ever increasing inflation. This is known as the Lucas critique. • So while the relationship estimated by Phillips seemed to suggest the existence of the trade off, but this collapsed as soon as the govt tried to exploit it. A stable PC only existed because govt did not systematically try to exploit. • Hence policy makers can only choose points on the vertical line above y at the ERU, this has led to the vertical long run PC.

15. Disinflation is costly • An important implication of the PC (π = π-1 + a (y-ye)) is that disinflation will be at a cost (unemp will be higher than ERU). Assume that inflation is high and constant, and unemp is at ERU. If inflation is to be lower than last period, uenemp must be pushed up above ERU. When unemp is above ERU, there is a negativegap between WS curve and PS curve. From the PC equation: π = π-1 + a (y - ye), => (π - π-1) = a (y - ye), If (π - π-1) < 0 (disinflation), Then a (y - ye) < 0, => y < ye (higher unemp) • Look at fig 3.5. the economy at B with high inflation 8%. The central bank wishes to reduce inflation to target 2%.

16. Figure 3.5

17. The only points on the curve with inflation below 8% are to the left of B, i.e. higher unemp. Disinflation is costly. • The PC (πl = 8), assume that the CB has chosen to raise unemp to F. Inflation falls to 6%, and a new PC (πl = 6) arises. The CB can then chose a point on PC (πl = 6),F’. This leads to a downward shift in the PC (not shown), eventually the objective of 2% inflation is achieved and the economy remains at the ERU.

18. Disinflation and central bank preferences • Which point along the PC curve the central bank would choose when implementing disinflation. Given inflation target 2%, at one extreme the CB could choose point C on fig 3.6. although this brings down inflation to target in the next period, but the cost is a steep rise in unemployment (low output at C). The PC shifts to PC (πl = 2) and the CB safely cut i to stabilize y at ye. The economy would move from B to C to A. • A less harsh point for the CB is to choose point F. the fall in inflation and the rise in unemp will be less than if C is chosen. As the CB is willing to sacrifice a rise in unemp to get a given reduction in inflation we will move along the PC from B to C. inflation aversion rises as the CB chooses a point closer to C.

19. The CB preference between a deviation of inflation from πTor unemp from ERU can be represented with indifference curves as shown in fig 3.6. indifference curves of the CB of the more inflation averse CB are flatter than the lees inflation averse. • The more inflation averse CB chooses point D because it is willing to sacrifice a bigger increase in unemp to get inflation lower more, and the other one chooses F on PC(πl = 8). As the PC shifts down, the CB chooses its preferred position where the indifference curve is tangential to the new PC. In this way the economy adjusts to point A. • The inflation averse CB guides the economy down the path from D to A. the less inflation averse CB guides the economy down the path from F to A. since the most preferred position is with π=πT and y=ye, the indifference curves shrink to a point at A.

20. Figure 3.6 Inflation averse

21. Costless disinflation and rational expectations • If the influence of the past on wage is absent, it would be possible for the economy to jump from B to A in fig 3.5 without any rise in unemp. Additional assumptions to eliminate the cost of disinflation: • Inflation inertia is absent. No nominal rigidities in the economy in wage or price setting behavior or institutional inertia, and adaptive expectations play no role in WS. Instead rational expectations hypothesis holds. Hence we have π = πE + a (y-ye) + ɛ (ɛ is a random shock term) • When the CB announces a low inflation target πTit is believed by market participants, or CB policy announcement is credible. π = πT + ɛ • Inflation remains at the target, apart form unforeseen shocks ɛ.

22. Rational expectations of inflation mean the only difference between expected and actual inflation is something random: agents do not make systematic errors, or agents subjective equal objective expectations given all information is available at the time of forming expectations. The rational expectations hypothesis means that πE = Eπ = E(πT + ɛ) = πT + Eɛ = πT πE = πT (rational expectations of inflation) • E is the objective expected value and the PC is now π = πT + a (y-ye) + ɛ (PC; rational expectations). Rearrange: y-ye = 1/a(π - πT - ɛ) = 1/a(π - πE) • Hence y=ye + 1/a(π - πE), (π – πE) inflation surprise y=ye+ζ(Lucas surprise supply equation) • ζ (ksi is a random error)

23. Output only deviates from eq when there is a surprise to inflation. Surprise or unanticipated inflation is normally interpreted as pushing output from eq, as firms will find it difficult to know whether there is a rise in inflation in general, or in its product relative to the general price level. It will not be possible for firms to distinguish with certainty between the general and the relative price change. • In a world of rational expectations, and credible inflation target, random shocks to inflation (surprises) will lead output to deviate from its eq level, there will not even be temporary movements along the PC in response to announced changes in govt policy. Disinflation will not be costly. • The distinction between the two approaches should be noted: • When using inertia augmented PC, causality goes from a deviation in output from its eq to a change in inflation relative to lagged inflation

24. ΔAD → Δy relative to ye → Δπ relative to π-1 • In the Lucas surprise supply eq causality goes from a deviation in inflation from its expected value to a change in output relative to eq. Δπ relative to πE → Δy relative to ye • The Lucas supply equation highlights that systematic monetary policy is ineffective in altering the level of economic activity, and there is no need for it because the economy returns directly to eqonce a shock to inflation has disappeared (strong assumptions).

25. The 3 equation model: IS-PC-MR • (1) The IS equation: simplify the IS equation to be: y=A-arIS Equation • We will be interested in r that equates y to ye ye = A – ars Stabilizing interest rate • rs changes whenever y or ye changes. y-ye = -a(r - rs) (IS, output gap form) • This eq makes it clear that output will deviate from eq to the extent that the r differs from the stabilizingrs. The CB is going to choose r so as to influence output gap as it seeks to achieve its stabilization objective. Instantaneous change in y can’t be achieved by altering r. it takes time for r changes to feed through to affect I and y.

26. (2) the inertia-augmented Phillips curve equation π = π-1 + a (y-ye) (PC) • (3) The third eq the MR is deviated from the CB’s output inflation tradeoff. This can be written as: y-ye = -b(π – πT) (MR) • This equation shows the combination of y and πthat the CB will choose given the PC it faces. Whenπis high, it will choose to reduce AD (by raising r), see fig. 3.6. a higher b is associated with a move inflation-averse central bank. • To construct the MR line simply take a PC to find the CB best output inflation combination along the PC. Find the tangency between the CB indifference curves and the relevant PC constraint it faces. At each point of tangency the MR equation will hold. Note also that the MR line will go through y=ye and π = πe. • In fig 3.6 the MR is found by joining up points D, D’ and A.

27. For the less inflation averse CB by joining points F, F’ and A. • Whenever the economy shifted away from the (ye, πT), by a shock, the CB will use a change in r to get the economy onto the MR line, once on the line, it must continue to adjust r until the economy returns to (ye, πT). Look at fig 3.7. at point B inflation rise to 6%, to get inflation back to target, y is going to be below eq. the MR shows that the CB will choose point F by raising r, AD falls below ye, and adjusts back to point Z. • If inflation falls below the target at point B’, the CB prefers point G, y goes above its eq to push inflation up to 2% until point Z. • The CB is going from chosen y on the MR line to the IS curve to see r that CB must set.

28. Figure 3.7

29. An inflation shock • Look at fig 3.8, the top diagram is the IS and the MR and PC in the bottom diagram. Starting at point A with y=ye and πTis 2%. We assume that there is an inflationary shock to the economy, which pushes inflation to 4%, the economy moves to point B on PC(πl = 4), the CB choosesr’ on the IS curve (point C’) to achieve point C on PC(πl = 4). In the next period the PC shifts down as a result of falling inflation, the new PC(πl = 3). • The economy is guided down the MR line to the south east as the CB implements the MR. we also see the path where the CB reduces r back towards stabilizing rs. Eventually the economy returns to eq with target inflation at Z. frequent adjustments of r are required by the monetary policy rule.

30. Figure 3.8

31. A temporary demand shock • See fig 3.9, if the economy starts off eq with πTis 2%, and the economy is disturbed by a temporary AD shock. The IS that reflects the shock is IS’ and remains IS’ for only one period. y is pushed up y’>ye. Inflation rise above target (to 4%), i.e. PC(πl = 4), along which the CB must choose its preferred point C. by going vertically up to point C’ in the IS diagram. The CB can work out that the appropriate r is r’. The subsequent adjustment path down the MR line to point Z is exactly the same as the case of the inflation shock. • The economy is shifted from A to B as a result of AD shock. Inflation is above target, which eliminated by pushing output below equilibrium. The CB raises r in response to AD shock to depress interest sensitive demand and reduce output.

32. Figure 3.9

33. A permanent demand shock • The IS shifts permanently to IS’. See fig.3.10 The economy starts at eq with inflation target 2%. The initial stabilizing r is rs. The IS shifts rightwards to IS’. Output goes up to y’: the economy is at point B on the PC diagram and at B’ in the IS diagram. Because the IS shock is permanent, the stabilizing interest has risen to r’s. with higher exogenous demand, a higher r is required to dampen AD so that y=ye. • In order to get the economy onto the MR line at point C, the CB has to set r at r’, considerably higher than was necessary in the case of the temporary demand shock. Once the economy is at points C and C’, adjustment along MR and IS’ takes place in the usual way, the new eq is Z in PC diagram and Z’ in the IS diagram.

34. Figure 3.10

35. The MR and the real interest rate • See fig 3.10 again. To steer inflation back to the target the CB raises r and the economy moves to C and C’ which is a rise in r from rsto r’. Contrast this with two alternatives: keeping r unchanged and keeping the nominal interest unchanged. If r is unchanged at rs, y remains at y’ above eq and inflation will continue to rise as the PC shifts upward each period. If nominal interest is unchanged the economy moves from B’ to a point on the IS’ to the south east of point B’. The rise in inflation is signaled by the persistence of y above ye, reduces r with a given nominal interest and higher inflation, r falls. (i=r+πE, and r=i- πE). This will boast y taking the economy further away from the inflation target.

36. Sacrifice ratios and disinflation strategies • Unemployment can be a consequence to a fall in inflation. “Cold turkey” or “shock therapy” are applied to this strategy in contrast to the gradualist approach, disinflation takes longer. Is cumulative unemployment higher under cold turkey or gradualism. • If PCs are linear and parallel, cumulative unemployment to reduce inflation to target is the same under both strategies, i.e., sacrifice ratio (cumulative unemployment to achieve a given reduction in inflation) is independent of the degree of inflation aversion of the CB. • Assume a government operates a simple MR y-ye = -b(π- πT),b=toughness of response to high inflation • assume that cumulative unemployment is independent of b. this assumption is that inertia augmented PC is linear

37. Figure 3.11

38. π = πl + a (y-ye) with πl= π-1 • Look at figure 3.11. first assume maximum toughness so that b=∞ the preference is to bring inflation back immediately. MR is horizontal (MR1). If there is an upward shock to inflation i.e., πl = π0 > πT. With MR1, y falls to y0 as the sharp rise in r takes effect. π falls from π0 to πT, next periodπl = πT, so the CB can safely cut r back to the stabilizing r and y rises back to ye. There is unemployment of ye-y0for one period, after which unemployment is zero again: cumulative unemp is simply ye-y0. • If the govt has more lenient MR (MR2), as a result of inflation shock, y is cut from ye to y1 so that in the first period πlfalls fromπl = π0 to πl = π1. using MR2, the PC withπl = π1 implies that y rises from y1 to y2. unemployment in the second period is (ye-y2). Cumulative unemployment after 2 periods is (ye-y1) + (ye – y2).

39. The proof of the assertion that cumulative unemp does not depend on the value of b can be seen from fig 3.11. (ye-y0) is exactly (yA-y0) on the horizontal axis, (ye-y2) is exactly (yB-yA). If we add the unemp created in each subsequent period in the gradualist case to (yA-y0)+(yB-yA)+…, the total is exactly (ye-y0), i.e., it is equal to the cumulative unemp in the cold turkey case with b=∞. • The proof depends on the linearity of the PCs. Look at figure 3.12. to see what happens when the PC is convex we use the MR with b= ∞and PC(πl = π0). This reflects the empirical finding that inflation becomes less sensitive to a rise in unemp the higher unemp is. This implies a reduction in y greater than the fall to y0. hence cumulative unemp with a more inflation averse MR will ge greater with a weaker one. Hence the strategy of a very inflation averse CB of reducing inflation to the target very fast will be more costly than a gradualist one. • With non linear PCs the sacrifice ratio is higher for a more inflation averse CB. With a linear PCs, the reduction of inflation to target has the same total unemp cost.

40. Figure 3.12

41. Inflation at the medium run equilibrium • Two monetary policies • Interest rate rule (MR approach) • In the 3 eq model, as long as the CB objective is to stabilize the economy at ERU, inflation at the medium run eq is equal to the target set by the CB π = πT. Since the CB is constrained to choose a point on the inertia-augmented PC, it will have to raise r to set the economy on the path toward the new inflation target. There will be a phase of costly disinflation before the new inflation is achieved. • Money supply rule (LM approach) • MS is under the control of the CB. The growth rate of MS determines the rate of inflation in the medium run eq. We assume the approximation holds so that: i = r + πE • the medium run eq, π = πE so that i = r + π

42. Next we take money market eq condition Ms/p = L(i,y) = L(r + π, y ) • y is determined by WS and PS curves at ye. The IS is fixed by AD. Hence r associated with ye is fixed at rs. Since in the medium run πis constant the real demand for money is constant. MS/P must also be constant, which requires P to grow at the same rate of MS which is under the control of CB. Assume that MS growth γM is constant atγMpar(exogenous): γMpar = M-M-1/M-1 π = γMpar

43. How the MR relates to the LM curve. • What is the relationship between MR approach and LM approach. There are two key points: • First the approach to use depend on the type of M policy, if interest rate based MR, the correct model is the 3 eq with MR. this is called an inflation targeting regime. If the target is to set γMparor Mspar. A money supply rule requires the use of the LM curve approach. • Second the LM condition does not disappear when the MR approach is being used. We need to distinguish between LM condition Ms/p = L(i,y) and the money supply rule, which assumes that MS is set exogenously. The LM condition must always hold irrespective of whether the govt is using MS rule or MR based on r. otherwise r would not remain at desired level. The LM curve is present in the background but it plays no role in fixing the position of the economy y,π or r.

44. Inflation in the IS/LM model • The IS/LM presents a different picture of policy making from the 3 eq model. When using MR the CB is forward looking and setting r to guide the economy back to eq. by contrast using MS rule implies that M policy is passive. • When the economy is subjected to a shock, the new medium term eq will be identical in both models. However the adjustment path with MS rule will be different. The CB is assumed to stick to a constant MS growth. r then changes as a result of interaction between the CB fixed money supply growth and the evolution of inflation. If there is a permanent AD shock, adjustment takes place in the IS/LM as follows: • 1. A RHS shift of IS will raise y and Md. In the short run MS growth and inflation are equal, and MS/P is constant. The LM stays fixed, there will be a sale of bonds and r rises. This is a movement along LM to its intersection with the new IS.

45. 2. higher y leads to a rise in inflation, which reduced MS/P causes the LM to shift to the left. This dampens AD. • 3. as inflation increases it must end up back to its original level in the new medium run eq. the inertia in inflation implies that y will have to fall below ye, y<ye. • 4. a spiral shaped adjustment path in the PC diagram will be traced as the economy moves first to the north east and then in a counter-clockwise spiral back to eq. See fig 3.13.

46. Figure 3.13