1. 2.3 IS-PC-MR model revisited “Workhorse of modern monetary macroeconomists” – IS: y – y e = -a(r – r s ) (AD –ve rels r and y) – PC: π E = π -1 + α(y – y e ) (+ve s-r rels between y and π) – MR: y – y e = -b(π - π T ) (CB’s policy trade-off between y and π) [implication of negative relationship: if π > π T then y must be less than ye (y < ye)]

2. The IS curve Simplified IS is given by : y = A – ar At the stabilising rate of interest (r s ) i.e. the real interest rate where y = y e => y e =A – ar s By subtracting ye from y, the IS can be written in output gap form as follows: y – y e = -a(r - r s ) Implication of the negative relationship: if r > rs then y will be less than ye (y < ye) CB chooses the interest rate (r) so as to influence the output gap as it pursues its stabilisation objective (as r rises the output y falls)

3. The PC Curve π = π -1 + α(y – ye) In the s-r: positive relationship between output and inflation (if y>ye then inflation rises) (if y<ye then inflation falls) In the l-r: inflation is stable at ye

4. Deriving the MR MR shows the path along which the economy will be guided by the actions of the CB to take it back to equilibrium output at the inflation target MR shows the combination of output and inflation that the CB will choose given the s-r Phillips curve that it faces: MR: y – y e = -b(π - π T ) When inflation is high π > π T CB will reduce AD (y < ye) by raising r and this will reduce inflation A higher b is associated with a more inflation averse CB, if b is 0 there will be 0 output sacrifice, but if b is high then output sacrifice will be high Fig 3.7 shows that to draw MR find and join tangents between CB’s indifference curves (for a given level of b) and the relevant Phillips curves (MR will intersect π T and y e )

5. MR curve (cont.) Whenever the economy moves away from equilibrium, the CB uses a change in interest rate (r) to get the economy onto the MR line and continues to hold r’ > rs until equilibrium is restored As per Fig 3.7 – Inflation has risen to 6%, point B is on the Phillips curve that shows the trade-off along which the CB can choose its preferred point – To get inflation to the 2% target output must fall below equilibrium at point F (y is down and r is up) – The economy then moves along MR by a process of step-by-step adjustments in r, π and y from F to F’ to A,Z NOTE: if inflation falls below target (e.g. 0%) then r must fall and AD and y must rise so that inflation rises to target e.g. from G to Z i.e. π r AD  => y  => π  to = πT

7. 2.4 IS-PC-MR model and shocks In practice, CB’s set the nominal interest rate but they do this in order to choose the real interest rate (r) on the IS curve that will deliver the chosen level of aggregate demand AD CB controls the nominal interest rate directly, but CB controls r indirectly (as it is based on nominal interest rate minus expected inflation r = i - π e ) AD management process: set r to manage AD to influence inflation (r  AD  y  π  ) Question how does the IS-PC-MR model show CB responses to various shocks? – inflation shock, – AD shock (temporary) – AD shock (permanent) and – supply shocks (next lecture)

8. (1) IS-PC-MR: Inflation shock In Fig 3.8 IS curve is in top diagram, Phillips curve and MR in bottom diagram Start at point A – y e and at IT (2%) Inflation shock pushes up inflation to 4% (point B) (for example, inflation expectations rise resulting in the PC shifting up as π -1 or π I has risen pushing up π in π = π I + α(y – ye) To bring down inflation CB chooses the interest rate (r’) on the IS curve (point C’) (this is equivalent to point C on PC) In the next period PC shifts down to (π I =3) Economy is guided down the MR line to D as CB implements the monetary rule The CB reduces r (movement down IS curve to D’) back to strabilising interest rate r s Eventually economy returns to point Z CB behaves in an active, but rules based fashion (known as instrument but not goal independence)

10. (2) IS-PC-MR: temporary demand shock In Fig 3.9, at A economy is in equilibrium Disturbed by a temporary aggregate demand shock (IS moves to IS’ for 1 period) Output rises so y’ > ye at B and B’ Inflation rises above IT to 4% (Demand shock pushes up inflation to 4% (point B) (for example, temporary investment boom (like 2010 World Cup) pushes up y so pushing up π in π = π I + α(y – ye) PC shifts up to PC (π I =4) CB chooses its preferred point C This indicates C’ in the IS diagram (which has shifted back to its original position) giving an interest rate of r’ There is a subsequent adjustment path down MR to Z Overall, this s-r AD shock causes output and inflation to rise and there must be an increase in r to reduce output (increase unemployment) and bring inflation back to IT

12. (3) IS-PC-MR: permanent demand shock In Fig 3.10. economy is in equilibrium at A Then there is a permanent increase in AD and IS shifts up to IS’ and stays there in future periods (eg due to permanent tax cut) Output goes up to y’ at B on PC and at B’ on IS’ Because the AD shock is permanent the stabilising interest rate has risen to r’ s As a result in order to get onto the MR at C the CB must set the interest rate at r’(at C’) – which is considerably higher than was the case with the temporary shock i.e. r’ > r’ s and r’ s > r s From C and C’ the economy adjusts back step-by-step to Z (on PC) and Z’ (on IS)

14. The “doing nothing” paradox CB sets a nominal interest rate in order to achieve a particular real interest rate (r) In Fig 3.10 the real interest rate rises from r s to r’ If CB keeps the real interest rate unchanged at r s then output remains at y’ and inflation will continue to rise as PC shifts upwards each period If CB keeps nominal interest rate unchanged (then the real interest rate will fall due to rising inflation r = i - π E ) (economy moves to a point SE of B i.e. with higher output and higher inflation) Paradox – doing nothing is doing something (i.e. keeping nominal interest rate unchanged in face of inflation means CB is reducing real interest rate which will have the effect of boosting y and promoting further inflation) Similarly - if there is expected inflation then CB must raise nominal interest rate to keep r unchanged r = i  - π E  (Fisher’s rule)

15. 2.5Sacrifice Ratios and disinflation Is cumulative unemployment greater under ‘cold turkey’ of ‘gradualist approach? ‘cold turkey’ where inflation-averse CB raises r more sharply thereby increasing unemployment more sharply but bringing a faster return to the inflation target and the ERU Gradualist where r is raised less sharply, unemployment rises by less but the process of disinflation takes longer Question – if we add unemployment for each period under the two approach under which is cumulative unemployment greater? Answer – if Phillips curve are linear and parallel the cumulative amount of unemployment is the same under both approaches (i.e. it α is constant – then responsiveness of inflation to changes in output is constant) Finding: under these circumstances the sacrifice ratio is independent of the degree of inflation aversion of the CB

16. Proof (Fig 3.11) If MR is : y – y e = -b(π - π T ) ie negative rels (-b) if π > π T then y < y e If b = ∞ – CB is totally inflation averse and wants to bring inflation back to target immediately and MR1 is horizontal at π T – When inflation rises the CB raises r and output falls sharply from y e to y 0 then inflation falls so that π 0 = π T and π I = π T in the next period, so in the next period r = r s and output rises back to ye – Unemployment is equal to y e - y 0 for one period, hence cumulative unemployment is y e - y 0 If b < ∞ – CB is more lenient on inflation following MR2 – When inflation rises, CB raises r (by less than where b = ∞) and output is cut from y e to y 1 (this is the measure of unemployment) – As inflation falls, r is decreased and in the second period unemployment is given by y e to y 2 – The cumulative unemployment after two periods is given by (y e - y 1 ) + (y e - y 2 )

18. Proof (Fig 3.11) Cumulative unemployment does not depend on the value of b (degree of inflation aversion – cold turkey vs gradualism), as: (y e - y 1 ) = (y A - y 0 ) and (y e - y2 ) + (yB- y A ) [Due to the geometric property that the opposite side of parallelograms are off equal length.] If we add the unemployment created in each period of the gradualist case (y A - y 0 ) + (yB- y A ) + … the total is equal to the cold turkey case (y e - y 0 )

19. Case of non-linear Phillips curves Empirical finding – inflation becomes less sensitive to a rise in unemployment the higher unemployment is (i.e. non- linear – where U is high – much higher U is needed to reduce inflation) (i.e. α is reduced – reduction in wages and prices less responsive to reduction in y) The convex Philips curve implies that a much higher fall in output (and much higher interest is required) to bring inflation down to π T (where b = ∞ on MR1 in Fig 3.12) Conclusion: in these circumstances cumulative unemployment will be greater with a more inflation- averse monetary rule b = ∞ (MR1) than with a weaker more gradualist monetary rule b < ∞ (MR2) Intuition is that a cold turkey strategy will be more costly than a gradualist one (if circumstances are such that Inflation responds less to rising U where U is high) As ye – yNonLinear > (ye-y1) + (ye-Y2) + …

21. 2.7 Akerlof’s Phillips curve (modelling behaviour during low inflation) Basic behavioural assumption: – When inflation is low, and relatively unimportant, it will be ignored or not given full weight – When inflation is high it will be the centre of attention and given its full weight in price and wage setting Effect for expectations augmented Phillips curve: – Effect of expected inflation on actual wage and price setting varies with the rate of inflation – Effect is small when inflation is low and close to one to one when inflation is high Where π = ϒπ -1 +α(y – y e ) and 0≤ϒ≤1 – ϒ is closer to 0 where inflation is low – ϒ is closer to 1 where inflation is high (as in IS-PC-MR)

22. Method and findings For the US economy, sorted the period from 1954 to 1999 into two samples: – Low inflation quarters, where CPI was below 3% (mean inflation 2%) – High inflation quarters, where CPI was above 4% (mean inflation 6,3%) Finding: – Coefficients on inflationary expectations are substantially larger for the high inflation sample, than for the low inflation sample – i.e. inflationary expectations play a larger role in price and wage setting when inflation is high

23. Theoretical Consequence: -Idea of NAIRU or Natural rate of unemployment is a special case that is relevant only at high inflation rates -At low or moderate levels of inflation, unemployment rate can be sustainably maintained below the unemployment rate associated with complete price stability (See Hypothetical Long-Run Phillips curve)

25. Why is moderate inflation associated with less unemployment First effect: At low inflation the cost to firms of paying less than full attention to inflation is low: – Therefore, at moderate inflation rates real wages paid to employees decline (increasing employment) and real prices charged for goods decline (increasing sales and output) – Consumers also have more to spend on other goods, raising total employment

26. Why is increasing inflation associated with increasing unemployment back to the NAIRU Second effect: At higher levels of inflation the cost to firms of not paying full attention to inflation increases. – Therefore, wages and prices rise – As a result real wages increase and unemployment levels rise (back to Nairu level) – Also prices increase reducing sales, output and consumer disposable income