1. Lecture 2 2.1 Introduction: Inflation and Phillips curves
2.2 Cost of Disinflation
2.3 IS-PC-MR model revisited
2.4 IS-PC-MR model and shocks
2.5 Sacrifice Ratios and disinflation
2.6 Akerlof’s Phillips curve and low inflation

2. 2.1 Introduction: Inflation and Phillips curves
In the model being developed - when unemployment is at it equilibrium level then inflation is constant
Phillips curve relations - negative relationship between unemployment (U) and inflation:
ERU – inflation constant
U < ERU – inflation rises (y > ye)
U > ERU – inflation falls (y < ye)
Phillips curve relations - Positive relation between output y  and inflation , hence upward sloping s-r Phillips curve in IS-PC-MR model
Question – is it possible in the IS-PC-MR model to run the economy sustainably at lower unemployment (higher output) but at higher levels of inflation
No, this is only a short-run relationship
In the long-run there is no trade-off between unemployment and inflation (i.e. if you hold output above ye then inflation will accelerate as wage setters will continue to push up their money wage to protect their real wage and the s-r PC curve will continuously shift upwards period after period)

3. Inflation and Phillips curves
Definitions:
Inflation is the rate of change of prices
The price level today reflects the pattern of past inflation
Deflation results in falling price levels
Disinflation results in a falling rate of inflation
If P is today’s price level and P-1 is the last period’s price level then inflation over the last period (π) is:

4. Inflation inertia The standard model is that inflation depends on:
past inflation (π-1) and
the output gap (between current output (y) and equilibrium output (ye) i.e. (y – ye)
There are two interpretations of past inflation (π-1):
Expectations interpretation (πE = π-1) i.e. wage setters expect inflation this period to continue to be what it was in the last period
(note: πE interpretation is not favoured as it implausibly implies that wage setters look entirely at the past when forming a view about the future)
Inertia interpretation (πI = π-1) i.e. wages setters incorporate past inflation into their current money wage claim to make up for the erosion of their real wage (living standards) since the last wage bargaining round

5. Inertia-augmented Phillips curve
The inertia-augmented Phillips curve (where πI = π-1) is given by :
Current inflation = inflation inertia + output gap
Phillips relation – positive relationship between y and π
higher y leads to higher π
lower y and lower π
Note: The inertia-augmented Phillips curve is equivalent to also called the expectations augmented Phillips curve where πE = π-1

6. Deriving Phillips curves
Each Phillips curve is defined by 2 characteristics π = π-1+ α(y – ye)
The height of the Phillips curve is determined by the lagged inflation rate (π-1). π-1 fixes the height of the Phillips curve at the level of output ye
The slope of the Phillips curve is determined by the degree of responsiveness of inflation to the output gap (given by α). If the WS curve is steeper then the Phillips curve will be steeper as wage demands increase more sharply for any given level of output.

7. Deriving Phillips curves (cont.)
The Philips curve is expressed in equation form as follows π = π-1+ α(y – ye):
If the output gap (y > ye) is positive this will raise inflation above the last period’s inflation
If the output gap (y < ye) is negative this will mean that inflation falls lower than the last period’s inflation
If y = ye this will mean that inflation is constant at the last period’s rate π-1

8. Deriving Phillips curves (cont.)
Why when unemployment deviates from equilibrium (ye) does the rate of inflation change?
In the labour market element of Fig 3.2 if employment is at E2 then the real wage lies 2% above the equilibrium real wage
If inflation is running at 0% then money wages will need to be raised by 2%
If money wages rise by 2% then firms will increase prices by 2% to preserve profits
But since money wages and prices both rise by 2% then the real wage will tend to move back towards equilibrium
Therefore, to keep employment at E2 and output at y2 money wages would have to rise again by 2% - again prices would rise and overall inflation would rise to 4%
If the economy then rested at E1 inflation would then remain constant at 4%, but if there is an attempt to keep employment at E2 then wages and price inflation would rise to 6%
To keep the economy at E2 there must be a spiral of ever increasing inflation. In Fig 3.2. this is represented by upward shifts in the Phillips curves as π-1 which sets the height of the Phillips curve rises each period

10. Deriving Phillips curves (cont.)
The short-run inertia- (or expectations-) augmented Phillips Curve is defined as a feasible set of inflation and output pairs for a given rate of lagged inflation
As the rate of lagged inflation (π-1) rises the Phillips curve shifts upwards to reflect the increasing quantum of inflation inertia e.g. from πI = 4%; πI = = 6%, etc.
The long-run Phillips Curve is vertical – as it is assumed that after wages and prices are allowed to adjust, output will return to ye (the “imperfectly competitive” equilibrium level of output determined on the supply side of the economy)

11. The original Phillips curve
Presented in Figs 3.3 and 3.4
Fig 3.3, shows an economy where:
average inflation is zero over a long period,
the economy experiences random shocks with output sometimes above and sometimes below ERU
Wage setters see price increases as temporary and do not incorporate past inflation into their wage claims i.e. (π-1= 0 and πI = 0)
Fig 3.4 shows the original Phillips curve for the UK economy between 1861 and 1913 with unemployment plotted on the horizontal axis resulting in a downward sloping curve

14. The original Phillips curve (cont)
Can the government use policy to move the economy from point A to point B (in Fig 3.3) i.e. reduce unemployment, increase output and increase inflation?
No - such policy intervention (such as increase money supply and reduced interest rates) would not be a random shock, but a concerted policy action
As a result of the concerted attempt to move the economy to point B workers will begin incorporating the prevailing inflation rate into their wage demands i.e. (π-1 > 0 and πI > 0) and the short-run Phillips curve would shift upwards
The government attempt to reduce unemployment will be associated with ever increasing inflation (as in Fig 3.2)
“A stable Phillips curve only existed because government’s did not systematically try to make use of it” – Lucas critique

15. 2.2 Cost of Disinflation
If authorities wish to reduce inflation then there will be a period of reduced output (y < ye) where unemployment is above the ERU
To lower inflation unemployment must be pushed up.
This is due the fact that: π = π-1+ α(y – ye) i.e. inflation is reduced if y < ye (or in other words if unemployment is pushed above ERU)
In the labour market higher unemployment means negative pressures on real wages and price (resulting in disinflation, falling inflation)

16. Disinflation => unemployment 
π = π-1+ α(y – ye)
=> (π -π-1) = α(y – ye)
if (π - π-1) < 0 (i.e. if there is disinflation)
then α(y – ye) < 0
=> y < ye (i.e. output is less then equilibrium output and unemployment is greater than ERU)

17. Disinflation (Fig 3.5)
The central bank wishes to reduce inflation form 8% to its 2% target
At point B the previous period’s inflation was 8%
To reduce inflation to 6% then y must be reduced and unemployment increased (Phillips curve π = π-1+ α(y – ye)) this leads to point F
With the previous period’s inflation at 6% this leads to a downward shift in the Phillips curve to PC (πI=6)
Then output must continue to to be less than ye (with higher unemployment (by CB keeping interest rates high) to point F’
At F’ inflation is reduced to 5% and there is a downward shift in the Phillips curve to PCPC (πI=5) (not shown in the diagram)
This continues until the inflation target is achieved at A (where there is an initial cost due to the disinflation, but ERU is restored in the longer-run)

19. Disinflation and Central Bank preferences
Central Banks (CB) are assumed to be attempting to minimise the summed deviations from the inflation target and equilibrium output (i.e. minimise L where L = α(π – πt)2 + β(y – ye)2 )
Within that optimisation problem CB’s have different preferences (i.e. different weighting for α and β)
“Inflation-nutter” / “strict inflation targeting” (α =1 and β=0) – CB is highly inflation averse and is prepared to induce high unemployment to rapidly achieve the inflation target
“flexible inflation targeting” (e.g. α = 0.5 and β = 0.5) - CB is more balanced in its aversion to both inflation and unemployment and will extend the time horizon over which the inflation target is achieved so as to avoid a sharp increase in unemployment

20. Central Bank preferences
Fig 3.6 inflation-nutter / strict approach - CB chooses to move from B to C to A – use a higher interest rate to bring inflation down to target in one period but with a large decrease in output and increase in unemployment (once high interest rate has achieved the inflation target, the interest rate can be reduced and output stabilises at ye)
A flexible approach – CB chooses to move from B to F to F’ to F’’… to A , this take a number of periods (longer time) but inflation target is met without the same sharp increase in unemployment
The inflation aversion of the CB rises / the willingness of the CB to sacrifice output and employment rises as we move along the Philips curve from B to C
CB chooses position where indifference curve is tangential to the Phillips curve
The indifference curves of the more inflation averse (inflation-nutter) CB’s is flatter (e.g. point D) with the indifference curve guiding the movement from D to D’ etc. to A (the most preferred position)
The indifference curves of the less inflation averse (balanced) CB’s is steeper (e.g. point F) with the indifference curve guiding the movement from F to F’ etc. to A (the most preferred position)

22. 2.3 IS-PC-MR model revisited
“Workhorse of modern monetary macroeconomists”
IS: y – ye = -a(r – rs) (AD –ve rels r and y)
PC: πE = π-1 + α(y – ye ) (+ve s-r rels between y and π)
MR: y – ye = -b(π - πT) (CB’s policy trade-off between y and π) [implication of negative relationship: if π > πT then y must be less than ye (y < ye)]

23. The IS curve Simplified IS is given by : y = A – ar
At the stabilising rate of interest (rs) i.e. the real interest rate where y = ye => ye =A – ars
By subtracting ye from y, the IS can be written in output gap form as follows:
y – ye = -a(r - rs)
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)

24. 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

25. 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 – ye = -b(π - πT)
When inflation is high π > πTCB will reduce AD (y < ye) by raising r and this will reduce inflation
A less steep MR curve is associated with a more inflation averse CB, and then output sacrifice will be high
A steeper MR curve is associated with a less inflation averse CB, and then output sacrifice will be low
Fig 3.7 shows that to draw MR find and join tangents between CB’s indifference curves and the relevant Phillips curves (MR will intersect πT and ye)

26. 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<πT => r<rs => AD => y => π to = πT

28. 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 - πe)
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)

29. (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 – ye 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 πI has risen pushing up π in π = πI + 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 (πI=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 rs
Eventually economy returns to point Z
CB behaves in an active, but rules based fashion (known as instrument but not goal independence)

31. (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 = πI + α(y – ye)
PC shifts up to PC (πI=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

33. (3) IS-PC-MR: permanent demand shock
In Fig 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 > rs
From C and C’ the economy adjusts back step-by-step to Z (on PC) and Z’ (on IS)

35. 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 rs to r’
If CB keeps the real interest rate unchanged at rs 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 - πE) (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 - πE (Fisher’s rule)

36. 2.5 Sacrifice 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

37. Proof (Fig 3.11)
If MR is : y – ye = -b(π - πT ) ie negative rels (-b) if π > πT then y < ye
If b = ∞
CB is totally inflation averse and wants to bring inflation back to target immediately and MR1 is horizontal at πT
When inflation rises the CB raises r and output falls sharply from ye to y0 then inflation falls so that π0 = πT and πI = πT in the next period, so in the next period r = rs and output rises back to ye
Unemployment is equal to ye- y0 for one period, hence cumulative unemployment is ye- y0
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 yeto y1 (this is the measure of unemployment)
As inflation falls, r is decreased and in the second period unemployment is given by yeto y2
The cumulative unemployment after two periods is given by (ye- y1 ) + (ye- y2)

39. Proof (Fig 3.11)
Cumulative unemployment does not depend on the value of b (degree of inflation aversion – cold turkey vs gradualism), as:
(ye- y1 ) = (yA- y0) and (ye- y2 ) + (yB- yA)
[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 (yA- y0) + (yB- yA) + … the total is equal to the cold turkey case (ye- y0 )

40. 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 πT (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) + …

42. 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 – ye) 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)

43. 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

44. 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)

46. 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

47. 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