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

2.1 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)

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:

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

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

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.

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

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

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)

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

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

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)

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)

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)

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

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)

Under what conditions is costless disinflation possible? In theory, disinflation can be costless (move immediately form B to A in diagrams) if the Phillips curve is expressed as follows: π = πT+ α(y – ye) + ε i.e. CB’s inflation target is totally credible i.e. πE = πT Inflation inertia is absent i.e. πE = πT so s-r Phillips Curve always intersects with (ye, πT) Rational expectations pertain (i.e. the only difference between what agents expect inflation to be and what it turns out to be is random (no systematic errors) If due to ε inflation rises this period it will return to πT at ye in the next period with no need for a sacrifice of output and employment

RE Phillips curve With rational expectations, when output is at equilibrium, inflation is at target apart from a random shock As a result there will be no temporary movements along the Phillips curve in response to changes in government policy, any deviation from IT will be immediately brought back to the IT and there will be no deviation from equilibrium output (from B to A on diagrams)