THE 3-EQUATION MODEL AND EXPECTATIONS
Stefania Paredes Fuentes Department of Economics, S2.121 University of Warwick
Money & Banking WESS 2016 THE ROLE OF EXPECTATIONS
expectations so far
• importance of uncertainty and expectations in macroeconomics - consumption, investment, central bank
• Phillips curve: expected inflation equals past inflation wage setters use past inflation as guide to how they expect prices to evolve - nominal wage increases that compensate workers for any erosion of the real wage due to unanticipated inflation in the previous period other ways: wage indexation, inflation forecasted by CB
• Uncertainty for the CB
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
Uncertainty is an ever-present feature of the economic landscape that monetary policy makers cannot escape. Broadly speaking, there are three types of uncertainty that confront us on the MPC: uncertainty about the data; about the nature and persistence of shocks; and uncertainty about the structure of the economy.
Charles Bean, UK MPC (2005) “Monetary Policy in an Uncertain World”
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
rational vs adaptive
• how inflation expectations are modelled?
• adaptive expectations: expected inflation equals past inflation
• rational expectations: expectations are forward looking agents use the model to form their expectations all available information is used and systematic errors are avoided
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
• Under rational expectations - people use all information at their disposal to make their best forecast of the coming rate of inflation (so they do not make systematic errors) - CB’s willingness to fight inflation becomes a crucial determinant of expected inflation - model-consistent expectations
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
• Under adaptive expectations - wage setters form inflation expectations in a backward-looking manner - in a period of rising inflation, agents using adaptive expectations make systematic errors
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
inflation and unemployment
Source: Phillips (1958)
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
Expectations: Adaptive or Rational?
US Inflation
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
Expectations: Adaptive or Rational?
Source: ONS
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
Expectations: Adaptive or Rational?
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
Expectations: Adaptive or Rational?
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
PC and adaptive expectations
⇥ = ⇥E + (y y ) t t t e E ⇡t = ⇡t 1 ⇥t = ⇥t 1 + (yt ye)
⇥t ⇥t 1 = ⇥t = (yt ye)
inflation will increase as long as output remains above equilibrium
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
PC and rational expectations
⇤ = ⇤E + (y y )+⇥ t t t e t
E ⇡ = ⇡ ⇤t = ⇤t + (yt ye)+⇥t t t
⇥ y = y t t e expectations on inflation are correct apart from the random shock term
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
CB adopts a new inflation target:
rational expectations adaptive expectations π π PC PC
π =π0 A π =π0 A
MR MR
ye y ye y
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
CB adopts a new inflation target:
rational expectations adaptive expectations
π π E E PC (πt =π0) PC (πt =π0)
E T PC (πt+1 =π )
π =π0 A π =π0 A
π =π1 B
T π =π Z MR MR
MR’ MR’
ye y y1 ye y
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
CB adopts a new inflation target:
rational expectations adaptive expectations
π π E E PC (πt =π0) PC (πt =π0) E PC (πt+1 =π1)
E T PC (πt+1 =π ) E T PC (πt+1 =π ) π =π0 A π =π0 A
π =π1 B C T π =π Z MR Z MR
MR’ MR’
ye y y1 ye y
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
PC and rational expectations
VPC(πE= πT) π
π =πT
MR
ye y
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
PC and rational expectations y = A ar IS under RE t t ⇤ = ⇤T + (y y )+⇥ PC under RE t t e t y y = ⇥(⇤ ⇤T ) MR under RE t e t when the CB announces a new low inflation target, this is believed by all participants T ⇡t = ⇡L + ✏t
E T T ⇥t = Et(⇥t)=Et(⇥L + t)=⇥L
Rational expectations on inflation
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
PC and rational expectations ⇤ = ⇤T + (y y )+⇥ PC under RE t t e t with rational expectations, when output is at equilibrium, inflation is at target apart from a random shock 1 1 y y = (⇤ ⇤T ⇥ ) = (⇡ ⇡E) t e t t ↵ t t 1 y = y + (⇥ ⇥E) t e t t inflation surprise
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
PC and rational expectations
⇤ = ⇤T + (y y )+⇥ PC under RE t t e t with rational expectations, when output is at equilibrium, inflation is at target apart from a random shock 1 1 y y = (⇤ ⇤T ⇥ ) = (⇡ ⇡E) t e t t ↵ t t 1 y = y + (⇥ ⇥E) t e t t
yt = ye + Lucas surprise supply equation
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
Disinflation strategies
• Under rational expectations - CB can achieve disinflation at no cost
• Under adaptive expectations - disinflation is costly
• due to delays in price and wage setting, inflation is persistent - lagged inflation does affect current inflation - trade-off between inflation and unemployment in the short run
• Disinflation is costly
• Sacrifice ratio: percentage point rise in unemployment experienced for a one percentage point reduction in inflation during a disinflationary episode
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
Disinflation strategies
• Ball (1994), Carvalho and Gonçalves (2009)
• cold turkey or gradualist approach?
• with linear PC, the sacrifice ratio is constant the cumulative amount of unemployment required to achieve a given reduction of inflation does not depend on the degree of CB’s inflation aversion
• PC are not linear - flatter as unemployment rises - cold turkey disinflation strategy (preferred by an inflation-averse CB) entails a higher sacrifice ratio
• disinflation (almost) costless after hyperinflation periods
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
CB credibility
• CB communication • keep inflation expectations anchored at the inflation target • easier to keep inflation under control sacrifice ratio lower in case of unexpected shocks
Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS
CB credibility ⇥ = ⇥E + (y y ) [standard PC] t t t e
E T [partially anchored ⇡t = ⇡ +(1 )⇡t 1 expectations]
T ⇥t =[⇤⇥ +(1 ⇤)⇥t 1]+ (yt ye) PC with partially anchored expectations
Stefania Paredes Fuentes Money and Banking WESS 2016 CB credibility =1 =0
A A r =rs r =rs
IS IS y y π π
PC PC
π =πT A π =πT A
MR MR
ye y ye y
Stefania Paredes Fuentes Money and Banking WESS 2016 CB credibility =1 =0
A A r =rs r =rs
IS IS π π y PC(inflation shock) PC(inflation shock)
E T PC(π 0 = π ) E T B π =π0 B PC(π 0 = π ) π =π0
π =πT A π =πT A
MR MR
ye y ye y Stefania Paredes Fuentes Money and Banking WESS 2016 r r CB credibility =1 C =0
A, Z A r =rs r =rs
IS IS y y π π PC(inflation shock) PC(inflation shock)
B B PC(πE = πT) PC(πE = πT) π =π0 0 π =π0 0
π =π1 C
π =πT A, Z π =πT A
MR MR
ye y y1 ye y
Stefania Paredes Fuentes Money and Banking WESS 2016 r r CB credibility =1 C =0 D A, Z A r =rs r =rs
IS IS y y π π PC(inflation shock) PC(inflation shock)
B B PC(πE = πT) PC(πE = πT) π =π0 0 π =π0 0
π =π1 C π =π2 D π =πT A, Z π =πT A
MR MR
ye y y1 ye y
Stefania Paredes Fuentes Money and Banking WESS 2016 r r =0 CB credibility =0.5 C C A A r =rs r =rs
IS IS y y π PC(inflation shock) π PC(inflation shock)
E PC(π 1 = π’) B B E T π =π0 PC(π 0 = π ) E T π =π0 PC(π 0 = π )
π =π1 C π =π’ C π =πT A π =πT A
MR MR
y1 ye y y1 ye y Stefania Paredes Fuentes Money and Banking WESS 2016 r r =0 CB credibility =0.5 C C A A r =rs r =rs
IS IS y y π PC(inflation shock) π PC(inflation shock)
E PC(π 1 = π’) B B E T π =π0 PC(π 0 = π ) E T π =π0 PC(π 0 = π )
π =π1 C π =π’ C π =πT A π =πT A
MR MR
y1 ye y y1 ye y Stefania Paredes Fuentes Money and Banking WESS 2016 r r =0 CB credibility =0.5 C C A A r =rs r =rs
IS IS y y π PC(inflation shock) π PC(inflation shock)
E PC(π 1 = π’) B B E T π =π0 PC(π 0 = π ) E T π =π0 PC(π 0 = π )
π =π1 C π =π’ C π =πT A π =πT A
MR MR
y1 ye y y’1 ye y Stefania Paredes Fuentes Money and Banking WESS 2016 r r r =0 =0.5
C C D A A r =rs r =rs
IS IS
y π y π PC(inflation shock) PC(inflation shock)
E PC(π 1 = π’)
E B B PC(π 2 = π’’) E T E T PC(π 0 = π ) π =π0 PC(π 0 = π ) π =π0
π =π1 C C π =π2 D π =π’’ D π =πT A π =πT A
MR MR
y1 ye y y1 ye y Stefania Paredes Fuentes Money and Banking WESS 2016 THE ROLE OF EXPECTATIONS CB credibility
• More firmly anchored inflation expectations will reduce the negative impact of stabilisation policy on the economy - lower the cost associated with disinflationary policies
• transparency and communication matter
• Will the central bank stick to its policy objective? - independence from political pressure
• Can the central bank help shape expectations of inflation? - keep PCs close to the inflation target
• Demerzis & Hughes Hallet (2007), Dincen & Eichengreen (2009) CB transparency reduces inflation variability
• Sturm & De Haan (2011); Blinder et al. (2008) better CB communication improves the predictability of monetary policy decisions
Stefania Paredes Fuentes Money and Banking WESS 2016 SOME READINGS
• Carlin & Soskice, Chapters 4
• Friedman (1968) The Role of Monetary Policy. The American Economic Review, 58(1):1-17
• Lucas Jr. R. E. (1972) Expectations and the Neutrality of Money. Journal of Economic Theory, 4(2):103-124
• Lucas Jr. R. E. (1975) An Equilibrium Model of the Business Cycle. Journal of Political Economy 83(6): 1113-44
• Phelps (1967) Phillips Curves, Expectations of Inflation and Optimal Unemployment over Time. Economica, 34(135): 254-81