Stefania Paredes Fuentes Department of Economics, S2.121 ...€¦ · Stefania Paredes Fuentes Money and Banking WESS 2016 Uncertainty is an ever-present feature of the economic landscape

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

Stefania Paredes Fuentes Money and BankingWESS 2016

• importance of uncertainty and expectations in macroeconomics - consumption, investment, central bank

• Phillips curve:expected inflation equals past inflationwage 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 periodother ways: wage indexation, inflation forecasted by CB

• Uncertainty for the CB

expectations so far



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”



• how inflation expectations are modelled?

• adaptive expectations: expected inflation equals past inflation

• rational expectations:expectations are forward lookingagents use the model to form their expectations all available information is used and systematic errors are avoided

rational vs adaptive



• 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



• 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



inflation and unemployment

Source: Phillips (1958)



Expectations: Adaptive or Rational?

US Inflation




Source: ONS









PC and adaptive expectations

⇥t = ⇥Et + �(yt � ye)

⇥t = ⇥t�1 + �(yt � ye)⇡Et = ⇡t�1

⇥t � ⇥t�1 = �⇥t = �(yt � ye)

inflation will increase as long as output remains

above equilibrium



PC and rational expectations

⇡Et = ⇡t

⇤t = ⇤Et + �(yt � ye) + ⇥t

⇤t = ⇤t + �(yt � ye) + ⇥t

yt = ye �⇥t�

expectations on inflation are correct apart from

the random shock term



CB adopts a new inflation target:

rational expectations adaptive expectations

y

πPC

MR

ye

A

y

πPC

MR

π =π0

ye

A π =π0




y

π

MR

ye

A

y

πPC (πtE=π0)

MR

π =π0

ye

A π =π0


Z

PC (πt+1E=πT)

MR’

π =πT

MR’

PC (πtE=π0)

Bπ =π1

y1





y

π

MR

ye

A

y

πPC (πtE=π0)

MR

π =π0

ye

A π =π0

Z

PC (πt+1E=πT)

MR’

π =πT

MR’

PC (πtE=π0)

Bπ =π1

y1

PC (πt+1E=π1)

C

PC (πt+1E=πT)

Z




y

π

π =πT

ye

VPC(πE= πT)

MR




yt = A� art

yt � ye = ��⇥(⇤t � ⇤T )

⇤t = ⇤T + �(yt � ye) + ⇥t

⇡t = ⇡TL + ✏t

⇥Et = Et(⇥t) = Et(⇥

TL + �t) = ⇥T

L

IS under RE

PC under RE

MR under RE

when the CB announces a new low inflation target, this is believed by all participants

Rational expectations on inflation




⇤t = ⇤T + �(yt � ye) + ⇥t

yt � ye =1

�(⇤t � ⇤T � ⇥t) =

1

↵(⇡t � ⇡E

t )

yt = ye +1

�(⇥t � ⇥E

t )

PC under RE

with rational expectations, when output is at equilibrium, inflation is at target apart from a random shock

inflation surprise




⇤t = ⇤T + �(yt � ye) + ⇥t

yt � ye =1

�(⇤t � ⇤T � ⇥t) =

1

↵(⇡t � ⇡E

t )

yt = ye +1

�(⇥t � ⇥E

t )

yt = ye + �

PC under RE

with rational expectations, when output is at equilibrium, inflation is at target apart from a random shock

Lucas surprise supply equation



• 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

Disinflation strategies



• Ball (1994), Carvalho and Gonçalves (2009)

• cold turkey or gradualist approach?

• with linear PC, the sacrifice ratio is constantthe 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

Disinflation strategies



• CB communication

• keep inflation expectations anchored at the inflation target

• easier to keep inflation under control sacrifice ratio lower in case of unexpected shocks

CB credibility



CB credibility

⇥t = ⇥Et + �(yt � ye)

⇡Et = �⇡T + (1� �)⇡t�1

⇥t = [⇤⇥T + (1� ⇤)⇥t�1] + �(yt � ye)

[standard PC]

[partially anchored expectations]

PC with partially anchored expectations


CB credibility

IS

y

y

πPC

π =πT

r =rs

ye

A

A

� = 1

MR

IS

y

y

πPC

π =πT

r =rs

ye

A

A

MR

� = 0


CB credibility

IS

r =rsA

� = 1

IS

y

r =rsA

� = 0

y

π

PC(πE0 = πT)

π =πT

ye

A

MR

y

π

π =πT

ye

A

MR

PC(πE0 = πT)

PC(inflation shock)

B

PC(inflation shock)

Bπ =π0

π =π0


IS

y

y

r

π

PC(πE0 = πT)

π =πT

r =rs

ye

A, Z

� = 1

MR

IS

y

y

r

π

π =πT

r =rs

ye

A

A

MR

� = 0

PC(πE0 = πT)

PC(inflation shock)

B

PC(inflation shock)

B

A, Z

C

C

y1

π =π0 π =π0

π =π1

CB credibility


IS

y

y

r

π

PC(πE0 = πT)

π =πT

r =rs

ye

A, Z

� = 1

MR

IS

y

y

r

π

π =πT

r =rs

ye

A

A

MR

� = 0

PC(πE0 = πT)

PC(inflation shock)

B

PC(inflation shock)

B

A, Z

C

C

y1

D

π =π0 π =π0

π =π1

π =π2

D

CB credibility


CB credibility

IS

y

y

r

π

π =πT

r =rs

ye

A

A

MR

� = 0

PC(πE0 = πT)

PC(inflation shock)

B

C

C

y1

π =π0

π =π1

� = 0.5

IS

y

y

r

π

π =πT

r =rs

ye

A

A

MR

PC(πE0 = πT)

PC(inflation shock)

B

C

C

y1

π =π0

π =π’

PC(πE1 = π’)


CB credibility

IS

y

y

r

π

π =πT

r =rs

ye

A

A

MR

� = 0

PC(πE0 = πT)

PC(inflation shock)

B

C

C

y1

π =π0

π =π1

� = 0.5

IS

y

y

r

π

π =πT

r =rs

ye

A

A

MR

PC(πE0 = πT)

PC(inflation shock)

B

C

C

y1

π =π0

π =π’

PC(πE1 = π’)


CB credibility

IS

y

y

r

π

π =πT

r =rs

ye

A

A

MR

� = 0

PC(πE0 = πT)

PC(inflation shock)

B

C

C

y1

π =π0

π =π1

� = 0.5

IS

y

y

r

π

π =πT

r =rs

ye

A

A

MR

PC(πE0 = πT)

PC(inflation shock)

B

C

C

y’1

π =π0

π =π’

PC(πE1 = π’)


rr

� = 0.5

IS

y

y

π

π =πT

r =rs

ye

A

A

MR

PC(πE0 = πT)

PC(inflation shock)

B

C

C

y1

π =π0

π =π’’

IS

y

y

r

π

π =πT

r =rs

ye

A

A

MR

� = 0

PC(πE0 = πT)

PC(inflation shock)

B

C

C

y1

D

π =π0

π =π1

π =π2

D

PC(πE1 = π’)

PC(πE2 = π’’)

D



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

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

Stefania Paredes Fuentes Department of Economics, S2.121 ...€¦ · Stefania Paredes Fuentes Money and Banking WESS 2016 Uncertainty is an ever-present feature of the economic landscape

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