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THE 3-EQUATION MODEL

AND EXPECTATIONS

Stefania Paredes Fuentes Department of Economics, S2. University of Warwick Money & Banking

Stefania Paredes Fuentes Money and Banking

• (^) 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 expectations so far

Stefania Paredes Fuentes Money and Banking

• (^) 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 rational vs adaptive

Stefania Paredes Fuentes Money and Banking

• (^) 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 inflation and unemployment Source: Phillips (1958)

Stefania Paredes Fuentes Money and Banking Expectations: Adaptive or Rational? US Inflation

Stefania Paredes Fuentes Money and Banking Expectations: Adaptive or Rational?

Stefania Paredes Fuentes Money and Banking Expectations: Adaptive or Rational?

Stefania Paredes Fuentes Money and Banking PC and rational expectations ⇡ E t = ⇡t ⇤t = ⇤ E t

• (yt ye) + ⇥t ⇤t = ⇤t + (yt ye) + ⇥t yt = ye ⇥t expectations on inflation are correct apart from the random shock term

Stefania Paredes Fuentes Money and Banking CB adopts a new inflation target: rational expectations adaptive expectations y π PC MR ye A y π PC MR π =π 0 ye A π^ =π 0

Stefania Paredes Fuentes Money and Banking CB adopts a new inflation target: rational expectations adaptive expectations y π MR ye A y π PC (πtE=π 0 ) MR π =π 0 ye A^ π^ =π 0 Z PC (πt+1E=πT) MR’ π =π T MR’ PC (πtE=π 0 ) π =π 1 B y 1 PC (πt+1E=π 1 ) C PC (πt+1E=πT) Z

Stefania Paredes Fuentes Money and Banking PC and rational expectations y π π =π T ye VPC(π E = π T ) MR

Stefania Paredes Fuentes Money and Banking PC and rational expectations ⇤t = ⇤ T

• (yt ye) + ⇥t yt ye =

(⇤t ⇤ T ⇥t) =

(⇡t ⇡ E t

yt = ye +

(⇥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

Stefania Paredes Fuentes Money and Banking PC and rational expectations ⇤t = ⇤ T

• (yt ye) + ⇥t yt ye =

(⇤t ⇤ T ⇥t) =

(⇡t ⇡ E t

yt = ye +

(⇥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