Monetary Policy

1
Monetary Policy

• Part 1. The Monetary Policy Rule

2
Role of monetary policy

• Role of monetary policy is to provide a nominal
  anchor to control inflation and inflation
  expectations. This should be done at a minimum
  cost in terms of output fluctuations.
• Objective reflected in Bank of England Act. .
  . to deliver price stability (as defined by the
  Governments inflation target) and, subject to
  this objective, to support the Governments
  economic policy, including objectives for growth
  and employment

3
3 equation model IS-PC-MR

• Many monetary policy issues can be analysed in a
  3-equation model of economy
• IS curve determines the relationship between
  the real interest rate and aggregate demand
• Phillips curve determines trade-off between
  output (unemployment) and inflation
• Monetary rule determines how central bank sets
  interest rates to hit inflation target given the
  central banks preferences and constraints it
  faces

4
IS curve
In absence of shocks, central bank targets the
neutral interest rater a/ß, consistent with
zero output gap and inflation at target
5
Phillips curve
6
Central bank loss functions
Loss function L (p pT)2 ?y2
?1
?lt1
?gt1
An inflation-averse central bank is characterised
by a lower ? ?0 ? strict inflation targeting
(inflation nutter) ?gt0 ? flexible inflation
targeting
Source Carlin Soskice, p49
7
Transmission mechanism
Current monetary policy affects the output gap
after one year the output gap, in turn, affects
inflation after one year
Source Carlin Soskice, p154
8
Optimal policy under inflation targeting

• Policy problem is to set the instrument rate to
  minimise the loss function subject to the
  constraint given by Phillips curve. Set up
  Lagrangean
• H (p pT)2 ?y2 ?(p pT dy)
• Lagrange multiplier ? measures the cost if the
  central bank deviates from its optimal solution.
  Minimise the Lagrangean with respect to the state
  variables y and p
• ?H/?y 2?y d? 0 ? ?2?y/d?H/?p 2(p
  pT) ? 0 ? ? 2(p pT)
• p pT ?y/d monetary rule

9
The monetary rule (MR)
To construct MR line, take a Phillips curve and
find central banks best output-inflation
combination along PC MR shows adjustment back to
equilibrium output at target inflation after a
shock
Source Carlin Soskice, p145
10
Slope of monetary rule
Monetary rule flatter when Phillips curve steep
(large d) and when central bank more averse to
inflation (small ?)
Source Carlin Soskice, p148
11
The IS-PC-MR model
Loss function(1) L (p pT)2 ?y2 IS
curve(2) y a ßr eD Phillips curve(3)
p pT dy eS Monetary rule(4) p pT ?y
d
r
rs
IS
y
p
VPC
PC(pe2)
pT2
MR
0
y
0
12
Six things to remember

• Equilibrium level of output determines position
  of vertical Phillips curve (VPC)
• Monetary rule (MR) line cuts VPC at inflation
  target
• Central banks preferences in loss function
  determine shape of loss ellipses and affect slope
  of MR line
• Slope of Phillips curve also affects slope of MR
  line
• Interest rate sensitivity of aggregate demand
  determines slope of IS curve
• Central bank adjusts interest rate relative to
  neutral interest rate must always analyse
  whether this has shifted, eg as a result of a
  shift in IS curve or due to a change in
  equilibrium level of output

13
Inflation shock and monetary rule
Suppose an inflation shock takes economy from A
to B. Central bank chooses r which corresponds
to C on the Phillips curve and C on the IS
curve. Economy adjusts back over time to Z.
Source Carlin Soskice, p83
14
Optimal monetary policy in response to shocks

• (5) y d eS d2 ?
• (6) p pT ? eS d2 ?
• (7) rOPT a 1 eD d eS
  optimal instrument rule ß ß
  ß(d2 ?)
• Optimal response to demand shock does not depend
  on preferences ? optimal response to supply
  shock does

15
Taylor rule

• Taylor (1993) found that US monetary policy could
  reasonably be characterised by the following
  interest rate rulei r p 0.5y 0.5(p
  pT)i is federal funds ratep is annual rate of
  inflation (Taylor uses GDP deflator)y is output
  gap ( 100(YY)/Y)Y is real GDPY is trend
  real GDPr is equilibrium real rate (assumed
  to be 2)pT is target inflation rate (assumed to
  be 2)

16
Taylor rule and US federal funds rate
Source Taylor (1993), p204
17
Simple interest rate rules

• r Fxwhere F is a coefficient matrix and x are
  variables of the model
• Coefficients not derived by minimising loss
  function. Rules of thumb e.g Taylor rule
• (8) r r ?p(p pT) ?yy
• Graphically, the Taylor rule gives an upward
  sloping interest rate line in r-y space. In p-y
  space, the Taylor rule leads to a downwards
  sloping aggregate demand function

18
Taylor rule response to shocks

• (9) y ß?p eS
  1 eD 1ß?ydß?p
  1ß?ydß?p
• (10) p pT 1ß?p eS
  d eD 1ß?ydß?p
  1ß?ydß?p
• (11) rTR a ?p eS
  d?p?y eD ß 1ß?ydß?p
  1ß?ydß?p
• Taylor rule depends on structural parameters ß
  and d as well as the TR parameters ?y and ?p
• Sub-optimal response to demand shocks

19
Comparing target rule with instrument rule

• Targeting ruleVar(y) d 2 Var(eS)
  d2 ?
• Var(ppT) ? 2 Var(eS)
  d2 ?
• Instrument rule
• Var(y) ß?p 2 Var(eS)
  1 2Var(eD) 1ß?ydß?p
  1ß?ydß?p
• Var(ppT) 1ß?y 2 Var(eS) d
  2Var(eD) 1ß?ydß?p
  1ß?ydß?p

20
Taylor curve
Var(y)

?0
Taylor curve
Feasible but inefficient trade-offs
Taylor rule

?0.5
Trade-offs not feasible

?1

Var(p)
21
Time inconsistency and inflation bias
There will be an inflation bias if central bank
tries to target output above the equilibrium
level.
Source Carlin Soskice, p162
22
Solutions to time inconsistency problem

• Time inconsistency arises under following
  circumstances(i) central bank has over-ambitious
  output target (yTgt0)(ii) wage and price setters
  have rational expectations(iii) central bank
  uses a rule-based reaction function but operates
  with discretion, ie it chooses its desired level
  of output after inflation expectations have been
  formed
• Solutions(i) central bank independence(ii)
  reputation building

23
Further reading

• Carlin and Soskice, Macroeconomics, Chapters 2,
  5
• For an overview of some of the practical issues
  relating to the conduct of monetary policy under
  inflation targeting, seeKing, M (2005),
  Monetary policy practice ahead of theory, Bank
  of England Quarterly Bulletin, Summer 2005,
  pp226-236http//www.bankofengland.co.uk/publicati
  ons/quarterlybulletin/qb0502.pdf
• For a discussion of recent research in to
  time-inconsistent monetary policies, seeDennis,
  R (2003), Time inconsistent monetary policies
  recent research, FRBSF Economic Letter, 2003-10
• http//www.frbsf.org/publications/economics/lette
  r/2003/el2003-10.html