Three Equation Model
IS-PC-MR
Monetary Macroeconomics
Motivation for the Model
• Over the last decade, many central banks have
adopted the policy goal of inflation targeting in
the conduct of monetary policy.
• Monetary policy is implemented through the use
of a nominal interest rate as its policy
instrument.
• Traditional macro models make monetary policy
actions appear exogenous rather than reflecting
the fact that most policy actions represent
endogenous reaction to the economy.
Motivation
• The model we will study assumes the monetary
policy authority (the central bank) acts
systematically to minimize fluctuations of output
around the full employment level (natural rate)
and inflation around its inflation target.
• Follows a Taylor Rule.
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Key Assumptions of the Model
• (1) The inflation process is persistent – slow to
change. In line with a wealth of empirical
evidence.*
π te = π t −1
• (2) In terms of adjustment lags, assume that it
takes one year for monetary policy to affect
output and a year for a change in output to
affect inflation – 2 years to have an impact on
inflation.
------------------------------*
Fed Governors Mishkin and Kroszner have given speeches recently citing studies that showing the inflationary
process to be less persistent.
Adjustment Lags
• “The empirical evidence is that on average it
takes up to about one year in this and other
industrial economies for the response to a
monetary policy change to have its peak effect
on demand and production, and that it takes up
to a further year for these activity changes to
have their fullest impact on the inflation rate.”
----------------------------------– Bank of England (1999) The Transmission of Monetary Policy p.9
http://www.bankofengland.co.uk/montrans.pdf
Key Assumptions of the Model
• (3) The central bank sets the nominal
interest rate (i). But with assumption (1), the
expected rate of inflation is given in the
short- run, so the central bank can set the
real rate (r) in the short- run. (think about
why?)
Assumption 1:
Real Interest rate:
From Assumption 1:
π te = π t −1
r = i −πe
r = i − π t −1
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The IS - Curve
y = C + I + G + (EX – IM)
•
•
•
•
•
•
•
C = Consumption
I = Investment
G = Government
EX = Exports
IM = Imports
EX – IM = Net Exports
y = real GDP
How does a change in the real interest rate (r) affect spending ?
• As r ↑ => C ↓ (Think about why!) => y ↓
• As r ↑ => I ↓ => y ↓
• As r ↑ => EX↓ and IM ↑ => y ↓
The IS–Curve shows an inverse relationship between r and y
r
IS
y
3
So the Central Bank can adjust r to determine y
r
r1
r2
r3
IS
y1
y2
y3
y
If they know the IS-curve relation
So the Central Bank can adjust r to determine y
1) If it can control the real interest rate, and (
big AND!)
2) If it knows the relationship between r and y
– This is to say, it knows the position and
the shape of the IS
- Curve.
Remember, the Fed controls the nominal FFR
(iFFR)
Shifts in the IS Curve
• We will refer to shifts in the IS curve as
“demand shocks”
• For example:
– Change in I
– Change in G
– Change in Consumer Confidence => change
in C
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Shifts in the IS Curve
r
C↑
I↑
C↓
G↑
I↓
G↓
IS0
IS1
IS2
y
There is a real interest rate (rs) consistent with full employment (ye)
r
rs
A’
IS
ye
y
We will refer to rs as the stabilizing real interest
rate. Or the neutral real interest rate (rn in Taylor
equation)
Inflation Process
(1)
(πe
= π-1) or (πe = π-1)
(2) π = πe + α(y – ye) or
(3) π = π-1 + α(y – ye)
(1)Represents inflation inertia. People look backwards in
forming expectations => expectations are slow to change.
(2) and (3) state, for a given πe, inflation rises as y rises above
full employment (ye ) and falls as y falls below ye .
Question: If y = ye, what can we say about inflation?
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= πI + α(y – ye) or
Phillips Curve: π = πe + α(y – ye)
Phillips Curve: π
π
VPC (Vertical Phillips Curve)
πe = πI = π-1 = 2%
y > ye
π=2%
y < ye
y
ye
Phillips Curve: π = πe + α(y – ye)
Movement along the curve
π
VPC
πe = πI = π-1 = 2%
π=3%
π=2%
π=1%
y2
ye
y
y1
When y rises above ye => the output gap ↑ => π↑
When y falls below ye => the output gap ↓ => π↓
Shifts in the Phillips Curve: π = πe + α(y – ye)
Inflation π
VPC
PC(πe=3)
PC(πe=2)
3
πT=2
ye
y
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Figure 1 – Full Employment Equilibrium
The economy is at a
constant inflation
equilibrium output level
with y = ye.
Inflation is constant at the
target rate π =πT = 2%.
The stabilizing interest
rate is rs.
VPC
Question: According to the
Taylor Rule, what is the
nominal FFR (iffr)?
Figure 2
Supply Shock
•Suppose an inflation
shock (supply shock)
takes the economy from
A to B. At B there is full
employment with high
inflation at 4%.
B
•Inflation is above the
central bank target
level: πT = 2%.
•The Fed wishes to
reduce inflation to the
target level of 2%.
What does the Phillips Curve show?
• The Phillips Curve [PC (πI = 4%)] shows —
given last period’s inflation — the inflation and
output trade
- off faced by the central bank.
• The only points on the Phillips Curve with
inflation below 4% are to the left of B, i.e. with
lower output and hence higher unemployment.
• The Fed must create an output gap in order to
reduce inflation.
• To do this, the Fed must increase the real
interest rate.
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Figure
Figure
3
3How does the central bank behave?
The Fed chooses
interest rate r' (at
point C') causing
income to fall to y1.
•As y falls, move
down along the PC,
inflation falls to 3%
(why?)
•Question: What
happens to the PC
over time as
inflation falls?
MR
Monetary Policy Reaction (MR) Function
• The Taylor Rule is an example.
• A nominal anchor defined in terms of an inflation
target provides guidance as to how the real
interest rate should be adjusted in response to
different shocks hitting the economy.
• The objective is stable inflation while minimizing
output fluctuations.
Figure 4
•The Fed raises the real interest
rate to slow down the economy.
Inflation falls to 3%
•As π falls, people adjust their
expectations downward and the
PC shifts down to a level
consistent with 3% expected
inflation.
•With lower inflation, the Fed can
now adjust the interest rate
downward as inflation falls.
•The economy moves down the IS
curve from C' to D' to A' and
along the MR curve from C to D
to A.
•Eventually the target rate of
inflation of 2% is achieved and the
economy is at full employment.
y1
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So what happened here?
• The MR line shows the level of output the central bank
will choose, given the Phillips curve constraint that it
faces.
• To implement its output choice, the central bank sets the
appropriate interest rate as shown in the IS diagram.
• As inflation gradually falls, the Phillips curve shifts down
and the central bank chooses an output level closer to
the equilibrium.
• This traces out the path down the MR along which the
economy moves back to equilibrium (i.e. along the MR
curve from C to D to A in the Phillips diagram; along the
IS curve from C′ to D′ to A′ in the IS diagram).
The Monetary Policy Rule and Central Bank Preference
Figure 5
y1
y2
•The more inflation-averse
central bank has a
relatively “flat” MR curve.
•Starting at point B, such a
central bank is prepared to
sacrifice a large reduction
in output to y1 in order to
deliver a given reduction
in inflation.
•The less inflation-averse
central bank has a
“steeper” MR curve. This
bank is less willing to
sacrifice a large fall in
output (y2) to deliver a
given reduction in
inflation.
The Monetary Policy Rule and Central Bank Preference
Figure 6
Inflation Shock
•Assume there is an inflation
shock to the economy that takes
inflation to 7%, i.e. to point B
and the central bank is faced
with the Phillips curve:
PC (πI = 7).
• The more inflation-averse
central bank chooses point D on
the PC curve, raises the real
interest rate to r1 and guides the
economy down the MR curve
from D to D' to A.
y1
y2
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The Monetary Policy Rule and Central Bank Preference
Figure 6
Inflation Shock
The less inflation-averse
central bank chooses point F on
the PC curve, raises the real
interest rate to r2 and guides the
economy down the MR curve
from F to F' to A.
y1
y2
Aggregate Demand Shock
• The previous slides show how an inflation shock is
handled.
• Let’s now look at aggregate demand shocks. The IS
curve shifts.
• It is assumed that the economy starts off with output at
full employment equilibrium and inflation at the target
rate of 2%.
• Let’s look at a positive aggregate demand shock such as
improved consumer expectations: the IS moves to the
right to IS′ - a permanent shift. (Fig.7).
Permanent Demand Shock
Figure 7
• Output rises above ye
(movement from A’ to B’)and
inflation will rise above target
— in this case to 4%.
• As inflationary expectations
adjust a new Phillips curve is
defined (PC (πI = 4)) along
which the central bank must
choose its preferred point for the
next period: point C.
• By going vertically up to point
C′ in the IS diagram, the central
bank can work out that the
appropriate interest rate to set is
r′.
• The adjustment path down the
MR-curve to point Z is exactly
as described in the case of the
inflation shock.
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Permanent Aggregate Demand Shock
• This example highlights the role of the stabilizing
real interest rate, rS.
rs'
• Following the shift in the IS curve, there is a new
stabilizing interest rate, r's and in order to
reduce inflation, the interest rate must be raised
above the new r's, for example to r′.
Aggregate Demand Shock
• If the demand shock is only temporary, the IS
curve shifts to IS′ for only one period before
returning to its initial position.
• In this case, there is no change to the stabilizing
interest rate and the central bank simply raises
the real interest relative to the original rS.
• This example illustrates the importance for the
central bank in being able to forecast the
persistence of such shocks.
To Summarize
• The rise in output builds a rise in inflation above
target into the economy.
• Because of inflation inertia, this can only be
eliminated by pushing output below and
(unemployment above) the equilibrium.
• The graphical presentation emphasizes that the
central bank raises the interest rate in response
to the aggregate demand shock because it can
work out the consequences for inflation. The
central bank is forward
- looking and takes all
available information into account.
• Its ability to control the economy is limited by the
presence of inflation inertia and by the time lag
for a change in the interest rate to take effect.
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To Summarize
• An aggregate demand shock can be fully offset by the
central bank even if there is inflation inertia if the central
bank’s interest rate decision has an immediate effect on
output.
• The economy then remains at A in the Phillips diagram
in which points A and Z coincide and goes directly from
A′ to Z′ in the IS-diagram. This highlights the crucial role
of lags and hence of forecasting for the central bank.
• The more timely and accurate are forecasts of shifts in
aggregate demand, the greater is the chance that the
central bank can offset such shocks and prevent the
impact of inflation from being built into the economy.
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