LECTURE 7
The AS-AD model
Øystein Børsum
28th February 2006
Overview of forthcoming lectures

Lecture 7: Aggregate demand and aggregate supply


Lecture 8: Stabilization policies



Goals for stabilization policies: Stable output and inflation
Optimal policy rule: Demand and supply shocks
Lecture 9: Limits to stabilization policies




Macroeconomic dynamics in the AS-AD model
Rational expectations and the Policy Ineffectiveness Proposition, the
Ricardian Equivalence Theorem and the Lucas Critique
Policy rules versus discretion: Credibility of economic policy
Real business cycles (section 19.4)
Lecture 10: Open economy
Overview of the AS-AD model with endogenous
monetary policy

On a compact form, the SRAS-LRAS-AD model can be analyzed as a
two-equation model in the (y;) space

A temporary, negative supply shock increases inflation and lowers
output. Adjustment to equilibrium is gradual

A temporary, positive demand shock increases inflation and temporarily
increases output. Output “undershoots” its long-run value in a gradual
adjustment to equilibrium

These dynamic development of the model after a temporary shock can
be computed by two first-order difference equations

Permanent shocks may change the long-run equilibrium values of output
and the real interest rate

Simulations show that a modified version of this AS-AD model can
reproduce stylized business cycle facts
Elements of aggregate supply and aggregate demand
yt  y  1  gt  g    2  rt  r   vt
rt  it  
e
t 1
it  r    h  t     b  yt  y 
e
t 1
*
t      yt  y   st
e
t
  t 1
e
t
Compact form of the AS-AD model

The AD curve can be re-written on a more compact form:
yt  y  yt *y
, t   zt ,

*zt 
t 
g1 gt  g 
2h

 2 h vt  1  gvtt 
  where  
,
zt  , zt 
1   2b 1   2b
1   2b 1   2b
AD:

1
t       yt  y  zt 

*
Replacing expected inflation in the short-run AS curve gives:
SRAS: t  t 1    yt  y   st
Graphical illustration of the AD-SRAS-AS relationships
Illustration of a short-run macroeconomic equilibrium where output below its natural, long-run value
Example 1: A temporary negative supply shock

Temporary negative supply shock: s1 > 0 (with s2, s3, … = 0)

Shifts the SRAS vertically by s1
SRAS: t  t 1    yt  y   st

The long-run AS is not affected (natural level of output unchanged)

Some possible interpretations: Industrial conflict, bad harvest,
(exogenous increase in production costs) or temporary producer
cartel (e.g. OPEC)
The path to long-run equilibrium after a temporary
negative supply shock is gradual
Illustration of the path from short to long-run macroeconomic equilibrium after a negative supply shock
Example 2: A temporary positive demand shock

Temporary positive demand shock: z1 > 0 (with z2, z3, … = 0)

Shifts the AD curve vertically by z1 / 
AD:
1
t       yt  y  zt 

*

Long-run supply is not affected (natural level of output unchanged)

Some possible interpretations: Temporary optimism about the
future growth potential of the economy
A temporary positive demand shock is followed by
a period of recession in order to curb inflation
Illustration of the path from short to long-run macroeconomic equilibrium after a positive demand shock

LRAS
SRAS2
SRAS1
1
2

E1
E2
Ē
AD1
z1
AD0 AD2
y
y2
y0
y1
Finding the dynamic solution to the AS-AD model

Define the output gap and the inflation gap:
yˆt  yt  y

ˆt   t  
*
Set st = zt = 0 and rewrite the AS-AD model as
1
AD: ˆt 1     yˆt 1 ,
 
SRAS: ˆt 1  ˆt   yˆt 1
2h

1   2b
The dynamic solution to the AS-AD model

Rearranged, this gives to linear first-order difference equations:
yˆt 1   yˆt ,

and
Solutions:
yˆt  yˆ 0  t ,
ˆt  ˆ0  t ,

1

1  
t  0,1, 2,.....
t  0,1, 2,.....
0 < β < 1 assures a stable long-run equilibrium
ˆt 1  ˆt
With plausible parameter values, the model
requires about four years to adjust half the shock
The adjustment to a temporary negative supply shock (s1=1).
Illustration of a quarterly AS-AS model calibrated with plausible parameter values
After a temporary demand shock, the model
“overshoots” the long-run equilibrium output
The adjustment to a temporary negative demand shock (z1= -1).
Illustration of a quarterly AS-AS model calibrated with plausible parameter values
Permanent shocks and long-run equilibrium values

Permanent shocks may change the long-run equilibrium values
of y and r

The AS-AD model relative to the initial values of natural output
and the natural interest rate:
yt  y0  vt   2  rt  r0  ,
vt  vt  1  gt  g 
t  t 1    yt  y0   st

Example 1: A permanent supply shock: Initial equilibrium with
s0 = 0 and thereafter st = s ≠ 0 for t = 1,2,…

Equilibrium condition: Inflation and output are stable
t  t 1 ,
yt  y ,
st  s
A permanent, negative supply shock reduces equil.
output and raises the equil. real interest rate

The effect of a permanent supply shock on natural output:
s
y  y0 


To equate demand and supply, the equilibrium real interest
rate changes

The effect of a permanent supply shock on the equilibrium real
interest rate:
s
r  r0 
 2
A permanent, positive demand shock raises the
equil. real interest rate and leaves output unchanged

Example 2: A permanent demand shock: Initial equilibrium with
v0 = 0 and thereafter vt = v ≠ 0 for t = 1,2,…

The permanent demand shock does not affect natural output.

The equilibrium real interest rate changes to curb the demand
shock.

The effect of a permanent demand shock on the equilibrium real
interest rate:
v
r  r0 
2
Illustration: A change in the natural level of output

Arbitrage
The Frisch-Slutzky paradigm


Stylized facts on business cycles (chpt. 14) raise two key questions:
o
Why do movements in economic activity display persistence?
o
Why do these movements tend to follow a cyclical pattern?
Our exposition of the AS-AD model follows the Frisch-Slutzky
paradigm
o
Unsystematic impulses (demand and supply shocks) initiate the
business cycles
o
The structure of the economy generate systematic fluctuations
(propagation mechanism)
Illustration: Simulations on the AS-AD model with
a simple stochastic shock process


Demand and supply shocks follow stable first-order stochastic
processes with positive persistence:
zt 1   zt  xt 1 ,
0   1
st 1   st  ct 1 ,
0   1
The innovations to the shock processes are independent and
identically distributed according to the normal distribution
xt
~
N (0,  x2 ) ,
xt i.i.d .
ct
~
N (0,  c2 ) ,
ct i.i.d .
Graphical comparison of actual and model
fluctuations
Model properties compared with actual stylized
business facts