Document 7609461
Download
Report
Transcript Document 7609461
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 yt *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