LECTURE 7

The AS-AD model

Øystein Børsum

28th February 2006

Overview of forthcoming lectures

Lecture 7: Aggregate demand and aggregate supply Macroeconomic dynamics in the AS-AD model

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 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

1 2t t t ty y g g r r v

1e

t t tr i

1e *

t t t ti r h b y y

et t t ty y s

1et t

Compact form of the AS-AD model

The AD curve can be re-written on a more compact form:

Replacing expected inflation in the short-run AS curve gives:

1AD: *

t t ty y z

1SRAS: t t t ty y s

12

2 2

1 1

t t t

t tt

y y * z ,

v g gh, zb b

12

2 2

1 1

t t t

t tt

y y * z ,

v g gh, zb b

where

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

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)

1SRAS: t t t ty y s

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 /

Long-run supply is not affected (natural level of output unchanged)

Some possible interpretations: Temporary optimism about the future growth potential of the economy

1AD: *

t t ty y z

SRAS1

SRAS2

LRAS

AD0 AD2

AD1

z1

ĒE2

E1

2

1

y0 y1y2

y

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

Finding the dynamic solution to the AS-AD model

Define the output gap and the inflation gap:

Set st = zt = 0 and rewrite the AS-AD model as

ˆ t ty y y *ˆt t

21 1

2

1ˆ ˆAD: ,

1t t

hy

b

1 1ˆ ˆ ˆSRAS: t t ty

The dynamic solution to the AS-AD model

Rearranged, this gives to linear first-order difference equations:

Solutions:

0 < β < 1 assures a stable long-run equilibrium

0ˆ ˆ , 0,1,2,.....tty y t

0ˆ ˆ , 0,1,2,.....tt t

1

1ˆ ˆ ,

1t ty y

1ˆ ˆt t and

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:

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

0 2 0 1 t t t t t ty y v r r , v v g g

1 0t t t ty y s

1 t t t t, y y , s 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:

To equate demand and supply, the equilibrium real interest rate changes

The effect of a permanent supply shock on the equilibrium real interest rate:

0

sy y

02

sr r

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:

02

vr r

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:

The innovations to the shock processes are independent and identically distributed according to the normal distribution

1 1 0 1 , t t tz z x

1 1 , 0 1t t ts s c

2(0, ) . . .t x tx N x i i d , ~

2(0, ) . . .t c tc N c i i d , ~

Graphical comparison of actual and model fluctuations

Model properties compared with actual stylized business facts