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EC201 Intermediate Macroeconomics
EC201 Intermediate Macroeconomics

Lecture 15-16: A Dynamic AD-AS Model

Lecture Outline:
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Introducing dynamic into the AD-AS model;

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Effects of shocks on the dynamic AD-AS model;

Essential reading:
Mankiw: Ch
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In particular, economic
fluctuations could arise because of changes in economic policy (fiscal and monetary
policy) and demand shocks that could shift the aggregate demand schedule or because
of supply shocks that could shift the aggregate supply
...
However, the model itself was intrinsically static
(no explicit dynamic was considered in writing the AD or the AS schedule)
...

This is interesting since the modern macroeconomic models are now in the form of
DSGE models
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There are 3 main ingredients of modern macroeconomics models:
1) Dynamic is explicitly modelled;
2) The economy is subject to exogenous unpredictable shocks (this is the
stochastic part);
3) Microfoundations: the models are built directly from consumers and firms’
optimization;
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Here we are going to consider only the first two elements
...

Even if we are going to build a dynamic AD-AS model most of the qualitative results
we have found before (in terms of what happens to output and prices after a change in
the AD or the AS curve) we still apply here
...
It represents the demand for goods and
service in period t (we know that we can derive the AD from the IS-LM model, here
we are going to do the same):
Yt = Yt − α (rt − ρ ) + ε t

1)

What is what? Yt is total output at time t
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rt
is the real interest rate in period t
...
Finally

ε t is a demand exogenous shock, so it is a random variable that is in average zero
(this does not mean that it is zero, it is zero on average
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5 and -5 with probability 0
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In average
the value of that random variable is 0
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5×(-5) =0
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Equation 1) implies a negative relationship between the real interest rate and real
output as in the usual IS curve
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The second equation of the model is the Fisher
equation:

rt = it − Etπ t +1

2)

Where it is the nominal interest rate in period t and Et π t +1 is the expectation formed at
time t for next period inflation
...
The third equation is the
Phillips curve (that is also equivalent to an aggregate supply curve as we know from
Lecture 12-13):

2

π t = Et −1π t + φ (Yt − Yt ) + υ t

3)

Notice that we have used output instead of unemployment (we used the Okun’s Law)
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The fourth equation tells us how agents form their expectations
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This is
what we have called inflation inertia
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However, we are
going to assume that monetary policy follows a Taylor Rule and so we replace the
LM curve with the following TR curve:

it = π t + ρ + ϕπ (π t − π t ) + ϕY (Yt − Yt )
*

5)

Where π t denotes the inflation target of the central bank (for example 2%), the
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parameter ϕπ > 0 measures how much the central bank adjusts the interest rate when
inflation deviates from its target and ϕY > 0 measures how much the central bank
adjusts the interest rate when output deviates from its natural rate
...
Those are the variables that will be
explained by the model
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Those are the variables that will affect the
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endogenous variables that cannot be explained by the model
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This means that in the long run we should have: ε t = υ t = 0 meaning that are
no shocks
...
If that is true expectations
are correct
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Those are the solution of the endogenous variables (as a function of the exogenous
variables) in the long-run equilibrium
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The Dynamic Aggregate Supply and the Dynamic Aggregate Demand
The dynamic aggregate supply is given by the Phillips curve in 3) once we put the
way expectations are formed into it:

π t = π t −1 + φ (Yt − Yt ) + υ t

6)

This is a dynamic equation since it links variables at two different points in time (t
and t-1)
...
It
is like the short run aggregate supply we have seen in previous lectures with the main
difference that we have inflation instead of the price level
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Higher is
real output, everything else constant, and higher is inflation
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4

The dynamic aggregate demand is slightly more complicated to derive
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First use the Fisher equation rt = it − Etπ t +1 to substitute rt into equation 1):
Yt = Yt − α (it − Et π t +1 − ρ ) + ε t
Then use the fact that Et π t +1 = π t to substitute the expected inflation:
Yt = Yt − α (it − π t − ρ ) + ε t
Then use the Taylor rule it = π t + ρ + ϕπ (π t − π t ) + ϕY (Yt − Yt ) to substitute the
*

nominal interest rate in the previous equation:

Yt = Yt − α (π t + ρ + ϕπ (π t − π t ) + ϕ Y (Yt − Yt ) − π t − ρ ) + ε t
*

That equation simplifies to:

Yt = Yt − α (ϕ π (π t − π t ) + ϕY (Yt − Yt )) + ε t
*

Then solve that equation for Yt :

Yt = Yt − A(π t − π t ) + Bε t
*

Where A =

7)

αϕ π
1
> 0 and B =
> 0 are two constants that depends on some
1 + αϕ Y
1 + αϕ Y

parameters of the model
...

We call equation 7) the DAD (Dynamic Aggregate Demand) in period t
...

Graphically:

5

So the dynamic AD-AS model is given by the following two equations:
DAS: π t = π t −1 + φ (Yt − Yt ) + υ t
DAD: Yt = Yt − A(π t − π t ) + Bε t
*

The short-run equilibrium
In each period, the intersection of DAD and DAS determines the short-run
equilibrium values of inflation and output
...
Obviously we could
have depicted a case where the short run is above the natural level or a case where the
short-run and the long-run equilibrium coincide
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For example an increase in υ t in period t and
then it returns to zero from t+1 onwards
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At time t there is an increase in υ t
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Consider as an example an increase in the price of oil
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Point B is an example of stagflation
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Give the DAS at time t:

π t = π t −1 + φ (Yt − Yt ) + υ t , is υ t >0, that curve shifts up
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By increasing the interest rate output falls
because investment falls
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There is inflation inertia
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Period t + 2: As inflation falls also inflation expectations fall and the DAS moves
downward
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This process continues until output returns to the natural level and the economy
moves back towards point A
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This is the essence of an impulse
response that works like the following:
1) First you solve for the equilibrium of a dynamic model (in our case we need to
solve for the equilibrium of the DAD and DAS, so we solve those two
equations for the equilibrium level of output and the equilibrium level of
inflation
...
After that we can find
the equilibrium value of all the other endogenous variables);
2) We consider plausible numerical values for the exogenous and the parameters
of the model
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25, ϕ π = 0
...
5
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For example, in our case the equilibrium level of inflation is:

πt =

π t −1 + φAπ t * + φBε t + υ t
1 + φA

Assume that you start from the long run equilibrium where π t −1 = 2 that is the target
inflation
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25 × 0
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15
=
= 2
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25 × 0
...
075

Where A =

αϕ π
= 0
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At t+1, the shock returns to zero (assume again that ε t +1 = 0
so no demand shock at t+1), however inflation at t+1 is given by:

π t +1 =

π t + φAπ t +1* + φBε t +1 + υ t +1
1 + φA

And using the numbers we have we obtain:

π t +1 =

2
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25 × 0
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86
1 + 0
...
3

One period after the shock inflation started to decrease but slowly because of the
inflation expectations are still high
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0
1
...
0
0
...
0
-0
...
0
-1
...
0

3
...
0
2
...
5
0
...
0

The first graph is the evolution over time of the aggregate supply shock, 1 in period t
and zero everywhere else
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We can do the same for the other endogenous variables in the model and represent
those impulse responses into a similar graph
...
5

99
...
0

6
...
5
5
...
5
4
...
5
t+11

t+9

t+7

t+1

t-1

t-3

3
...
Those impulse responses tell you the same
story of the DAD/DAS graph previously analysed, but now we can in principle see
the behaviour of all endogenous variables while in the DAD/DAS graph you see only
inflation and the real output
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This can be a war that increases government spending or a stock market
bubble that increases wealth of people and so increases consumption spending
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So at time t

ε t = 1 and then it stays at 1 until time t+4
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Graphically:

We start at point A before t (if nothing happens we stay there)
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t+4 (the demand is now higher that it stays
there until t+4)
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2) Time t+1: Higher inflation in t raised inflation expectations for t + 1, shifting
DAS up
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3) From t+2 until t+4: Higher inflation in previous period raises inflation

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expectations, shifts DAS up
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4) Time t+5: the DAD returns to the initial position and so it shifts back
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Inflation
decreases and output decreases
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Notice the dynamic effect of this aggregate demand shock
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Then inflation rises and output decreases and then output
increases and inflation decreases
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First output increases above the natural level, then it decreases below and
then it goes back to it
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Also for the case of an aggregate demand shock it is possible to make impulse
response functions for the endogenous variables
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13



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