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EC201 Intermediate Macroeconomics
EC201 Intermediate Macroeconomics

Lecture 17-18: The New Classical Macroeconomics

Lecture Outline:
- Rational Expectations:
- Policy Ineffectiveness Proposition;
- Lucas Critique;
Essential reading:
This lecture note
Introduction: The Basic Assumptions of the New Classical Macroeconomics

The New Classical Macroeconomics is a new school of macroeconomics that begins
in the early 70’s mainly with the works of R
...
Lucas and T
...
Sargent
...
For example, in
previous lecture notes we saw how Friedman and Phelps introduced the role of
adaptive expectations into a Phillips curve
...
This implied that any
policy that tries to reduce the natural level of unemployment would have only shortrun effects but after a while the result of that policy would create high inflation and
the same natural unemployment rate as before
...

The New Classical Macroeconomists bring those conclusions to more extreme
consequences by saying that even in the short-run a trade-off between inflation and
unemployment may not exist and policies may be completely ineffective even in the
short-run
...
So prices are always flexible and markets are

1

always in equilibrium
...
In practice,
the economy is continuously subject to random shocks;
3) Rational Expectations: economic agents take their decision on the base of
all information available and this information is used efficiently;

The main assumptions that make the new classical macroeconomics a new theory is
the idea of rational expectations
...

According to new classical macroeconomists, macroeconomic models should be built
on a framework with optimising agents (firms and consumers)
...
This is what we call “micro foundations” of
macroeconomics and it is now the way in which modern macro models are analysed
...
This is not very satisfactory if we deal with rational and optimising agents
...

For example, suppose we deal with expectations about prices:
P e = E[ Pt Φ t −1 ]

1)

t −1 t

Where

t −1

P e t is

Φ t −1 represents

the expectations made at t-1 of the price level at time t and

the set of all the information available at time t-1
...
For example, assume that the true model
that determines the price level is given by the quantity theory of money
...
F Muth in early 60’s to explain the movement

of prices
...


2

information set there will be the values of real income, money supply and the velocity
of money
...

In practice, under rational expectations the assumption is that the agents form their
expectations according to the relevant economic theory
...
This implies that the forecasting error should
be a serially uncorrelated random variable with mean equal to zero:

Pt − Pt = ε t
e

where ε t is an Identically and Independently Distributed (i
...
d
...

This process is also known as white noise and the notation ε t ~ WN (0,σ 2 ) simply
mean that

ε t is DISTRIBUTED as a white noise (WN) with zero mean and variance

σ 2
...

Furthermore,

errors

are

serially

uncorrelated

over

time,

meaning

that:

cov(ε t , ε t − j ) = 0
...

This implies that the error today is not correlated with the error made at any other
time period
...


Using the definition of the forecasting error we can see why expectations are correct
in average:

Pt − Pt = ε t
e

⇒ Pt = Pt + ε t
e

3

Applying the expected operator to both sides2:

E ( Pt ) = E ( Pt + ε t )
e

⇒ E ( Pt ) + E (ε t )
e

⇒ E ( Pt ) + 0
e

But the expectation of the expectation of a variable is simply the expectation of that
variable (Law of Iterated Expectations), so we can write:

E ( Pt ) = Pt

e

In average the expectation of P is exactly the expected value of the true value of P
...
Rational expectations are not sufficient for this result to
hold, there is the need of price flexibility as well
...
The parameters β i with i = 0,1,2 are positive constants
...
The last term is a random variable υ ~ WN (0, σ 2υ ) and
serially uncorrelated that captures aggregate demand shocks
...


2

We use the property that the expected value of a sum is the sum of the expected values:

E ( X + Y ) = E ( X ) + E (Y )

4

Furthermore we assume that cov(µ t ,υ t ) = 0 , the two shocks are uncorrelated with
each other
...
However, they
must also know how the policy authorities behave
...

We assume the following:

gt = γ g gt + θt
mt = γ m mt + ϑ t

2)

where γ g and γ m are positive constants
...

The terms

γ g g t and γ m mt are the SYSTEMATIC parts of those rules
...
Therefore, if the
agents are at time t-1, they know that at time t the policy rules implies γ g g t and

γ m mt
...
This part of
the rule is known to the agents
...
For example in some periods the central bank
would like to increase more the money supply in order to increase aggregate demand
and so aggregate output, or decreasing the money supply because of a positive shock
in the economy and so on
...

The parts

θ t ,ϑt are the STOCHASTIC elements of the policy rules and satisfy the

usual assumption that:

θ t ~ WN (0, σ 2θ ) , ϑt ~ WN (0, σ 2ϑ )

and they are serially

uncorrelated
...

In practice we are saying that policy rules are divided in two parts: one is a systematic
part that is known by the agents with certainty and the other is a stochastic part
...

Therefore, the expectations of the policy variables are:

gt = γ g gt
e

mt = γ m mt
e

The Forecasting errors are given by:

gt − gt = θt
e

mt − mt = ϑt
e

Consider the equilibrium implied by our AD-AS model (where AD=AS):

β 0 + β1 (mt − pt ) + β 2 gt + υt = y + α ( pt − pt e ) + µt
Solve for the equilibrium value of pt:

pt ( β1 + α ) = β 0 + β1mt + β 2 gt − y + υt − µt + αpt

e

Therefore:

pt =

β0

β1 + α

+

β1

β1 + α

equilibrium value for

mt +

β2

β1 + α

gt −

(υ − µt ) + α p e
y
+ t
The
β1 + α β1 + α β1 + α t

yt is found for example, by substituting the above expression

for

pt into the aggregate demand function:

yt =

β 0α + β1 y + αβ1mt + αβ 2 g t
βα
e
− 1
pt + ϕ t
β1 + α
β1 + α

6

υt − µt
is a shock that depends on demand and supply shocks
...
They know that the price at time t
is given by the expression for pt derived above
...
Therefore, the above expression can be written as:
E ( pt ) =

β0

β1

+

β1 + α

β1 + α

E (mt ) +

β2

β1 + α

E ( gt ) −

y
α
e
E ( pt )
+
β1 + α β1 + α

 (υ − µ t ) 
1
where we use the fact that: E  t
[E (υt ) − E ( µt )] = 1 [0 − 0] = 0
=
β1 + α
 β1 + α  β1 + α

Now notice that

E ( pt ) = pt
e

E ( pt ) = pt

e

by the law of iterated expectations

e

by definition of expectations

E (mt ) = mt = γ m mt
e

E ( gt ) = gt = γ g gt
e

Therefore

pt

e

is given by:
pt =
e

β0
β e y
e
+ mt + 2 g t −
β1
β1
β1

We can substitute this expression into the equilibrium level of

yt = y +
where

y t we obtain:

αβ1
αβ 2
e
e
(mt − mt ) +
( gt − g t ) + ξt
β1 + α
β1 + α

ξt is a shock that depends on demand and supply shocks
...


In equilibrium, with rational expectations and flexible prices, the level of aggregate
income fluctuates around the natural level and it does not coincide with it only for
stochastic elements

(η t )
...

The two levels do not coincide only because of stochastic terms that depend on:
1)

Shocks on the aggregate supply and the aggregate demand,

2)

( µ t ,υt )

Shocks on the policy rules, ( ϑt ,θ t )

Notice that the systematic parts of the policy functions do not appear into equation 3)
and therefore they DO NOT affect the equilibrium value of real output
...
With rational expectations and price
flexibility the equilibrium level of output fluctuates around its natural level and those
fluctuations depend only on stochastic (and so unpredictable) elements”

This result, as you may guess, is particularly strong
...
Or in other words: when economic agents are fooled by the policy authorities
that deviate from the systematic parts of their policy rules
...
Evidence
suggests that both anticipated and unanticipated policies affect the level of output
...

Furthermore, what is really important from this theory is to show us how the
introduction of expectations (in this case rational expectation) may affect the role of
economic policies
...
We have seen that with rational expectations and price flexibility, the
systematic part of a policy (the part of the policy that is known and perfectly
anticipated by the agents) has no real effects
...

Suppose we start at the long-run equilibrium where AD=LRAS=SRAS (aggregate
demand = long run aggregate supply = short run aggregate supply), like in point a in
the figure below
...

Suppose that agents believe that the announcement of the central bank is credible
...
They know the true model that relates all the
economic variables under analysis and they use that model to form their expectations
...
Agents
know that an increase in money supply that is systematic should increase the price
level without affecting the real variables of the economy
...

Starting from point a, when the policy is implemented agents will simply adapt their
expectations (they can do that because prices are flexible) and the economy will move
directly to point c on the long-run aggregate supply
...

Notice the difference with the case with adaptive expectations
...

For New Macroeconomic economists this movement is not rational and it is not likely
to happen
...

AD-AS model with Rational Expectations: the effects of Unanticipated Policies

Now we consider the case of an unanticipated monetary policy
...

Suppose an unexpected increase in money supply
...
The increase in m increases p
10

unexpectedly and so

p differs

p e can be wrong
...
Starting from a, the

increase in m will shift the aggregate demand to AD2
...
As soon as the agents

realise what happened in the economy they revise the expectations
...
This adjustment process is very similar to the one with
adaptive expectations
...
The main difference is that the
adjustment process now can be very short
...
There is no delay due to the partial
revision of errors as under adaptive expectations
...
However, if governments continue to make policies
that are not announced, this behaviour will become systematic and so also those
policies will stop having effects
...


Painless Disinflation and the Phillips Curve:
From the Phillips curve we know that if we want to decrease inflation in the short-run,
the price of this policy is an increase in the unemployment rate
...

The idea is exactly the sae as the one we have discussed in the case of an anticipated
policy
...
Suppose that the central
bank announces that in 6 months the growth rate money supply will be reduced to 0%
...
We know that in the short run there is a different Phillips
curve for any different inflation expectation
...
Suppose that agents believe that the
announcement of the central bank is credible (central banks that are politically
independent are typically more credible than those that are “puppets” to elected
officials
...
A very worthwhile reform, therefore,
would be for governments to give their central banks independence)
...

The movement will be from a to b after the policy is implemented and so in theory
there will not be effects on unemployment
...


Lucas’ Critique
The Lucas’ critique (R
...
Lucas, 1976) referred to a critique to the way
macroeconometric models were used to analyse and forecast the effects of economic
policies
...

The idea is the following: according to new classical macroeconomists, when a
government changes a policy or implements a new policy it should take into account
that also the behaviour of the agents will change
...

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According to new macroeconomists this is not realistic and can bring the analysis to a
wrong result
...
This in turn will change the result of the analysis
...
Indeed those coefficients may change with the change in the
policy
...

Governments should be aware that there is a sort of strategic interaction going on with
economic agents when deciding a particular policy
...
etc
...

1)

Rational expectations: the assumption of rational expectations is now
widely accepted by most of the macroeconomists
...

2)

The theory of efficient financial markets: many of the ideas developed by
the new classical macroeconomists have been applied successfully to
markets where continuous market clearing is a reasonable assumption, like
financial markets
...


3)

Greater understanding of economic policy: the idea that individuals have
rational expectations has improved our understanding of economic policy
...
For instance, wage negotiators who suspect that the
government will allow rapid inflation after a supply shock are likely to

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demand full cost-of-leaving adjustment in their contracts (what we call wage
indexation)
...


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