Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

EC201 Intermediate Macroeconomics
EC201 Intermediate Macroeconomics

Lecture 13-14: The Trade-off between Inflation and
Unemployment
Lecture Outline:
- The Phillips Curve:
- The relationship between inflation and unemployment;
- The Phillips curve as an aggregate supply;
Essential reading:
Mankiw: Ch
...
2
Introduction: The Original Phillips Curve
In an empirical paper in 1958 A
...
Phillips studied the relationship between the
change in nominal wages and the unemployment rate in UK for the period 1861-1957
...

According to Phillips’ findings, an increase (decrease) in nominal wages is associated
with a decrease (increase) in unemployment rate
...
Phillips found that associated with the
same unemployment rate there was the same change in the nominal wages over years
...

This means that the Phillips curve is the same in the short and in the long-run
...
Furthermore, we have that f ' < 0 and f '' > 0 , meaning that the relationship

&
between W and u is negative and convex
...

This means that at the Natural Rate of Unemployment we have that the number of
unemployed workers is equal to the number of job vacancies available in the
economy
...
In the
graph this is given by u0
...
The first attempt to
provide a theoretical foundation for the Phillips curve was done by Lipsey in 1960
...
Therefore, any other point on the
Phillips curve must be a point where the labour demand is larger than the labour
supply (like at point b) or vice versa
...
At point b,
according to Lipsey, there should be an excess of labour demand
...
As the wages increase more workers are willing to work and
unemployment decreases
...
Therefore, we should expect an economy to be
most of the time at u0 since disequilibrium situations should not last for long periods
and market forces should re-equilibrate the system
...


The Phillips Curve as a Relationship between Inflation and Unemployment
After the work of Phillips, many others have tried to estimate the same relationship
for other countries
...
However, their main contribution was to establish a Phillips
curve as a relationship between inflation and unemployment
...
The idea is: if the production costs for a firm increase, also the price of the
product produced should increases
...
Suppose that the
production requires only labour, then the nominal wage represents the marginal cost
for he firm (the cost of one unit of labour)
...
If this hold for all
the firms in the economy, then an increase (decrease) in the nominal wage in the
economy will be reflected in an increase (decrease) in the aggregate price level
...

where now P =
P
After the contribution of Samuelson and Solow, the Phillips curve is now referred as a
relationship between inflation and unemployment
...

The true importance of the Phillips curve is that it is consistent with the Keynesian
economic theory
...
If what matters in the economy is the aggregate demand,
then when aggregate demand is low unemployment should be high but inflation
should be low (low demand puts downward pressure on prices that should decrease)
...


The Phillips Curve and Economic Policy
If the Phillips curve is stable as Phillips believed and many economists in the 60’s,
then it provides a trade-off between inflation and unemployment rate
...


4

∆P/P

b

u1

u

This trade-off provides a clear result for economic policy: if a government wants to
reduce unemployment, it can do it at the price of increasing inflation (for example at
point b)
...
Governments can do that by affecting
aggregate demand using policies
...
How do we choose
the optimal trade-off? It depends on the preferences of the society
...
Then a government would have
an incentive to choose a point on the Phillips curve where inflation is higher and
unemployment is lower
...
Using data for the US economy between 1970 and 2000,
the relationship between Inflation and Unemployment in a scatter plot would look
like:

5

What happened?
The behaviour of inflation changed in the 60s and it became more persistent
...

The inflation rate in US looks like:

When inflation is always positive, wage setters start to expect higher price level in the
future
...

The idea of Friedman and Phelps is: suppose we start at point u1 in the figure below
and suppose we move to point b where inflation is now higher and unemployment

6

lower
...
In particular, since prices are increasing, also
expectations will increase
...
This increase in nominal wages will increase prices further
...

∆P/P
Long run Phillips Curve

c

Short run Phillips Curves
b
u1

u

This implies that the Phillips curve shifts up when expectations increase
...
This means that the Trade-off between inflation and
unemployment holds only in the short-run while in the long-run there is no trade-off
...

Friedman and Phelps assume that expectations are ADAPTIVE
...


7

Long run Phillips Curve

∆P/P

e
d
Short run Phillips Curves

c

b
u1

u

Adaptive expectations are formed according to:

P e t = P e t −1 + a ( Pt −1 − P e t −1 )
e
where P t is the expectation made at t-1 of the price level at time t, P e t −1 is the

expectation made at t-2 for the price level at time t-1, and 0 ≤ a ≤ 1
...
This implies that INFLATION increases (remember the relationship
between inflation and money growth from the quantity theory)
...
After a while, agents will start to revise
their expectations according to the formula above
...
According to
the formula above, the new expectations when we are at point b will be:

P e t = 0 + a ( Pt −1 − 0) ≡ a ( Pt −1 )
If a < 1, then agents will increase their expectations by less then the actual price level
...
So
from point b we move to point c
...
At point c agents will revise their expectations, but again they
will not fully correct them and we will move to another Phillips curve and to a point
like d
...
On that
curve, by the definition of the long run P = P , and so the expectations are (in
e

average) correct
...
Notice that we have defined

8

adaptive expectations in terms of the expected price LEVEL and not in terms of
inflation
...
Therefore, by changing the
expectation of the price level we change also the expectation of the inflation rate
...

According to this view, the Phillips curve in the short run should be written as:

π t = π e t − f (u − u )
where we assume that

1)

f ' (u − u ) < 0 and f (0) = 0
...

Notice that when

π t e = 0 , meaning that wage setters expect the price level in period

t to be equal the one in period t-1, then we go back to the original Phillips curve
described by Samuelson and Solow
...
This implies that
expectations are given by:

P e t = Pt −1
Therefore, in terms of inflation we can assume that agents form their expectations as:

π e t = π t −1
Agents expect for tomorrow the same inflation as today
...

Under this assumption about expectations, the Phillips curve becomes:

π t = π t −1 − f (u − u )

1)

In this particular case the natural level of unemployment is also called NAIRU, Non
Accelerating Inflation Rate of Unemployment that is the rate of unemployment at
which inflation remains constant
...

Suppose a situation where the government wants to reduce unemployment from u1 to
u2 permanently
...
Now the
government increases aggregate demand to decrease unemployment
...
At point b agents revise their expectations for the next period to be equal to
the actual rate of inflation
...
At
point c, inflation has increased again
...
At point d the inflation is higher than at c
and so agents revise their expectations
...

This implies that in order to keep a lower unemployment rate than the natural level
inflation must accelerate over time
...


According to this view, any expansionary policy creates problems in terms of
inflation and should be avoided
...

Using US data from 1970 to 2000 we have:

10

There is indeed a negative relationship between the change in the inflation rate and
the unemployment rate
...
0u t is a regression line estimated from
the data in the graph
...
After 1970 we have θ = 1
...


The Modern Version of the Phillips Curve
After the contribution of Friedman and Phelps, the modern form of the Phillips curve
is the following:

π t = π e t − β (u − u ) + ν
where β > 0 is a constant and

ν

2)

is a supply shock (a random variable)
...
So we can
interpret equation 2) as the log-linear version of a non-linear Phillips curve
...
Adverse supply shocks
typically raise production costs and induce firms to raise prices, “pushing” inflation
up
...
Positive shocks to
aggregate demand cause unemployment to fall below its natural rate, which “pulls”
the inflation rate up
...
Write the aggregate supply in the logs of the variables and with a
supply shock in it:

pt = p e t +

1

α

( y − y ) +ν

where the small letters now denote the natural log of a variable
...

This law relates the change in real output with changes in unemployment
...


This says that deviations of real output from its natural level are

inversely related with deviations of unemployment from its natural level
...
From the Okun’s Law define γ = βα
...

Sacrifice Ratio
Given the trade-off in the short-run implied by the Phillips curve, to reduce inflation,

1

The original Okun’s Law is given by: (Percentage change in real GDP) = 3
...


12

policymakers can contract aggregate demand, causing unemployment to rise above
the natural rate
...
A typical estimate of the ratio is 5
...
Example: To reduce inflation from 6 to 2 percent,
we must sacrifice 20 percent of one year’s GDP:
GDP loss = (inflation reduction) x (sacrifice ratio) = 4 x 5
This loss could be incurred in one year or spread over several, e
...
, 5% loss for each
of four years
...
One could use Okun’s law to
translate this cost into unemployment

---