The Medium Run III:The Phillips Curve

¿Cómo se relacionan entre sí la Tasa de Inflación y la Tasa de Paro en el Corto y en el

Mediano Plazo?

Precedents and Purpose

The AD AS model leads to an equilibrium where inflation is zero (and the price level stabilizes). This is not what happens in modern economies.

In this unit we extend the AS analysis to understand the link between unemployment and inflation (instead of the price level and the employmet level).

The chapter expands the notion of the natural rate of unemployment. In the context of the accelerationist Phillips curve, the natural rate is the unique rate of unemployment consistent with a constant rate of inflation. For this reason, the natural rate is sometimes called the nonaccelerating inflation rate of unemployment (NAIRU).

In this unit we see that the economy cannot operate at an unemployment rate below the natural rate without a continual increase in the rate of inflation. By the same token, if the central bank wishes to reduce the inflation rate, it cannot do so without increasing the unemployment rate above the natural rate.

In the next unit we recover the aggregate demand in terms of the growth rate of money, develops a relationship between the unemployment rate and output growth, and considers in detail the policy tradeoffs facing the central bank.

Inflation, ExpectedInflation, and Unemployment

The above equation is the aggregate supply. This relation can be rewritten to establish a relation between inflation, expected inflation, and the unemployment rate.

P P F u ze ( ) ( , )1

F u z z( , ) 1 uFirst, the function F, let us assume the form:

P P e ( )( )1 1 u + z

Then, replace this function in the one above:

The appendix to this chapter shows how to go from the equation above to the relation between inflation, expected inflation, and the unemployment rate below:

P P F u ze ( ) ( , )1

e z( ) u

Inflation, ExpectedInflation, and Unemployment

According to this equation: An increase in the expected inflation, e,

leads to an increase in inflation, . Given expected inflation e, an increase in the

markup, , or an increase in the factors that affect wage determination, z, lead to an increase in inflation .

Given expected inflation, e, an increase in the unemployment rate, u, leads to a decrease in inflation, .

e z( ) u

Inflation, ExpectedInflation, and Unemployment

When referring to inflation, expected inflation, or unemployment in a specific year, the equation above needs to include time indexes, as follows:

e z( ) u

te

t tz ( ) u

The variablesThe variables , , eett, and , and uutt refer to inflation, refer to inflation,

expected inflation and unemployment in year expected inflation and unemployment in year tt. . and and zz are assumed constant and don’t have time are assumed constant and don’t have time indexes.indexes.

Inflation, ExpectedInflation, and Unemployment

Inflation, ExpectedInflation, and Unemployment

Friedman and Phelps questioned the trade-off between unemployment and inflation. They argued that the unemployment rate could not be sustained below a certain level, a level they called the “natural rate of unemployment.”

The natural rate of unemployment is the unemployment rate such that the actual inflation rate is equal to the expected inflation rate.

0 ( ) z u n then,then, uz

n

Inflation, ExpectedInflation, and Unemployment

This is an important relation because it gives another way of thinking about the Phillips curve in terms of the actual and the natural unemployment rates, and the change in the inflation rate.

u zn then,then,uz

n

e z( ) uGivenGiven te

t n tu uthen,then,

Finally, assuming that Finally, assuming that eett is well approximated by is well approximated by

t-1t-1, then: , then: t t t nu 1 ( ) u

Inflation, ExpectedInflation, and Unemployment

The equation above is an important relation for two reasons: It gives us another way of thinking about the

Phillips curve: as a relation between the actual unemployment rate ut, the natural unemployment rate un, and the change in the inflation rate

It also gives us another way of thinking about the natural rate of unemployment. The non-accelerating-inflation rate of unemployment, (or NAIRU), is the rate of unemployment required to keep the inflation rate constant.

t t t nu 1 ( ) u

t t 1

The Phillips Curve: A Graphical Analysis

Tasa de paro

Ta

sa d

e I

nfla

ció

n

e

uun

t = t e + (µ+z)-ut

A

For a given expected inflation (e ), The effective inflation rate is a decresing function of the unemployemnt rate.

The Phillips curve crosses by a point where the effective inflation rate is equal to the expected inflation rate (The corresponding unemployment rate is the (NAIRU).

If the effective unemploymet rate is lower than the NAIRU then effective inflation will be higher than the expected inflation rate.

z

uif nett

:

t – te = - (ut – un)

The Phillips Curve is not Stable along Time

Tasa de paro

Ta

sa d

e I

nfla

ció

n

e

uun

A

If, for any known circumstance, the natural unemployment rate increases then the Phillips Curve will shift rigthward.

e’A’

Tasa de paro

Ta

sa d

e I

nfla

ció

n

e

u

un

A A’

If expected inflation increases the Phillips Curve Shift Upwards.

u’n

Some Economist Had The Impression of Having Seen the Phillips Curve

The steady decline in the U.S. unemployment rate throughout the 1960s was associated with a steady increase in the inflation rate.

Inflation versus Unemploymentin the United States, 1948-1969

But the Illusion Soon Disappeared

Beginning in 1970, the relation between the unemployment rate and the inflation rate disappeared in the United States.

Inflation versus Unemploymentin the United States since 1970

Why the Phillips Curve Vanished

The negative relation between unemployment and inflation held throughout the 1960s, but it vanished after that, for two reasons: Many things have changed since the 60s: the

oil crises, work market reforms, globalization, …, but more importantly,

Change in the way wage setters formed expectations due to a change in the behavior of the rate of inflation.• The inflation rate became consistently

positive, and• Inflation became more persistent.

Mutations

Suppose expectations of inflation are formed according to

et t 1

The parameter captures the effect of last year’s inflation rate, t-1, on this year’s expected inflation rate, e

t.

The value of steadily increased in the 1970s, from zero to one.

Mutations

We can think of what happened in the 1970’s as an increase in the value of over time: As long as inflation was low and not very

persistent, it was reasonable for workers and firms to ignore past inflation and to assume that the price level this year would be roughly the same as the price level last year.

But, as inflation became more persistent, workers and firms started changing the ways they formed expectations.

Mutations

In the equation above, when equals zero, the relation between the inflation rate and the unemployment rate is:

t t tz u 1 ( )

When is positive, the inflation rate depends on both the unemployment rate and last year’s inflation rate:

t tz u ( )

t t tz u 1 ( ) When is positive, the inflation rate depends

on both the unemployment rate and last year’s inflation rate:

t t tz u 1 ( )

Mutations

When =1, the unemployment rate affects not the inflation rate, but the change in the inflation rate.

Since 1970, a clear negative relation emerged between the unemployment rate and the change in the inflation rate.

t t tz u 1 ( )

Mutations and Methaphysical Econometrics

The line that best fits the scatter of points for the period 1970-2000 is:

But if you do the same in Spain you get this:

Does it make sense? NO

Since 1970, there has been a negative relation between the unemployment rate and the change in the inflation rate in the United States.

Change in Inflation versus Unemployment in the United States since 1970

ttt u %61

ttt u %,601

Mutations

The original Phillips curve is:

The modified Phillips curve, also called the expectations-augmented Phillips curve, or the accelerationist Phillips curve, is:

t t tz u 1 ( )

t tz u ( )

Let’s summarize what we have learned so far: The aggregate supply relation is well captured

in the United States today by a relation between the change in the inflation rate and the deviation of the unemployment rate from the natural rate of unemployment.

When the unemployment rate exceeds the natural rate of unemployment, the inflation rate decreases. When the unemployment rate is below the natural rate of unemployment, the inflation rate increases.

A Summary and Many Warnings8-3

Variations in the Natural Rate Across Countries

The factors that affect the natural rate of unemployment above differ across countries. Therefore, there is no reason to expect all countries to have the same natural rate of unemployment.

uz

n

Variations in the Natural Rate of Unemployment Across Countries

The Japanese Unemployment Rate

The average unemployment rate in Japan since 1960 has been 2.1%, compared to 6.1% in the U.S. One of the main reasons for this difference appears to be the widespread reliance on lifetime employment in the Japanese labor market.

Table 1 Cumulative Number of Jobs Held by Males of Different Ages, In Japan and the United States.

Age Group 16-19 20-24 25-29 … 55-64

Japan 0.72 2.06 2.71 … 4.91

United States

2.0 4.40 6.15 … 10.95

Variations in the Natural Rate Over Time

A high unemployment rate does not necessarily reflect a high natural rate of unemployment. For example,

If inflation is decreasing fast, the actual rate of unemployment is far above the natural rate.

If inflation is stable, the actual and the natural rates of unemployment are roughly equal.

t t tz u 1 ( )

Variations in the Natural Rate Over Time

Change in Inflation versus Unemployment: Euro Area since 1961 (Squares denote the 1960’s, diamonds the 1970’s, triangles the dates since 1980)

The Phillips curve relation between the change in the inflation rate and the unemployment rate has shifted to the right over time, suggesting a steady increase in the natural unemployment rate in Europe since 1960.

High Inflation and thePhillips Curve Relation

The relation between unemployment and inflation is likely to change with the level and the persistence of inflation.

When inflation is high, it is also more variable.

The form of wage agreements also changes with the level of inflation. Wage indexation, a rule that automatically increases wages in line with inflation, becomes more prevalent when inflation is high.

High Inflation and thePhillips Curve Relation

Let denote the proportion of labor contracts that is indexed, and (1 ) the proportion that is not indexed.Then, becomes:

te

t t nu ( ) u t t

et t nu u [ ( ) ] ( )1

The proportion of contracts that is indexed The proportion of contracts that is indexed responds to responds to tt, while the proportion that is not , while the proportion that is not

responds to responds to eett..

When When =0, all wages are set on the basis of =0, all wages are set on the basis of expected inflation (equal to last year’s inflation), expected inflation (equal to last year’s inflation), then:then: t t t nu 1 ( ) u

High Inflation and thePhillips Curve Relation

When is positive,

t t t nu u

1 1( )

( )

According to this equation, the higher the According to this equation, the higher the proportion of wage contracts that is indexed—the proportion of wage contracts that is indexed—the higher higher --the larger the effect of the --the larger the effect of the unemployment rate on the change in inflation.unemployment rate on the change in inflation.

When When is closer to 1, small changes in is closer to 1, small changes in unemployment can lead to very large changes in unemployment can lead to very large changes in inflation.inflation.