978-0133780581 Chapter 8 Lecture Note

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Chapter 8. The Phillips Curve, the Natural Rate of Unemployment and Inflation

I. MOTIVATING QUESTION

How are the inflation rate and the unemployment rate related in the short run and

the medium run?

Since 1970, the U.S. data can be characterized as a negative relationship between the unemployment rate

and the change in the inflation rate. This relationship implies the existence of an unemployment rate—

called the natural rate of unemployment—for which the inflation rate is constant. When the

unemployment rate is below the natural rate, the inflation rate rises; when the unemployment rate is above

the natural rate, the inflation rate falls.

II. WHY THE ANSWER MATTERS

The material in this chapter provides a way to think about the central issue of U.S. macroeconomic policy,

namely, whether the Federal Reserve should change the interest rate (equivalently, the money supply) and

if so, in what direction. According to the framework developed in this chapter, the economy cannot

operate at an unemployment rate below the natural rate without a continual increase in the rate of

inflation. This limits the ability of the central bank to stimulate the economy. 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. The next chapter recasts 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.

III. KEY TOOLS, CONCEPTS, AND ASSUMPTIONS

1. Tools and Concepts

i. The chapter introduces the original Phillips curve and its modern, expectations-augmented or

accelerationist variant.

ii. 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).

2. Assumptions

In the context of the modern Phillips curve, the chapter assumes that expected inflation equals lagged

inflation. This assumption gives rise to the accelerationist Phillips curve.

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IV. SUMMARY OF THE MATERIAL

Prior to 1970, there was a negative relationship between the unemployment rate and the inflation rate in

the United States. In the 1970s, this relationship broke down. Since 1970, the U.S. data can be

characterized by a negative relationship between the unemployment rate and the change in the inflation

rate. The original relationship is called the Phillips curve, after A.W. Phillips, who first discovered the

relationship for the United Kingdom. The modern form is usually called the accelerationist or

expectations-augmented Phillips curve.

1. Inflation, Expected Inflation, and Unemployment

Impose the specific functional form F(u,z)=1–u+z, and use the price determination equation (7.3) from

Chapter 7 to derive

π= πe + (m + z) – u, (8.2)

where  refers to the inflation rate and πe to the expected inflation rate. An appendix to Chapter 8

presents the full derivation of equation (8.2).

It is important to understand the effects at work in equation 8.2. which are;

An increase in expected inflation (πe) leads to an increase in actual inflation (π).

Given expected inflation (πe) an increase in markup (m), or an increase in the factors that affect

wage determination (an increase in z) leads to an increase in actual inflation (π).

Given expected inflation (πe) a decrease in the unemployment rate (u) leads to an increase in actual

inflation (π).

2. The Phillips Curve

Two explanations are commonly offered for the breakdown of the original Phillips curve in the 1970s.

First, there were significant supply shocks in the 1970s. Since the Phillips curve is the aggregate supply

curve in terms of inflation, supply shocks affect the Phillips curve. The oil price shocks in 1973 and

1979, which the text models as increases in , would have affected the original Phillips curve.

Second, the way workers form inflation expectations may have changed over time. The text models

expected inflation as πet=πt-1 and argues that it is plausible that  was zero in the early postwar period

because inflation was not consistently positive. However, as the inflation rate became consistently

positive and more persistent, it is unlikely that workers failed to take notice. The text argues that the

evidence supports a value of 1 for  since 1970. Under this interpretation, the original Phillips curve,

πt = π + (m + z) – ut, (8.4)

evolved to

πt–πt-1 = (m + z) – ut. (8.6)

Equations (8.4) and (8.6) describe fundamentally different relationships between the inflation rate and the

unemployment rate. In the former equation, there is a permanent tradeoff between inflation and

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unemployment. In the latter equation, the unemployment rate is a constant when the inflation rate is

constant or more generally, when the inflation rate equals the expected rate of inflation. Note that

equation (8.6) uses the change in inflation instead of inflation. Data since 1970 show there is a negative

relationship between the change in the inflation rate and the unemployment rate. High unemployment

leads to decreasing inflation and low unemployment leads to increasing inflation. The relationship

modeled in equation 8.6 is often called the modified Phillips curve, the expectations-augmented Phillips

curve, or the accelerationist Phillips curve.

3. The Phillips Curve and the Natural Rate of Unemployment

The unemployment rate defined by correct inflation expectations is called the natural rate of

unemployment. For this reason, the natural rate is also known as the non-accelerating inflation rate of

unemployment (NAIRU).

To derive the natural rate, solve for the unemployment rate when the inflation rate is constant in equation

(8.6) or when the expected inflation rate equals the actual inflation rate in equation (8.2). Either method

produces the following expression:

un= (m +z)/. (8.8)

In this chapter the authors also revisit the notion of the neutrality of money. The implication of this

analysis is that money growth affects only the inflation rate in the medium run. Money growth has no

effect on medium-run output growth or unemployment. By the same token, inflation is ultimately

determined by monetary policy.

4. A Summary and Many Warnings

The text notes three limits on the use of the accelerationist Phillips curve as a characterization of the

economy. First, the natural rate, such as we can measure it, varies across countries. European economies,

for example, have much higher unemployment rates, on average, than does the United States. Some

economists attribute high European unemployment to labor market rigidities, a term applied to a

collection of policies, including generous unemployment insurance, a high degree of worker protection,

bargaining rules that protect unions, and high minimum wages. A box in the text argues that the

relationship between such policies and unemployment is not straightforward. For example, Denmark and

the Netherlands have low unemployment rates despite generous social insurance programs for workers. It

seems that low unemployment can be consistent with generous social insurance, as long as such insurance

is provided efficiently.

Second, the natural rate of unemployment varies over time. The text argues that the U.S. natural rate fell

in the last half of the 1990s as a result of a variety of factors, some of which may have temporary effects

on the natural rate and some permanent. Note that the interpretations of the changes in the natural rate

tend to come after the fact. Such changes are difficult to predict.

Third, suppose policymakers wish to reduce inflation. The Phillips curve implies that a reduction in

inflation will require an unemployment rate higher than the natural rate for some time. The issues are the

size of the unemployment cost and how the structure of a disinflation program affects the cost.

Fourth, the relationship between inflation and unemployment may depend on the degree of inflation. For

example, if workers will accept real wage cuts only from inflation, and not from cuts in the nominal

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wage, the Phillips curve may break down when inflation is very low (or negative). In this case, high

unemployment may not lead to much reduction in inflation. This point is relevant today because many

countries have low inflation. In addition, this reasoning may help to explain why U.S. deflation was so

limited during the Great Depression, even though unemployment was unusually high.

On the other hand, when inflation is very high, the relationship between unemployment and inflation may

become stronger, because wage indexation becomes more prevalent. Suppose that a proportion () of

wage contracts is indexed to the actual inflation level, so that wages depend on the inflation rate. A

proportion (1-) of wage contracts is not indexed. Wages in these contracts depend on expected inflation,

assumed to equal past inflation. Given these assumptions, the Phillips curve becomes

πt=[πt + (1–)πt-1] – (t – un) (8.11)

πt– πt-1 =[-/(1–)](ut – un)

An increase in the degree of wage indexation () leads to an increase in the coefficient on the

unemployment rate, and so increases the effect of the unemployment rate on inflation.

V. PEDAGOGY

1. Points of Clarification

i. The AS Curve and the Phillips Curve. Chapter 8 may well seem to be something completely

new. It is useful to emphasize that the AS curve and the expectations-augmented Phillips curve essentially

capture the same relationship, one in terms of the price level, the other in terms of inflation. A subtler

point is that the assumption that expected inflation equals lagged inflation is not equivalent to the

assumption that the expected price level equals the lagged price level. The former assumption generates

an equilibrium inflation rate (when embedded in the full medium-run model); the latter assumption

generates an equilibrium price level.

ii. Graphical Presentation. The material in this chapter is presented algebraically. An alternative is

to employ a graphical approach. Instructors could show the downward-sloping Phillips curve and explain

that increases in expected inflation and the price of oil both shift the Phillips curve to the right. Moreover,

the natural rate of unemployment intersects the Phillips curve where actual inflation equals expected

inflation. If unemployment is lower than the natural rate, so that inflation is higher than expected,

expected inflation increases and the Phillips curve shifts right. For a given state of aggregate demand,

inflation and the unemployment rate both increase as the economy moves back toward the natural rate of

unemployment. If unemployment is higher than the natural rate, expected inflation falls, the Phillips

curve shifts left, and inflation and the unemployment rate fall as the economy moves back to the natural

rate. Note that an increase in the price of oil also increases the natural rate.

The graphical presentation has some advantages. One is that is easy to show that an attempt by

policymakers to maintain an unemployment rate below the natural rate will result in increasing inflation,

since expected inflation will continue to increase, and the Phillips curve will continue to shift up. Another

is that the econometric collapse of the Phillips curve is easy to illustrate. As the Phillips curve shifts over

time, we collect data from different Phillips curves. The result is a collection of points that do not

illustrate a downward-sloping Phillips curve.

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VI. EXTENSIONS

Instructors could introduce rational expectations by considering the consequences of π=πe in equation

(8.6). Under this assumption, the unemployment rate equals its natural rate.

VII. OBSERVATIONS

In the medium run, there is no inflation in the AD-AS model. By contrast, the Phillips curve introduced in

this chapter implies a constant (not necessarily zero) rate of inflation when unemployment is at its natural

rate. In the AD-AS model, monetary policy is conceived in terms of the level of the money stock. In the

medium-run model, monetary policy is conceived in terms of the growth rate of the money supply.

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