CHAPTER 8. THE NATURAL RATE OF
UNEMPLOYMENT AND THE PHILLIPS CURVE
I.
MOTIVATING QUESTION
How Are the Inflation Rate and the Unemployment Rate Related in the Short and
Medium Run?
Since about 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 increases; when the
unemployment rate is above the natural rate, the inflation rate decreases.
II.
WHY THE ANSWER MATTERS
The material in this chapter provides a framework 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 and
accelerationist variants.
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 (also known as adaptive expectations or backward-looking expectations). This assumption gives
rise to the accelerationist Phillips curve.
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.
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1.
Inflation, Expected Inflation, and Unemployment
Impose the specific functional form F(u,z)=1-u+z, and use the AS relation from Chapter 7 to derive
π= π e+( +z)-u.
(8.1)
Note that π e refers to the expected inflation rate. An appendix to Chapter 8 presents the full derivation of
equation (8.1).
The intuition for the relationships in equation (8.1) is the same as the intuition developed in the
presentation of the aggregate supply relation. Given the price level in the previous period, an increase in
the current price level implies an increase in the inflation rate, and an increase in the expected price level
implies an increase in the expected inflation rate. Thus, an increase in the unemployment rate, which
tends to reduce wages (because it reduces the relative bargaining power of workers) and thus to reduce
prices (through the price-setting mechanism), also tends to reduce the inflation rate.
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 π et=π t-1 and argues that it is plausible that  was zero in the early postwar period
(prior to the 1970s), when inflation was roughly zero on average. However, as the inflation rate
increased, 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 characterization of expectations, the original Phillips curve,
π t= (+z)-ut ,
(8.2)
evolved to
π t- π t-1= +z-ut.
(8.3)
Equations (8.2) and (8.3) describe fundamentally different relationships between the inflation rate and
the unemployment rate. In the former equation, there is a permanent tradeoff between inflation and
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. The
unemployment rate defined by correct inflation expectations is called the natural rate of unemployment.
To derive the natural rate, solve for the unemployment rate when the inflation rate is constant in equation
(8.3) or when the expected inflation rate equals the actual inflation rate in equation (8.1). Either method
produces the following expression:
un= ( +z)/.
3.
(8.4)
A Summary and Many Warnings
The text notes three limits on the use of the accelerationist Phillips curve in equation (8.1) as a
characterization of the economy. First, the natural rate, such as we can measure it, varies across
countries. Japan, for example, has historically had a lower average rate of unemployment than the
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United States, because of the tradition of lifetime employment in Japanese firms. The text argues that
international competition may erode such employment protection in the future.
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. Europe's natural rate, on the other hand, seems to have risen
steadily since the 1960s. One interpretation of the rise in Europe's natural rate of unemployment has to
do with the slow adjustment of wage demands to declines in productivity growth. This interpretation is
presented in Chapter 13. Note that the interpretations of the changes in the natural rate tend to come
after the fact. Such changes are difficult to predict.
Third, 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
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. Japan actually has negative 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.
By contrast, when inflation is very high, the relationship between unemployment and inflation may
become stronger, because wage indexation becomes more prevalent. Suppose that a share  of wages in
the economy are indexed to the actual inflation level, and the remainder are set according to expected
inflation, assumed to equal past inflation. In this case, the Phillips curve becomes
πt=πt+(1-)πt-1+(+z)-u
or
πt- πt-1 =(+z)/(1-)-[/(1-)]u.
(8.5)
Indexation increases the effect of the unemployment rate on the inflation rate.
For all these reasons, economists must be careful when using the natural rate as a guide for policy.
V.
PEDAGOGY
1.
Points of Clarification
i.
The AS Curve and the Phillips Curve. The jump from the AS curve of Chapter 7 (in price levels)
to the expectations-augmented Phillips curve of Chapter 8 (in inflation rates) will be difficult for some
students. In particular, students have difficulty with the difference between the level of a variable and its
growth rate. Chapter 7 itself required a big conceptual jump by analyzing wage-price dynamics. Chapter
8 may well seem to be something completely new. Time is required for this transition. It is useful to
point out 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 more subtle 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 of Chapter 9); the latter generates an
equilibrium price level.
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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 oil prices 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, and inflation is higher than expected, then
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 oil prices 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 collection of points that do
not illustrate a downward-sloping Phillips curve.
But this does not deny the existence of a Phillips curve. It means instead that at any point in time it can
be difficult to determine the position of the Phillips curve currently ruling the economy
VI. EXTENSIONS
Instructors could introduce rational expectations by considering the consequences of π=πe in equation
(8.3). Under this assumption, the unemployment rate equals its natural rate. Chapter 9 effectively
discusses rational expectations, although it does not use the term, in the context of the credibility of
monetary policymakers.
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. The reason for this difference will become clear in the next chapter. In the AD-AS model,
monetary policy is conceived in terms of the level of the money stock. In the medium-run model
introduced in Chapter 9, monetary policy is conceived in terms of the growth rate of the money supply.
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