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.
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)/. (8.4)
3. 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 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.
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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