《宏观经济学》课程教学资源（英文版）Chapter 10 The Phillips Curve

Chapter 10: The / Phillips Curve 10-1: Inflation, Expected Inflation and Unemployment s10-2: The Phillips Curve 9 10-3: A Summary and many Warnings 2003-7-20

2003-7-20 1 Chapter 10: The Phillips Curve 10-1: Inflation, Expected Inflation, and Unemployment 10-2: The Phillips Curve 10-3: A Summary and many Warnings

10-1: Inflation, Expected Inflation and Unemployment e We have already known the function in chapter 9 Pt= Pt(1+p)F(ut, z) e It will be convenient here to assume a specific form for the function F F(u1,2)=1-au+z e Replacing in the earlier equation gives t=Pe(1+p)(1-ut+2) 心 To continue 2003-7-20

2003-7-20 2 10-1: Inflation, Expected Inflation, and Unemployment We have already known the function in chapter 9: Pt = Pt e (1+μ) F (ut , z) It will be convenient here to assume a specific form for the function F: F (ut , z)= 1 - αut + z Replacing in the earlier equation gives: Pt = Pt e (1+μ)(1 - αut + z) To continue

e With a few manipulation, this relation can be rewritten as a relation between the inflation rate, the expected inflation rate, and the unemployment rate e+(u+z)-au 10.1) Where J. denotes the inflation rate and e denotes the corresponding expected inflation rate e In short, equation(10. 1) tells us Higher expected inflation leads to higher inflation Given expected inflation, the higher the markup chosen by firms, u, or the higher the factors that affect wage determination, Z, the higher inflation Given expected inflation, the higher unemployment, the lower inflation 2003-7-20 3

2003-7-20 3 With a few manipulation, this relation can be rewritten as a relation between the inflation rate, the expected inflation rate, and the unemployment rate πt =πt e + (μ+z) - αut (10.1) Where πt denotes the inflation rate, and πt e denotes the corresponding expected inflation rate. In short, equation (10.1) tells us: ⚫ Higher expected inflation leads to higher inflation ⚫ Given expected inflation, the higher the markup chosen by firms, μ, or the higher the factors that affect wage determination, z, the higher inflation. ⚫ Given expected inflation, the higher unemployment, the lower inflation

10-2: The phillips curve The early Incarnation ● Mutations e Back to the natural rate of unemployment 2003-7-20

2003-7-20 4 10-2: The Phillips Curve The Early Incarnation Mutations Back to the Natural Rate of Unemployment

The Early Incarnation e Think of an economy where inflation on average equals to zero, it is reasonable for people to expect that inflation rate will be equal to zero over the next year as well Assuming that j t=0 in equation(10. 1), then J t =(u+z)-au (102) e This is precisely the negative relation between unemployment and inflation The story behind it is simple Given expected prices, lower unemployment leads to higher nominal wages Higher nominal wages lead to higher prices 2003-7-20 5

2003-7-20 5 The Early Incarnation Think of an economy where inflation on average equals to zero, it is reasonable for people to expect that inflation rate will be equal to zero over the next year as well. Assuming that πt e =0 in equation (10.1), then πt = (μ+z) - αut (10.2) This is precisely the negative relation between unemployment and inflation. The story behind it is simple:Given expected prices, lower unemployment leads to higher nominal wages. Higher nominal wages lead to higher prices

Wage-price spiral This mechanism has sometimes been called the wage-price spiral, and this phrase captures well the basic mechanism at work o Low unemployment leads to higher nominal wages e In response to higher wages, firms increase their prices o In response to higher prices, workers ask for higher nominal wages e Firms further increase prices, so workers ask for further Increases In wages And so on, with the result being steady wage and price inflation 2003-7-20 6

2003-7-20 6 Wage-price spiral This mechanism has sometimes been called the wage-price spiral, and this phrase captures well the basic mechanism at work: ⚫ Low unemployment leads to higher nominal wages. ⚫ In response to higher wages, firms increase their prices. ⚫ In response to higher prices, workers ask for higher nominal wages. ⚫ Firms further increase prices, so workers ask for further increases in wages. ⚫ And so on, with the result being steady wage and price inflation

Mutations e From 1970 on, the original Phillips curve relation broke down there are two main reasons The change in the price of oil. The effect of this increase in nonlabor costs was to force firms to increase their prices given wages, to increase p An increase in u leads to an increase in inflation, even at a given rate of unemployment o Wage setters changes the way they formed expectations. This change came from a change in the process of inflation itself. This is the main reason for the breakdown of Philips curve relation 2003-7-20 7

2003-7-20 7 Mutations From 1970 on, the original Phillips curve relation broke down. There are two main reasons: ⚫ The change in the price of oil. The effect of this increase in nonlabor costs was to force firms to increase their prices given wages, to increase μ. An increase in μ leads to an increase in inflation, even at a given rate of unemployment. ⚫ Wage setters changes the way they formed expectations. This change came from a change in the process of inflation itself. This is the main reason for the breakdown of Philips curve relation

The importance of expectation e Suppose expectations are formed according to e=0 t-1 (103) e To see the implications of different values of e for the relation between inflation and unemployment, replace equation(10.3)in equation/ (10.1). Doing so gives 丌e t1+(u+Z) )-u o When e equals zero, we get the original Phillips curve When e is positive, the inflation rate depends not only on the employment rate but also on last year's inflation rate C To continue 2003-7-20 8

2003-7-20 8 The importance of expectation Suppose expectations are formed according to πt e =θπt-1 (10.3) To see the implications of different values ofθfor the relation between inflation and unemployment, replace equation (10.3) in equation (10.1). Doing so gives πt e πt = θπt-1 + (μ+z) – αut ⚫ When θ equals zero, we get the original Phillips curve. ⚫ When θ is positive, the inflation rate depends not only on the employment rate but also on last year’s inflation rate. To continue

The importance of expectation o When/ 0 equals 1, the relation becomes (+z)-u (10.4) So, when 0 =1, the unemployment rate affects not the inflation rate but rather the change in the inflation rate: High unemployment leads to decreasing inflation; low unemployment leads to increase inflation To distinguish equation(10.4)from the original Phillips curve(equation [10.2), it is often called the modified Phillips curve 2003-7-20 9

2003-7-20 9 The importance of expectation ⚫ When θ equals 1, the relation becomes πt -πt-1 = (μ+z) – αut (10.4) So, when θ =1, the unemployment rate affects not the inflation rate, but rather the change in the inflation rate: High unemployment leads to decreasing inflation; low unemployment leads to increase inflation. To distinguish equation (10.4) from the original Phillips curve (equation [10.2]), it is often called the modified Phillips curve

Back to the natural rate of Unemployment o by definition, the natural rate of unemployment is that unemployment rate such that the actual price level turns out equal to the expected price level./ More conveniently here, the natural rate of unemployment is the unemployment rate such that the actual inflation rate is equal to the expected inflation rate Denote the natural unemployment rate by un. Then imposing the condition that actual inflation and expected inflation be the same(t =t t )in equation (10. 1)gives To continue 2003-7-20 10

2003-7-20 10 Back to the Natural Rate of Unemployment By definition, the natural rate of unemployment is that unemployment rate such that the actual price level turns out equal to the expected price level. More conveniently here, the natural rate of unemployment is the unemployment rate such that the actual inflation rate is equal to the expected inflation rate. Denote the natural unemployment rate by un . Then, imposing the condition that actual inflation and expected inflation be the same (πt =πt e ) in equation (10.1) gives To continue