# Phillips Curve. Macroeconomics Cunningham

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1 Phillips Curve Macroeconomics Cunningham

2 Original Phillips Curve A. W. Phillips (1958), The Relaion Beween Unemploymen and he Rae of Change of Money Wage Raes in he Unied Kingdom, , Economica. Wage inflaion vs. Unemploymen New Zealander a London School of Economics Missing Equaion of Keynesian economics? 2

3 5½ % = zero inflaion 3

4 5½ % 4

5 Phillips Conclusions There exiss a sable relaionship beween he variables. The relaionship has no subsanially changed for over 100 years. Negaive, nonlinear correlaion. Wages remain sable/saionary dw ( =0) when unemploymen is 5½%. w 5

6 Conclusions, Coninued From he dispersion of he daa poins, Phillips concluded ha here was a counercyclical loop : Money wages rise faser as du/d decreases, Money wages fall slower as du/d increases Implies an inflaionary bias, and is consisen wih sicky wage heory. dw w slower faser u 6

7 Problems wih Phillips Sudy Empirical mehod suspec. Is his an empirical resul in search of a heory? To ie o heory, need a way o relae his o real wages in order o connec his o labor marke condiions. R.G. Lipsey (1960) aemps o address hese poins in The Relaionship Beween Unemploymen and he Rae of Change of Money Wage Raes in he UK, : A Furher Analysis. 7

8 Lipsey s Phillips Curve Derives he Phillips curve from supply-demand analysis of he labor marke. N s = N + U N d = N + V Where U refers o he number unemployed, V refers o he number of job vacancies. Excess demand N d N s = X = V U. So X N s = V N s Where v is he vacancy rae and u is he unemploymen rae. U N s = x = v u 8

9 Lipsey,, Coninued Sep One. Wage Adjusmen Funcion w d dw N N = = k s dn N This amouns o saying ha he change in he money wage rae is proporional o he excess demand for labor. Sep Two. Esablish a heoreical negaive correlaion beween he excess demand for labor and he rae of unemploymen. s 9

10 Lipsey,, Coninued Individual Labor Marke Condiions N x = d N N s s Asympoic (u=0 no possible) dw w wage inflaion dw w u f u Individual labor marke u f unemploymen u N x = d N N s s 10

11 Lipsey,, Coninued The resul is a Phillips curve for an individual marke. Nex, aggregae across markes for he aggregae Phillips curve. 11

12 Samuelson-Solow Solow (1960) P. Samuelson and R. Solow. The Problem of Achieving and Mainaining a Sable Price Level: Analyical Aspecs of Ani-Inflaion Policy, American Economic Review (May 1960), Popularized he curve. Made relevan o policymakers. Relaion is general price level inflaion vs. unemploymen. Recommended o policymakers as a rade-off. 12

13 Samuelson-Solow Solow,, Coninued Key ransformaion from Phillips-Lipsey o S-S is hrough mark-up pricing. Firms se prices by adding a fixed mark-up o labor coss. The mark-up = he indusry-wide profi margin + depreciaion of fixed K mark-up WN P ( 1+ a) y = uni labor coss 13

14 Samuelson-Solow Solow,, Coninued Subsiuing: In logs: P y = ( 1+ a) W nominal oupu (GDP) N nominal wage bill y Le Λ = N (labor produciviy) W P = (1 = a) Λ logp = log(1+ a) + log logλ W 14

15 Samuelson-Solow Solow,, Coninued This implies: or P P W Λ = W Λ = w λ inflaion rae = wage inflaion rae growh rae of labor produciviy Increases in wages mached by produciviy increases are no inflaionary. There is a relaionship beween wage inflaion and goods price level inflaion. 15

16 Samuelson-Solow Solow,, Coninued Generalize furher in he form of a Phillips curve relaion: w = e + bu 1 demand pressure + βλ, inflaion expecaions (assumed sable, i.e., equal o zero) Subsiue: = w λ b > 0, 0 β 1 offseing produciviy gains 16

17 Samuelson-Solow Solow,, Coninued = e + bu 1 (1 β) λ This is he modern Phillips curve. Technical relaion beween inflaion and unemploymen. Each poin is an equilibrium sae of he economy. 17

18 Friedman-Phelps Phillips Curve Milon Friedman. The Role of Moneary Policy, American Economic Review (March 1968), Edmund Phillips. Phillips Curves, Expecaions of Inflaion and Opimal Employmen Over Time, Economica (Augus 1967), ) They quesion he sabiliy of he relaionship. They conclude: The rade-off is shor-run. Differen Phillips curves exis for differen inflaion raes Changes in inflaion expecaions shif he shor-run Phillips curve. 18

19 Friedman-Phelps Phillips Curve LRPC = f ( u) + Shor run Phillips curves e U 1 U* e = 1 e =0 U Naural Rae of Unemploymen or NAIRU 19

20 Friedman s Acceleraionis Hypohesis = f ( u) + e Acceleraionis Hypohesis: le f ( u) = b( u u*) Use adapive expecaions: e e = θ 1 + ( 1 θ) 1 So ha = θ Problem: e 1 + ( 1 θ) 1 b( u u*) e 1 is no observable. 20

21 Friedman s Acceleraionis Hypohesis Lag one period, muliply by ( 1 θ) e ( 1 θ) = (1 θ) 1 b(1 θ)( u 1 1 u Subrac from he original equaion: = + b( 1 θ)( u 1 u*) b( u 1 1 u *) *) Replaces he expeced inflaion erm When inflaion is fully anicipaed, = e, = 1, and u = u 1. 21

22 Friedman s Acceleraionis Hypohesis Subsiuing, = bθ( u u*) b(1 θ)( u u 1) 1 Bu and So and u = = u = bθ( u u = u *. u u*) u 1 1 = 0 = 0. Which implies ha unemploymen revers o he naural rae a he long run Phillips curve once inflaion is fully anicipaed. 22

23 Anoher view: Keynesian Perspecive AS 2 AS AD 2 AD 1 23

24 More Friedman In his Nobel lecure, Friedman offered he possibiliy of a posiively-sloped Phillips curve: Sabilizaion policy increases he inflaion rae and variabiliy. This requires nominal conracs o be renegoiaed o shorer lenghs. Efficiency is lowered. Invenories grow. Unemploymen rises. The broadcas abou relaive prices is, a i were, being jammed by he noise coming from he inflaion broadcas. 24

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