Unemployment and Inflation
P h illip s (1 9 5 8 ) estim ated a n eg ativ e relatio n b etw een th e w ag e
rate an d u n em p lo ym en t rate u sin g th e d ata set fo r th e U K
eco n o m y fro m 1 8 6 1 -1 9 5 7 .
w h ere g  0 , w h ere
w  g u 
w
(1 )
w is th e ch an g e in th e u n em p lo y m en t rate an d
w
u is th e u n em p lo y m en t rate
L ip sey (1 9 6 0 ) slig h tly altered th is relatio n in clu d in g ex cess


w  g  N S  N D 
lab o u r su p p ly in relatio n to lab o u r fo rce w
.


LF

Macroeconomic Themes:9

1
Friedman (1966, 1968) and Phelps (1967) natural
rate of unemployment hypothesis
  e w h ere   0
(2 )
t
N

w h ere  t is th e actu al in flatio n ,  e is th e ex p ected in flatio nu
is
t
N
 t    u t  u




th e n atu ral rate o f u n em p lo y m en t th at is g ro u n d o u t b y th e
W alrasian syste m o f th e g en eral eq u ilib riu m , an d u t is th e actu al
u n em p lo y m en t rate.
S in ce  t   te    u t  u
N






an d   0 th e in v erse relatio n
b etw een u n em p lo ym en t an d in flatio n im p lies
 t  e

t

t
t
 e
t
 e
t

 yt  y *
N
u t  u  yt  y *
(3 )
N
ut  u  y  y*
t
N Macroeconomic
Themes:9
ut  u
2
Rational and Adaptive Expectation about
Inflation
T h e ratio n al ex p ectatio n m eth o d
 e  E  t | I
t 1 t

t 1




w h ere
 e is th e p rice in p erio d t as ex p ected in p erio d t-1 ,
t
t 1
w h ere I
t 1
is th e in fo rm atio n set w h ich in clu d es p ast v alu es o f
all en d o g en o u s v ariab les an d p aram eters.
A d ap tiv e ex p ectatio n (learn in g fro m p ast m istak es)

 e   
t


  e    e
t 1
t 1 
t 1
(4 )


  e  an d learn in g o ccu rs b ecau se
t 1 
 t 1
0    1 .N o tice  e  
  1 th is is a co m p letely
if
t
t 1
P ast m istak e 
b ack w ard lo o k in g ex p ectatio n .
Macroeconomic Themes:9
3
Backward Looking Expectation of Inflation

 e   
t


  e    e
t 1
t 1 
t 1
(4 )


  e  an d learn in g o ccu rs b ecau se
t 1 
 t 1
0    1 .N o tice  e  
  1 th is is a co m p letely b ack w ard
t
t 1 if
P ast m istak e 
lo o k ing ex p ectatio n .
 e d ep en d s o n p ast v alu es of actu al in flatio n
t

 e   

  e    e
t
t 1 
t 1
 t 1
2
n 1
 e  
  1   
  1    
 ..   1   
 tn
t

 t2




t 1
t 3
(5 )
Macroeconomic Themes:9
4
Aggregate Supply and Demands
Y t  N  in lo g s y t   n t (6 )
t
Yt
wt


1
N

L ab o u r d em an d :
p t tak in g lo g it can b e
t
N t




w ritten as w  p  ln α    α  1ln  n 
(7 )


t
t
 t
Mt
 k t Y t w h ere k is a m o n etary p o licy
A g g reg ate D e m an d :
t
Pt
A g g reg ate S u p p ly

p aram eter k t  e t w h ere  is a ran d o m v ariab le. N o w tak in g
t
 
lo g o f th is d em an d m t  p t  ln  k   y t o r
m t  pt   t  yt
(8 )
Macroeconomic Themes:9
5
Labour Market with Rational Expectation
L ab o u r su p p ly d ep en d s o n ex p ected real w ag e rate w
pe
. w  w if
pe
p
p e  p . W o rk ers k n o w th eir w ag e rate b u t th ey d o n o t k n o w th e
cu rren t p rice lev el. T h ey h av e ex p ectatio n ab o u t th e cu rren t p rice
lev el co n d itio n al u p on in fo rm atio n av ailab le u p to p erio d t-1 .




s
*
n    wt  E
 p 
t

t 1  t  
w h ere *
t 1



(9 )
p t  is th e p sych o lo g ical ex p ectatio n o f th e p erio d t

p rice lev el h eld at tim e t-1 .
L ab o u r m ark et clearin g co n d itio n :
ns  nd
t
t
Macroeconomic Themes:9
(1 0 )
6
Labour Market Equilibrium and Aggregate
Supply
S olve (4) for the w age rate w t and substitute the result for
the w t term in (2).
w t  1 n s  E *  p t 
 t
t 1  
1 n s  E *  p   p  ln      1  n 





t
 t

 t 
t 1  t 




1
1






*


n t  1     p t  E
 1   
 p   ln   let  






 t 
t

1








1





*
*
p  E
nt   p t  E
 p   ln   and y 
 p   ln  
t
t
t
t







t

1
t

1



(11)
Macroeconomic Themes:9
7
Macroeconomic Equilibrium
nt 
p

1
 E t  1  p t   ln 
*
t
 and
yt 
p


 E t  1  p t   ln 
*
t

(11)
AS: y t 
p


 E t  1  p t   ln 
*
t

*
P rice p t  E t  1  p t 
p t  E t 1  p t
*

p t  E t 1  p t
*
AD:

yt  y
*
y
*



ln 

yt  mt  pt  t
yt  y
*
O utput
t t

ut  u N  yt  y
*
t t

ut  u N  yt  y
*
ut  u N  yt  y
*
e
e
t 
e
t

Macroeconomic Themes:9
8
Unemployment and Inflation
P h illip s C u rve in th e U K , 1 9 7 0 -2 0 0 2
16
14
Inflation rate
12
10
URATE
8
L in e a r (U R A T E )
6
4
2
0
0
5
10
15
20
25
30
U n e m p lo ym e n t ra te
Macroeconomic Themes:9
9
Unemployment and Inflation
In fla tio n a n d u n e m p lo ym e n t ra te in th e U K
30
25
RPI
15
URATE
10
5
Macroeconomic Themes:9
1998
1993
1988
1983
1978
1973
0
1970
P ercent
20
10
Unemployment and inflation: New Keynesian Theory
Adverse Supply Shock and Stagflation in 1970
C an d e m and m ana ge m en t p o lic y increase the le vel o f o utp ut in the lo ng run?
D yna m ic ad justm e nt p ro cess after a p o sitive
D yna m ic ad justm e nt p ro cess o f e xp ansio nary
sup p ly sho c ks
m o netary and fiscal p o lic y
Y
LAS
AD2
s
e
; z)
P  (1   ) P N ( 1 
L
AD1
a
D
SAS
b
P
c
P
c
b
AS1
a
Y  F(
M
,G ,T )
AS3
P
Y
Yn
A g gregate d e m a nd and ag grega te sup p ly
AD
AS2
Y
Yn
A g gregate d e m a nd and ag grega te sup p ly in the
sho rt and the m ed iu m run
Macroeconomic Themes:9
11
Fix Target and Optimal Choice Approach to
Control Inflation and Unemployment
Inflatio n
*
S o cial w e lfare fu nctio n
P o licy co nstraints
u*
une m p lo ym e nt rate
Macroeconomic Themes:9
12
Barro and Gordon (1983) Unemployment Inflation
Policy choice Model
  0 (1 )
U t  U n    t   e 
t
t 

N atu ral rate o f u n em p lo y m en t: U n   U n  1   U  
t
t

t 1 
0    1 (2 )
2
2




n
a,b  0
Z

a
U

kU

b





S o cial co st fu n ctio n : t
t
t 
 t 

0  k  1 (3 )
P h illip s cu rv e:
O v erall o b jectiv e fu n ctio n g iv en in fo rm atio n set














Zt

Zo  E 
I
t
0
t  0 1  r 


(4 )
e
e
P riv ate secto rs ex p ectatio n o f in flatio n  t  h  I t 1 

Macroeconomic Themes:9

(5 )
13
Barro and Gordon (1983) Unemployment Inflation
Policy choice Model
B y su b stitu tin g (2 ) an d (5 ) in (1 )


  (6 )
U t   U n  1   U   t    t  h e  I



t 1
 t 1  

N o w su b stitu te (6 ) in to th e o b jectiv e fu n ctio n (3 )
2

2








n
e
n


  kU
Zt  a U
 1   U   t    t  h  I

b






t 
 t 
t 1 
 t 1  





A g ain su b stitu tin g term



 


 
U
n
t
an d b y rearran g in g th is alters to







Z t  a 1 k  U n  1  U   t   t  h e I
t 1
t 1










  
 

  
2
 b  t 

2

(7 )
N o w p o licy m ak ers lik e to m in im ise th e so cial w elfare fu n ctio n in
(7 ) b y ch o o sin g th e o p tim al in flatio n rate
Z t




  
    2b 
  2 a  1  k    U n  1   U   t     t  h e  I

t 0




t

1
t 1

  

 t



Macroeconomic Themes:9
14
Barro and Gordon (1983) Unemployment Inflation
Policy choice Model


 


aa





e
n


ˆ
ˆ


 1  k    U
 1   U   t  
  
    h  I

 t
t


 
t 1 
 t 1  
b 
 

(8 )
U n d er th e ratio n al ex p ectatio n p eo p le ex p ect in flatio n rate to b e th e
 .
sam e as d eterm in ed b y th e p o licy m ak ers ˆ t  h e  I

 t 1 

aa
T h erefo re th e ˆ t 
b
ˆ t  aa 1  k U
b






 


1  k    U n  1   U   t   

 
 
t 1 
(9 )
H o w ev er n o tice th at p o licy m ak ers h av e an in cen tiv e to ch eat an d
m ay set in flatio n rate h ig h er th an p eo p les ex p ectatio n s o n ce th ese

e
ex p ectatio n s are m ad e ˆ t  h  I t 1   0 .


Macroeconomic Themes:9
15
Inflation Policy Game
.......... .......... .......... .
Government
Sector
Pr ivate


H

 L
Sector
H
 3,0
 5, 3
L 

3,  3

0 , 0 
.
P o lic y o p tio n s a n d its o u tc o m e
P olicy O ptions
A
B
C
D
A ctual inflation
L ow
L ow
H igh
H igh
E x pected inflation
L ow
H igh
L ow
H igh
Macroeconomic Themes:9
U nem plo ym ent rate
u = un
u > un
u < un
u = un
16
Inflation Policy Game
LP C
In flation 

PC2  t  
e
 b u t  u n 
PC1
C (3 ,-3)
D (-3,0)
A (0,0 )
B (-5,-3)
un
U nem plo ym ent rate, u.
Macroeconomic Themes:9
17
Variation in unemployment rate across OECD countries
(57 time series observations for each country)
Mean
S t.D e v
V a ria nc e
M in im u m
M a xim u m
C o e ff o f
(1 9 8 8 )
(2 0 0 1 )
va r.
2 .2 7 08
5 .6 3
1 0 .7 7
0 .1 8 95
A u s tralia
7 .9 5 37
1 .5 0 69
A u s tria
4 .0 3 68
0 .3 0 31
9 .1 9 E -02
3 .4 2
4 .6 3
0 .0 7 51
B e lg ium
1 2 .1 76
2 .1 0 35
4 .4 2 47
9 .5 6
1 9 .9 1
0 .1 7 28
Canada
8 .8 9 02
1 .4 8 64
2 .2 0 94
6 .7
1 1 .7 3
0 .1 6 72
C heck R ep
2 .8 1 7
1 .6 5 33
2 .7 3 35
0 .4
5 .3 3
0 .5 8 69
D e n m a rk
8 .6 6 3
2 .4 3 59
5 .9 3 35
5
1 2 .5 3
0 .2 8 12
9 .1 1 75
1 .0 4 63
1 .0 9 47
7 .4
1 0 .7
0 .1 1 48
1 8 .5 2
3 .5 5 93
1 2 .6 69
1 2 .7 7
2 4 .5 8
0 .1 9 22
F in lan d
1 0 .3 95
4 .5 0 04
2 0 .2 54
2 .9
1 7 .8 7
0 .4 3 30
F ra n ce
1 0 .5 61
1 .2 6 78
1 .6 0 73
8 .6
1 2 .3
0 .1 2 00
G7
6 .3 2 28
0 .5 3 38 6
0 .2 8 50 1
5 .4
7 .2
0 .0 8 44
G re a t B ritain
6 .3 1 75
2 .1 5 98
4 .6 6 48
3 .1 3
9 .9
0 .3 4 19
Ire la nd
1 0 .9 55
4 .4 2 77
1 9 .6 05
3 .6
1 6 .5
0 .4 0 42
Ita ly
1 1 .0 91
0 .8 7 06 5
0 .7 5 80 3
9 .1
1 2 .1 7
0 .0 7 85
J a p an
3 .2 9 58
1 .0 7 92
1 .1 6 47
2 .0 7
5 .4
0 .3 2 75
L u xu m b e rg
2 .3 4 28
0 .4 9 33 8
0 .2 4 34 3
1 .5 2
3 .3 2
0 .2 1 06
M e xic o
3 .3 7 56
1 .1 5 48
1 .3 3 36
2 .0 3
6 .9 9
0 .3 4 21
5 .1 8 3
1 .8 5 75
3 .4 5 04
1 .8 7
7 .5 5
0 .3 5 84
N o rw a y
4 .5 6 81
1 .0 2 83
1 .0 5 74
2 .6
6 .4
0 .2 2 51
N e w Z e a la n d
7 .3 7 11
1 .6 3 28
2 .6 6 61
5 .2 4
1 1 .0 1
0 .2 2 15
P o rtu g al
5 .1 6 65
1 .2 8 93
1 .6 6 24
1 .8 9
7 .4
0 .2 4 96
Sweden
5 .3 5 72
2 .4 2 9
5 .9 0 02
1 .4
8 .6 4
0 .4 5 34
USA
5 .5 4 44
1 .0 4 9
1 .1 0 03
3 .9 7
7 .6 3
0 .1 8 92
A g g re g ate
7 .9 5 37
1 .5 0 69
2 .2 7 08
5 .6 3
1 0 .7 7
0 .1 8 95
EU
S p a in
N e th e rlan d
Macroeconomic Themes:9
18
References
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Macroeconomic Themes:9
Y ellen J. L (1 9 8 4 ) E fficienc y w a g e m o d els o f u ne m p lo ym e nt, A E A p ap ers and p ro ceed ings vo l.7 4 N o .2 ,
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19