Aggregate Supply and Potential
Output
Assaf Razin
Tel Aviv University and Cornell
University
Aggregate Supply and Potential
Output
The tradition in the monetary literature is that •
inflation is primarily affected by: (i) economic
slack; (ii) expectations; (iii) supply shocks; and
(iv) inflation persistence.
The paper extends the standard New- •
Keynesian aggregate supply relationship to
include also fluctuations in potential output, as
an additional determinant of the relationship.
It discusses whether potential output could be
made a target for optimizing interest rules.
Aggregate Supply and Potential
Output
The New-Keynesian aggregate supply derives from microfoundations an inflation-dynamics model very much like the
tradition in the monetary literature.
Inflation is primarily affected by: (i) economic slack; (ii)
expectations; (iii) supply shocks; and (iv) inflation persistence.
This paper extends the New Keynesian aggregate supply relationship
to include also fluctuations in potential output, as an additional
determinant of the relationship.
Optimizing Monetary Rules
Consider a micro-based loss function which is the discounted
value of a weighted sum of squared deviations of inflation from a
zero level (so as to minimize distortion price dispersions among
firms of identical technologies and demand schedules), the squared
deviations in output from target output, and the level of the output
target. The target output level is likely to be different from
potential output under monopolistic competition because of the
existence of a wedge between the marginal productivity of labor
and the leisure/consumption marginal rate of substitution.
A quadratic-linear optimal problem:
minimize a micro-based loss function, subject to the constraints: (1) Aggregate
supply relationship; (2) Government debt dynamics, and 3) the dynamic low
governing the potential accumulation of the stock of capital.
Conjecture: Optimizing interest rules would respond to potential output
changes in addition to inflation surprise and output gap.
Literature
Understanding why nominal changes have real consequences (why a
short run aggregate supply relationship exists) has long been a central
concern of macroeconomic research. Lucas (1973) proposes a model in
which the effect arises because agents in the economy are unable to
distinguish perfectly between aggregate and idiosyncratic shocks. He
tests this model at the aggregate level by showing that the Phillips curve
is steeper in countries with more variable aggregate maximal demand.
Following Lucas, Ball, Mankiw, and Romer (1988) show that stickyprice Keynesian models predict that the Phillips curve should be steeper
in countries with higher average rates of inflation and that this prediction
too receives empirical support. Loungani, Razin, and Yuen (2001), and
Razin and Yuen (2001) show that both Lucas’s and Ball-MankiwRomer’s estimates of the Phillips curve slope depend on the degree of
capital account restrictions.
Consumer’s Welfare



Et   s t u C s ;  s    10 v(hs ( j );  s dj   ( M s / P ) ,
s t
C is the Dixit-Stiglitz (1977) index of household consumption, P the Dixit-Stiglitz
price index:

  1
 1
1
Ct    ct  j   dj
0

1
1
1
Pt   pt  j 1 dj 
0

,
,
The Budget Constraint
n
p
t
(i )ct (i ) di 
0
 it

1 i
t



 M t  Bt  M t 1 

n
(1  it 1 ) Bt 1 

t
(i ) di
0
n

 w (i )h (i )di
t
t
0
n
Pt yt 
n
 w (i )h (i )di   
t
0
t
0
t
(i ) di
First Order Conditions
u m (ct ;  t )
it

uc (ct ;  t ) 1  it
uc (ct ;  t )
  (1  r )
uc (ct 1 ;  t 1 )
vh ( ht (i );  t ) wt (i )

uc (ct ;  t )
Pt
Consumption, Output, and Investment

 pt ( j ) 

ct ( j )  Ct 
 Pt 
yt ( j )  At f (ht ( j ))
I t  j   I kt 1  j  / kt  j kt  j ,

  1
1 i  1
I t  j     I t  j   di
0

,  1
Firm’s Optimization:
Nominal
VC  wt (i ) ht (i )  wt (i ) f
MC  S t (i )  wt (i ) (
(
Real
yt (i )
)
At
f '( f
mc  st (i ) 
1
(
yt (i )
)
At
yt (i ) 1
)
At
At
1
1
(
yt (i )
))
At
wt (i )
y (i ) 1
( t )

Pt
At
At
vh ( ht ;  t ) 1
y (i )
( t )
uc (Ct t ;  t ) At
At
Real Marginal Cost
st ( j ) 
wt ( j )
Pt At f ' ( f 1 ( yt ( j ) / At ;  t ))
vh ( f
~
s ( y , C ;  t , A) 
ytd  Yt (
1
( y / A ;  ))
uc (C ;  ) Af ' ( f
1
( y / A ;  t ))
pt (i ) 
)
Pt
p1t
 s ( y1t , Ct ;  t , At )
Pt


 1
1
  p1t
1    p2 t
Flexible prices
Set price one period in advance
Preset Nominal Prices
1
MaxEt 1
 t (i ) 
1  it 1
 1
MaxEt 1 
[ p2t y2t  wt ht ] 
1  it 1
1

 1
Y
P
p
MaxEt 1 
[Yt Pt p2t (i )1  wt f 1 ( t t 2t )]
At
1  it 1

1
Et 1
 t (i )
 1
1  it 1
 p2 t
 0  Et 1 
Yt Pt (
 s ( y2t , Ct ;  t , At )]  0
p2t (i )
Pt
1  it 1
Et 1  uc ( yt ;  t ) yt [   s ( yt ; yt ;  t )]  0
1
~
The Labor Market
W/P
Figure 1: Labor Market
Equilibrium
Marginal Factor Cost
Labor Supply
Mark
Down
Marginal Productivity
h
Investment
1 Pt 1
I '[kt 1 ( j ) / kt ( j )]  Et (
)
{qt 1 ( j )
1  it Pt
 (kt  2 ( j ) / kt 1 ( j )) I '[kt  2 ( j ) / kt 1 ( j )]  I [kt  2 ( j ) / kt 1 ( j )]}
 f  At ht ( j ) / kt ( j )   At ht ( j ) / kt ( j )    At ht ( j ) / kt ( j )  

qt  j   wt  j 
At f  At ht ( j ) / kt ( j ) 




1
*(1 ) 1
Pt  n[p11t  (1   )p12t  ]  (1  n) t p t
 1
pt
[np ]
1
1 /(1 )
 s (Yt N , CtN ;  t , At )
t
CtN  Yt N 
pt
[np ]
1
1 /(1 )
 s (Yt N , Yt N ;  t , At )
t
n 1
1  s ( KYt N , Yt N ;  t , At )
Potential Output


1  s K t , Yt , Yt  I t ;  t , At .
n
n
Steady state:
 (1  r )  1
 t  o, At  A, pt  p, Ct  C.

xt  log(

xt

x
)
xt  x

x
Log-linearized Model
log-linearize the marginal cost function around the deterministic steady state
equilibrium:
n
st  st



  yˆ t  yˆ tn   1

 n 

yˆ t  yˆ tn   1 Iˆt   p  k t  k t 





  w   p
 
cucc
uc
C Y I
w 
vhh
f 
, p   2
vh
f
Log-linearizing the two price-setting equations ,
the investment rule, [equation (7)], and using equation (8), yields:









log P1t   log Pt      1 yˆ1t  Yˆt n   1 Iˆt   p kˆ1t  kˆtn


log P2t   Et 1 log Pt      1 yˆ 2t  Yˆt n   1 Iˆt   p kˆ2t  kˆtn
 t  Et 1  t   log Pt   Et 1 log Pt 
     1  ˆ ˆ n  1 ˆ  p ˆ 
 t  Et 1 t  
Y Y 
I 
K

1     1    t t 1   t 1   t 


Aggregate Supply and
Investment




log P1t   log Pt      1 yˆ1t  Yˆt n   1 Iˆt   p kˆ1t  kˆtn





log P2t   Et 1 log Pt      1 yˆ 2t  Yˆt n   1 Iˆt   p kˆ2t  kˆtn
 t  Et 1  t   log Pt   Et 1 log Pt 
 t  ln Pt / Pt 1 
     1  ˆ ˆ n  1 ˆ  p ˆ 
 t  Et 1 t  
Yt  Yt 
It 
Kt 


1     1   
1   1   




Investment and Potential Output

1  s k , y , Yt  I t ;  t , At
Yˆt n1 
n
t
n
t
n

1
ˆ n   1 I n  u

K
p
t 1
t 1t
t
   1



A
ut 
d t 
dAt


 p Kˆ tn1   1I tn1  (   1 )Yˆt n1  ut
Aggregate Supply and Potential Output


1
    1 




n
n
ˆ
ˆ
ˆ
 Yt  Yt 
 t  Et 1  t  
Yt  ut 

1     1   
1  


 
cucc
uc
C Y I
  w   p
vhh
f 
w 
, p   2
vh
f
,
Conclusion
The paper demonstrates that potential output improves the inflationoutput gap trade-off. My intuition is that the task of the monetary authority,
which trades off inflation and output gaps is facilitated if they target
potential output, as well as the inflation fluctuations and the output gaps.
In so doing the monetary authority should be independent, so as not to
get trapped in Barro-Gordon dynamic inconsistencies. A Taylor-like rule
makes interest rate respond not only to the fluctuations in inflation
rates and output gaps, but also the fluctuations in potential output is
bound to raise the measure of consumer.
The Open-EconomyPhillips Curve

N

N

 N
s t  s t   ( y t  Y t )   1 (C t  C t )
  w   p
y
y
1
vhh ( )
f ' ' ( f (.))( )
A ,  
A
w 
p
vh f '
f ' ( f 1 (.)) f (.)
ucc y
 
uc
‘where
 uc (C ;  )
y
1

, ( ) 
A
1 y
ucc (C ;  )C
f ' ( f ( ))
A
Elasticity of marginal product of
labor wrt output
y
y
y
vhh ( f ( );  ) ( ) y  ' ( ) y
A
A 
A

y
1 y
vh ( f ( );  ) A
 ( )y
A
A
1
Elasticity of wage demands,
wrt to output, holding
marginal utility of income
constant
Log-linearization of real mc:
s ( yt ; yt ;t ) 
y (i )
y (i )
vh ( t ;t ) ( t )
At
At
uc ( yt ;t )
 F ( yt (i );t )
_
_ y
1 F
yt (i )
1 F
1 F
t
log( si )  log( si ) ss 
( A  At ) 
ss ( yt (i )  yt (i )) _ 
ss ( yt )  yt ) _ 
si yt (i )
si yt
si At ss t
yt (i )
yt



n
st (i )   y t (i )   1 y t  (   1) y t
Partial-equilibrium relationship?
Aggregate Supply

1  s k tn , y tn , Yt n  I t ;  t , At
Yˆt n1 


1
 p Kˆ tn1   1 I tn1t  u t
1
 
ut 



d t  A dAt


 p Kˆ tn1   1I tn1  (   1 )Yˆt n1  ut
 t  Et 1  t  


    1 

   1 ˆ n
 Yˆt  Yˆt n 
Yt  ut 

1     1   
1  


 t  Et 1  t  


    1 

 Yˆt  Yˆt n 

1     1   



N
 N

log( p1t )  log( Pt )   ( y1t  Y t )   (Ct  C t )

1
N

 N
log( p2t )  Et 1[log( Pt )   ( y2t  Y t )   (Ct  C t )]
1
log( Pt )  n[ log( p1t )  (1   ) log( p2t )]  (1  n) log(  t pt* )
Pt
Pt *
 t  log(
),  t  Et 1 ( t )  log( Pt )  Et 1 log( Pt ), et   t
Pt 1
Pt
  n  H  N
(1  n)  F  N
 1  F  N 
 t  Et 1 ( t )  (
) (
)(Y t  Y t )  (
)(Y t  Y t )  (
)(C t  C t ) 
1    1  
1  
1  


1 n  1
(
) (
) log( et )  Et 1 log( et ) 
n  1 


N

 N
log( p1t )  log( Pt )   ( y1t  Y t )   (Ct  C t )

1
N

 N
log( p2t )  Et 1[log( Pt )   ( y2t  Y t )   1 (Ct  C t )]
W

y jt  Y t   [log( p jt )  log( Pt )]
W
H
F
Y t  n Y t  (1  n) Y t
W
N

 N

1
1
log( p1t )  log( Pt ) 
(Y t  Y t )  
(Ct  C t )
1  
1  
W
N

 N

1
log( p2t )  Et 1[log( Pt ) 
(Y t  Y t )   1
(Ct  C t )]
1  
1  
log( p2t )  Et 1 log( p1t )
log( Pt )  n[ log( p1t )  (1   ) log( p2t )]  (1  n) log(  t pt* )
log( Pt )  Et 1 log( Pt )  n[ log( p1t )  Et 1 log( p1t )]  (1  n)[log(  t pt* )  Et 1 log(  t pt* )]
 n[ log( p1t )  log( p2t )]  (1  n)[log(  t pt* )  Et 1 log(  t pt* )]
 1 
*
log( p2t )  
[log( Pt )  n log( p1t )  (1  n) log(  t pt )]
n
(
1


)


 
log( Pt )  Et 1 log( Pt )  
1  
P*
et   t t
Pt


1  n  1
[log( p1t )  log( Pt )]   n  (1   ) log( et )  Et 1[log( et )] 




W
N

 N 
   

1
1  n  1
1
 (
log( Pt )  Et 1 log( Pt )  
(
Y

Y
)


(
C

C
) log( et )  Et 1[log( et )] 
t
t
t ) 

t



1  
1    1  

  n  1  
P
 t  log( t ),  t  Et 1 ( t )  log( Pt )  Et 1 log( Pt ),
Pt 1
 t  Et 1 ( t )  (
(
H
N
 n
(1  n)  F  N
 1  F  N 
) (
)(Y t  Y t )  (
)(Y t  Y t )  (
)(C t  C t ) 
1    1  
1  
1  



1 n  1
) (
) log( et )  Et 1 log( et ) 
n  1 

Perfect Capital Mobility


N
 (1  r*)  Ct  0  C 
t
  n  H  N
(1  n)  F  N 
 t  Et 1 ( t )  (
) (
)(Y t  Y t )  (
)(Y t  Y t ) 
1    1  
1  


1 n  1
(
) (
) log( et )  Et 1 log( et ) 
n  1 

Closing the capital account:

H
 N
N
Ct  Y t ,Ct  Y t 
 n   1  H  N
(1  n) 1  F  N 
 t  Et 1 ( t )  (
) (
)(Y t  Y t )  (
)(Y t  Y t ) 
1    1  
1  



1 n  1
(
) (
) log( et )  Et 1 log( et ) 
n  1 

Closing the trade account:
n 1
    1  H  N 
 t  Et 1 ( t )  (
) (
)(Y t  Y t ) 
1    1  


Sacrifice Ratios in Closed vs.
Open Economies: An Empirical
Test
Prakash Loungani, Assaf Razin, and
Chi-Wa Yuen
Background
Lucas (1973) proposed a model in which the effect arises
because agents in the economy are unable to distinguish
perfectly between aggregate and idiosyncratic shocks; he
tested this model at the aggregate level by showing that the
Phillips curve is steeper in countries with more variable
aggregate demand. Ball, Mankiw and Romer (1988) showed
that sticky price Keynesian models predict that the Phillips
curve should be steeper in countries with higher average
rates of inflation and that this prediction too receives
empirical support
DATA
The data used in the regressions reported in this paper are taken from
Ball (1993, 1994) and Quinn (1997).
Sacrifice ratios and their determinants: Our regressions focus on
explaining the determinants of sacrifice ratios as measured by Ball. He
starts out by identifying disinflations, episodes in which the trend
inflation rate fell substantially. Ball identifies 65 disinflation episodes
in 19
OECD countries over the period 1960 to 1987. For each of these
episodes he calculates the associated sacrifice ratio. The denominator
of the sacrifice ratio is the change in trend inflation over an episode.
The numerator is the sum of output losses, the deviations between
output and its trend (“full employment”) level.
Sacrifice ratios and their determinants: Our
regressions focus on explaining the
determinants of sacrifice ratios as measured
by Ball. He starts out by identifying
disinflations, episodes in which the trend
inflation rate fell substantially. Ball identifies
65 disinflation episodes in 19 OECD countries
over the period 1960 to 1987. For each of these
episodes he calculates the associated sacrifice
ratio. The denominator of the sacrifice ratio is
the change in trend inflation over an episode.
The numerator is the sum of output losses, the
deviations between output and its trend (“full
employment”) level.
For each disinflation episode identified by Ball, we use as an
independent variable the current account and capital account
restrictions that were in place the year before the start of the
episode. This at least makes the restrictions pre-determined with
respect to the sacrifice ratios, though of course not necessarily
exogenous.
Capital Flow Restrictions
Quinn (1997) takes the basic IMF
qualitative descriptions on the presence of
restrictions and translates them into a
quantitative measure of restrictions using
certain coding rules. This translation
provides a measure of the intensity of
restrictions on current account
transactions on a (0,8) scale and
restrictions on capital account
transactions on a (0,4) scale; in both cases,
a higher number indicates fewer
restrictions. We use the Quinn measures,
labeled CURRENT and CAPITAL,
respectively, as our measures of
restrictions.
Sacrifice ratios and Openness Restrictions
Independent variable
(1)
(2)
(3)
(4)
Constant
-0.001
(0.012)
-0.059
(0.025)
-0.033
(0.022)
-0.058
(0/026)
Initial inflation
0.002
(0.002)
0.003
(0.002)
0.003
(0.002)
0.003
(0.002)
Length of Disinflation
0.004
(0.001)
0.004
(0.001)
0.004
(0.001)
0.004
(0.001)
Change of inflation
during episode
-0.006
(0.003)
-0.007
(0.003)
-0.006
(0.003)
-0.007
(0.003)
CURRENT
0.008
(0.003)
CAPITAL
0.010
(0.006)
OPEN
0.006
(0.002)
Adjusted R-Square
0.16
0.23
0.19
0.23
Number of
observations
65
65
65
65
Numbers
In parantheses
are
standard
errors
Conclusion
In our earlier work we showed that restrictions of
capital account transactions were significant
determinants of the slope of the Phillips curve, as
measured in the studies of Lucas (1973), Ball-MankiwRomer (1998), and others.
The findings of this note lend support to this line of
work, in particular to the open economy new
Keynesian Phillips curve developed in Razin and Yuen
(2001). We find that sacrifice ratios measured from
disinflation episodes depend on the degree on
restrictions on the current account and capital
account. Of course, to be more convincing this finding
will have to survive a battery of robustness checks,
such as sub-sample stability, inclusion of many other
possible determinants (such as central bank
independence) in the regressions, and using
instruments to allow for the possible endogeneity of
the measures of openness.