Download Globalization

Globalization and Disinflation: A Note
by
Assaf Razin
[email protected]
11/16/2004
Abstract
We analyze how globalization forces induce monetary
authorities, guided in their policies by the welfare
criterion of a representative household, to put greater
emphasis on reducing the inflation rate than on
narrowing the output gaps.
I.
Introduction
Ken Rogoff (2003, 2004) elaborates on some favorable
factors that have been helping to drive down global
inflation in the 1990s.
An hypothesis, which he put
forth, is that the “globalization—interacting with
deregulation and privatization—has played a strong
supporting role in the past decade’s disinflation.” But, a
significant portion of the improved performance of
inflation is possibly because resulted from a reorientation
of central bank policies towards a greater emphasis on
keeping inflation low. Thus, it is interesting to explore
what has guided monetary authorities in the pursuit of
low inflation in the 1990s, in the presence of strong
forces of globalization.
This note considers how the output-gap and inflation
weights, in a utility-based loss function of the monetary
authority, are affected by opening of the country to trade
and by the liberalization of the international capital
flows.
II. Utility Based Welfare Criterion
Michael Woodford (2003, Chapter 6) demonstrates how
to derive a quadratic loss function from a standard
welfare criterion of a representative household. The
welfare criterion, from which he derives a quadratic loss
function, is the expected utility of the representative
household, given by
 

E   tU t 
 t 0

Where,
1
U t  u (Ct ; t )   w(ht ( j );  t )dj 


0
Ct
.
is an index of differentiated products that constitutes
aggregate consumption,
At f (ht ( j )) is
ht ( j ) is
the labor supply to, and
the production function of variety j, and ( At ,
t )
are
productivity and preference shocks. The aggregate output is
specified as Y
t

   yt ( j )
 0
1
 1


dj 


 1
, and
Pt
is the corresponding
aggregate price level.
Let
 ( yt ( j ))  w( f 1 ( yt ( j )
condition
1
).
At
Then, using the closed economy
C=Y,
function y ( j)  A
t
t
f (ht ( j )) ,
and
the
production
we get:
1


U t  u(Yt ;  t ))    ( y t ( j );  t , At )dj  .
0


Real marginal costs are:
s( y ( j ), Y ;  , A)  v y ( y ( j );  , A) / uc (Y ; ) .
It follows that the elasticity of
v y ( y ( j );  , A)
with respect to y
is given by  , and the elasticity of real marginal cost s with
respect to Y is given by
 1  
Y ucc
 0.
uc
Efficient Level of the Output Gap
The steady state level of output is given by
s (Y , Y ;0,1)  v y (Y ;0,1) / uc (Y ;0) 
(1   )

 1 
,

The symbol
Summarizes the overall distortion in the steady
state output level as a result of both taxation and market power:
(1)  is the Woodford-Rothemberg sales-subsidy (financed by
lump sum taxes) that aims at neutralizing the monopolistic
competition inefficiency in the steady state); and
(2)


 1
is the mark up as a result of producers’ market
power.
Efficient (zero mark up) output is thus given by
s(Y *,Y *;0,1)  1 .
Note that
Y /Y *
Is a decreasing function of  , equal to one
when   0 .
This property enables us to get the approximation
log( Y / Y *)  (   1 )
.
We can naturally define
x*  log( Y / Y *)  (   1 )
efficient level of the output gap.
as the
Quadratic Approximation for U
A quadratic approximation of the utility function is given by



1
2
1
(   )( x t  x*)  (   ) var j y t ( j )


n




y ( j)
y t ( j )  log( t ); x t  Y t  Y t ; Y t  log( Yt / Y )
Y
*
Y
x *  log( )
Y
Ut  
Y uc
2




.
(3)

var j y t ( j )   [ y t (1)  E j y t ( j )] 2  (1   )[ y t (2)  E j y t ( j )] 2



E j y t ( j )   y t (1)  (1   ) y t (2)
(See derivation in the Appendix).
Cross-Variety Dispersion Measure in the Utility Criterion
Equation (3) can be rewritten
Ut  
Y uc
2



1
2
1
(   )( x t  x*)  (   ) var j y t ( j ) .


Where, the term (   1 )( xt  x*) 2 originates from


u(Yt ;  t ))  ,



And the term (   1 ) var j y t ( j ) originates from
1
  ( y ( j );  , A )dj .
0
t
t
t
The familiar Dixit-Stigliz preferences over differentiated goods
imply

 p j) 
y t ( j )  Yt  t 
 Pt 
log y t ( j )  log Yt   (log p t ( j )  log Pt )

var j log y t ( j )   2 var j log p t ( j )
Ut  

.
Y uc
(   1 )( x t  x*) 2   (1   ) var j log pt ( j )
2
Inflation and Relative Price Distortions
We postulate a
( ,1   ) split
between the goods prices that are fully
flexible (group 1) and the good prices that are set one period in
advance (group 2).
The aggregate supply relationship is:
 t  E t 1 t  x t

  1  
1   1  
.
Now we exploit the property that
log p t( 2 )  E t 1 log p t(1)
log Pt   log pt(1)  (1   ) log pt( 2 )

 t  Et 1 t   [log pt(1)  E t 1 log pt(1) ]
  [log pt(1)  log p t( 2 ) ]

var j log p t ( j )   (1   )[log pt(1)  log pt( 2 ) ] 2

1

[ t  E t 1 t ] 2
And substituting this relationship into U, yields
U t  (cons tan t ) Lt
1
1



Lt  ( t  Et 1 t ) 2 
( xt  x*)2
 1   1  
x*  (   1 ) 1 
.
This means that Aggregate output and inflation
variations are proper arguments in the welfare
function. It is the output gap and the unexpected
inflation); and the relative weight that is placed
upon the two objects is related to slope of the
aggregate supply.
III. The Open Economy
Razin and Yuen (2002) extended this closedeconomy
framework
to
an
open
economy.
Specifically, they derive the slope of the aggregate
supply relationship for various openness regimes.
Perfect Capital Mobility
If capital is perfectly mobile, then the domestic agent has a
costless access to the international financial market. As a
consequence, household can smooth consumption similarly
in the rigid price and flexible price cases.
=>
Cˆ t  Cˆ tN
The Aggregate-Supply curve is:
 t  E t 1 t 

  n ˆ h ˆ N (1  n) ˆ f ˆ N  1  n  1

(Yt  Yt ) 
(Yt  Yt ) 
eˆt  E t 1 eˆt 

1   1  
1  
n 1 


,
where, ê is a proportional deviation of the real exchange rate from
its corresponding steady state level, and
Yˆt f
is a proportional
deviation of the rest-of-the-world output from its corresponding
steady state level.
The approximate utility function is:
U t  (cons tan t ) Lt
Lt  ( t  E t 1 t ) 2 
1 
n
( x t  x*) 2
 1   1  
x*  (   1 ) 1 
Where, n denotes the number of domestically produced
goods, and 1-n denotes the number of imported goods. .
Closing the Capital Account
If the domestic economy does not participate in the
international financial market, then there is no possibility of
consumption smoothing, and we have that:
Cˆ t  Yˆt ; Cˆ tN  Yˆt N
In this case, the Aggregate-Supply Curve is:
 t  E t 1 t 

  n   1 ˆ h ˆ N (1  n) ˆ f ˆ N  1  n  1

(Yt  Yt ) 
(Yt  Yt ) 
eˆt  E t 1 eˆt 

1    1  
1  
n 1 


, where, e denotes the real
exchange rate.
The Loss function is:
U t  (cons tan t ) Lt
Lt  ( t  E t 1 t ) 2 
1  1 
n
( x t  x*) 2
 1    1   1  
x*  (   1 ) 1 
Closing the Trade Account (Back to the Closed
Economy)
If both the capital and trade accounts are closed, then the
economy is an autarky, completely isolated of the rest of
the world. In this case, all the goods in the domestic
consumption index are produced domestically, which
means that n = 1.
The Aggregate Supply Curve becomes:
 
1 
 t  E t 1 t  
    1  ˆ h ˆ N
(Yt  Yt )

 1   
The loss function is:
U t  (cons tan t ) Lt
Lt  ( t  E t 1 t ) 2 
1  1   1  
( x t  x*) 2
 1    1   1  
x*  (   1 ) 1 
IV. Comparing the Output Gap and Inflation Weights
in the Loss Function
The weight of the output gap in each one of the openness
scenarios is given by:
(i)
1 
n
 (1   )(1   )
1
Goods Mobility)
(Perfect International Capital and
(ii)
2 
1  (n   1 )
 (1   )(1   )
(Closed Capital Account and Open
Trade)
(iii)
1  (   1 )
3 
 (1   )(1   )
(Fully Closed economy)
We can see that,
1  2  3 .
(Note that we implicitly assume that the price-setting
fractions
( ,1   )
across the different openness scenarios are the
same; empirically this assumption can be relaxed1).
This means that successive rounds of opening reduce the
output gap weight in the utility-based loss function.
1
The degree of inflation persistence is indicated in the model by the vector ( ,1   )
.A
recent ECB's
inflation study found that retail prices changed, on average, only once every year in the Euro-zone,
compared with every second quarter in the US. When price changes occur in the Euro-zone, they tend to
be large - between 8 and 10 per cent in the retail sector.
V. Conclusion
Global inflation has dropped from 30 percent a year to
about 4 percent a year. At this period a massive
globalization process also swept emerging markets in Latin
America and East Asia. This note put forth the hypothesis
that globalization induces the monetary authority, guided in
its policy by the welfare criterion of a representative
household, to put more emphasis on reducing inflation, at
the expense of larger output gaps. In such an endogenous
policy set up, globalization motivates central banks to
engage in pro-active disinflation policies.
References
Razin, Assaf and Chi-Wa Yuen (2002), “The "New Keynesian"
Phillips Curve: Closed Economy vs. Open Economy,” Economics
Letters, 75, May 2002, pp. 1-9.
Rogoff, Ken (2003), “Disinflation: An Unsung Benefit of
Globalization?” December 2003, Volume 40, Number 4: 5556.
Rogoff, Ken (2004), "Globalization and Global Disinflation," in
Federal Reserve Bank of Kansas City, Monetary Policy and
Uncertainty: Adapting to a Changing Economy, forthcoming
in 2004.
(Paper presented at a symposium sponsored by the Federal
Reserve Bank of Kansas City, at Jackson Hole, WY, August
28-30, 2003.)
Woodford Michael, (2003), Interest and Prices:
Foundations of a Theory of Monetary Policy, Princeton
University Press.
Appendix:
Derivation of Equations (2) and (3)
Approximate


Yt
 1  Yt  (Yt ) 2 . Then,
Y


~

1
1 
ucc (Yt ) 2  uc Y t  ( t , At )' u ( t , At )
2
2
_







1
1
1 
 u uc Y  (Y t  (Y t ) 2 )  u  t  (Y ) 2 ucc (Yt ) 2  uc Y  t Yt  ( t , At )' u ( t , At )
2
2
2



2
2
1
 Yt uc Y  (Y uc  Y ucc ) (Yt ) 2  Y ucc g t (Yt ) 2
2



1
 Y uc [Yt  (1   1 ) (Yt ) 2 ]   1 g t (Yt )
2
_
u(Yt ;  t , At )  u uc Y  u  t 

_
u  u(Y ;0,1); Yt  Yt  Y

gt  
Using
uc  t
Y ucc
v y (Y ;0,1) / uc (Y ;0) 
(1   )

we get an approximation for the term:

v ( yt ( j );  t ) :
_
_




1
v ( y t ( j );  t )  v  u c Y [ y t ( j )  (1   )( y t ( j )) 2  q t y t ( j )]
2



1
 uc Y [(1   ) y t ( j )  (1   )( y t ( j )) 2  q t y t ( j )]
2


y t ( j )  log(
yt ( j)
Y
); q t  
v y  t
Y v yy
.
1 




1
2
v
(
y
(
j
);

)

u
Y
[(
1


)
E
y
(
j
)

(
1


)[
E
(
y
(
j
))

var
y
(
j
)]


q
E
y
t
t
c
y
j
t
j
t
t
t
j
t ( j )]
0
2





1
1
Y uc [(1   y ) Y t  (1   )[(Y t ) 2  q t Y t ]  [( 1   ) var j y t ( j )]
2
2





var j y t ( j )   [ y t (1)  E j y t ( j )] 2  (1   )[ y t (2)  E j y t ( j )] 2



E j y t ( j )   y t (1)  (1   ) y t (2)
, where,

E j ( yt ( j ))
is the mean value of
differentiated goods, and

var yt ( j )

y t ( j ) across
all
is the corresponding variance.
Finally, going back to U, we get:




1
1
U t  Y uc [( y ) Y t  ( 1   )[(Y t ) 2  ( 1 g t  q t )(Y t )  [( 1   ) var j y t ( j )] 
2
2

Yu 

 c ( 1   )( x t  x*) 2  ( 1   ) var j y t ( j )
2 


 n
xt  Y t  Y t
 n
Yt 
 1 g t  q t
 1  
 log(
Y
)  ( 1   ) 1 
Y*