Transcript Trade in Capital Goods By Jonathan Eaton and Samuel Kortum There are a couple of good recent papers that look at equipment.

Trade in Capital Goods
By
Jonathan Eaton and Samuel Kortum
There are a couple of good recent papers that look at equipment prices
and growth or productivity
Greenwood, Hercowitz, and Krusell, 1997. "Long-Run Implications of
Investment-Specific Technological Change". American Economic Review
873, 342-362. Uses Gordon's (1982) quality-adjusted prices for
equipment to measure technological progress in capital goods production.
Includes this in a standard neoclassical model and finds that it is
large. Leads to a puzzle in that the productivity slowdown is even more
severe once this quality correction is made. Nice paper.
Restuccia and Urrutia, "Relative Prices and Investment Rates."
http//www.chass.utoronto.ca/~diegor/research.html I think this paper is
coming out in the JME. It argues that differences in the relative price
of capital have strong explanatory power for differences in investment
rates and provides a model and calibration of this.
Jovanovic and Rob, "Solow versus Solow"
http//www.econ.nyu.edu/user/jovanovi/
Argues that a vintage capital model (Solow 1960) does a better job of
explaining differences in income levels across countries than a Solow
1956 model. Relative price of capital/equipment is used to measure
distortions to capital across countries.
Six Stylized Facts:
Rich Countries are specialized in
equipment production;
ºPoor countries import most of their equipment from only
a FEW developed countries;
ºEquipment trade displays
home bias;
ºEquipment investment as a share of GDP
has no relation to income per capita;
ºThe relative price of equipment goods in terms
of consumption goods decline with income per capita;
Stylized Facts
• A small group of R&D intensive countries
are the most specialized in equipment
production;
• Poor countries import much of their
equipment, most of which comes from just
a few large exporters;
(continue)
• Equipment is traded more than manufactures as
whole, yet this trade displays home bias and other
effects of geography;
• The price of equipment (relative to the price of
consumption goods) declines dramatically over
time, and with development, reflecting
technological innovations.
A Textbook North-South Model
Qik  Ai F ( K ik , Lki )
Qiy  F ( K iy , Liy )
i  N, S
trade  costs :
dk,d y 1
AN  AS
.
.
AN AS

g0
AN AS
Simplifying assumption:
no international borrowing, implying that:
Yi  Pi k Qik  Pi yQiy  Pi yCiy  Pi k Ii
TRADE
PSy  1
P d
y
N
y
P  P / AN  d / AN
k
N
y
N
y
PSk  d k PNk  d k d y / AN
YS  F ( K S , LS )  LS f (k S )
YN  P AN F ( K , L )  P L f (k N )
k
N
k
N
k
N
y
N
y
N
 P AN L f (k N )  P L f (k N )  d LN f (k N )
k
N
k
N
y
N
y
N
y
Per Capita Income
yS  (YS / P ) / LS  f (k S )
y
S
k  k  kN
k
N
y
N
y N  [ P AN L f (k N )  P L f (k N )] /[ L  L ]
k
N
 d f (k N )
y
k
N
y
N
y
N
k
N
y
N

U i   e  it ln Ci (t )dt
0
f (k )  k 
dk d log(k  )
k  1 dk
gy   
 
k dt
dt
k dt
dk

  (g y  g)
kdt
.
ri   i 
Ci

 i 
g
Ci
1
Pi k K i
Pi k K i
Pi k 1
i 
 y 1   y (k )
Yi
Pi Li K i
Pi
ki  yi
i 
k

Pi
(
y
i
Pi y
1

 k 
)  yi   k i y 
 Pi / Pi 

1
Rental price of capital compensate the owner of
for the cost of capital,r, depreciation, and the falling price
g
k
of capital, g.
q  (r    g ) P  [  
  ]P k
i
i
i
i
1
i  N, S
Ki
  qi
Yi
i 
ºHigher price of y in
the North by a factor
ºFalling price of
capital at rate g

g
[ i 
 ]
1
AS f ' (k S )(ri    g )d k d y
AN f ' (k N )(ri    g )
rS  rN
d k d y  1  k N  k S  y N  yS
i
K t 1  K t

g
 gy  g  (
 1) g 
Kt
1
1
I t 1 K t 1  K t


K t 1
Kt
I
g
 
K
1
g
 ( 
)
Yi  Pi y Ci Pi k I i
1
si 


g
Yi
Y
i   
1
s=Saving rate


si

yi  
g Pi k
) y
 ( 
1   Pi

i  N, S







1
ºReal output per capita grows in parallel, driven by
ºtechnological change occurs in the North
ºSouth specializes in y
ºNorth diversifies in y and k
Ii
Pi y
ºreal investment are higher in the rich country N Yi / Pi y  si Pi k
ºsaving rates are similar across s and N
ºNo borrowing across S and N; interest rates are higher in S
It is the difference in the relative price of capital, not
differences in in saving rates, that drive the correlation
between output per capita and investment rate.
Income per capita is negatively associated with
the relative price of capital goods, which fall overtime
at a rate g.
Consistent with Young(1995), the model
show no TFP growth, but in contrast, it is the technological
change that drives capital accumulation, not thrift.
An expanded model captures the feature that developing
countries buy capital goods, which are heterogeneous, from
wide range of sources, including themselves.

 1
 1
1


K t    K ( j , t ) dj
Composite capital
0

Country i provide type j with quality z
zi ( j , t )
d ni  1
Shipping cost from i to n
p ( j , t )  cit d ni / zi ( j , t )
Buying j, from I by
pnk ( j , t )  min pnik ( j , t )
Lowest effective cost
k
ni
i
P r[zi  z ]  e
Tit z 
Extreme-value distribution
P r[p ( j , t )  p ]  1  e
k
ni
P r[pnk ( j , t )  p ]  1  e
Tit cit d ni p

Distribution of cost
N
Tit cit d ni p
i 1
Distribution of
Minimum cost
Three equations for the empirical implementation:
X nik Ti ci d ni

X nk
n
1
N

Pnk    Ti ci d ni 
 i 1



1


sn


yn  
k 
P
g
)( ny ) 
 ( 
1   Pn 

ln yn  an 
Ti 

ci 
n 
Dni 
N

ln  Ti ci Dni
(1   ) i 1
Stock of knowledge
Variability of quality
Production cost
Distribution of lowest cost source
In place of bilateral trade share
Implications for Equipment Prices:
How equipment prices differ across countries

  
 ln P   ln Ti ci d ni 
 i 1

N
k
n
ºEstimations:
ºProduction of Manufactures and equipment across countries
ºTrade in Manufactures and equipment
ºInvestment and prices
ºBilateral trade: gravity parameters
Empirical Strategy
First stage:Use trade volume and Price Equations to generate
Infered Capital Good Price Series
k

X
T
c
k
xni  ln nik  ln i i   ln d ni
X nn Tncn
Si  ln Ei  ln Ti   ln ci
xnik  Si  S n  mn  d k  b  l   ni
N
Pnk   [ Ti ci d ni ]
i 1

1

Second Stage:Connecting Steady State Productivity Levels with Savings
and Relative Price of Capital Goods