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PAPER SERIES
CONSUMPTION,
NON-TRADED
GOODS AND REAL EXCHANGE RATE:
A COINTEGRATION-EULER
EQUATION
APPROACH
Kenneth S. Lin
Working Paper 5731
NATIONAL
BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
August 1996
This paper was presented at the NBER East Asian Seminar on Economics.
This work is part of the
NBER’s project on International Capital Flows which receives support from the Center for
I thank Professor Ching-Sheng Mao and participants in the
International Political Economy.
Seminar for helpful discussions on an earlier draft. I also thank Professors Takatoshi Ito and Gian
Maria Milesi-Ferretti whose comments led to an improvement of the paper, and Ms. Chia-Wei Hong
for excellent research assistance. Any opinions expressed are those of the author and not those of
the National Bureau of Economic Research.
@ 1996 by Kenneth S. Lin. All rights reserved. Short sections of text, not to exceed two paragraphs,
may be quoted without explicit permission provided that full credit, including @ notice, is given to
the source.
NBER Working Paper 5731
August 1996
PRIVATE CONSUMPTION,
NON-TRADED
GOODS AND REAL EXCHANGE RATE:
A COINTEGRATION-EULER
EQUATION
APPROACH
ABS TRACT
This paper presents an empirical study of real exchange rate movements from a consumer’s
perspective.
Trade between two countries creates a link between real exchange rate and terms of
trade. It is the private consumption of non-traded goods that induces an equilibrium relationship
between real exchange rate and private consumption of traded and non-traded goods. We use Ogaki
and Park’s (1989) cointegration-Euler equation approach to explore long-run implications from the
equilibrium relationship. Given the stationary preference shocks assumption, the testable restriction
is that real exchange rate and private consumption of traded and non-traded goods in the home and
foreign countries are cointegrated. The empirical evidence suggests that private consumption in the
home and foreign countries accounts for a significant fraction of the long run movements of real
exchange rate in South Korea and Taiwan. Accounting for real government consumption does not
overturn the result.
Kenneth S. Lin
Department of Economics
National Taiwan University
21, Hsu-Chou Road
Taipei
TAIWAN
Private
Consumption,
Non-Traded
Goods and Real Exchange
A Cointegration-Euler
Equation
Kenneth
Rate:
Approachl
S. Lin
1. Introduction
This paper
presents an empirical
ments from consumer’s
perspective.
optimal choice of consumption,
study of real exchange
For the private agent’s intertemporal
the marginal rate of substitution
sumption
of two goods
exchange
rate is the relative price of the home country’s
must equal the corresponding
ket in terms of the foreign country’s
two countries
consumption
rium relationship
between
traded and non-traded
relative price.
Real
consumption
bas-
basket.
of non-traded
real exchange
goods
rat e and private consump tion of
goods.
tries and the bilateral real exchange
fluctuations.
rate all exhibit
Large, persistent
movements
and small cross-country
correlation
been separate
topics in international
research
few attempted
consumption
Trade between
that induces an equilib-
As displayed in Figures 1 and 2, private consumption
prisingly
for the con-
creates a link between real exchange rate and terms of trade.
It is the private consumption
different
rate move-
of aggregate
to account
in different coun-
clear trends and have
of real exchange
private consumption
macroeconomics.
for the comovement
rate
have
But sur-
between
private
in different countries and real exchange rate both in the short
run and in the long run.
one
exception
exchange
economy
country,
is Backus and Smith (1993).
with one traded
and an arbitrary
ing is that fluctuations
country
in aggregate
itive correlation
the discrepancy
and fluctuations
countries,
for each
ratio between
correlated
over time.
There
theory and evidence.
rate
However,
for the pos-
are two possibilities
First, preference
find-
foreign
in bilateral real exchange
they found little evidence
in the time series data.
between
good
One main theoretical
consumption
and are positively
based upon eight OECD
one non-traded
number of countries.
and home country
have similar dynamics
good,
They studied a dynamic
for
shocks are
1 This paper ww presented at the NBER Emt Asian Seminar on Economics,
This
work is part of the NBER’s project on International Capital Flows which receives support
from
the Center
Mao
and participants
thank Professors
an improvement
for International
Political
in the Seminar
Takatoshi
Economy,
for helpful
I thank Professor
discussions on earlier
Ito and Gian Maria Milesi-Ferretti
of the paper,
and Ms. Chia-Wei
1
Ching-Sheng
draft.
I also
whose comments
Hong for excellent
led to
research assistance.
not admitted
in their model.
When endowment
shock, it can only generate positive correlation
sumption
between changes in the con-
ratio and changes in the real exchange
identical preferences
In this paper,
Euler equation
approach
the Ogaki and Park’s
between
one testable
real exchange
Given the assumption
restriction
Here preference
an identifying
goods
via elements
of various
of stationary
preference
of these vari-
in the sense that they are
correlation
in different countries,
Preference
parameters
in the construction
in the theoretical
preferences
preferences
and weights used in the construction
but also
and weights as-
of price index determine
cointegrating
erogeneous
vector.
Het-
across countries induce dissimilarityy. When agents’
of price index are identical
across the two count ries, the real exchange rate becomes
to the cross-country
from the equilib-
shocks not only induce negative
assumption.
signed to non-traded
cointegration-
on the long run movements
between real exchange rate and consumption
the similarity
agents have
rate and consumption
ables is that they have similar trend properties
provide
(1989)
to explore long-run implications
goods in different countries,
cointegrated.
rate. Second,
across countries.
we adopt
rium relationship
shocks,
shock is the sole external
consumption
related to the cross-country
positively
related
disparity in traded goods, but negatively
consumption
There is very little empirical
disparity in non-traded
evidence
goods. z
that any known fundamentals
have reliable effects on the real exchange rate, Most previous studies on real
exchange
rate movements
the most popular
son (1964).
country
were taken from producer’s
hypothesis
is originated
It states that real exchange
difference
traded sectors.
in the productivity
Since significantly
sector is expected
tivit y growth
should
be evident
And
and Sameul-
reflect the cross-
differential between traded and non-
higher productivity y growth in the traded
growth economies,
of export
The real exchange
competitiveness.
growth mechanism
development
the positive
disparity in produc-
in those economies.
relation and underlying
tral research topic in economic
Symansky
rate movements
rate and cross-country
rat e has been a natural indicator
the positive
by Balassa (1964)
to occur in the export-led
relation between real exchange
perspect ive.3
Establishing
has become
(For example,
a cen-
Ito, Issard and
(1996))
2 Lucas (1982) also studied
rank the exportable
goods
a two-country
and importable
model
goods
in which the representative
according
to its preferences
agent
and must
use currency to purchase the goods.
The relative price of between these two goods
determined by the cross-country
difference in the endowments of these two goods.
3 Examples
include
Isard and Symsnsky
Alder
(1996),
and Lehman
(1983),
Hsieh (1982),
Kravis and Lipsey (1987)
2
Huizinga
and Strauss (1996).
(1987),
is
Ito,
Adler and Lehman
a stochastic
trend,
ity growth
evidence
biased
(1983) found that the real exchange
and argued that this might be due to the productivtoward
traded
sector.
for the role of productivity
elling the non-stationarity
rate. Recently,
between
Hsieh’s
differential
of productivity
differential
rate and productivity
Even though productivity
for a significant
fraction of the long-run movement
to justify
nation of real exchange
movement.
and real exchange
of non-traded
goods,
spending
exists
between
traded
can account
of real exchange
of real exchange
rate, it
approach
rate.
Re-
in the expla-
They found that the cross-country
can account
consumption
for the real exchange
is concentrated
an increase in government
relative price of non-traded
rate appreciates
movement
rate movement.
Since government
relationship
differentials
(1991) took an alternative
in government
mod-
growth rate in the traded sector would
the long-run
cent ly, Froot and Rogoff
provided
explicitly
differentials
goods.
seems a much higher productivity
study
without
and non-traded
difference
(1982)
Strauss (1996) found that a cointegrating
real exchange
be required
rate contains
in the purchase
consumption
goods to traded goods.
rate
increases the
Thus, the real exchange
in the country with a high growth rate of government
con-
sumption.
As documented
correlation
of output
productivity
account
the shocks produce
than fluctuations
for this discrepancy
have introduced
consumption
markets
in consumption
between
correlation
theory
(Kollmann
(1991))
of aggregate consumption
That is, the non-traded
shocks.
consumption
et al. (1992)),
When
the
component,
could be less imper-
is less imperfect.
goods can account
To
recent studies
cent ains the non-traded
do not share but consume
This is so
their own non-traded
for small cross-country
of consumption.
The remainder
of the paper is organized
derive the stationarity
restriction
rate and private consumption
tertemporal
that are less highly
in the model.
simply because
correlation
econ-
(Devereux
goods
goods.
In a single goods
and evidence,
fect if that of non-traded
countries
and
and productivity
utility function
basket in each country
the cross-country
countries.
cross-country
of consumption
output fluctuations
the non-separable
and the incomplete
(1992),
is larger than such correlation
shocks for many industrial
omy, however,
correlated
in Backus, Kehoe and Kydland
optimization
for the cointegration
the econometric
on the trend properties
from the Euler equation
problem.
These restrictions
Euler Equation
specifications
as follows.
approach.
concerning
3
In section
2, we
of real exchange
for the agent’s
in-
are the foundation
In section
the trend property
3, we describe
of individual
series like private consumption
of traded and non-traded
implications
for the stationarity
and reports
empirical
results.
restriction.
Section
The countries
goods
and their
4 explains
the data
under consideration
include
Japan, South Korea, Taiwan and United States. Japan, Taiwan and South
Korea ran huge trade surplus with United States, while Taiwan and South
Korea ran significant
tions are examined
country.
trade deficits with Japan,
with South Korea and Taiwan each serving as the home
The bilateral
real exchange
ties, and there is the cross-country
interesting
rates exhibit
disparity in private consumption.
for the long run movements
Korea and Taiwan.
Consider
two countries
is populated
goods.
Goods
Equation
in period
Yt” units of importable
goods
rate in South
remarks.
Approach
in a large world economy.
in the home country
export able goods,
of real exchange
with an infinitely-lived
It is
and non-traded
The last section cent ains concluding
2. A Cointegration-Euler
household
different trend proper-
to know the role of private consumption
in accounting
economy
Two sets of bilateral rela-
Imagine that each
representative
t is endowed
household.
with X:
The
units of
goods and Z; units of non-traded
Xt and Yt are costlessly traded in the world markets, while
Zt is only traded domestically.
The household
cording
ranks its consumption
stream, { (Xt Yt Zt )’, t ~ O} ac-
to its lifetime utility function:
[m
E~ ~~~u(xt,
t=o
Y~, Zt)
1
,
in which ~ is a constant discount factor with O < ~ < 1, and Et denotes the
mathematical
expectation
conditioning
on the information
the beginning
of time t, Ot. The intra-period
utility function,
set available at
U(X~, Y~, Z~),
is assumed to take the form:
x:-a=
_ ~
U(xt,Yt,Zt)= ~zt ~_ ~
Y:-”’
+ ~yt
the household
Let P.t,
goods
carried
for i = T, y, z, and preference
utility via the stationary
respectively.
from
period
goods
~ztz::”a-
in period
1
z
shocks are allowed to influence
processes:
{u~t, ~yt, U.t, t ~o},
Pvt and P,t be the prices of exportable
and non-traded
currency,
+
I–ag
x
Here ai >0,
– 1
t measured
goods,
importable
in units of domestic
Let bt+ 1 be the real value of international
t to period
t + 1 measured
4
asset
in units of exportable
and let rt be the real interest rate measured
household’s
budget
bt+l =
constraint
at time t is
;(Z; - Zt) + ~(u”– +
–Xt)
+(1 +
optimization
problem
Yt)
z
(X:
z
The representative
agent’s int ertemporal
mize the lifetime utility function
necessary
in units of export ables.
first-order
conditions
Et ~
[
subject
function,
au
1
(l+rt)-&
Euler equations
and the
are
=0,
and the budget constraint holds. Under our specification
utility
is to maxi-
to the budget constraint,
for this problem
axt+l
rt-l)bt
in the first-order
of the intra-period
conditions
can be ex-
pressed as
Uztxt–ffx
Y -~v
~yt
Pz t
‘G’
t
Pz~
—
– %“
aztzt–a=
Oztxt–a’
Taking the natural logarithm
where xt z logXt,
on both sides of the above equations
Pxt – Pyt + ~xxt – ~yYt = Uyt,
(1)
pzt
(2)
–pzt
+
axzt
–
ffz2t
=
Uzt,
yt = logYt, zt z log Zt, pit G logPEt7 for i = x, y, z, and
uzt = logaxt — Zogait, for i = y, z. In equilibrium,
must satisfy equations
If uzt is stationary
stationarity
restriction
goods,
prices and consumption
(1) and (2).
for i = y, z, then equations
(1) and (2) imply the
of both pZt —pyt + aZxt —avyt and pzt —pzt + azxt —aZzt. This
allows for different
depending
the restriction
goods
yields
trend properties
upon preference parameters.
allows goods
X consumption
i consumption
of consumption
of various
For example, when ai > a.,
to grow at a slower rate than
for any given path of relative price and preference
shocks and i = y, z. This is because
a given change in pit – pzt induces a
5
greater response of goods i consumption.
in home country
is described
Pt =
Suppose that general price index
by
ezpzt
+ gypvt
+ ezpzt
+
Uptl
in which pt is the logarithm
of the domestic
price index at time t, and 19Z
is the weight given to goods
i in the index with 8Z > 0 for i = z, y, z, and
8X+ 19Y+ d= = 1. The error term, uPt, captures the third country effect, and
is assumed to be uncorrelated
to eliminate pZt in equation
Pt
=
(ox
+
with pit, for i = x, y, z. We se this definition
(2):
‘Z)pzt
+
‘ypyt
+
axezxt
–
a.ezzt
in which Vzt z @zuzt — uPt. The foreign country’s
(3) is
.
fit
=
(6.
(3)
‘Zt,
counterpart
of equation
.
.
+
–
ez)j.t
+
‘y$yt
+
‘X6Zit
–
‘ZeZ2t
–
‘.17
.
in which
tizt s
parameters
t9ZtiZt — tiPt.
Here and from now on, all variables
pert aining to foreign country
For our purpose,
the real exchange
are designated
and
by a hat.
rate at time t, qt, is defined as
(4)
qt=pt–st–$t,
in which st is the logarithm
of nominal bilateral exchange
in st means an appreciation
parity (PPP)
between
doctrine
domestic
ments indicate
of domestic
states that nominal
and foreign prices.
deviations
the role of non-traded
currency.
To sharpen
rate moveour focus on
we assume that the law of one price holds for
the goods that are traded between the two countries.4
the following
power
rate equals the ratio
real exchange
from the PPP for pt.
goods,
The purchasing
exchange
Therefore
rate. A decrease
This is captured
by
relationship:
Pit = St + Fit,
for i = x, y. The assumption
of the law of one price may not be as restrictive
as it appears, we can easily abandon
in pat — St
— fiat,
this assumption by allowing movements
If these deviations
contain
a trend component,
that is,
4 The law of one price obtains if 1) markets are competitive,
2) there are no t ransportation costs, and 3) there are no barriers to trade, such as tariffs or quotas. Hsieh
(1982),
sumption
Fisher and Park (1991)
and Strauss
for the traded goods.
6
(1996)
among
others also adopted
this ~-
the PPP
for pzt or pYt does not hold in the long run, v.~ in equation
(3) will contain
in equation
trend component,
(3) is stationary
misspecification
provides
a diagnostic
equation
(3) and its foreign
(4) for pt and jt, respectively
country’s
two countries imposes an equilibrium relationship
terms of trade, and private consumption
If vt is stationary,
the comovement
perspective
of
qt,
equation
p.t
–
Xt,
(5) that trade between
among real exchange rate,
it,
,zt
the restriction
We call this restriction
the stationarity
restriction,
of cointegration-Euler
this restriction
does not require any use of budget constraint
equation approach.
relating to the intertemporal
cointegration-Euler
equation
approach
which is
The derivation
of
and first-order
choice of consumption.
allows for the existence
Hence the
of liquidity
or other financial market imperfections,
The stationarity
comovement
regulating
and ;t from the consumer’s
the foundation
constraints
into
of various goods in the two coun-
(5) imposes
pyt,
counterpart
that
is stationary,
conditions
for possible
yields
in which Vt s —vzt + tizt. It is clear from equation
tries.
analysis
residuals
errors.
Substituting
equation
Hence, checking if estimated
restriction
of individual
trend properties
has different long run implications
variables
of individual
in equation
variables.
(5), depending
for the
upon the
For example, if the PPP for pt holds
in the long run (that is, qt is stationary), then the stationarity restriction
.
requires that pzi — pyt, ~t, xt) Zt and ;t be cointegrated with the cointe,.
a
grating vector: (iv – 13y,H’)’, in which H’ = (aZ6’z, –&z6z, –azdz, &zOz).5
Suppose there is a change in nominal exchange rate caused by nominal factors, Both traded and non-traded
have a deterministic
influence
goods consumption
on the general price index in each country.
As a result, changes in consumption
of various goods in both countries have
to manage to maintain the long run relationship
5 Here we adopt the definition
in the two countries
of cointegration
between price ratios in the
given in Campbell
and Perron (1991,
p 164). An n x 1 vector of variables, St, is said to be cointegrated if there exists at least
one non-zero n-element vector ~ such that ~’S~ is trend stationary. This definition does
not require that each of individual
series in St contain
be trend stationary.
7
a unit root; some or all series can
two countries
and nominal exchange rate, and the nominal factors have ef-
fects only on the short run movements
if qt contains a trend component
grated with the cointegrating
restriction
of consumption.
and pzt —pvt, Zt, it, Zt and ;t are cointe-
vector:
implies that private
driving force for the long-run
On the other hand,
(eV – @y, H’)’,
consumption
movement
As argued in Hsieh (1982),
then the stationarity
in equation
(5) cannot
be a
of qt.
different weights (Hi) used in the construc-
tion of the price index can cause the movement
of qt. To see it, assume that
the law of one price holds for both goods X and goods Y and that there is
.
no non-traded goods in the world economy (0= = 19z= O). Then equation
(5) becomes
.
qt = (@y –
~y)(pzt
Clearly, it is the private consumption
link between
real exchange
Pyt)
changes with the real exchange
correlation.
economy,
then 6Y = 19y= 1 and equation
real exchange
in the model,
links terms of trade
.
19y# t9y and vt. = O,
When
say goods Y, in the world
(5) becomes
in Backus and Smith (1993),
qt = Vt, That
terms of trade can account
is,
the PPP for pt does
due to the presence of preference
rate movements
It is the
rate and terms of trade have
If there is only one goods,
hold exactly
that creates a
rate have similar dynamics.
imperfect
Even though
goods
the two countries
shocks that make real exchange
unlike the result obtained
~t.
consumption
rate changes.
terms of trade and real exchange
not necessarily
+
of non-traded
rate and private
On the other hand, trade between
preference
–
for a significant
here, the real exchange
shocks.
fraction
of
rate (qt ) does not
necessarily
have positive
correlation
with the terms of trade.
The sign of
correlation
is determined
by that of jy – 8V. To see this, consider an increase
in terms of trade (pZt – pyt ) caused by a lower price of import ables.
consumption
of importable
in foreign
country
domestic
currency
(in terms of a basket of goods)
negatively
units of foreign currency.
it is optimal
of import ables,
in home country
than
in the sense that 8V > 4V, then the value of a unit of
that of the equivalent
appreciates,
goods is more important
If
for private
must rise relative
When real exchange
agents to increase
rate
the consumption
For this case, terms of trade and real exchange
correlated
to
rate are
over time.
To identify other sources for the movement
of qt, assume that house-
holds in the two countries have identical preferences (ai = &i, for i = x, y, z)
and that the weights used in the construction
8
of price index are the same for
the two countries.
Given those assumptions,
equation
(5) can be reduced
to
gt = Qzoz(zt
It is obvious
– it) – azoz(zt
that the cross-country
and non-traded
cross-country
consumption
disparities for the traded
goods account for the movement
of qt: qt increases with the
consumption
disparity in traded goods but decreases with the
cross-count ry consumption
experienced
disparity in non-traded
a real appreciation
of its currency
rapid growth in private consumption
in that of non-traded
goods.
goods.
A country
had enjoyed
that
either a more
of traded goods or a less rapid growth
Since non-traded
expensive in the fast growing economies,
experience
– ~t) + Vt.
goods will be relatively more
the currency of these countries will
a real appreciation.
Clearly, without
preference
shocks and the third country
demand side, we cannot derive the long-run restriction
effect in the
on equilibrium
rela-
tionship among real exchange rate, terms of trade and private consumption.
For the productivity
differential models (for example,
(1982) and Sameulson
For example,
mobile
(1964)),
in Hsieh’s
between
productivity
(1982)
the tradable
model,
goods,
Balassa (1964),
Hsieh
shocks did not play such a role.
the supply of labor is fixed but is
and labor is the only input factor
production.
Then
the real exchange
rate is a deterministic
the following
variables:
non-tradable
sectors in both countries
function
in
of
productivity y differentials between the tradable and
and cross-country
disparity
in the
unit labor costs of the traded goods.
3. Econometric
The stationarity
restriction
strictions from the consumer’s
equilibrium
consumption
Specifications
summarizes
perspective.
Ogaki
(1992)
Instead of modeling
consider open exchange
achieved
shocks have stochastic
the production
economies
nities imply that the consumption
production
technology
of both exportable
side. For example,
the identification
in the supply side, we
in the world markets.
Trading opport u-
of goods X and Y in each country
in equilibrium.
may
For highly open economies
goods and importable
9
by
trends.
such as South Korea and Taiwan, the trend properties
sumption
parameters
restriction if the supply side exhibits
and Park (1989)
assuming that productivity
not equal domestic
and preference
in the long run than the demand
and Ogaki
re-
In the closed exchange economy,
equals its production,
can be identified from the stationarity
much more volatility
the long run equilibrium
of equilibrium
con-
goods are unlikely to be
closely related to their domestic
of preference
parameters,
shocks have stochastic
export
and import
duction.
production.
To achieve the identification
it is not sufficient to assume that the productivity
trend.
This can be done if the trend properties
activities
And productivity
do not offset those of the corresponding
shock is the dominant
of
pro-
driving force in the long
run,
In empirical
sumption
investigation,
of exportable
it is difficult to obtain the data on the con-
and importable
focus will be on the two goods
Let Xt denote
equation
case: traded goods
the traded goods.
(5) can be reduced
for the countries under study, The
Equation
goods
a.ezxt
–
.
‘Z”zit
–
~ztizzt
+
According
(1991)
even though
qt,
Zt,
ft,
+
(6)
Vt.
of various
movement
to the Campbell
of real
and Perron’s
the stationarity
and ;~ are cointegrated,
Zt
it
on the long-run
exchange rate in the two countries.
of cointegration,
&.@.
if private consumption
are capable of placing restrictions
implies that
restriction
not all the individual
series are required to contain a unit root. The stationarit y restriction
states that there exists at least a 5
;t such that Vt in equation
of trend stationary
For example,
x
1 vector:
Allowing
(6) has important
the presence
implications.
If
variables are trend stationary, it is trivially cointegrated.
if qt is trend stationary,
then one trivial cointegrating
unit vector which selects the trend-stationary
true, another cointegrating
trend components,
vector is
When the model is
That is, even private consumption
the st ationarit y restriction
that private consumption
variable.
vector is (1, H’)’ with a. dzxt –dz~z~t
&z19z2t being trend stationary.
real exchange
simply
(1, —H’) for qt, Ztl it, zt and
(6) is trend stationary.
variables in equation
some of individual
case,
to
(6) will be used to determine
definition
goods.
Since pzt = pvt in the two goods
.
qt =
and non-traded
–azdzzt
cent ains
does not necessarily
is a driving force for the long-run
+
imply
movement
of
rate.
To assess the empirical
across countries,
significance
of heterogeneous
we follow the tradit ion in international
utility function
trade and assume
ai = ~i for i = z, z and 6= = ~,. Then equation (6) can be further simplified
to
qt
If real exchange
=
–
it)
–
azez(zt
rate and the cross-country
it and Zt – 2t contain
restriction
azoz(zt
different
(7)
– ~t) + vi,
consumption
trend components,
disparity,
then the stationarity
implies that qt, xt — it and Zt — ;t are cointegrated.
10
xt –
However,
when qt is stationary,
the stationarity
the stationarity
restriction does not necessarily imply
of yt – ~t and Zt – ~t for the following
Zt — ;t can be cointegrated
with the cointegrating
that aZ8z(zt –it ) – azOz(zt – it) is stationary,
a lower income elasticity
qt forces Zt –it
than goods
vector:
yt – jt and
(aZOz, —azdz ) so
For this case, if goods X has
Z (aZ > a=), then the stationarity
to grow at a faster rate than Xt –it,
do not have long run effects on qt. In general,
Zt — it
reason.
and Zt — 2t does not imply
but private consumption
the cointegration
the stationarity
azOz(zt —it ), the absence of arbitrage opportunities
between
of aZ6z (zt – it)
in the non-traded
of aZ /az
and &Z/~Z can be identified
–
goods
between the two countries is very likely to induce the non-stationarity
Finally, the estimates
of
of qt.
in the above
two specifications.
4. Data
and Empirical
Results
As displayed in Figures 1 and 2, consumption
traded goods
and bilateral real exchange rate all exhibit clear trends.
focus here is to explore
the stationarity
restriction
that these series contain trend components,
for the trend property
tegrating
of both traded and non-
of individual
The
under the assumption
We first present statistical tests
series, and then estimate various coin-
regressions under the two specifications
and the weights given in the construction
of preference
parameters
of pt.
Data
The countries
Two
involved
sets of bilateral
are Japan, South Korea, Taiwan and the U.S.
relations
are examined
wan each serving as the home country.
with South Korea
Data on the exchange
and Tai-
rate of New
Taiwan dollars against U, S. dollar and Japanese Yen were taken from
wan Monthly
Financial
Stati~tics, while the exchange
rates of Korean Won
against the two foreign currencies were taken from International
Statistics
(IFS).
To study the sensitivity
of empirical
Tai-
Financial
results with respect
to the use of price index as the measure of general price level, the two selections of pt are: CPI and WPI (or PPI). Japan and South Korea price series
were taken from IFS. Taiwan price series were taken from Taiwan Natioanl
Income
Accounts,
while U.S. series were taken from BuTeau of Labor Statis-
tics. Let qj denote the real exchange rate when CPI is the measure of price
index, and let qiWdenote the real exchange
rate when WPI is the measure.
Following Kakkar and Ogaki (1993), the real consumption
on durable,
semi-du,rables
and non-durables
11
expenditure
is defined as the consumption
of traded goods,
while the real consumption
fined as the consumption
of non-traded
expenditure
goods.
and Zt were taken from Na-tional Accounts,
on services is de-
South Korea
published
data on Xt
by Bank of Korea,
while Taiwan series were taken from the Taiwan Natioanl Income
The Japan series on it and ;t were taken from OECD
Accounts,
of Commerce,
and services is constructed
tion expenditure
number
period
Quarterly
National
and U.S. series were taken from Survey of CuTTent Bu9ine~s, pub-
lished by Department
goods
Accounts.
by appropriate
by total population.
is 1975:1-1994:4
The per capita real consumption
as follows.
on
We deflate nominal consump-
price index, and then divide the resulting
All data are quarterly
series.
The sample
for Taiwan and U. S., and 1975:1-1993:4
for Japan
and South Korea.
Evidence
from time series data
The real bilateral
exchange
rates are displayed
in Figure 1, the plots
of zt, .zt, it and ~t in Figure 2, and those of Xt — it and Zt — ;t in Figure
3.
Three
points
a real appreciation
period.
First, Taiwan generally
worth mentioning.
of its currency
The nominal
depreciation
dollars caused a real depreciation
experienced
against U.S. dollars during the sample
of New Taiwan dollars against the U.S.
of Taiwan’s
currency
from 1981 to 1986,
and then the real value of New Taiwan dollars was pushed up under the
pressure of the U, S. when Taiwan enjoyed a sizable current account surplus
in the 1986-1989 period.
On the other hand, the bilateral exchange
rate of
Korean Won against the U.S. dollars exhibits a less clear upward trend. The
real depreciation
of Korean Won in 1980 and in the 1982-1986 was caused
by the continuing
nominal depreciation
of Korean Won against U.S. dollars.
When South Korea began to enjoy sizable current account
Korean
surplus in 1986,
Won was under pressure by the U.S. to have an unprecedented
appreciation
against the U.S. dollars through
depreciation
of the Won against the U.S. dollars were mainly due to two
factors:
the deterioration
and the appreciation
1989. After 1989, mild real
of South Korean international
payment
position
of Japanese Yen against the U.S. dollars since 1991.
As a result, the real value of Korean won against U.S. dollars fell to the level
of the late 1970s in 1993-1994.
South Korea and Japan exhibited
1975-1994
exchange
period.
The bilateral
rate between
a similar and clear upward trend in the
Unlike the real exchange
rate between
real exchange
rate in South Korea,
Taiwan and Japan exhibits a downward
volatile fluctuations.
12
the real
trend with
Second, the real per capita private consumption
goods and non-traded
goods contain different trend components
count ries. Third and finally, the cross-country
that the per capita real consumption
development.
expenditures
This evidence
in the private consumption
on traded
in the four
evidence in Figure 2 indicates
of services increases with economic
is also shown in the cross-country
on traded goods
and non-traded
disparities
goods
in four
pairs of countries.
Testing
the PPP
foT
doctTine
We first test the trend property
home country
and foreign country.
tain a trend component,
Otherwise,
property
If the real exchange
of bilateral
rate does not con-
then the PPP doctrine for pt holds in the long run.
it does not hold in the long run.
exchange
trine. For this purpose,
tests.
of bilateral real exchange rate between
Therefore,
rate is equivalent
to testing the PPP
we use Park and Choi’s (1988)
The null of difference
stationary
testing the trend
doc-
J(p, q) and G(p, q)
around the linear time trend is re-
jected when the J(I; q) statistic is smaller than the critical values tabulated
in Park and Choi (1988 ).6 We also report Park and Choi’s
test for the stationarity
stationarity).
tribution
According
(1988)
G(I, q)
of those series around the linear time trend (trend
to Park and Choi (1988),
G( 1, q) converges
in dis-
to a Xz(q – 1) random variable under the null of trend stationarity.
We reject the null when G(I, q) test statistic is larger than critical values.7
Table 1 displays test results for the trend property of bilateral real exchange
rate.
For qj and q~ between
2,3,4
cannot
reject
Taiwan and U. S., the J(l, q) tests with q =
the null of difference
time trend at the 10 % significance
of the trend stationarity
st ationarit y around
the linear
level. There is evidence against the null
of qj at the 5% significance
level in terms of G(I, 2)
and G(I, 4) tests. On the other hand, the G(I, q) tests with q = 2,3,4
weaker evidence
against the trend stationarit y of q:.
For q: between
difference
6 The
(ADF)
Taiwan and Japan,
stationary.
J(p,
an advantage
q)
The
test in that neither
J(l, 3) and J(I, 4) tests even reject it at the
and Perron’s
by the ADF
bandwidth
Carlo simulations.
variance,
estimator
variance
nor the order of autoregression
also show that the
test in small samples
small
and has
Dickey-Fuller
J(p,
q)
test has a
in terms of powers.
q when the sample size is small according
Here, we chose g = 2,3 and 4. For estimation
we use Andrews’
parameter
parameter
Carlo experiments
7 Kahn and Ogaki (1992) recommend
of the long-run
Za (Zt ) test and Augmented
the bandwidth
The Monte
stable size and is not dominated
long-run
J(l, q) tests all reject the null of
test does not require the estimation
over the Phillips
needs to be chosen.
to their Monte
yield
(1991)
based
quadratic
on AR(l).
13
spectral
of the
kernel with the automatic
1% significance
improved
level.
evidence
When
WPI
is the measure of pt, there is slightly
for the null of difference stationarit y for
The J( 1, 3)
q:.
and J(I, 4) tests still reject the null, and only J(I, 2) fails to reject it at
the 10% significance
evidence
level.
On the other hand, we did not find significant
against the null of trend stationarity
for both
q:
and
in terms
qtw
of the G(17 q) tests. a
There is conflicting
Korea and Japan.
stationarity,
also support
q =
2,3,4
null of trend stationarity
2,3,4
q:
The
q:.
all fail to reject the null of difference stationarity
level. Only the G(17 3) test fails to reject the
for q: at the 10% significance
level.
Finally, for
South Korea and U. S., both J(I, q) and G(I, q) tests with q =
provided
However,
On the other hand,
evidence for the difference stationarit y of
of q: at the 10% significance
q; between
But results of the G(I, q) tests with
the null of trend stationarity.
there is more consistent
J( 1, q) tests with
of qj between South
We found that the J(I, 2) and J(I, 4) tests cannot reject
the null of difference
q = 2,3,4
evidence for the trend property
significant evidence
for the null of difference
there is slightly weaker evidence for the difference
in terms of the J(1> q) tests.
onlY the G(172)
stationarit y.
stationarity
of
and G(l> 3) tests fail to
reject the null of trend stationarity.
Our empirical
lateral exchange
Korea/Japan,
findings
can be summarized
rates contain
First, the bi-
a unit root and linear time trend in South
South Korea/U.S.
and Taiwan/U.
tween Taiwan and Japan are stationary
results are generally
as follows.
consistent
S. cases. And q; and
around a linear time trend,
with the findings
in Corbae
These
and Ouliaris
(1988) and Fisher and Park (1991) using the data in other countries.
test the stationarity
of real exchange
that nominal exchange
coint egrat ing vector
the stationarity
in testing the trend property
long-run
by equation
of real exchange
deviation
They
rate based upon the null hypothesis
rate and price are cointegrated
implied
be-
q:
rate.
with the normalized
(4), and found evidence
Second,
of real exchange
of PPP for pt. Recently,
the measure of
against
pt
chosen
rate does not matter for the
based upon the data in other
count ries, Kim (1990) and Kakkar and Ogaki (1993) found more favorable
evidence
for the long-run
PPP when WPI is used as the measure of
pt
than
when CPI is used. They argued that a large weight given to the non-traded
8 We report the ADF test in Table 3 because it was widely used in the literature.
tests reject the null of difference stationary for both q; and q: in the
None of the ADF
Taiwan/J
apan and Taiwan/U
.S. cases.
In the following
discussion,
and G(p, q) test results when there is no conflicting
and the ADF test.
J(p,
q)
14
evidence
we only present
between
the
these tests
goods
in CPI could be the reason that the long-run
PPP
doctrine
based
upon CPI did not receive much empirical support.
Testing
the trend property
foT
of
private
consumption
Given the trend property of real exchange rate presented above, private
consumption
in different countries are required to exhibit trends in order to
account for the long-run movement
arity restriction.
of real exchange rate under the station-
Table 2 presents test results for the trend property
.zt, it and ;t, Here Zt and Zt are the home country’s
tion expenditures
on goods (durables,
services, respectively,
semi-durables
of zt,
real private consumpand non-durables)
while it and ~t are the foreign country’s
and
counterparts
of Zt and Zt, respectively,
First, for both Zt and Zt in Taiwan,
around
the linear time trend cannot
the null of difference
be rejected
level in terms of J(I, q) tests with q = 2,3,4,
q
=
2,3,4
all significantly
the difference
difference
at the 107o significance
and the G(I, g) tests with
reject the null of trend stationarity
stationarit y at the 1% significmce
stationarity
stationary
level. Second,
in favor of
the null of
for both Zt and Zt in South Korea received
strong
supports
from the J(I, q) tests, and the G(I, q) tests also yield significant
evidence
against the null of the trend st ationarit y for these two series, In
the light of the above results, we assume that both Zt and Zt in South Korea
and Taiwan contain a unit root and linear time trend.
we found
For the U.S. series of ;t,
difference
stationary
trend stationarity
around
weaker evidence
the linear trend.
for the null of
Even though
the null of
is rejected
at the 10% significance
level in terms of the
G(I, q) tests with q = 2,3,4,
both J(l, 2) and J(1,4)
tests reject the null
of difference
stat ionarit y at the 107o significance
there is significant
evidence
level. On the other hand,
for the null of difference
U.S. series of it. These results are also confirmed
tests.
stationarity
by results of the G(l, q)
For it and ;t in Japan, there is mixed evidence
stationarity.
stationarity
for the
for the difference
First, both J(l, 2) and J(I, 3) tests reject the null of difference
for it at the 10% significance
with q = 2, 314 cannot
the 10% significance
reject
level.
level.
Second,
the null of difference
They are consistent
the J( 1, q) tests
stationarity
of ;t at
with results of the G(I, q)
tests in Table 2. Based upon the test results on the trend property
of ~t, we
assume that it in Japan and U.S. contains a unit root and linear time trend.
Since the G(p, q) test tends to over-reject
the null when the autoregressive
root is close to one, the above findings can be viewed as conclusive
for the trend stationarity
of it in Japan and U.S.
15
evidence
Recently,
Ogaki and Park (1989) found significant evidence for the null
of the difference stationarity
for the U.S. data on ;t in terms of both J(I,
test and the Phillips and Perron’s
Za (Zt ) test, and evidence
against the
trend stationarit y of ;t in terms G( 1, q) tests at the 570 significance
level.
They used seasonally
adjusted monthly data on durables, non-durables
services
Income
in National
period
is from January
period
is used (February
stationarity
durable,
Testing
1959 to December
be rejected.
stationarity
cross-country
If preference
parameters
consumption
disparity
If domestic
disparity
(1992)
cointegrating
and it (and between
in different
the test
countries.
on traded goods
(non-
cointegrating
vec-
disparity for traded goods
in testing
the coin-
variable
the H(O, 1) statistic
restriction.
According
con-
under the null of
can be used to test the
to the H(p, q) statistics
against the cointegration
between
xt
Zt and it) for all possible pairs of home and foreign
the deterministic
cointegration
H(O, 1) test, while the stochastic
restriction
cointegration
the H(I, q) tests with q = 2,3,4
disparity
was rejected
restriction
obtained
for traded and non-traded
level.
These
in Figure
all clearly indicated
by the
was rejected
at the 1% significance
with visual impressions
test results and visual impressions
consumption
for the long-run
we conduct
H(p, q) statistics
to a X2(p – q) random
In particular,
sults are consistent
to account
consumption
pt
the cross-country
with the normalized
in Table 3, we found much evidence
countries:
country,
of
Park (1992) showed that the H(p, q) statistic
verges in distribution
deterministic
and non-
contains a trend component.
relationship.
cointegration.
on the
our results.
and foreign consumption
Here we use the Park’s
tegrating
on durables
private consumption
are not cointegrated
goods)
the null of the trend
For this purpose,
tor: (1, – 1), then the cross-country
(non-traded
consistent
and foreign
rate.
between
consumption
traded goods)
1986),
must be nonstationary
of real exchange
for the cointegration
1986. When the shorter sample
and weights used in the construction
across home country
and
The sample
Given the mixed evidence
consumption
are identical
movement
(NIPA).
for the consumption
their findings are generally
for
Accounts
1968 - December
for it cannot
null of difference
and Product
q)
4.
by
re-
Both
the cross-country
goods
contains
a trend
component.
One possibility
intertemporal
for the cross-country
elasticity of substitution
are two approaches
consumption
rises as an economy
to generate the time-varying
16
disparity is that the
is richer. There
intertemporal
elasticity of
substitution.
economy
market,
First, the time-varying
is richer.
rate of time preference
Facing the same real interest rate in the world credit
agents wit h lower rate of time preference
postpone
their current consumption
time preference
is subsistence
rate induces higher consumption
The marginal utility of consumption
discourages
saving. When an economy
of substitution.
For example,
subsistence
Taiwan
data provided
elasticity
Testing
of substitution.
Jtationarity
for
(6) simply
ing vectors,
cointegration
without
for this implication
stationarity
consumption
with the cointegrating
countries
The hypothesis
of
the real exchange
rate included.
coun-
H’ and they are the
that private
with other cointegrat-
here is that we conduct
in different countries
for the set of variables excluding
the
with and
qt, but reject the
qt, then the long run movements
of
qt
in different countries.
the H(O, q) and H(I, q) tests for the null of cointe-
for the four private
consumption
as the home (foreign)
the null of deterministic
cointegration
in different
in
If the test results fail to reject
cannot be driven by private consumption
tests with q = 2,3,4
restriction
It is possible
qt.
testing strategy
null for the set of variables including
designated
vector:
is cointegrated
tests for private consumption
the null of cointegration
gration
of the
for the intertemporal
of qt, the stationarity
implies that private
in different
Table 3 reports
the importance
and found that Japan, South Korea and
force for the long run movement
consumption
elasticity
restriction
tries is not cointegrated
driving
intertemporal
so that
g
Given the difference
equation
for future consumption
Lin (1996) emphasized
evidence
re-
shoots off to infinit y, which
induces an increasing
level of consumption,
is near
begins to grow, agents become more
current consumption
requirement
growth rate. Second, there
is meeting the subsistence
quirement.
the subsistence
Hence, lower
When the level of consumption
level, agent’s major concern
willing to substitute
have more intent ives to
for future consumption.
level in consumption.
the subsistence
(Ot) falls as an
series,
country,
cointegration
When
Taiwan
(U. S.) is
the H(O, 1) test fails to reject
for zt, it, zt and 2t, and the H(1, ~)
also provide strong evidence
restriction.
When
for the null of stochastic
Japan is the foreign country,
test rejects the null of the deterministic
cointegration
the H(O, 1)
for zt, it, Zt and it
g Using the Indian villages’ panel data, Atkeson and Ogaki (1991) found that the rate
of time preference is constant across poor and rich households, while the intertemporal
elasticity
of substitution
However,
as shown in Lin (1996),
estimation
is higher
for rich households
the subsistence
procedure.
17
than it is for poor
requirement
will drastically
households.
change the
at the 107o significance
strongly
level.
favor the stochastic
We found
However,
cointegration
much evidence
cointegration
not be rejected
q) tests with q = 2,3,4,
restriction.
against the null of cointegration
and ;f in the South Korea/Japan
deterministic
the H(l,
and South Korea/U.
restriction
Zt, it,
S. cases.
Zt
Only the
in the South Korea/Japan
case can-
by the H(O, 1) test. There are more than a single source of
non-stationarity
in generating
the long-run
movements
of zt, it,
Zt
and
~t
here,
Next, we apply the H(p, q) tests to qt, x~, it, Zt and it, and the results
are given in Table 3. Using both measures of pt, we found little evidence
against the stationary
cases:
neither
restrictions
the deterministic
in the Taiwan/Japan
cointegration
the H(O, 1) test, nor the stochastic
by the H(l,
S.
was rejected
by
restriction
cointegration
q) tests with q = 2,3,4.
and Taiwan/U.
Despite
restriction
was rejected
private consumption
series
are cointegrat ed in these two cases, the above finding clearly suggests that
the private
consumption
run movements
of real exchange
are cointegrated
subsections,
in different
countries
evidence
for the long-
rate and the private consumption
with the cointegrating
we found
can account
vector other than II’.
series
In previous
for the trend stat ionarit y of qt between
Taiwan and Japan and it in Japan and U.S. These results apparently
not affect the test results for the stationarity
There is mixed evidence
Korea/Japan
restriction.
for the stationarity
case in terms of
H(p,
q)
did
restriction
in the South
tests in Table 3. When
CPI is the
measure of pt, the H(O, 1) test fails to reject the deterministic
cointegration
for qt, Zt, it,
cointegration
restriction
When
z~ and tt.
was rejected
WPI
On the other hand, the stochastic
by the H(I, 2) test at the 10% significance
is the measure of p~, the stationarity
by the H(O, 1) test but cannot be rejected by H(l,
For the South Korea/U,
tionarity
q
=
restriction:
2,3,4
reject
Even though
against the sta-
neither the H(O, 1) test nor the H(ll q) tests with
cointegration
private consumption
was rejected
q) tests with q = 2,3,4.
S. case, we found little evidence
the null of cointegration
ference stationarity
restriction
level.
at the 10% significance
exists for the four consumption
of qt and the stationarity
accounts
level.
series, the dif-
restriction together imply that
for the long run movement
of real exchange
rate.
When we assume that preference
construction
of pt are identical
the stationarity
consumption
restriction
parameters
and weights used in the
across home country
in equation
and foreign
(7) implies that the cross-country
disparity account for the long-run movement
18
country,
of real exchange
rate. Next we present the H(p, q) test results in Table 3, First, we found significant evidence
for the stationarity
and weaker evidence
cointegration
test, but the stochastic
be rejected
Cointegrating
regression
coefficient
the stochastic
2,3,4
=
exists between
ble 4 reports the cointegrating
the model imposes
real exchange
rate and private
of the performance
econometrically
parameters,
of the model.
(1990)
FM procedure.
pt are identical
CCR
As noted by
regressions
and dz /&Z, can be estimated
without
parameters
the assumption
con-
that regressors
are
and weights used in the construction
across home country
which experienced
or relatively
aZ /aZ
Ta-
exogenous.
When preference
ther relatively
the sign of
regression results using Park’s (1992)
and Phillips and Hansen’s
by these procedures
restrictions
Even tbough the
Ogaki and Park (1989), one remarkable feature of cointegrating
sistently
restric-
in the South
it is necessary to investigate
estimates as an evaluation
is that structural
by the
cases.
restriction,
in different countries,
procedure,
q
cointegration
in the coint egrating regressions.
relationship
consumption
S.
results
to stationarity
on the sign of coefficients
in the Taiwan/U.
cannot be rejected
by the H(l, q) tests with
and South Korea/U.S.
case,
was rejected by the H(O, 1)
restriction
Second,
Korea/Japan
cointegrating
restriction
cointegration
H(I, q) tests with q = 2,3,4.
In addition
in the Taiwan/Japan
for the st ationarit y restriction
case: the deterministic
tion cannot
restriction
an appreciation
and foreign country,
in real exchange
less rapid growth in private consumption
For the South Korea/Japan
and South Korea/U.
those countries
rate have enjoyed
more rapid growth in private consumption
of
ei-
of traded goods
of nontraded
goods.
S. cases, the cointegrating
regression results in Table 4 clearly indicate that estimates of at 0= and a= 0=
have the theoretically
preciations
period,
correct signs, South Korea experienced
mild real ap-
against both U.S. donor and Japanese Yen during the sample
and zt – it and z~ – ~t exhibit
cases. Hence the mild real appreciation
clear upward trends in these two
of Korean Won can be attributed
more rapid growth both in Xt and in Zt for South Korea.
Note that az /a.
measures the ratio of income elasticities of .zt and Zt in South Korea.
instability
of the ratio across the two cases indicates
to
The
that the model does
not perform
well in this aspect.
On the other hand, we had the theoret-
ically wrong
signs for estimates
of axe= and azOz in the Taiwan/Japan
case.
Unlike the other three real exchange
real exchange
rates in Figure 1, the bilateral
rate between Taiwan and Japan exhibits
19
a downward
trend,
which reflects the depreciation
Facing the continuing
Japan are expected
creasing
real appreciation
goods.
relatively
However,
of Japanese Yen, private agents in
to increase their consumption
the imports
substitute
of New Taiwan dollars against Japanese Yen.
from Taiwan,
cheaper
and Zf as clearly displayed
and those in Taiwan
non-traded
Taiwan enjoyed
of traded goods
are expected
goods for more expensive
relatively
more rapid growth
traded
in both Zt
for the declining
pattern of bilateral real exchange rate. That is, the substitution
not be a crucial element in the determination
reason.
effects can-
of real exchange rate. Finally,
S. case, we found that the coefficient
have wrong signs for the following
appreciation
to
in Figure 3. As a result, the sign of coefficient
estimates for Zt — i ~ and zt — ;t must change to account
for the Taiwan/U.
by in-
estimates
of a.~z
Since Taiwan experienced
a real
against U,S, dollars, the model predicts that private agents in
Taiwan enjoy less rapid growth
As displayed
in the consumption
of non-traded
in Figure 3, Taiwan had more rapid growth
goods,
in Zt. It forces
the sign of az~z estimate to change.
We had consistent
cointegrating
regression
These results at least make two points clear.
can account
for the long run movement
we take the restrictions
seriously,
private
results in equation
First, private consumption
of real exchange
on the signs of coefficients
it is necessary
(6).
rate.
imposed
to refine the specifications
Second,
if
by the model
of the model
so that
consumption
can deliver the reliable effects on the real exchange
consumption
vs. government
rate.
Private
An alternative
explanation
consumption
of the long run movement
rate is that of government
consumption
Froot
The channel linking between
and Rogoff
sumption
When
expenditure
and real exchange
a larger fraction
of government
the non-traded
ernment
goods
appreciation
recently
consumption
Therefore,
government
those countries
by
con-
as follows.
expenditure
falls on
an increase in gov-
increases the real appreciation
currency.
proposed
rate can be described
than does private consumption,
consumption
against foreign
growth
(1991).
expenditure
of real exchange
of domestic
currency
that experienced
real
against the foreign currency have enjoyed relatively more rapid
in government
consumption
expenditure,
Table 5 shows the results of cointegrating
change rate on private consumption
regressions
and government
of the real ex-
consumption
expen-
diture:
.
qt =
axezxt
–
‘Xez?t.
–
a.ezzt
20
+
&z fizit
+
Tgt
–
?@t
+
V:,
(8)
in which g~ and ~t are per capita real government
in the home country
sumption
and foreign country, respectively.
expenditure
then the movement
is assumed
estimates
the private consumption
the cointegrating
The evidence
If government
consumption
of non-traded
spending.
of traded and non-traded
goods
rate and private
by the presence of government
ing regressions.
consumption
consumption
that ~ >0
and ~ >0.
between
are not significantly
expenditure
affected
in the cointegrat-
The data show no evidence of the government
consumption
effects on real exchange rates. Some of coefficients on government
tion in the home country
consump-
and foreign country are not statistically
from zero and are even of the wrong signs.
com-
is a regressor in
in Table 5 indicates that the empirical relationships
real exchange
goods,
from zero once
goods
In general, we expect
con-
Hence, we expect
of ~ and ~ are insignificant
regressions,
expenditure
to totally fall on the non-traded
of the private consumption
pletely reflects that of government
that the coefficient
consumption
The inclusion
different
of government
consumption
regressors in (8) has little effects on the estimates of aZt9Z,
.
~Zf?z, azOz and &Zdz. This remains as statistically significant as before,
with the signs for coefficient
estimates unchanged.
To access the empirical
government
consumption,
significance
gt – jt,
of cross-country
in the cointegrating
Table 5 also presents the results of the following
qt =
~zez(~t
–
it) –
azoz(zt
–
it)
We have similar results for the cross-country
sumption
effects on the real exchange
domestic
and foreign
statistically
private
significant
+
in real
regression
of (7),
cointegrating
~(gt
–
gt)
+
regression:
(9)
v;’.
disparity in government
rate as above.
consumption
disparity
become
when gt — jt is included.
The coefficients
consumption
consumption
But the wrong signs for
affects. the long run movement
of real exchange
rate.
Remarks
The empirical evidence suggests that private consumption
countries
provide
on the long run movement
wan.
Based
regressions,
fundamental
upon
for
does not seem to overturn the result that private
5. Concluding
and foreign
on
larger and even more
the estimates of Xt – it and Zt – ;t remain quite severe. Thus, accounting
government
con-
a significant
of real exchange
the signs of coefficient
component
of the explanation
rate in South Korea and Taiestimates
it seems that the private consumption
in the cointegrating
may not be a reliable
that has reliable effects on the real exchange
21
in the home
rate.
It is useful to incorporate
ductivity
differentials
determination,
the supply-side
in a general equilibrium
elements such as the promodel of real exchange
and explore the trend and cyclical implications
rium relationships
obtained
in the model.
Since fluctuation
rate
from equilibin the relative
price of traded goods accounts for a significant fraction of the real exchange
rate movement,
equation
another int cresting topic for future research is to estimate
(5).
22
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,
1
!
m
m
I
UI
m
m
m
4
—.
-+-
m
7
.z
./
-/
/
./
-/
\
m
r-
I
I
6’1
8“1
L I
9“1
g I
?“I
E“ 1
9‘“o-
g~-
n~-
2’T–
fiT -
\
i
G“?
ti’z
E’Z
Z“z
6’1
O’z
I“z
1
U)
m
;;
L
i
m
m
r
m
In
m
(7
m
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i
1
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)
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“1
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J
t“o T
0“01
96
Z“6
9“9
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FE
0’9
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0’11
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f7’6
Table
Statistics
1: Tests
Taiwan/Japan
for
Trend
Property
Taiwan/USA
Price Index:
of Real
Exchange
S. Korea/Japan
Rate
S. Korea/USA
CPI
Null: Difference Stationarity
0.007*
0.397
0.026
0.257
J(1,3)
0.008***
0.414
0.098*
0.484
J(1,4)
0.048***
1.144
0.341
3,194
J(I,
2)
Null: Difference Stationarity
ADF(l)
-2.352
-1,798
-2.204
-1.295
ADF(2)
-2.628
-1.936
-2.571
-1.583
ADF(3)
-2.683
-1.895
-2.554
-1.770
Null: Trend Stationarity
G(1, 2)
0.135
5.586**
0,487
G(1,3)
0.171
5.750*
1.710
5.794*
G(1,4)
0.951
10.483**
4.869
13.520***
Price
Index:
3.628*
WPI
Null: Difference Stationarity
J(I, 2)
0.053
0,168
0.193
0.028
J(1,3)
0.073*
0.248
0,226
0.164
J(1,4)
0.096**
0.622
0.500
1.648
Null: Difference Stationarity
ADF(l)
-2.612
-1.894
-2.331
-1.822
ADF(2)
-2.429
-2.274
-2,537
-1.775
ADF(3)
-2.673
-2.469
-2.694
-1.885
Null: Trend Stationarity
G(l,
2)
0.511
1.128
2.806+
3.098*
G(1,3)
1.509
3.871
3.538
2.598
G(1,4)
1.947
7.463*
6.395*
11.487***
Note:
1. J(P, g) and G(p, q) denote Park and Choi’s (1988) tests with the time polynomial
in the null hypothesis
2. ADF(p)
and the time polynomial
denotes Dickey and Fuller’s (1984) test with the time polynomial
in the null hypothesis
of order p
of order q in the fitted regression.
of order 1
and p lagged first difference terms in the fitted regression.
3. CPI and WPI
denote consumer price index and wholesale price index, respectively.
at 570 level, ~d *** signifi~mt at 170 level,
4. * Significant at 1070 level, ** Sigfifi-t
29
Table
Z: Tests
for Trend
Property
of Private
Consumption
Null: Difference Stationarity
Statistics
J(1,2)
J(1,3)
J(1,4)
ADF(l)
Null: Trend Stationarity
ADF(3)
ADF(2)
G(1,2)
G(1,3)
G(1,4)
Japan
0.008*
0.025**
1.573
-1.993
-2.156
-2.206
0.175
0.530
13.184***
1.063
1.153
1.323
-1.760
-2.296
-2.066
10.105***
10.502***
11.165**
South
Korea
2.331
2.346
9.972
-1.041
-1.126
-1.438
12.407***
12.432***
16.115***
1.986
3.135
3,175
-2.487
-2.357
-2.241
12.829***
14.622***
14.668***
Taiwan
1.065
1.072
3,601
-1.590
-0.925
-1.276
9.980***
10.O13***
15.144***
2.131
2.179
6.300
-1.106
-0.769
-1,446
12.723***
12.814***
16.132***
United
O.000***
0.427
Note:
States
0.164
0,172*
-1.563
-1.922
-2.106
0,000
2.730
2,843
0.550
0.831
-1.744
-1.639
-1.957
5.951**
7.048**
9.021**
1. zt and zt denote per capita real consumption on traded and nontraded goods, respectively.
2. * Significant at 10% level, ** Significmt at 5~0 level, and *** Significant at l~o level.
30
Table
3: Tests
for
Cointegration
Null: Cointegration
Variables
H(o,
1)
H(o, 2)
South
Korea
19.104***
15.529***
15.538***
16.584***
6.900***
10.029***
10.356**
1.231
10.621***
11.737***
11.761***
17.770***
0.862
12.060***
14.586***
14.690***
14.004***
1.136
5.078*
3.325*
3.339
3,491
2.872*
5.232*
1.834
2,085
2.367
4.671**
4.833*
0.552
0.973
4.234
7,275***
7.326**
0.019
1.695
4.309
16.226***
Korea
–it,
17.612***
14.819***
14.932***
14.189***
16.994***
12.207***
14.243***
14.632***
4.117**
9.964***
7,764***
9.424***
12.677***
1,136
5.629*
4.003**
8.967**
11.601***
0.637
0.688
0.009
0.225
2.287
0.639
0,642
0.000
0.279
2.396
0.030
1.936
1.281
1.291
4.383
3.747*
4.253
0.597
0.961
3.491
/ Japan
12.466***
20.772***
14.266***
14.357***
15.436***
9.408***
16.151***
11.388***
11.396***
15.564***
zt,;,)
2.842*
3.004
0,108
0.130
5.350
13.770***
14.074***
4.987**
7,893**
8.720**
0.397
1.320
0,493
0.651
1.438
0.818
1.811
0,527
1.071
2.671
zt-2t)
0.069
0.133
0.019
0.083
2.839
zt –it)
0.320
0.752
0%068
0.371
2.978
Taiwan
/ U.S.
16.968***
17.812***
13.980***
13.980***
15.998***
9.136***
17.143***
13.803***
13.843***
15.588***
1.764
1,608
6.534**
1,316
1.306
Note:
/ U.S.
14.152***
(Z,,2, )
zt-jt)
(q;, zt-it,
16,676***
/ Japan
(Xt,
it)
(9:, zt!it,
zt,5t)
(q~,~t,~t,zt,jt)
(qy)zt
H(1,4)
3.154*
Taiwan
(Zt, i,,
H(1,3)
14.361***
South
(Ct-it,
H(1,2)
2.056
0.744
1.494
3 .393*
5.130*
5.132
2.159
0.360
0.720
0,723
9.456***
2.808
0.798
1.848
2.594
6.756***
6.914**
0.488
1.666
1.828
2.953*
2.966
0.054
2.153
2.170
1. qt denotes real exchange rate, zt and Zt denote per capita real consumption
2. * Significant
goods, respectively.
at 5~0 level, and ***
at 10% level, ** Sjgnifi_t
on
traded and nontrded
31
Significant at 1~o level.
Table
4: Cointegrating
Regressions
ffz e=
Equation
of Red
Exchange
&zoz
South
Rates
~zez
on Private
Consumption
&zOz
Korea/Japan
Price Index: CPI
Equation
(6)
1.502*/ 1.462*
Equation
(7)
1.669*/ 1.628*
Equation
(6)
1,341*/ 1.267*
Equation
(7)
1.241*/ 1.209*
-0.686 /-0.804
2.778*1 2.775*
1.159 / 1.057
2.488+/ 2.452*
Price Index: WPI
-0.591 /-0.786
3.546*1 3.543*
1.298 / 1.113
2,756+/ 2.728*
South
Korea/U.S.
Price Index: CPI
Equation
(6)
2.657*/ 2.653*
Equation
(7)
2.061+/ 2,057+
1.477*/ 1.503*
1.864*/ 1.826*
2.662+/ 2.767*
1.625*/ 1.601*
Price Index: WPI
Equation
(6)
1.686*/ 1.682*
Equation
(7)
1.427*/ 1.424*
1.233+/ 1.236*
1.728*/ 1.707+
2.425*/ 2.439*
1.721*/ 1.700*
Taiwan
/Japan
Price Index: CPI
Equation
(6)
-8,731*/-8.476*
Equation
(7)
-1.222 /-1.232
0.032 /-0.073
-5.225 */-5.O8~
3.r70*/
3.749*
-0.342 /-0.331
Price Index: WPI
Equation
(6)
-5,414 */-5.33l*
Equation
(7)
-1.364 /-1.343
-0.476 /-0.498
-3,114 */-3.O68*
2.923*/ 2.964*
-0.270 /-0.255
Taiwan/U.S.
Price Index: CPI
Equation
(6)
-0.791
Equation
(7)
0.657*\
/-0.943
1.462+) 1.475*
-1.841 */-l .945*
2.784*/ 2.824*
-0.673 */-O.7OO*
0.646*
Price Index: WPI
Equation
(6)
0.149 /-0.064
Equation
(7)
0.226 / 0.215
Note:
* Significant
0.698*/ 0.741*
-0.815 /-0.961
-0,487 */-O.5l2*
at 5% level.
32
2.078+/ 2,213+
Table
5: Cointegrating
on Private
Equation
Lvzez
Regressions
Consumption
&=ez
of Real
and
azez
South
Exchange
Government
Rates
Consumption
&zQz
?
?
1.011 / 0.834
-0.076 /-0.067
-0.235 /-0.468
Korea/Japan
Price Index: CPI
Equation (s)
1.671*/ 1.655*
Equation
(9)
1.214*/ 1.272*
Equation
(8)
1.564*/ 1.513*
Equation
(9)
0.785*/ 0.839*
-0.774 /-0.832
2.886*/ 2.743*
0.227 / 0.182
2.335*/ 2.348*
Price Index: WPI
-0,629 /-0.746
3.513*/ 3.285*
0.948 / 0.665
South
-0,067 /-0.051
-0.586 /-0.934
0.233 / 0.192
2.644*/ 2.658*
Korea/U.S.
Price Index: CPI
Equation
(8)
2.304+/ 2.327*
Equation
(9)
1.611*/ 1.666*
1.367*/ 1.306*
l.llo*/
1.171*
3.749*/ 3.585*
0.005 / 0.003
0.912*/ O.91O*
0,299*/ 0.260*
1.292*/ 1.343*
Price Index: WPI
Equation
(8)
1.536*/ 1.562*
Equation
(9)
1.279*/ 1.295*
1,311*/ 1.241*
1.437*/ 1.513*
3.091*/ 2.894*
-0.001 /-0.002
o.lo4*/
1.677*/ 1.685*
0,239 / 0.240
0.091*
Taiwan/Japan
Price Index: CPI
Equation
(8)
Equation
(9)
-9.457*/-9333*
3.070*/ 2.803*
0.440 / 0.286
-5.555*/-5.495*
4.775*/ 4.691J*
1.694*/ 1.588*
0.542 / 0.515
1.066 / 1.029
0.838 / 0.785
Price Index: WPI
Equation
(8)
-5.715*/-5.635*
Equation
(9)
0.148 / 0.051
1.534*/ 1.365*
-3.316*/-3.255*
3.591*/ 3.471*
0.619 / 0.584
Taiwan
o,818*/ 0.794*
0.362 / 0.347
0.633 / 0.621
/U.S.
Price Index: CPI
Equation
(8)
-0.451 /-0.569
Equation
(9)
0.912*/ 0.908*
2.111*/ 2.114*
-1.645 */-l.755*
3.653*/ 3.716*
-0.163 /-0.231
-0.672 */-O.6ll*
-0.260 /-0.257
-0.620 */-O .635*
Price Index: WPI
Equation
(8)
0.693 / 0.604
Equation
(9)
0.783+/ 0.775+
Note:
1. * Significant
1.847+/ 1.830*
-0.644 /-0.708
-0.352 /-0.370
at 570 level.
2. Sample period:
1975:1-1993:4.
33
3,561*/ 3.565*
-0.406 */-O.426*
-0.557 */-O.529*
-1.029 */-O.992*