Revisiting the Issues: Free Trade and Demographic Transition
Guohan Zhu1, Marcel Mérette2
1
2
Department of Economics, University of Ottawa, KIN 6N5 Canada
Faculty of Social Science, Department of Economics, University of Ottawa, KIN 6N5 Canada
gzhu063@uottawa.ca, mmerette@uottawa.ca
ABSTRACT
Over the next several decades, countries around the world will experience varied degrees of population aging due
to the unequal population growth rates. Meanwhile, the accelerating process of globalization is making the national
markets more and more integrated through international trade. This paper employs an overlapping generations
computable general equilibrium model to investigate the evolution of trade and its welfare implications for two open
economies during demographic transition. We assume the two economies are identical in every aspect except for the
population growth rate. Two scenarios are considered for different types of demographic transition. Under both
scenarios, one of the two economies becomes comparatively older than the other. The resulting changes of relative
factor abundances give rise to different production prices across economies and create incentives for trade. Armington
assumption is applied into the model for the trade case, where the two economies are assumed to export and import both
capital-intensive and labor-intensive goods. Opposite to the result presented by Sayan (2005), our model shows that the
older economy becomes better off and the younger economy becomes worse off after opening to trade. Furthermore, we
find that the welfare gap between the old and the young economy is positively correlated with the steady-state
population growth rate. Our result cast some light on the continued average welfare gap between the developing and the
developed world during the process of globalization.
JEL classification: F11; F43; D58; D91; J10
Keywords: Demographic transition; International trade; Overlapping generations
the share of international trade in Gross Domestic
1. INTRODUCTION
Product (GDP) has increased dramatically.
Standard
The world population is experiencing a dramatic
Heckscher-Ohlin (HO) model indicates that given
demographic transition: population growth is slowing
different factor intensities in the production of tradable
down and the portion of the elderly keeps increasing.
goods, an economy produces more and exports the goods
This process of aging will be further accelerated after
that use its abundant factors intensively (Pugel and
2010 when the baby boom generation 1 begins to retire
Lindert 2000). Unequal population growth rate and the
(Mérette 2002, 2004). According to International
resulting divergence in the elderly dependency ratio
Monetary Fund (IMF, 2004), the improvement in life
(EDR) 2 have a direct impact on the factor abundances
expectancy and decrease of fertility rate are expected to
across countries. On global market, the existing
drag down the overall population growth rate from
dissimilarities in relative factor abundance between
around 1.25% in 2000 to 0.28% by 2050. Besides major
capital-abundant economies in North America, Europe
OECD
developing
and East Asia and the rest of the world will continue to
economies are also encountering a significant decline in
grow in the coming decades (UN 2001). Consumption,
population growth rates in the coming decades. In China
production, investment and the related prices may
for example, the net growth of population has already
change according to different age structures. Thus it is
declined
of
highly relevant to investigate how and to what degree
implementation of the “one child policy” since the late
rapidly changing and unequal population growth rates
1970s. Based on the present pattern of population growth,
could affect the pattern of trade and the welfare
the growth rate of Chinese population is expected to
implications of trade during the demographic transition.
industrial
to
economies,
0.68%
in
some
2004
after
decades
decline to -0.3% during the five years between 2045 and
2050. In other developing regions like West Asia and
Using a two-country, two-good, two-input, two-
Africa, population growth is also slowing down but less
generation (2*2*2*2) overlapping generations com-
rapidly. Overall, the world population is under a process
putable general equilibrium (OLG-CGE) model, this
of accelerating aging. However, we observe unequal
paper investigates the evolution of trade and the welfare
population growth rates not only between the developing
implications
and the developed world, but also among the developing
demographic transition. Except for population growth
economies. This divergence of population growth rates
rate, the two economies are identical in all other aspects.
will be further enlarged in the next fifty years. Figure 1
Consequently, one of them is developing into an older
shows the differentiated population growth rates by
economy with lower population growth rate. In contrast
regions projected by United Nations (UN, 2002).
to Sayan (2005) and Sayan et al. (2001), Armington
0.03
Growth Rate
2000
two
open
economies
during
assumption is applied into our trade case to generate a
Fifure 1 Projections on population growth rates
more
0.025
0.02
for
2050
realistic
trade
capital-abundant and
0.015
0.01
pattern
in
which
labor-abundant countries
both
are
trading both capital-intensive and labor- intensive goods.
0.005
Furthermore, a constant elasticity substitution with the
0
-0.005
Region
/Country
-0.01
-0.015
-0.02
West
Europe
East
Europe
North
America
East Asia
China
Southcentral
Asia
West Asia
Africa
average
World
average
elasticity different from one (CES) utility function,
which is widely used in general equilibrium studies, is
introduced into the intertemporal maximization of
lifetime utility for a typical consumer. The simulation
We also have observed a new phase of globalization
results of our model give rise to a welfare implication of
over the past decades. National markets have become
trade that is just opposite to that presented by Sayan
more and more integrated with the rest of the world and
2 The EDR is defined as the ratio of people aged 65 and over to the working –age
1 The baby boom generation refers to the cohorts born between 1946 and 1966.
population (15 to 64 years old).
2
(2005). We find that the older economy gains from trade
economy deteriorates while that for an individual in the
while the younger economy loses. The gap of average
younger economy improves compared to autarky. When
welfare is positively correlated with the steady-state
full labor mobility is allowed, the destination (older)
population growth rate. This result casts some light on
economy loses while the sending (younger) economy
the continued welfare gap between the developing and
gains in welfare. Based on the same model, Sayan (2005)
the developed world during globalization. It also offers a
focuses on the interactions between free trade and
brief projection on the evolution of many variables for an
demographic transition applying population growth rates
open economy during projected demographic transition.
data projected by UN (2001) 3 . Incentives for trade is
generated by the fact that two countries become either
This paper is organized as follows. Section 2
relatively capital abundant or labor abundant with
reviews the latest literatures on related issues by Sayan.
unequal population growth rates. The older country is
Section 3 briefly describes the OLG-CGE model and
assumed to specialize in producing and exporting the
Section 4 presents simulation results and comparisons.
capital-intensive good when the younger one specializes
Section 5 concludes.
in the labor-intensive good. On the consumption side, A
Cobb-Douglas (CD) utility function is applied into the
2. REVIEW ON RELATED LITERATURE
intertemporal maximization of lifetime utility for a
representative individual. It is shown that for an older
According to the standard HO theorem, differences in
country with a faster aging process, the welfare for a
factor abundances across countries give rise to different
representative individual in the economy falls below the
production prices and thus create incentives for trade.
autarky level under free trade. An individual in the
Indeed, an economy has comparative advantage in
younger country however, will enjoy a higher welfare
producing and exporting the commodity that uses its
level. The welfare loss for individuals in the older
abundant factor intensively. It is predicted that all
economy can be observed under both demographic
participating economies gain from free trade given that
scenarios 4 . Thus Sayan concludes that “Contrary to
resources are more efficiently used in production.
those predictions (of the static HO model), however,
Compared with autarky, trade partners benefit from the
trade
favorable terms of trade leading to a higher value of their
improvement over the state of autarky” (p.1491).
would
not
necessarily
represent
a
Pareto
export goods and less expensive imported goods for local
consumers. Over the past decades, there were a few
Both Sayan and Uyar (2001) and Sayan (2005)
studies that introduce dynamic concepts into standard
incorporate demographic shocks to test the standard HO
HO model. Many attempts have been put into testing the
predictions. Results of the papers support the previous
predictions of traditional HO model using dynamic
arguments that welfare implications predicted by
general equilibrium frameworks. Related papers include
traditional HO model might not hold under different
Fried (1980), Buiter (1981), Chen (1992), Galor and Lin
dynamic scenarios. However, the welfare loss for
(1994, 1997), Guillo (2001). Sayan et al. (2001) and
individuals in the old economy is explained as “a result
Sayan (2005) are the first to introduce demographic
shocks into a dynamic trade model and test the validity
of welfare predictions of standard HO model.
3 The unequal population growth rates are 1950 values of average population
growth rate for “more-developed regions” and “less developed regions” projected
by UN (2001).
Sayan and Uyar (2001) employ a two-country,
two-good, two-input dynamic OLG-CGE model to
investigate the welfare implications of free trade and full
labor mobility for two open economies with unequal
population growth rates. Their paper shows that under
free trade, the welfare for an individual in the older
4 Sayan (2005) considers two demographic scenarios Under scenario one, one
country has a lower initial population growth rate which declines faster during the
dynamic. Another country has a higher initial population growth rate which
declines at a lower speed. Under scenario two, one country has a lower constant
population growth rate when the other country’s population has a higher constant
growth rate.
3
of these changes in relative commodity and factor
parameters for both goods are assumed to be identical,
prices” (Sayan 2005, p.1488), which remains for further
which means each individual has identical preference for
discussion.
both Sec1 and Sec2.
In
3. MODEL DESCRIPTIONS
the
assumption
5
trade
model,
we
apply
Armington
(Armington 1969) to generate a more
realistic picture of trade. A good (Sec1 or Sec2) produced
This paper also uses an OLG-CGE model to
in Cou1 is no longer a perfect substitution for that
investigate the welfare implication for two open
produced in Cou2. After opening to trade, the preference
economies during demographic transitions in both the
parameters are assumed to be identical for four
autarky and the trade cases. In the model, we have two
differentiated goods. In other words, a consumer is likely
countries (Cou1, Cou2), two homogenous consumption
to consume the same quantity of locally produced Sec1,
or investment goods (Sec1, Sec2), two inputs (capital and
imported Sec1, locally produced Sec2 and imported Sec2.
labor labeled as L
dem
dem
, K
) and two generations (the
Consequently, incentives for trade exist when two
working generation gi and the retied generation gn) of
countries are perfectly symmetric because both of them
population. The productions of two goods have different
demand locally made and foreign made goods. During
factor intensities and require both labor and capital
demographic transitions, the changes in relative factor
inputs. Technologies are assumed to be identical across
abundance make production prices different across
countries. The OLG-CGE model is a simple economy
countries.
and the government sector is not included. Inheritance
differentiated goods change overtime. The appendix
and bequest are not taken into account.
offers a detailed model description.
Accordingly,
demands
for
the
four
Consumers in both countries are forward looking
Demographical transitions are modeled as the
and have perfect foresights. A representative individual is
following. In an arbitrary period t, the fertility rate for
born in the first period as the only labor force in the
the first generation is labeled as NNFt. We denote the
economy. Part of his or her labor income is saved as
number of individuals living in period t as Popgi,t and the
investment in capital stock and the rest is consumed. In
population of the old generation as Popgn,t. The
the second period, this individual spends all his or her
population regenerates according to the following
wealth, including investment in the first period and the
equation (22) and (23):
interest income, on consumption. The portfolio of
P o p g i , t + 1 = P o p g i , t (1 + N N Ft )
(22)
consumption and investment is decided immediately
P o p g n ,t +1 = P o p g i ,t
( 2 3)
after birth to maximize his or her lifetime utility based on
a CES utility function. The first order condition is the
scenarios. Under the first scenario (A), two countries
following equation (9):
Con g +1,t + g
In this paper, we consider two demographic
⎡ (1 + Rrett + g ) PgCon
⎤
,t + g −1
=⎢
⎥
Con
⎣⎢ (1 + ρ ) Pg +1,t + g ⎦⎥
start from different initial fertility rates labeled as
1
( )
θ
Con g ,t + g −1
(9)
NNFCou1,t0 and NNFCou2,t0. From the second period on (t1),
fertility rates for both of them decline towards zero but at
of
different speed. Population of Cou1 with a lower NNFt0
is the
declines faster and this country turns to be older than
aggregate consumption price that is a weighted sum of
Cou2. Under the second scenario (B), Cou1 also has a
production prices for Sec1 and Sec2. ρ is the discount
lower initial fertility rate that is constant overtime. The
rate which is assumed to be identical for both countries.
population of Cou2 starts from a higher initial fertility
where
Cong,t
is
the
aggregate
consumption by generation g at time t.
quantity
Pg,tCon
Consumers across countries have an identical utility
rate and grows at a constant rate before the fifth period
function. An autarky consumption bundle only consists
of locally produced Sec1 and Sec2. The preference
5 Internationally traded products are differentiated by country of origin.
4
(t5). After t5, Cou2’s fertility rate declines at a constant
Under both scenarios, Cou1 is growing into an old
speed and converges to that of Cou1. To make the results
capital-abundant country and Cou2 becomes younger but
more comparable, we use the same initial population
labor abundant. Table 1 and Figure 2 show different
growth rates for Cou1 and Cou2 as in Sayan (2005).
scenarios of demographic transition for the two countries.
Table 1 Evolution of population growth rates
NNFCou1,t
NNFCou2,t
NNFCou1,t
Scenario A
Scenario B
NNFCou1,t0=0.012
NNFCou2,t0 = 0.0205
NNFCou1,t =0.5872*NNFCou1,t-1
NNFCou2,t = 0.6258*NNFCou2,t-1
for t>0
for t>0
1.025
NNFCou2,t
0.012 for all t
0.0205 for 0<t<6
NNFCou2,t-0.012
=0.7*(NNFCou2,t-1 -0.012)
for t >=6
1+NNF
Figure 2 Population growth rates in scenario A and B
1.020
1.015
1.010
1+NNFCou1,t-A
1.005
1+NNFCou2,t-A
1+NNFCou1,t-B
1+NNFCou2,t-B
1.000
t
0.995
t1
t2
t3
t4
t5
t6
t7
t8
t9
t10 t11 t12 t13 t14 t15 t16 t17 t18
The model is solved based on the following strategy.
stock. The effective labor supply (Lsup) in the economy is
Given some common consumption and production
0.5 units (the younger generation) and is equal to the
parameters, we first solve the autarky model with zero
labor demanded (Ldem). Based on the above settings, we
population growth. The calibrated values, including
use some critical parameter values to solve the prototype
consumption, investment, rate of return on capital and
autarky model (Table 2).
discount rate, are used as initial steady-state values.
In Table 2, ALK is the parameter to show factor
Based on these values, we introduce the regional-specific
fertility rates into the model and solve the autarky case
intensities in production. It is shown that Sec1 is
for two counties. Then we allow trade between the two
assumed to be a capital-intensive good and Sec2 is a
countries and the trade model is solved based on
labor-intensive good in our model. EOS stands for the
Armington assumption.
elasticity of substitution and the assumed EOS values are
used in both model calibration and simulation. The
Before calibration, two countries are assumed to be
depreciation rate is set as 0.6. The intertemporal EOS
perfectly symmetric. In each of them, 0.5 units of Sec1
and the depreciation rate may seem high but recall that in
and Sec2 are produced, 0.4 units of Sec1 and Sec2 are
our simple two-generation OLG model, we assume the
consumed by 1 unit of people (0.5 units of young people
working life begins at age 16. An individual retires at the
and 0.5 units of old people). The extra 0.2 units of Sec1
age 45 and lives for another thirty years. Thus each
and Sec 2 are used as investment goods to build capital
period t is equivalent to 30 years.
Table 2 Critical parameter values used in calibration
σs
σInv
θ
share of capital in
EOS for consumptions
EOS for investment
Inverse of intertemporal
production
across sectors
goods across sectors
EOS
2.5
3.0
1.5
ALKSec1
ALKSec2
DepR
Depreciation Rate
0.6
0.4
0.6
5
4. SIMULATION RESULTS
0.334
Figure 4 Capital-Labor ratios in autarky
k
0.332
4.1 The prototype autarky case
0.33
0.328
0.326
We first show the evolutions of effective labor
k-cou1-A
k-cou2-A
k-cou1-B
k-cou2-B
0.324
0.322
supply and capital-labor ratios (k) for both countries in
autarky under demographic transition scenarios A and B:
0.66
0.64
0.6
t3
t4
t5
t6
t7
t8
t9
t10
t11
t12
t13
t14
t15
t16
t17
t18
case are presented and compared with the trade case in
Lsup-Cou1-A
Lsup-Cou2-A
Lsup-Cou1-B
Lsup-Cou2-B
0.62
t2
Results of other important variables for the autarky
Figure 3 Effective labor supply in autarky and trade
Lsup
t
0.32
the next section.
0.58
0.56
4.2 The trade case
0.54
0.52
t
0.5
t2
t3
t4
t5
t6
t7
t8
t9
t10
t11
t12
t13
t14
t15
t16
t17
t18
When Armington assumption is applied, a tradable
We set the initial population for both countries
good is not only differentiated by the technology used in
equal to one. In the first period (t0), the effective labor
its production but also by its country of origin. Thus,
supply is 0.5 for both of them. Unequal population
there are four differentiated goods on world market: Sec1
growth rates make two countries’ effective labor supplies
made in Cou1, Sec1 made in Cou2, Sec2 made in Cou1
different from the second period on. The growth rate of
and Sec2 made in Cou2. The preference parameter for all
Cou1’ population declines to one at a speed faster than
these goods is set to be identical for consumers across
that of Cou2 under scenario A. Under scenario B, Cou1
countries. When two countries are perfectly symmetric, a
has a constant population growth rate dominated by that
consumer in Cou1or Cou2 demands 0.25 units of each of
of Cou2 overtime though Cou2’s population growth rate
the four goods for either consumption or investment. In
converges to that of Cou1 in the long run. Under both
other words, incentives for trade exist when two
scenarios, Cou2 is younger than Cou1. As shown in
countries are perfectly symmetric because each country
Figure 3, the absolute value of effective labor supply in
has comparative advantages in producing and exporting
Cou2 dominates that of Cou1 overtime.
locally produced Sec1 and Sec2. Unequal population
growth rates bring changes to the relative factor
With a positive rate of population growth, the
abundances and the production prices of two goods.
aggregate demand in the economy will increase, which
International goods mobility between these countries
requires more capital stock. As a result, the rate of return
turns to be affected by each country’s comparative
on capital (Rret) is increasing, which creates incentive
advantage in producing and exporting Sec1 compared to
for the young people to smooth more current
its comparative advantage in producing and exporting
consumption to his or her second half of life. Population
Sec2. In this case, demand for locally produced Sec1, the
growth rates for both countries converge to an identical
capital-intensive good, is higher than the demand for
and constant level under both scenarios. Consequently,
locally produced Sec2 for a capital- abundant country.
the capital-labor ratio (k) will settle down towards a
This can be shown by the changes of the ratio of the
constant level after periods of gradual adjustment.
export of Sec1 over the export of Sec2 for countries with
Ceteris paribus, the steady-state k level is determined by
different factor abundances.
the steady-state population growth rate as predicted by
conditional
As shown in section 3, Cou1 turns into a capital-
convergence. The steady-sate population growth rate
abundant older country and Cou2 becomes a labor-
under scenario A is lower than it is under scenario B, so
abundant and younger country under both scenarios. In a
countries under scenario A have a higher autarky
traditional HO framework with two homogenous goods
steady-state k level (Figure 4).
and two inputs, Cou1 (Cou2) specializes in the producing
the
Solow-Swan
growth
model
of
6
and exporting the capital (labor) intensive Sec1 (Sec2)
country in production. The capital (labor)-abundant Cou1
and is exporting Sec1 (Sec2). After opening to free trade,
(Cou2) is more efficient than the labor (capital)
national markets are fully integrated and locally
-abundant Cou2 (Cou1) in producing the capital (labor)
produced Sec1 (Sec2) is a perfect substitute for imported
-intensive good, Sec1 (Sec2). The relative production
Sec1 (Sec2). The marginal product of each input is
price of Sec1 (Sec2) is also cheaper in Cou1 (Cou2). The
equalized across countries, and so are factor prices. In
evolution
this case, free trade successfully transmits the relative
demographic transitions is shown in Figure 6.
factor abundances across counties. The capital-labor
relative
production
prices
during
Figure 6 Relative price of production
PQS1/PQS2
1.01
ratios of the two countries share a unique evolutionary
of
1.005
path that lies between their autarky levels.
1
PQS1/PQS2-cou1-A
PQS1/PQS2-cou2-A
PQS1/PQS2-cou1-B
PQS1/PQS2-cou2-B
0.995
When Armington assumption is applied into the
trade model, the identical preference parameter for both
0.99
t
0.985
locally produced and imported Sec1 or Sec2 means the
t2
t3
t4
t5
t6
t7
t8
t9
t10
t11
t12
t13
t14
t15
t16
t17
t18
homogenous good Sec1 or Sec2 produced in two
In a traditional HO model, countries export goods
countries are no longer perfect substitutes. As a result,
with comparative advantages and a capital (labor)
marginal products of capital input and labor input are no
intensive country exports only capital (labor) intensive
longer equalized across countries, neither are factor
good. In the Armington case however, each country has
prices on markets. Different from traditional dynamic
the comparative advantage in both locally produced Sec1
HO model, the capital-labor ratios of both countries are
and Sec2. In addition, demands for locally produced or
no longer equalized after opening to trade. As shown in
imported goods are affected by the relative production
the following Figure 5, the simulated capital-labor ratios
prices across countries. To maximize lifetime utility, a
of Cou1 and Cou2 converge to different steady-state
consumer tends to consume more imported goods with
values overtime. Under both scenarios, the capital-
lower production prices. Clearly, after opening to trade,
abundant country turns to be more capital abundant than
the quantity of export or import are not only affected by
the labor-abundant younger country at steady state. The
consumers’ preference, but also affected by different
gap between their capital-labor ratios is positively
production prices. Figure 7 shows that Cou1 is exporting
correlated with the steady-state population growth rate.
more Sec1 than Sec2 because Sec1’s relative production
0.336
price is cheaper than it is in Cou2 and there is more
Scenario A (declining NNF)
k
demand for Sec1 made in Cou1. For the labor-abundant
0.334
Cou2, the ratio of the export of Sec1 over the export of
0.332
0.33
Sec2 is dominated by that of Cou1 under both scenarios,
k-cou1-Trade
0.328
k-cou2-Trade
0.326
k-cou1-Aut
t
k-cou2-Aut
country’s export portfolio.
0.324
t2
t3
t4
t5
t6
t7
t8
t9
t10
t11
t12
t13
t14
which means there is a smaller portion of Sec1 in this
t15
t16
t17
t18
1.01
0.335
1
Scenario B (constant NNF)
k
Figure 7 The evolution of export ratios
Exp-S1/Exp-S2
0.99
0.33
0.98
0.325
ExpSec1/ExpSec2-Cou1-A
0.97
0.32
k-cou1-Trade
k-cou1-Aut
k-cou2-Aut
0.31
ExpSec1/ExpSec2-Cou2-A
ExpSec1/ExpSec2-Cou1-B
0.96
k-cou2-Trade
0.315
t
t
ExpSec1/ExpSec2-Cou2-B
0.95
t2
t3
t4
t5
t6
t7
t8
t9
t10
t11
t12
t13
t14
t15
t16
t17
t18
0.305
t2
t3
t4
t5
t6
t7
t8
t9
t10
t11
t12
t13
t14
t15
t16
t17
t18
Figure 5 The evolution of capital-labor ratio under scenario A and B
Now we show the evolution of per capita welfare,
measured by the lifetime utility for a representative
The differential in production prices across
individual, during demographic transitions. Simulation
countries represents the relative efficiency of each
results for the average welfare have the same pictures as
7
those of GDP per capita levels. In this paper, we present
other hand, this country is producing more Sec1
the evolution of GDP per capita levels under both
compared with autarky because it produces Sec1 more
scenarios overtime in Figure 8.
efficiently and the production price of Sec1 is lower than
1.01
it is in Cou2. The demand for locally produced Sec1
Scenario A (declining NNF)
GDP Pcap
turns to be higher than it is for locally produced Sec2,
1.01
1.00
which requires more capital stock in productions.
1.00
0.99
Consequently, the rate of return on capital in Cou1 is
PCap GDP-cou1-Tra
0.99
PCap GDP-cou2-Tra
0.98
Pcap GDP-cou1-Aut
Pcap GDP-cou2-Aut
0.98
slightly higher than it is in Cou2 at steady state even
t
though Cou1 is more capital abundant. With the
0.97
t2
1.02
t3
t4
t5
t6
t7
t8
t9
t10
t11 t12
t13 t14
t15 t16
t17 t18
assumption that the quantity and quality of the labor
supply for representative individuals are identical across
Scenario B (constant NNF )
GDP Pcap
countries, the labor income for an individual in the older
1.01
1.00
economy is higher. Without capital mobility across
0.99
0.98
0.97
PCap GDP-cou1-Tra
0.96
PCap GDP-cou2-Tra
0.95
Pcap GDP-cou1-Aut
Pcap GDP-cou2-Aut
countries, an individual in Cou1 at period t saves more to
build capital needed for production in period t+1 because
t
the demand for locally produced capital- intensive good
0.94
t2
t3
t4
t5
t6
t7
t8
t9
t10
t11
t12
t13
t14
t15
t16
t17
t18
is more than it is in autarky. As a result, the interest
Figure 8 The evolution of GDP per capita under scenario A and B
income for individuals in the old generation in Cou1 is
In the autarky case, Figure 8 shows that GDP per
higher than it is in Cou2. The resulting lifetime wealth
capita levels of Cou1 and Cou2 converge to an identical
(Linc) for a representative individual in the old economy
steady-state level. This steady-state level of GDP per
is higher than the younger economy (Figure 11). As
capita is 1 under scenario A and 0.994 under scenario B
shown in Figure 8, the average welfare for individuals in
with a higher steady-state population growth rate. The
the old country is higher than its autarky level, which
convergence of per capita welfare can be explained by
means this country gains from trade. The younger
the
economy, however, is made worse off. This finding is
observation
that
the
steady-state
levels
of
capital-labor ratio and autarky factor prices (wage and
rate of return on capital) of both countries will converge
to an identical level. These levels are determined by the
observed under both scenarios.
0.675
W/R
W/R-Scenario A (declining NNF )
0.67
steady-state population growth rate. Consequently, the
0.665
steady-state lifetime wealth for an individual is equalized
0.66
across countries. Given that consumers in Cou1 and
W/R-Cou1-Aut
W/R-Cou2-Aut
0.655
W/R-Cou1-Tra
W/R-Cou2-Tra
Cou2
have
an
identical
utility
function,
their
t
0.65
t2
t3
t4
t5
t6
t7
t8
t9
t10 t11
t12
t13
t14
t15
t16
t17
t18
consumption bundles are equal at the steady state and so
are the average welfare levels.
0.665
W/R
W/R-Scenario B (constant NNF )
0.66
In the trade case with Armington assumption, the
capital-labor ratios and factor prices in Cou1 and Cou2
no longer converge to an identical level though their
population growth rates are identical at steady state.
Figure 9 shows that the wage-rental ratio of Cou1
dominates that of Cou2 under both scenarios overtime. In
0.655
0.65
0.645
W/R-Cou1-Aut
W/R-Cou2-Aut
W/R-Cou1-Tra
W/R-Cou2-Tra
0.64
0.635
t
0.63
t2
t3
t4
t5
t6
t7
t8
t9
t10 t11
t12
t13
t14
t15
t16
t17
t18
Figure 9 The evolution of wage-rental ratios under scenario A and B
addition, the absolute values of wage and rate of return
on capital stock in Cou1 are also higher than those in
Cou2 at steady state (Figure 10). The scarcity of labor
endowment makes labor more expensive in Cou1. On the
8
1.01
W
It is also shown that the welfare gap between a
Evolution of wage levels (Scenario A)
1.005
young and an old economy increases with the
1
steady-state population growth rate. Under scenario A,
0.995
0.99
0.985
W age-cou1-Tra-A
0.98
W age-cou2-Tra-A
the steady-state population growth rate is 1 and is lower
than it is under scenario B (1.012). Correspondingly, the
0.975
t
0.97
t2
1.005
t3
t4
t5
t6
W
t7
t8
t9
t10
t11
t12
t13
t14
t15
t16
t17
t18
gap between steady-state GDP per capita levels is
enlarged from 1.58% to 3.58%.
Evolution of wage levels (Scenario B)
5. CONCLUSION REMARKS
0.995
W age-cou1-Tra-B
0.985
W age-cou2-Tra-B
0.975
Using an OLG-CGE model, this paper revisits the
0.965
evolution of trade during demographic transition and the
0.955
t
welfare implications. A CES utility function with the
t18
elasticity different from one is introduced into the
0.945
t2
1.515
t3
t4
t5
R
t6
t7
t8
t9
t10 t11
t12 t13
t14 t15
t16 t17
intertemporal maximization of life time utility for a
Evolution of rental levels (Scenario A)
representative individual. In the real world, tradable
1.51
Rental-cou1-Tra-A
1.505
goods are differentiated not only by factor intensities in
Rental-cou2-Tra-A
1.5
production, but also by country of origin. Armington
1.495
assumption is applied into our trade model to generate a
1.49
t
1.485
t2
1.52
t3
t4
t5
R
t6
t7
t8
t9
t10
t11
t12
t13
t14
t15
t16
t17
First, our findings for the autarky case are quite
Evolution of rental levels (Scenario B)
1.515
similar to the related literature. Except for the total
Rental-cou1-Tra-B
number
Rental-cou2-Tra-B
1.51
of
population,
all
variables
including
capital-labor ratios, wage-rental ratios and GDP per
1.505
capita levels for the two economies converge in the long
1.5
t
1.495
t2
t3
t4
t5
t6
t7
t8
t9
t10
t11
t12
t13
t14
t15
t16
t17
t18
Figure 10 The evolution of factor price levels under scenario A and B
2.28
more realistic picture of international trade.
t18
that a representative individual in the old economy has a
higher level of welfare than autarky and gains from trade.
The average welfare for the younger economy however,
Lifetime income-A (declining NNF )
Linc
run. After opening to trade, our simulation results show
2.27
deteriorates. This result supports the argument that trade
2.26
would not necessarily represent a Pareto improvement
2.25
welfare change for the old and the young economy are
LInc-Cou1-Aut-A
LInc-Cou2-Aut-A
2.23
2.22
t2
2.28
over the state of autarky. However, the directions of
LInc-Cou1-Tra-A
LInc-Cou2-Tra-A
2.24
t3
t4
t5
t6
t7
t8
t9
t10
t11 t12
t13
t14
t15 t16
t
t17
t18
we provide some explanations of the average welfare gap
observed in the simulation results. We find that under
Lifetime income-B (constant NNF )
Linc
opposite to those shown by Sayan (2005). Furthermore,
different scenarios of demographic transition, both the
2.26
long-run wage rate and the long-run rental price in the
2.24
2.22
capital-abundant (older) economy are higher than they
LInc-Cou1-Tra-B
LInc-Cou2-Tra-B
2.2
are in the labor-abundant (younger) economy. The
LInc-Cou1-Aut-B
LInc-Cou2-Aut-B
2.18
2.16
t2
t3
t4
t5
t6
t7
t
t8
t9
t10
t11 t12
t13 t14
t15
t16 t17
Figure 11 The evolution of lifetime income under scenario A and B
t18
resulting lifetime wealth for an individual in the older
economy is higher and so is the average welfare. This is
the source of the average welfare gap between the two
economies with unequal population growth rates. Finally,
9
it is shown that the average welfare gap between the
gains from technical change and from international
older economy and the younger economy is positively
trade”, Canadian Journal of Economics, Vol. 13,
correlated with their steady-state population growth rate.
No.1, pp65-18, 1980.
[5] Galor, O., Lin, S., “Terms of trade and current
This model can be applied into studies on trade
account dynamics: a methodological critique”.
between a younger labor-abundant economy, such as
International Economic Review, Vol. 35, No. 4, pp
China, and the comparatively older capital-abundant
1001-1014, 1994.
economies such as EU economies. Our simulation results
[6] Galor, O., Lin, S., “Dynamic foundations for the
suggest that as the population growth rate of a younger
factor endowment model of international trade”, In:
developing economy is projected to be continuously
Jensen, B.S., Wong Dynamics, K. (Eds), Dynamics,
higher than its developed trade partners, the welfare gap
Economic Growth and International Trade (Studies
between them is expected to be persistent overtime.
in International Economics), University of Michigan
Compared to other developing economies with high
Press, 1997.
population growth rates, the growth rate of Chinese
[7] Guillo, M. D., “The trade balance and the terms of
population is moderate. In the coming decades, this rate
trade in a two-country two-Sector OLG economy”,
is projected to be even lower than some of the developed
Spanish Economic Review, Vol. 3(1), pp71-80, 2001.
economies. Accordingly, the welfare gap between China
[8] IMF, “How will demographic change affect world
and the developed world is expected to be persistent but
economy”, World Economic Outlook: the Global
decreasing overtime.
Demographic Transition, Chapter 3, September,
2004.
The model used in this paper can be extended for
[9] Mérette, M., “The bright side: a positive view on the
many future studies. A multi-regional model will be built
economics of aging”, Economic Growth Choices
to investigate the evolution of trade among many
IRPP, Vol. 8, March, 2002.
economies with different patterns of demographic shock.
[10] Mérette, M., “Population aging and international
In this paper, we assume two economies have an
mobility of labor: a review of issues report including
identical capital-labor ratio before calibration, which
a multi-country numerical model”, 2004.
doesn’t reflect present relative factor abundances for the
[11] Pugel, T. A., Lindert, P. H., International Economics
developing and the developed economies. Real data will
(the 11th edition), Irwin McGraw-Hill Companies,
be collected and applied into this model to simulate a
2000.
more realistic picture of trade. The robustness of our
results remains to be tested in the future work.
[12] Sayan S. Uyar A. E., “Directions of trade flows and
labor movements between high and low population
growth countries: an overlapping generations GE
analysis”,
REFERENCES
Bilkent
University
Department
of
Economics Discussion Paper No.01-08, April, 2001.
[1] Armington, P. S., “A theory of demand for products
[13] Sayan S., “Heckscher-Ohlin revisited: implications
distinguished by place of production”, IMF Staff
of differential population dynamics for trade within
Papers, Vol. 16, pp159-176, 1969.
an overlapping generations framework”, Journal of
[2] Buiter, W. H., “Time preference and international
lending
and
borrowing
in
an
overlapping-
generations model”, Journal of Political Economy,
Vol. 89, No. 4, pp769-797, 1981.
[3] Chen, Z., “Long-run equilibria in a dynamic
Heckscher-Ohlin model”, Canadian Journal of
Economics, Vol. 25, pp923-943, 1992.
Economic
Dynamics
&
Control,
Vol.
29,
pp1471-1493, 2005.
[14] United Nations, “World population prospects: the
2000 revision highlights”, UN Population Division
Report No.165, United Nations, New York, 2001.
[15] United Nations, World Population Aging 1950-2050,
United Nations, New York, 2002.
[4] Fried, J., “The intergenerational distribution of the
10
APPENDIX. DETAILED MODEL DESCRIPTIONS
Household’s problem
An
Allais-Samuelson
overlapping
generation
framework characterizes households, so that this model
is based on the life-cycle theory of savings. The
Firm’s problem
In each country, there are two industry sectors (s),
so two goods (Sec1 and Sec2) are produced according to
different technologies. We assume different parameters
Scs,tQ and αsk in the productions functions to differentiate
technologies used by productions of two goods. Scs,tQ is a
scaling constant and αsk is the expenditure share
measures the intensity of use of capital in production. As
shown in Section 3, Sec1 is assumed to be a
capital-intensive good and Sec2 is a capital-intensive
good. Technologies, or production functions, are
assumed to be identical across countries. A representative
firm’s problem is to minimize the production cost subject
to the embedded constraint that characterizes the firm’s
technology:
M in m iz e R e n tt K
K
s ,t , L s ,t
dem
s ,t
(1)
,α
(2)
s .t . Q s , t = C D ( K , L , S c
k
s
)
In equation (1), Rentt and wt represent rental prices
and wage levels respectively. Ls,tdem is the labor
demanded by production sector s and Ks,tdem is the capital
demanded. In equation (2), Qs,t is the quantity of
production of good s at time t. CD(Sc,α) means the
technology employed is represented by a Cobb-Douglas
production function in which the sum of expenditure
shares for capital and labor inputs is equal to one. We
assume that input factors are perfectly mobile across
sectors in each country. Consequently, the wage levels
and
rental
prices
are
equalized
across
sectors.
Furthermore, we assume that all firms hire factors and
sell outputs competitively on the markets, so the price for
each factor is set to be equal to its the marginal product.
Differentiating equation (1) with respect to equation (2),
we get the following equation (3) and (4) as first order
conditions for producers in the economy:
R e n t j ,t = S c
w
j ,t
= (1 − α
Q
s ,t
k
s
α K
k
s
k −1
dem α s
j , s ,t
− α sk
) S c sQ, t L dj e, sm, t
income, demographic characteristics, rate of return on
capital and many other variables in the economy. At an
arbitrary period of time t, each economy is populated
with two generations (the working generation gi and the
retired generation gn) and a representative individual is
born and working in period t and retires at t+1. The
working life begins at age 16 and an individual is
assumed to live another 30 years after the retirement at
age 56. Correspondingly, each period t represents 30
years in our model. An individual’s problem is to
maximize his or her lifetime utility subject to the budget
constraint:
Maximize U t =
+ w t L ds e, tm
Q
s ,t
determinants of individual saving include life-time
Con g ,t , Con g ,t +1
1
1−θ
2
1
∑ (1 + ρ )
g =1
g
Con1g−,tθ+ g −1
Con
s.t . Wt = PgCon
, t + g −1Con g .t + g −1 + Pg .t + g Con g ,t + g
(5)
(6)
In our model, we assume a time-separable CES
form utility function and consumption is the only
component in an individual’s utility. The aggregated
lifetime utility is shown by equation (5), which includes
the present values of current and future consumptions. In
this equation, Ut is the lifetime utility for a representative
individual and Cong,t is the quantity of aggregate
consumption by an individual in generation g at time t. θ
is the inverse of intertemporal elasticity of substitution
which stands for the degree of substitutability of
consumption across different generations. ρ is the pure
rate of time preference and
indicates the degree to
which the household would prefer current consumption
rather than future consumption. The larger ρ, the more of
its lifetime resources a household will spend in the first
stage of life and the less it saves. This pure rate of time
preference is assumed to be identical across countries
overtime. Furthermore, we assume that labor supply is
(3)
exogenous and leisure is not included in the utility
(4)
function. In both countries, each individual supplies an
identical quantity and quality of labor in the first half of
life. The wage income is allocated into either current
consumption or future consumption as shown in equation
(6). In this equation, Pg,tCon is the aggregate consumption
11
price for generation g at time t. Wt is the present value of
lifetime wealth represented by the following equation
P gC, to n
1 − σ sC o n
=
∑α
C ons
s,g
C o n S s , g ,t = α
t
1
⎪⎧
⎪⎫
Wt = ∑ ⎨
⎬ LInc g ,t + g −1
g =1 ⎪
⎩ 1 + Rre t t + g −1 ⎪⎭
(1 0 )
s
(7):
2
C on
Ps1, −t σ s
C ons
s,g
(7)
⎡ P gC, to n ⎤
⎢
⎥
⎣⎢ Ps , t ⎥⎦
σ
C on
s
C o n g ,t
(1 1)
where σsCon is the Dixit-Stiglitz elasticity of
where LIncg,t is the labor income for an individual
substitution for consumption across sector s.
in generation g at time t. Rrett is the rate of return on
In our model, individuals across generations in both
Cou1 and Cou2 are assumed to have an identical
capital stock.
In our model, there is no government and no tax
preference parameter αs,gCons for each good s. In other
imposed in the economy. Bequest and inheritance are not
words, a consumer demands the same amount of Sec1
taken into account in people’s wealth. Assuming no
and Sec2 given that there is no difference between their
borrowing constraint and perfect capital market in each
prices.
economy, the present value of an individual’s wealth is
the labor income earned in the first half of life:
W
t
= L In c
g i ,t
Investor’s problem
In each period t, part of output produced in the
(8 )
economy is saved by individuals in the first generation in
The intertemporal maximization problem is as
the form of investment in physical capital demanded by
follows. Immediately after birth, an individual in gi
production in the next period t+1. The law of motion of
decides on the allocation of his or her labor income into
capital stock can be represented by the following
either current consumption or future consumption. In
equation (12):
other words, an individual could smooth part of current
K stock t +1 = Inv t + (1 − D epR ) K stock t
consumption by investing before he or she retires. After
(12)
retirement, this individual spends all principle and
interest income of investment on consumption goods.
In equation (12), Invt is the aggregate investment at
Differentiating an individual’s utility function with
time t which includes both Sec1 and Sec2 used for
respect to the budget constraint yields the following first
investment purpose. The capital stock in the economy at
order condition for the aggregate consumption Cong,t:
time t+1, represented by Kstockt+1, is positively
Con g +1,t + g
⎡ (1 + Rret t + g ) PgCon
⎤
, t + g −1
=⎢
⎥
Con
(1
)
P
+
ρ
g + 1, t + g
⎣⎢
⎦⎥
(
1
θ
correlated with investment in the previous period and
)
Con g , t + g −1
negatively correlated with depreciation rate (DepR). The
(9)
expected rate of return on capital on a unit of physical
capital invested at time t, Rrett, is then defined by the
In a second optimization step, an individual has to
decide on a portfolio of consumption expenditures on
two final goods Sec1 and Sec2. We assume a
consumption
parameter
αs,gCons
representing
following equation (13):
R r e tt =
consumption goods s. Then the aggregate consumption
price Pg,t
(1 3)
the
preference of a consumer in generation g on different
Con
R e n t t + (1 − D e p R ) Pt In v
Pt −In1v
where Rentt is the rental for capital input at time t.
Inv
Pt is the aggregate price for investment goods.
is a weighted sum of consumption prices for
The decision on how much should be invested is
Sec1 and Sec2. The quantity of consumption of good s is
made by a perfect-foresight representative individual
positively correlated with preference parameter αs,g
Pg,tCon
Cons
based on his or her expectation on the next period’s rate
over
of return on capital stock. As mentioned before, we
the consumption price for good s (Ps,t). The following are
assume both Sec1 and Sec2 can be used for investment
the first order conditions for the secondary optimization
purpose in our model. In other words, capital stock is
of consumption:
built using an investment technology that allows for
and the ratio of aggregate consumption price
12
substitution between different good s. An investor
chooses the optimal portfolio of investment goods on the
σ cj ,s
Ei , j ,s,t = α
E
i , j ,t
market according to the following equation (14):
I n v S s ,t = α
In v s
s
⎡ Pt I n v
⎢
⎢⎣ P s , t
⎤
⎥
⎥⎦
σ
⎡ Pj ,s ,t ⎤
⎢
⎥
⎢⎣ Pqi,s ,t ⎥⎦
⎧
⎫
⎨∑∑ Pop j , g ,t ConS j ,s, g ,t + InvS j ,s ,t ⎬ (17)
⎩s g
⎭
Here, αEi,j,s shows an individual (in country j)’s
In v
In vt
(1 4 )
preference on goods s produced either by a local
producer or a foreign producer. σj,sc is the elasticity of
where αsInvs is the given share of good s in aggregate
substitution between consumption of Sec1 and Sec2 and
investment and it is assumed to be identical across
it is assumed to be identical across countries. In our
Inv
is the elasticity of substitution
model, we assume αEi,j,s is identical across countries and
for investment good which shows the degree of
sectors. In other words, a consumer is assumed to
substitutability between consumption and investment.
demand the same amount of good s produced in Cou1 or
sectors and countries. σ
Inv
The price of investment good, Pt , is a weighted sum of
Cou2 when both countries are assumed perfectly
consumption prices for good s labeled as Ps,t (equation
symmetric. As mentioned before, Pj,s,t is the consumption
15):
price for good s in country j at time t. Pqi,s,t is the
Pt Inv
1− σ Inv
=
∑ α sInv Ps1,−t σ
production price of good s in country i, the country of
Inv
(15)
s
for good s produced in country i increases with the
The above equation (14) shows that the actual share
of good s InvSs,t in aggregate investment Invt increases
Invs
with αs
origin. Equation (17) shows that the demand by country j
aggregate local demand and the ratio of consumption
price over local production price.
and the ratio of price of investment good over
the consumption price of good s.
Equilibrium conditions
A general equilibrium solution is one in which all
economic behaviors (production, consumption and
Foreign trade with the rest of the world
In our model, trade with the other country is a
investment) are consistent with both current prices and
portion of aggregate demand in the economy. The
future prices and all markets clear. To close our model,
aggregate demand is defined as:
we impose equilibrium conditions for all four markets:
∑∑
s
Pop
j , g ,t
C onS
j , s , g ,t
+ In v S
j , s ,t
(1 6 )
g
the good market, the market for labor input, the market
for capital input and the asset market.
where ConSj,s,g,t and InvSj,s,t are the quantities of
The equilibrium condition for good market in each
consumption demand and investment demand for good s
country is that the quantity of good s produced in country
at time t respectively. Popj,g,t is population of generation
j must be equal to the quantity demanded by all
g living in country j at time t. In international trade, we
countries:
allocate demand by consumers in country j for goods
Q j , s ,t =
produced by country i based on the Armington
assumption. In other words, even though individual
∑E
(18)
i , j , s ,t
i
For labor market, we assume full employment and
producers are microscopic price takers, goods of sector s
labor supply equals demand in each country j:
are assumed differentiated in demand by country of
Pop j , gi , t Lsup
j , gj =
origin. Thus each country in our model produces, exports
∑L
dem
j , s ,t
(19)
s
and imports both goods (Sec1 and Sec2). Accordingly,
where Lsupj,gj is the effective labor supply provided
the importers in each country choose an optimal portfolio
by an individual in the working generation gj in country j.
of domestic and imported goods in both sectors. In
In this paper, this effective labor supply is assumed to be
period t, the demand for good s from consumers and
identical across countries. However, with unequal
investors in country j from country i (Ei,j,s,t) is defined by
populations in the working generation at time t, Popj,gj,t,
the following equation (17):
the aggregate labor supply in the economy varies across
countries. The aggregate labor supply in an older
13
capital-abundant country is less than it is in a younger
labor-abundant country.
On capital markets, capital stock must be equal to
demand in each country j:
Kstock j ,t =
∑K
dem
j , s ,t
(20)
s
Based on the aggregate value of capital stock
demanded and population of the old generation at time
t+1, a representative individual make decision on saving
part of output as investment to build capital stock
required by productions at time t+1. Without capital
mobility across countries, the equilibrium condition for
the asset market requires that the value of lending by
individuals at time t+1 equals to the value of capital
stock in the economy at time t+1in each country j:
Pop j , g +1,t +1 Lend j , g +1,t +1 = Pinv j ,t Kstock j ,t +1
(21)
where Lendj,g,t is the value of lending by an
individual in generation g at time t.
14